Lecture Notes Physics 106

Module 2: Physics of the small

Simon Knapen

July 3, 2013

Contents

How to use these notes 2

Introduction 4

1 Introduction to quantum physics 61.1 The world of the small . . . . . . . . . . . . . . . . . . . . . . . . 61.2 Wave mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.3 The double slit experiment . . . . . . . . . . . . . . . . . . . . . 111.4 Wave-particle duality . . . . . . . . . . . . . . . . . . . . . . . . . 14

2 Quantum Mechanics and Probability 172.1 Common sense and determinism . . . . . . . . . . . . . . . . . . 172.2 Uncertainty from coarse graining . . . . . . . . . . . . . . . . . . 192.3 Uncertainty from Quantum Mechanics . . . . . . . . . . . . . . . 23

3 E = mc2 & the atomic bomb 283.1 E = mc2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.2 Unlocking the nucleus . . . . . . . . . . . . . . . . . . . . . . . . 303.3 Germany . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.4 America . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.5 Epilogue: reaching for the stars . . . . . . . . . . . . . . . . . . . 41

4 Radioactivity (workshop) 454.1 Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.2 Radioactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.3 Some examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.3.1 Problem 1: Estimate your annual radiation dose . . . . . 494.3.2 Problem 2: Carbon dating . . . . . . . . . . . . . . . . . . 504.3.3 Problem 3: Cell phone radiation . . . . . . . . . . . . . . 51

5 The Fukushima disaster 545.1 Nuclear reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . 545.2 55 reactors on the Ring of Fire . . . . . . . . . . . . . . . . . . . 585.3 The Fukushima disaster . . . . . . . . . . . . . . . . . . . . . . . 615.4 Aftermath . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

1

5.5 Other incidents with nuclear reactors . . . . . . . . . . . . . . . . 68

6 Introduction to modern particle physics 706.1 The forces of nature . . . . . . . . . . . . . . . . . . . . . . . . . 706.2 The lego box of the universe . . . . . . . . . . . . . . . . . . . . . 736.3 What’s all the extra stuff for? . . . . . . . . . . . . . . . . . . . . 756.4 The Large Hadron Collider (LHC) . . . . . . . . . . . . . . . . . 786.5 Now what? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

Epilogue 85

2

How to use these notes

This document is contains many interactive links and the margins are wide foran easier read, which contributes to the overall amount of pages. The notes aremeant to be read electronically, and I highly encourage you not to waste anymoney and paper by printing them.

These notes are intended as a study aid, to provide you with some back-ground material for the lectures and to help you improved your understanding.Please do not attempt to memorize these notes. Questions like

In what year was radioactivity discovered?

will not appear on the exam. Instead you should read these notes, understandthem and remember the key points of each lecture. I tried to highlight these keypoints as much as possible, to help you distinguish them from less importantdetails. Add the end of each lecture I added a list of ”take home points” and alist of questions under the name ”Test your understanding”. You can considerboth as example exam questions.

To further help you process the content, I marked important points withthese three pictograms:

An important definition or a new concept to be understood andremembered.

A common pitfall or mistake. Proceed with care!

A question or puzzle that will deepen your understanding or testyour knowledge.

It is really important that you try to solve the questions marked with the

symbol. I highly encourage you do discuss the answers with your peers,in particular on the Sakai forum. I will look at the Sakai forum at regularintervals myself, and steer the discussion in the right direction if needed. Atleast one of these questions will be included as an exam question.

Moreover lecture notes are sprinkled with links with useful information,mostly interactive demos or simulations. Some of these are added to improveyour understanding of the subjects in class, while others are merely references

3

for you if you wish to explore a subject more for your own interest. I expect youto take a look at the links marked in red and understand what they are about.Links marked in green are optional, and will not be part of the exam material,although occasionally they may relate to material covered in other modules.

Finally, this is the first version of a set of notes written by a non-nativeEnglish speaker in a limited amount of time. I thank you for your understandingfor the language imperfections and the typos that I have not yet been able tocorrect. You can contribute to the improvement of these notes by flagginglanguage mistakes or unclear passages in the designated section on the Sakaiforum.

Simon KnapenJanuary 1st 2013

4

Introduction

In module 2 we explore the fascinating world of the smallest length scales knownto us. The fundamental question we would like to formulate an answer to is

What are the smallest building blocks of Nature?

This question was already being contemplated by the ancient Greek philosophersin 6th century BC. We have come a long way since then, and we will explorethe current state of the art answer to this question in the last lecture. Althoughthe question seems highly abstract and of academic interest only, the road tothe answer led us past many surprises, many of which have revolutionized theway we live today. Modern communication, computers, smartphones, lasers,televisions, medical imaging devices and nuclear technology, just to name a few,are all spin-offs from this the search towards this one fundamental question.Because of their enormous relevance for society, it is not more than appropriateto dedicate some time and energy to a selection of these important applicationsand their impact on our lives.

This module is divided into three parts: In the first two lectures we willexplore some of the most important and counterintuitive features of quantummechanics, which is the framework in which we currently understand the worldof the very small. Lectures 3, 4 and 5 are dedicated to nuclear physics and itsapplications. I think this is a particularly relevant subject at this time, as policymakers are about to make decisions which will affect many future generationsof humans. In the final lecture we will talk about our current understanding ofwhat the smallest of the small really is.

5

Chapter 1

Introduction to quantumphysics

”Anyone who is not shocked by quantum theory has not understood it.”NIELS BOHR 1885-1962

1.1 The world of the small

In the first two lectures of this module we will explore the foundations thetheory named quantum mechanics. Quantum mechanics describes how natureworks on the very small scales. It provides physicists with a complete set ofrecipes to calculate the properties and the interactions of molecules, atoms, andeven smaller objects. It is hard to overestimate the importance of quantummechanics in our modern understanding of nature. Most branches of physicswould not exist without it. Without quantum mechanics, we would not knowwhy the sun emits light, where X-rays come from or even why atoms exist1.Even outside fundamental physics the implications of quantum mechanics areenormous. Quantum mechanics is key in the design of things like communicationsystems, nuclear facilities, lasers and the microchips in our smart phones, justto name a few. For a particularly neat application, see figure 1.1. Withoutquantum mechanics we would not understand DNA, molecular biology wouldnot exist and chemistry would still be in its dark age. In this sense quantummechanics has implications that are far more significant and far reaching thanfor example general relativity.

Besides it wide applicability, quantum mechanics is also one of the mostpredictive and experimentally tested theories in all of science. Over the pastcentury it has been confirmed in numerous experiments, of which the mostimpressive one is perhaps the measurement of the magnetic dipole moment of

1In a universe without quantum mechanics the negatively charged electron would simplycrash into the positively charged nucleus because their electric attraction. No atoms cansurvive in such a universe.

6

Figure 1.1: The IBM logo produced with a Scanning Tunneling Microscope(STM). STM’s are capable of both detecting and relocating single atoms at atime. Each blue dot in the figure is a single atom. The total size of the logo isabout 0.0000001 cm. (Image courtesy IBM Corp)

the electron:ge = −2.0023193043622± 0.0000000000015

Theory and experiment agree to an astonishing accuracy of 12 decimal places.As it stands, this is probably the most precisely predicted and measured quantityin all of science.

Finally a word of caution before we begin our journey through along thesmallest constituents of our world. The things we will encounter will look likenothing you have seen before, and will appear very counterintuitive or evenplain wrong. The pioneers of the theory themselves were at first extremelyconfused and shocked by their own findings, and it took them over 30 years todevelop the basic framework and to understand the fundamentals. With thebenefit of hindsight, this is maybe not so surprising. After all, our senses arenot designed to detect such small objects, and all the intuition about physicsthat we built up since our childhood is based on the motion of large things likecars and tennis balls. There is a priori no reason why an atom should behaveas a tennis ball, and our naive intuition might not carry over to length scalesto small for us to observe. In fact, we will see it does not, and that the laws ofthe small are far stranger than anything we could have imagined. Therefore Iask you to approach these two lectures with an open mind and a healthy doseof persistence. It is likely that you will need to read certain things multipletimes, maybe even in different places. I’ll try to provide alternative referenceswhenever possible. I advise you to continuously attempt to come up with goodquestions to ask yourself, your classmates and your teachers. You will find thatthis is the best way to improve your understanding of this fascinating subject.

7

1.2 Wave mechanics

In the first module you already familiarized yourself with the concept of a ”par-ticle”. Recall that a particle is perfectly point like and has a well defined speedand position. We used the concept of a particle as a simplified picture, a modelfor a more complicated object, like a snooker ball, a planet or an electron. Inthis section you will add a second model to your toolbox, which will be essentialto understand quantum mechanics:

A wave is a disturbance or oscillation that travels through spaceand time, accompanied by a transfer of energy. A longitudinalwave is wave where the disturbance takes place along the directionof motion. A wave for which the disturbance is orthogonal to thedirection of motion is called a transverse wave.

You already know many examples of waves in various forms from every-day experience. On the ocean, on a rope or the wave in a sport stadium.These are examples of transverse waves, because the individual constituents(water/rope/spectators) move up and down, while the wave itself moves side-ways. For a demo about transverse waves click here. Other less obvious butvery important examples are sound and light. A sound wave is a longitudinalwave in the density of the air. Little packets of denser air bump into packetswith less dense air, a process which increases the density of the originally lessdense packet. In its turn that packet bump into the next one, hence transmit-ting the wave. This very analogous to the chain reaction that occurs when acar crashes into the rear end of a traffic jam. Although each individual car onlymoves by a small amount, the effects of the first crash can be transmitted a longway. The fact that the last car was damaged as well is evidence that energywas transmitted in the process. For a simulation you can click here. (Noticethat the packets of densely spaced lines propagate over the whole length of thesimulation, but that the red line by itself does not move much.)

Light waves are a manifestation the same principle, but here it are electricand magnetic fields that are oscillating, rather than the density of the air. Adetailed treatment of lightwaves is beyond the scope of this course and for nowit is enough to remember that light is transverse wave. If you are interested,you can find more information by clicking on this link.

Most waves that we know of in daily live must propagate througha medium, for example sound waves in air or a wave on a piece ofrope, but some waves do not need a medium. Light waves are anexample of a wave that can travel in vacuum.

Do you know any other examples of waves? Are your exampleslongitudinal or transverse waves? Do they need a medium or canthey travel in vacuum?

Waves are further classified by their wavelength and frequency:

8

The wavelength of a wave the distance over which the wave’s shaperepeats. The frequency of a wave counts how many times persecond the wave’s shape repeats.

The wavelength characterizes how ”long” a wave is. Waves on water typicallyhave a wavelength of several meters. The wavelength of sound waves can rangefrom a few milimeters to several meters, while light waves always have an ex-tremely small wavelength (You will learn more about light in module 3). Thefrequency of a wave tells you how fast its pattern is changing. For a wave on astring for example, the frequency tells you how many up and down vibrationsthere are each second. Frequency is most often expressed in terms of Hertz (Hz),which is the amount of oscillations per second. The human ear is a sophisticateddevice to convert the frequency of sound waves into our common notion of a”high pitch” (2.0× 104 Hz) and ”low pitch” (20 Hz) , which correspond to highand low frequencies respectively.

A high frequency wave does not necessarily travel faster than a lowfrequency wave. For example, sound waves always travel at the samespeed, regardless their frequency.

You can familiarize yourself with the concepts of wavelength and frequencyby following this link. It will lead you to an interactive simulation where youcan vary the frequency yourself. What happens to the wavelength if you do so?You will see a knob for something called amplitude. Play around with thisknob too, and find out how the shape of the wave changes if you do.

Can you estimate the wavelength and frequency of a wave in a sportstadium? Do the same exercise for the examples you found for theprevious question.

Before we set our first steps into quantum mechanics, we need to discuss twoimportant phenomena involving waves: diffraction and interference. You arealready familiar with both of these concepts in one way or another. Let us startwith diffraction

Diffraction is the apparent bending of waves around small obstaclesand the spreading out of waves past small openings. The longer thewavelength, the more the wave will undergo diffraction.

Diffraction is a phenomenon that only occurs for waves. Particles can changetheir direction of travel when they collide with another object, as snooker ballsdo, but they do not spread out in space after the collision. The diagram in figure1.2 is a schematic representation of what happens when a beam of particles anda beam of waves encounter a narrow slit. All the particles will get stopped bythe wall, except for those aligned with the slit. Waves on the other hand spreadout after they passed through the slit and can be detected everywhere.

You should keep in mind that diffraction is not something exotic, but aneveryday phenomenon. You can hear a person walking down a hall, even if he

9

Figure 1.2: Scattering of particles (left) and waves (right) by a narrow slit. Theblue arrows indicate the direction of the motion. Observer A detects both thewaves and the particles, while observe B can only see the waves.

or she is not precisely in front of the door of your room. This happens becausethe door acts as a slit to the sound waves of that person’s footstep, causing thesound wave to diffract into your room. You find two more examples in figure1.3.

If someone drops an object behind a corner, why can you hear it butnot see it?

To conclude our introduction to waves, we need to understand what happenswhen two waves collide. Unlike particles, waves usually pass straight througheach other, but nevertheless something interesting happens at the collision point.The incoming waves combine to a single wave, with height2 the sum of theheights of the incoming waves.

Interference is a phenomenon in which two waves collide to forma resultant wave of greater or lower height. When the resultingwave has a greater height the incoming wave, this is refered to asconstructive interference. When the resulting height is smallerwe speak of destructive interference.

You can find a simulation of constructive and destructive interference in theSakai resources folder. The simulations are simplified representations in onedimension. More realistic examples in two or three dimensions can give rise tocomplicated, and sometimes beautiful patterns, but the basic mechanism is thesame as in the one dimensional examples. For more realistic example, click thislink. If you like, you can easily find more examples on Youtube.

In the next section we will see the principles of diffraction and interferenceat work in one of the most significant experiments from the 20th century.

2Physicists use the term ”amplitude” instead of height.

10

(a) Diffraction of water waves (b) Diffraction of light waves

Figure 1.3: Examples of diffraction. The disc engraved with a grid of tinyscratches, that cause the light waves to diffract, similar to the diffraction ofwater waves by the spacing between the islands. The angle under which a wavebends after it is refracted depends on its wavelength, which in the case of lightcorresponds to color. This is why you see a colorful shine on the DVD in thepicture on the right.

1.3 The double slit experiment

We already saw in figure 1.2 what happens when we send a plane wave to awall with a narrow slit. The wave diffracts, resulting into a circularly spreadingwave on the other side of the wall. Now what happens if we would use two slitsinstead of just one, separated by just a small distance? The wave will undergodiffraction at both slits, resulting in two overlapping circular waves, as shown infigure 1.4. This experiment is easily carried out with water waves, but it werethe Englishman Thomas Young and the Frenchman Augustin Fresnel in 1804who (independently) carried out the experiment using light. Young3 shined alight source on two very narrow slits in a dark room, and put the a photographicplate4 on the other end. You can see a schematic representation of Young‘s ex-periment in figure 1.4. What they found was a peculiar collection of alternatingdark and bright fringes. However from the perspective of wave mechanics thisobservation is hardly surprising at all: The circular waves emitted from thetwo slits interfere, and dark fringes correspond to destructive interference, whilebright fringes point to constructive interference. With this experiment Youngand Fresnel unambiguously proved that light had to be a wave. Neverthelesstheir experiments were not taken serious at first, especially not in England. The

3Fresnel’s experiment was slightly different, as it employed diffraction in thin oil films,much like the DVD disc in figure 1.3b.

4A photographic plate becomes brighter and brighter when it accumulates light. Theprinciple is the same as that of old-fashioned photograph, but with a very long shutter speed.

11

famous physicist Isaac Newton had shown in 1672 that light had to consist ofparticles, and in 18th century England Newton was still no less than a superstar.Newton being wrong was simply inconceivable at that time. It was only whenthe Frenchman Andre Foucault showed that the speed of light differed in waterand in air, that the wave hypothesis became generally accepted.

Figure 1.4: A schematic representation of Young‘s famous double slit exper-iment. The yellow line represents the photographic plate, on which Youngobserved the dark and bright fringes, represented by the bands on the right.The experiment conclusively demonstrated that light is capable of undergoinginterference, and hence must be a wave.

There is nothing special about two slits. The experiment wouldwork just as well with three, four, or more slits. As you increase thenumber of slits, there a more sources to interfere with each otherand the pattern on the photographic plate becomes more and morecomplicated.

Despite the early resistance by the British scientific community, the waveparadigm of light did not come as a big shock. The idea had been around for

12

many years, first proposed by the Dutch physicist Christean Huygens, who wasa contemporary of Newton. However something really surprising happens whenthe experiment is repeated using an electron beam instead of light. The electronhad been discovered by Thompson and his team in 1897, and it was shownlater that electrons could be knocked out of their atoms by other electrons,like snooker balls. Moreover they could be trapped in a magnetic field andtheir location and trajectories could be predicted. The general consensus in thescientific community was thus that electrons had to be particles.

As such, it is very surprising that an electron beam exhibits the very sameinterference behavior that Young and Fresnel observed for light. It is evenpossible to determine the wavelength of the electron beam and showed that itdepends on the speed of the electrons. The first proposal to explain this peculiarobservation was that electrons are particles, however when a lot of them are puttogether they behave like a wave. From our everyday experience this is notcrazy at all: We know water consists of billions of tiny particles, that are ableform a wave when put together. So could the interference effect observed inthe electron beam a similar manifestation of a collective phenomenum5, wherea huge number of particles work together to produce a totally new effect that asingle particle can not possibly produce?

Technology improved, and soon enough the experiment was repeated, nowwith a source firing a single electron at a time. The general belief was that nowthe electrons should behave like particles again (left panel in figure 1.5), nowthat they had no more companions to form a wave with. The opposite turnedout to be true! Despite the electrons now being lonely, they still produced theinterference pattern associated with a wave. (middle panel of figure 1.5) Thismeans that the electron itself must be wave. How could this be? On the onehand Thompson and his lab had provided indisputable evidence that electronsare particles, while the double split experiment demonstrated that they had tobe waves. How could it be possible for something to be both a wave and particle?

A single electron always produces a single dot on the screen. How-ever when many electrons are fired at the screen, all these dots willarrange themselves to form the bright and dark fringes. What theprevious paragraph is intending to convey, is that it is irrelevantwhether all the electrons are fired together or one-by-one with largetime intervals in between. These two simulations should help clear-ing it up for you: simulation 1 and simulation 2. (The second one isa little silly, but it illustrates the physics very well.)

It got even stranger. In order to settle the matter, the experimentalists addeda detector close to one of the slits, to register precisely what slit the electronwas traveling through. Surprisingly, the interference pattern disappeared afterthe detector was added and the electrons behaved once again as particles. (rightpanel in figure 1.5). So not only do electrons exhibited both particle and wave

5Collective phenomena play a important role in modern physics, and you will learn muchmore about them in module 4.

13

Figure 1.5: A schematic representation of double slit experiment carried outwith electrons. The photographic plate becomes bright when hit by an electron(white fringes) and remains black when it isn‘t (black fringes). The left paneldisplays what the researchers expected to observe, the middle panel shows whatthey actually observed and the right panel displays the same experiment witha detector (red box) added.

properties, they also seemed to ”know” how they are being measured, and adapttheir behavior to the experiment. This apparent paradox is called the wave-particle duality and has no analogue in the world of tennis balls, sports cars andairplanes.

It did not stop with electrons. It was shown that all other particles (protons,neutrons and even atoms) behave like a wave if probed in the correct way. Evenmore importantly, in 1905 Albert Einstein6 showed that light, of which Youngand Fresnel showed it was a wave, can behave as a particle as well. (In 1921Einstein received the Nobelprize for this realization.) Today we know that inthe world of the small everything is simultaneously a wave and particle.

If you didn’t like my explanation or you just want a second reference, youcan also read the story here.

1.4 Wave-particle duality

We established that electron, atoms, light etc all exhibit both wave and particleproperties. But what does that mean? In particular, how do these objects”know” which option to choose, depending on the experiment? I will presentto you the modern viewpoint, to which the vast majority of physicist adhere.If you want to learn about more exotic interpretations like the ”Kopenhageninterpretation” or the ”Many worlds interpretation”, I refer you to the book byJohn Gribbin, referenced at the end of this chapter. Both of these interpretationtry to address the question ”What is reality?” Today most physicists take amuch more pragmatic point of view. The question to the nature of reality is

6Einstein realized that a phenomenon called the photo-electric effect could only be ex-plained if light could behave as a stream of particles. Although it is not hard to understand,a treatment of the photo-electric effect is beyond the scope of this course because of timeconstraints. You can read about it here.

14

mostly left to philosophers, while physicists rather attempt answer the question”How do we describe reality?” This goes back to idea of modeling. Nature isfundamentally too complicated for us to be understood in all its detail with asingle set of ideas. Therefore what physicists do is focus on the property orobject they want to measure, and come up with an idealized, oversimplifieddescriptions of this object. We call such a simplified description a model. Whena simple model does not suffice do describe the data correctly, one can eithertry a entirely new model, or add more details to the existing model to better fitthe experiment.

You already learned various different examples of models. What arethey? Can you think of any others?

The choice of the model always depends on the question asked: What am Itrying to explain? Nature is too complex to be understood entirely by a singlemodel. Instead physicists have a variety of models in their toolboxes, and applya different one depending on the problem at hand. For example, if you areinterested in computing the motion of the earth around the sun, it is very goodapproximation to model the earth as a point particle. If on the other hand,you are interested in the weather patterns in New Jersey, there is no harm inapproximating the earth as a flat disc. In a sense, neither of these models aretrue, but they just work excellent in describing the specific problems for whichthey were conceived.

Wave particle duality can be understood in a similar fashion. The models”wave” and ”particle” work well do describe a different set of experiments. Wedon‘t really know what the thing we call ”electron” really is, but we know thatit is something we can often describe very well as a particle, while sometimesthe wave picture is more appropriate.

I hope I convinced you that quantum mechanics is challenging our every dayintuition on a fundamental level. In the next lecture we will learn that wave-particle duality is only the tip of the iceberg, as we will discover an even morecounterintuitive feature of reality: it is fundamentally random.

Take-home points

• Quantum mechanics provides a framework to understand the motion andinteractions of the smallest constituents know to us. It is extremely pre-dictive and lead to numerous practical applications.

• The model of a wave and its properties. Longitudinal vs transverse waves,frequency and wavelength. You should know and understand several ex-amples of waves and come up with some examples yourself. When given annew example of a wave, I expect you to be able to determine its properties(Estimate wavelength, frequency, transverse or longitudinal wave).

• Understand the concepts of diffraction and interference and illustrate withexamples.

15

• Young’s double slit experiment for light waves

• The double slit experiment for electrons and its implications.

• Wave particle duality and the concept of modeling. Illustrate modelingthrough examples.

Test your understanding!

• How do we encounter quantum mechanics in our daily lives? Use theinternet to find some examples that are not referenced in the text.

• What are some important differences between particles and waves?

• Give some extra examples of diffraction and interference. Use the internetif needed.

• What would happen if we would repeat the double slit experiment withoranges instead of electrons or light?

• Why is the double slit experiment important for our understanding ofquantum mechanics?

• What is wave particle duality and what is its modern interpretation?

Respources

• You can find an excellent explanation of the double slit experiment on theblog Emperical Zeal.

16

Chapter 2

Quantum Mechanics andProbability

”I don’t demand that a theory correspond to reality because I don’t know whatit is. Reality is not a quality you can test with litmus paper. All I’m concerned

with is that the theory should predict the results of experiment.”STEPHEN HAWKING 1942-...

In the previous lesson you learned about wave-particle duality, a first coun-terintuitive feature of quantum mechanics. In this lesson we will explore asecond fundamental feature of the theory namely its interpretation in terms ofprobabilities. On an intuitive level you are of course very familiar with proba-bilistic events from things like rolling dice and other games of chance. In thefirst part of this lecture we will see how probability plays a central role in all ofscience through the principle of coarse graining. In the second part we will findthat quantum mechanics implies a new source of probability, which cannot bederived from the coarse graining principle. In this aspect quantum mechanicsis fundamentally different from every other field of science.

2.1 Common sense and determinism

To properly understand the significance of probability in science, we have to goback a few centuries, when great minds like Galileo, Kepler and again Newtonconstructed the fundamental principles behind the motion of things like cars,baseballs and planets1. Galileo understood that nature had to be inherentlypredictable: you could repeat the same experiment over and over again, withthe same outcome every time. You can drop a rock 100 times from a tower, andyou know in advance that the rock will end up on the ground 100% of the time

1Newton first understood that the movements of planets must be governed by the samelaws of physics as the movements of objects here on earth. Today this sounds all prettyobvious, but it was an enormously bold step to take at his time.

17

and will never start floating around in the air. You can claim that this all quiteobvious, and it is. We have seen so many objects fall down in our lifetime, thatthe notion got hardwired in our brain. We would be shocked or at least verysurprised to see an object that didn‘t follow our intuition about what nature issupposed to do. (This is of course the whole idea behind magic tricks.) HoweverGalileo wanted to take this idea one step further. He reasoned that it shouldbe possible to also predict exactly where the rock would land. This is far lessobvious, as such a prediction requires a number of non-trivial things:

1. A detailed understanding of the laws that govern the motion of the object.In this case it would require an understanding of gravity.

2. A set of mathematical tools that allow you to perform the calculationsneeded to predict where the rock will land.

3. and finally an accurate measurement of the initial position and velocityof the rock. (Obviously a rock throw at high speed will end much furtheraway else than a rock that is just dropped. The question is how muchfurther.)

Of these three ingredients, Galileo only had the third at his disposal2. Keplermade some significant progress by deriving a set of equations that predict theorbits of planets around the sun, but he lacked a detailed understanding of whyhis equations worked. It was finally Newton who filled in requirements 1 and2 from the list above, by writing down the theory of gravity and by inventingcalculus3 respectively. Newton’s laws of motion are valid for objects on earthand in the sky alike, and calculus proved an extremely powerful tool to convertthe equations into a concrete prediction. These developments equipped Newtonand his contemporaries with the tools to in principle predict the outcome of anyconceivable experiment at the time, provided that the initial conditions couldbe measured to sufficiently high precision. This led them to develop what iscalled the mechanical world view :

The mechanical world view states that the universe is best un-derstood as a completely mechanical system - that is, a system com-posed entirely of matter in motion under a complete and regularsystem of laws of nature. The future of the universe is completelypredetermined by its initial conditions. The mechanical world viewoften goes under the name of determinism.4

2Not entirely accurate: Galileo came up with a set empirical equations to predict forexample the touch down point of a cannon ball. However he obtained the equations fromexperience, rather than driving from a fundamental law of nature.

3In the interest of fairness we say that the German scientist Leibniz invented calculusroughly at the same time. It is not entirely clear who was first and to what extend bothscientists where influenced by each others work. We do know that a fierce rivalry betweenboth emerged after the publication of the papers.

4In philosophy determinism has important implications for the notion of ’free will’.

18

Sir Isaac Newton1642-1727

The Englishman Isaac Newtonrevolutionized both physics

(with his famous laws ofmotion and the theory ofgravity) and mathematics

(with the invention ofcalculus). Newton was the first

to realize that the motion ofstars and objects on earth

must be governed by the samelaws and made important

contributions to the theory oflight. Together with Einstein

he is considered to be the mostinfluencial physicist of all time.

Newton fact believed that universe was asomething like giant clock designed by God,which operated according to a fixed set ofprinciples, which the determine the entire fu-ture of universe. In principle one could thuspredict every single instance in the future ofthe universe, provided that one would haveenough computing power and a perfect mea-surement of all particles in the universe. Thisidea was famously formulated by the Frenchphilosopher and mathematician Pierre SimonLaplace, a contemporary of Newton:

We may regard the present stateof the universe as the effect of itspast and the cause of its future.An intellect which at a certainmoment would know all forces thatset nature in motion, and all po-sitions of all items of which na-ture is composed, if this intellectwere also vast enough to submitthese data to analysis, it wouldembrace in a single formula themovements of the greatest bodiesof the universe and those of thetiniest atom; for such an intellectnothing would be uncertain andthe future just like the past wouldbe present before its eyes.Pierre Simon Laplace, A Philosophical Essay on Probabilities

From your everyday experiences is this world, the mechanical world viewshould sound pretty much like common sense. If nature would randomly decideto violate its own laws, it would be impossible for us to get cars on the road orrobots on Mars. Nevertheless we cannot predict the future to arbitrary precision.(A 3-day weather forecast is already a challenge.) A mechanist would say thatthis is just due to our imperfect understanding of the initial conditions and ourlimited computing power. This problem is partially overcome by introducingthe concept of coarse graining, which is the subject of the next section.

2.2 Uncertainty from coarse graining

The concept of coarse graining is central in all of science, not just physics.Moreover your brain does it for you every second of your life, by filtering theenormous amount of information that comes in through your senses and by

19

assembling a simplified picture of the situation which is suitable for decisionmaking. All of science, social and natural, is based on this same premise:

The world is way too complicated to be understood in all its detail bya single analysis.

Therefore we must make approximations in everything that we do as scien-tists. The real craft of a good scientist is to understand what information canbe safely ignored in which situation. If I am for example interested in the func-tioning of an aircraft, I can not possible account for the motion of all the atomsaround the aircraft. Even if I could somehow obtain the position and velocityof each particle at a certain time, no computer would be even close to powerfulenough to perform this computation. Similarly, if you would be interested inpredicting the results of the presidential election, it is completely intractable toask every single American in advance for his or her voting preference. (This isof course what the actual election is for.) Instead pollsters will carefully selecta small sample of people from who they suspect they accurately represent thewhole population. This type of procedure is extremely common and is what iscalled coarse-graining:

A Coarse-grained description of a system is a description werea number of details are ignored, and the system is described by asmall number of variables. Coarse graining always results in someloss of information. This additional uncertainty is man-made, andparametrized by the use of statistics.

The context of physics, the most important example of coarse-graining is thestudy of thermodynamics: Nobody would get the idea of trying to describe abox of air (∼ 1027 atoms) by tracking each and every particle, but you can learnan awful lot by just considering simple variables as the pressure, the densityand the temperature of the gas in the box. The concept of coarse graining laysat the foundations of an important branch of physics, called statistical physics.This will be topic of module 4.

So how do scientists apply coarse-graining to extract quantitative answersfrom their data? For this we need statistics. The more complicated the coarse-graining, the more complex the statistical techniques can get, but we can easilyillustrate the concept with our simple example of Gallileo’s rock: Lets say wewant to launch a rock under a certain angle with a speed of 2.0m

s and measurewhere it ends up. Say we repeat the measurement three times, and our resultsare 34.5 m, 36.4 m and 32.8 m. First of all you notice that the rock doesnot always end up precisely at the same spot. We now have to reconsider ourassumptions and figure out why this is happening. In particular, our launchingdevice is certainly not perfect: sometimes it will launch the rock it little bitfaster than 2.0m

s , while sometimes the speed of the rock will be a little bitslower. This results in different measurements for the distance each time wetry the experiment. Let say we calibrated our launching device carefully andwe know that, although it doesn’t launch the rock with exactly the right speed

20

every time, the average launching speed is close to 2.0ms . This means that the

chances of the rock being fired too fast are roughly equal to the chances of therock being fired too slow. Remember we are interested in knowing how far therock would fly, if fired at 2.0m

s . Since there is no way to know precisely at whatspeed the rock was launched, the best we can do is to estimate the real distanceby averaging over our results:

average distance =34.5 m+ 36.4 m+ 32.8 m

3= 34.6m

This is our best guess for how far a rock fired at 2.0ms should fly. This is already

a nice achievement, but as a scientist you cannot be satisfied yet. The estimateyou made is not meaningful, unless you can say something about how closethe estimate is to the real value. In this example you might worry that you gotunlucky and the launching device fired the rock all three times too fast/too slow,and you are overestimating/underestimating the true distance by averaging yourresults. To quantify this possibility, you could compute a quantity called thestatistical error or statistical uncertainty:

Statistical error or statistical uncertainty5 is the uncertaintyintroduced by one‘s imperfect knowledge of all the conditions andcircumstances of a particular experiment.

So what if I would repeat rock launching experiment a 100 times. It is nowvery unlikely that the rock was always fired too fast/too slow. In contrary, onewould expect that roughly 50 times to rock was fired a little bit too fast, androughly 50 times it was fired a little bit too slow. So you would expect when youaverage all 100 results, your estimate of the true distance must be better thanwhen you just averaged the 3 results we had before. This idea is illustrated infigure 2.1. This is indeed the case, and is a manifestation of the most importantprinciple in statistics:

The more an experiment is repeated, the smaller the statistical un-certainty on all the experiments combined. This is called the thelaw of large numbers.

A second very important subtlety about coarse-graining that you should keepin mind is the following: The way coarse-graining itself is implemented dependson the judgement of the researcher! Sometimes the strategy is obvious: for thepurpose of throwing the rock I can safely ignore the atomic structure of therock and treat it as a solid sphere of uniform mass. However should I ignore theair resistance of the rock as well? Clearly, air resistance slows the rock down,causing to fly less far. By how much? A good scientist must estimate this effectand either show that it is not important or include it in his or her model. Oftenthe choice of coarse-graining is very tricky, and a bad choice makes the finalresult worthless. Lets go back to the example of the poll for the presidential

5In statistics texts this is often referred to as the standard deviation or standard error.

21

æ

ææ

ææ

ææ

28303234363840

distance HmL

æ

æ

æ

æææ

æ

æ

æ

æ

æ

æ

æ

æ

ææ

æ

æ

æ

ææ

æ

æ

æ

æ

æ

æ

æ

æ

æ

æ

æ

æ

æ

ææ

ææ

æ

æ

æ

æ

æææ

æ

æ

ææ

æ

æ

æ

ææ

æ

æ

æ

ææ

æ

æ

æ

æ

æ

ææ

æ

æ

æ

æ

æ

æ

æ

æ

æ

æ

æ

æ

æææ

æ

æ

æ

æ

æ

æ

æ

æ

æ

æ

æ

ææ

æ

æ

æ

æ

æ

æ

ææææ

28303234363840

distance HmL

Figure 2.1: The law of large numbers applied on the example with the flyingrock. The blue dots represent the spots where the rock landed, the red dot isthe average over all the experiments and the green dot is the true value. We seethat the average value approximates the true value better when the experimentis repeated 100 times (graph on the right), with respect to when the experimentis only repeated 3 times (graph on the left).

election. If person performing the poll for example decided to contact peopleover e-mail only, one might worry that mostly young people will be reached,who are known (on average) to vote in a different fashion than older people.So in this case you want to question the result of the research because of thedubious choice of coarse-graining. This is an example of what scientists call abias:

If the set of assumptions (coarse-graining) tends to erroneously favorone result over the other, we call this a systematic uncertainty orbias. When designing a study, scientists always attempt to reducethe effect of bias as much as possible, but it is almost never possibleto eliminate all forms of bias entirely. Any good scientific study willalways clearly state all potential sources of bias, and estimate theireffect on the final result. In contrast to the statistical uncertainty,the systematic uncertainty or bias cannot be reduced by repeatingthe experiment.

This last statement is very important. If I decide not to account for airresistance when throwing the rock, my expectation of where the rock will landwill always be greater than reality, and I am making this mistake every timeI repeat the experiment. So if I would repeat the experiment 100 000 times, Icould greatly reduce the statistical uncertainty, but the bias/systematic uncer-tainty would remain the same. (In the example or the rock it turns out thatthe effect air resistance is usually very small, and we can conclude the bias dueto air resistance is negligible.)

You should make a clear distinction between the scientific term bias,and the popular meaning of the same term. In daily life we refer toa person as being biased, when he or she made up his or her mind

22

beforehand, and is not likely to change his or her opinion based onthe available data. When the term ”bias” is used in a scientific con-text it does not refer to the scientists being biased in the mannerjust described, but rather to a potential error due to coarse-grainingthat must be studied carefully and kept under control. Every scien-tific study contains sources of bias, but often they are negligible. Itis the researcher’s job to show that this is indeed the case. This useof terminology regularly causes confusion in the press, in particularwith respect to the topic of global warming.

Find an example of a scientific study in news or a popular sciencearticle and answer the following questions6:

• What question is the research trying to answer?

• What kinds of coarse-graining were used?

• What types of bias could have been introduced by the coarse-graining?

• Does the study clearly document all the sources of bias youthink?

2.3 Uncertainty from Quantum Mechanics

Time to get back to quantum mechanics. Recall the double slit experiment fromthe previous lecture, and how we can fire individual electrons to a wall with twoslits and study where they end up. We saw that when we fire an individualelectron at the two slits, it can end up in various places, but if we repeat theexperiment many times, an interference pattern emerges. Newton and friendswould have been unsatisfied with this state of affairs. They would claim itshould be possible to predict the exact point of impact of every single electron,provided enough information about the electron was know. They would invokecoarse-graining, and state ”Ah, indeed the electrons do not end up at the samespot 100% of the time, but perhaps you are ignoring some details on how you areprecisely firing them to screen, and this is causing the apparent ”randomness” ofthe electrons.” So, pretty much like the example with the rock. Maybe we don’texactly control where the electron is going, because we didn’t really know forsure how fast and at what angle we fired it? Maybe the slits are not as smoothas we think they are, and some electrons are bouncing off small aberrations.These considerations were precisely the considerations made by the scientistswho did the experiments. So how does a scientist settle this matter? He or sheapplies for a new grant, gets a fancier piece of equipment with better precisionand redoes the experiment.

6This could be a potential exam question, where I provide you with a short article.

23

The experiment got upgraded over and over again and repeated by severalindependent groups7, but the result remained unchanged, to the point where theexperimenters where confident that aberrations in experimental setup could notaccount for the effect. More importantly, various other types of experiments8

probing these small scales were performed, and these experiments too found thatuncertainties in the measuring apparatus could not account for the amount ofrandomness observed in the system.

Niels Bohr 1885-1962

Niels Bohr made importantcontribution to the

development of quantummechanics, in particular to the

structure of the atom, forwhich he received to Nobel

Prize in 1922. He was apassionate soccer player.

This lead a schism in the physics commu-nity in early 1900’s. One school of thoughtstill held on to the idea that either the exper-iments or their interpretation had to be flawedin a yet unexposed way. Albert Einstein wasthe most influential member of this school.The other school of thought, lead by the Dan-ish physicist Niels Bohr, proposed that in-stead the 17th century mechanical world viewhad to be wrong and had to be replaced byan indeterministic world view:

In an indeterministic world-view certain events are notcaused by prior events, but in-stead happen randomly.

The idea had gained solid experimental sup-port, but was highly controversial on philo-sophical grounds. (The idea that every eventhas to be caused by an earlier event is as oldas Aristotle.) This controversy is nicely il-lustrated by one of Einstein’s most famousquotes, from a discussion with Niels Bohr in Copenhagen:

God9 does not play dice. - A. Einstein

Einstein and others eventually had to accept outcome of the experiments, butinstead proposed that quantum mechanics was somehow ”unfinished”. Therehad to be some yet undiscovered laws of physics that steer the electron one wayor another. They reasoned that the electrons appear to be subject to randombehavior, just because we have not yet understood all of their dynamics yet. I

7This is a good example how good science is always the result of a slow, painstaking processof check, cross checks, cross checks on the cross checks, and most importantly independentconfirmation of the results by other scientists.

8I am not really doing justice to the history of physics here, by implying that the doubleslit experiment was decisive. In reality the random nature of quantum mechanics was alreadywell established by other experiments by the time the double slit experiment was performedwith electrons. (It’s an easy experiment with light, but very tricky with electrons.)

9By ”God” Einstein means Nature in this context. This quote is now often misused a assignall sorts of scientifically unfounded metaphysical interpretations to quantum mechanics.

24

think this was a very valid piece of criticism to Bohr’s idea of indeterminism,but it also illustrates the unwillingness of a generation of scientists to give upon a paradigm had worked beautifully for centuries. In 1964 John Stewart Bellderived a set of experimentally verifiable consistency conditions that had to besatisfied for every interpretation of quantum mechanics involving hidden lawsof physics. In 1981 it was demonstrated by experiments that Bell’s consistencyconditions were violated, forever refuting the hidden dynamics hypothesis as anexplanation for the probabilistic nature of quantum mechanics10.

Niels Bohr was right all along. The world is of the small is full of randomness,and even if you would know everything about an electron, an atom or moleculethat there is to know, you could still not exactly say what its properties willbe next time when you would measure them. In fact, it turns out it is noteven possible to precisely determine where a particle is, not even if you wouldhave an arbitrarily accurate measuring device. (This is something known as”Heisenberg’s uncertainty principle”. If you want more information, you canfind it here.)

These ideas go often under the name of ”quantum uncertainty”,which is a common source of confusion. It is important to under-stand that the term just refers to the source of the uncertainty. Anytype of uncertainty quantum or coarse-graining, is described by thesame branch of mathematics that we call probability theory. Themathematical concept of probability that you deal with while rollingdice is precisely the same as for electrons traveling through two slits.For instance, in both cases there is no negative probability and themaximum possible probability is 100%. What is different is the phys-ical origin: in the case of the dice you use probability to deal withyour lack of knowledge about the exact conditions in which the dicewhere thrown, while in the case of the electrons you use probabilitybecause Nature forces you to do so.

Does this mean all hope of making predictions is lost? Not really. Althoughit is true that we cannot predict the precise path of a single electron, we canpredict what the most likely path of the electron will be. If we dan repeatthe experiment many times, like in the double slit experiment, we can makea very accurate prediction about how the electron should behave on average.This allows us to still make very accurate predictions, like the magnetic dipolemoment of the electron in lecture 1, despite the fundamentally indeterministicnature of quantum mechanics.

Let’s recap what we learned:

• The macroscopic world of tennisballs and airplanes is deterministic. If Iknow enough and if I have enough computing power I can in principlepredict whatever I want.

10This does not mean there can not be any hidden feature of quantum mechanics left over.Bell’s theorem only states that such hidden features can not be responsible for the probabilisticbehavior that we observe in experiment.

25

• In practice this doesn’t work, because our knowledge is always incom-plete. We deal with this by making, sometimes crude, approximations(coarse graining). Our approximations introduce (statistical and system-atic) uncertainty in our actual results. We must study these uncertaintiesto understand whether our results were meaningful or not.

• At very small length scales, quantum mechanics rules the world. Quantummechanics comes with a new source of uncertainty that is fundamentallydifferent from the uncertainty from coarse-graining. Quantum uncertaintyis hardwired into Nature, while uncertainty from coarse-graining is merelyan artifact of our imperfect understanding of Nature.

• Although we cannot predict stuff for a single particle, we repeat the ex-periment many times and predict very accurately what will happen onaverage.

This concludes our introduction to quantum mechanics. There is of coursemuch more that we don’t have time for, and I gladly refer interested studentsto the book by John Gribbin, which is referenced at the end if this chapter.Although I do not agree with some of his more controversial points, I greatlyenjoyed this book as a high school student.

In a sense, the rest of the module will be less abstract than the first twolectures, as we will move closer to real world applications. For most of ourdiscussion about nuclear and particle physics we will obtain some good insightswith (semi-)classical models, and quantum mechanics will be less on the fore-front of our discussions. However it is essential to keep in mind that it applieseverywhere throughout this module and physicists cannot not get any of thisapplications to work out without considering the subtleties of quantum mechan-ics. This being said, I would like to finish our discussion of quantum mechanicswith some popular wisdom:

Doing exactly the same thing twice and expecting different resultsin the definition of insanity. In the realm of the small, this is notinsanity but law.

Take-home points

• Until the 1900’s, scientists believed that nature was deterministic on afundamental level.

• It is not.

• The idea of coarse-graining is crucial for the way we as humans try tounderstand the world, but comes at the price of some uncertainty. Under-standing this uncertainty is the core business of all scientific research.

• Uncertainty from coarse-graining is man-made, uncertainty from quantummechanics is hardwired in Nature.

26

• We cannot predict the behavior of a single particle at one instance, butwe can predict its average behavior.

Test your understanding!

• Explain in your own words the difference between determinism and inde-terminism.

• Explain in your own words the difference between statistical uncertaintyand systematic uncertainty/bias. Illustrate this with an example that youfound yourself.

• Explain in your own words what the scientific term ”bias” means. Comeup with a few examples of bias of your own. How does it differ from ourevery day usage of the word ”bias”?

• Explain in your own words the difference between a coarse graining prob-ability and a quantum probability.

• What is the difference between Bohr’s worldview and Newton’s worldview?Why is Bohr’s worldview so counterintuitive?

References

• In Search of Schrodinger’s Cat: Quantum Physics and Reality - JohnGribbin

27

Chapter 3

E = mc2 & the atomic bomb

”The release of atom power has changed everything except our way ofthinking...the solution to this problem lies in the heart of mankind. If only I

had known, I should have become a watchmaker. ”ALBERT EINSTEIN 1879-1955

Recap: Atomic structure

This chapter relies heavily on a basic understanding of the structure of matter.Important concepts are atoms, protons, neutrons, electrons etc. If you are notcomfortable with these things you should refresh them before proceeding. Youcan do so by watching this video or in any other basic physics or chemistryreference that you like. There are also plenty of recourses on the web.

3.1 E = mc2

E = mc2 is undoubtably one of the most famous equations in all of science, as itcarries an aura of both power and deep mystery. E = mc2 describes some of ourdeepest understanding of nature in a remarkable simple form, which contributesto its beauty. The equation comes forth from Albert Einstein’s famous theory ofspecial relativity, which has mind boggling consequences but is no less beautifuland deep than E = mc2. A detailed treatment of special relativity is beyondthe scope of this course, but I think you will find E = mc2 by itself surprisinglyeasy to understand. Let’s start by breaking the equation in to its components:

• E: stands for energy. Energy can come in a variety of forms, of whichthe most familiar to you are probably heat, electrical energy, gravitationalenergy and kinetic energy. Recall from module 1 that the latter is theenergy associated with the speed of an object.

• = Has the obvious meaning of ”is equal to”. We will see shortly that inthe case of E = mc2 we can take this definition very literally.

28

• m: stands for mass. It is a measure how much stuff (the correct term is”matter”) something is made off. Mass is measures, in kilograms, ounces,tons, etc.

• c2: stands for the speed of light squared. The speed of light is always aconstant, which means it is the same at all times and under all circum-stances. What is important here is that c2 is in fact a huge constant:

c2 = 9× 1016m2

s2 .

So what does the equation mean? On the left hand side we have energy, whileon the right hand side have mass, which is the amount of matter, multiplied bythe absurdly large number c2. It means nothing less than that energy and massare one and the same thing. Moreover the presence of the huge constant c2 tellus that a tiny amount of mass must be equal to an enormous amount of energy.You can thus think of mass as extremely densely packed energy. For example,the energy stored in your pencil is about 1016 Joules, or equivalent to burningroughly 8 million gallons of gasoline.

Use E = mc2 to estimate the total energy content of your lunch.How does that compare to the amount of useful energy for yourbody? (This is usually expressed in calories.) How many gallons ofgasoline would this correspond to?

Albert Einstein 1879-1955

Einstein is often regarded asone of the most influential

physicists of all time, for hiscontributions to quantumphysics and the theory of

relativity. In 1921, Einsteinreceived the Nobel Prize for his

explanation of thephoto-electric effect. He never

won a Nobel Prize for thetheory of relativity.

If matter and energy are really two sidesof the same coin, then one way or anotherit should be possible to turn matter into theenergy or visa versa. This simple fact is thekey to all of nuclear and high energy physics.

If mass can be turned into energy,why doesn‘t all mass convert inthis way? Why do we not spon-taneously explode in bursts of en-ergy? E = mc2 only prescribesthat mass in principle can beturned into energy, however otherlaws of nature dictate preciselyhow this must happen. If youdid the previous exercise correctly,you have found a huge amount ofenergy in your lunch. Howeverall that energy is safely lockedaway into the nuclear structureof your sandwich, inaccessible forour body to use. The amount

29

of useful energy1 in your lunch ismuch much less. This ”useful” energy is a form of chemical energy,and unrelated to E = mc2. However it turns out that we can seeE = mc2 in action under some very special circumstances. We willencounter several examples throughout the course, some of whichoccur in nature, while others are man-made.

In fact a first important example was already known several years beforeEinstein wrote his famous papers. In 1896 and 1898 Henri Becquerel and MarieCurie discovered some peculiar properties of Uranium and Thorium respectively.These exotic materials continuously kept pouring out heat (a form of energy!)at a constant rate. Now at the time this sort of behavior was already knownabundantly in chemistry, however in chemical reactions the material alwaysundergoes some sort of change and a different material emerges after the reactionis over. The materials studied by Becquerel and Curie behaved fundamentallydifferent. Nobody could detect any change in the materials and the energy justkept streaming out seemingly endlessly. They were deeply puzzled by this effect,which got eventually named radioactivity. Only several years later, physicistsrealized that in fact the materials do change: the nucleus converts a tiny littlespeck of its mass into energy through E = mc2. Because the amount of massconverted is so small, neither Becquerel nor Curie could have detected the changewith the instruments available to them. Moreover, because the transition frommass to energy is so extremely economical, an clump of for example Uraniumcan keep emitting energy for multiple hundred thousand years with hardly anyloss in intensity.

Now that you have a sense for the magnitudes involved here, you can alreadyunderstand where the tremendous power of an atomic bomb comes from. If youcould arrange tiny fraction of the material to be transferred into pure energythrough E = mc2, an gigantic amount of energy would be released, exactlybecause the constant c2 is such an enormous number. But we are jumpingahead. In the years after Einstein published the formula, neither his colleaguesnor Einstein himself had yet realized the destructive potential of E = mc2. Itwas not until 1938 when the brilliant Lise Meitner and her nephew Otto Frischfirst understood how to crack open the nucleus and how to unleash its power.

3.2 Unlocking the nucleus

The star of this story is the element Uranium. Uranium is an extraordinarily fatnucleus with 92 protons and between 141 and 142 neutrons. In comparison, theelement Oxygen has only 8 protons and 8 neutrons. Uranium is radioactive anda so-called α-emitter -we will learn to distinguish between α, β and γ emitters

1This is the kind energy that restaurants sometimes quote in their menus, expressed incalories. A calorie is just another unit for energy, you could convert it to Joules by a simplerescaling.

30

in the work session- and has an extraordinarily long lifetime of about sevenhundred million years2.

Use the internet to find some more basic properties of Uranium.(How it decays, most common applications, where it is mined etc.)This information will be useful in lecture 5 when we talk aboutnuclear reactors.

Lise Meitner 1878-1968

The Austrian physicist LiseMeitner was the main person

responsible for the discovery ofnuclear fission, but neverreceived the Nobel Prize.

Instead the Nobel Prize wasawarded to her collaborator

Otto Hahn, who undertook alifelong campaign to minimize

Meitner’s contributions. In1982 the element Meitnerium

was named in her honor.

In the late 1930’s, the primetime of LiseMeitner’s career, the radioactive properties ofUranium where already known for a while,but a good explanation was still lacking. Atthe time she was the director of the theoreticalphysics group in the famous Kaiser Wilhelminstitute in Berlin. However being Jewish,Lise Meitner had to flee from Nazi Germanyin 1938 and settled in Stockholm. Howeverbeing the intellectual leader of the team, shekept on coordinating the experiments of hercollaborators in Berlin, Otto Hahn and FritzStrassmann. In the Fall of that same year,Hahn and Strassmann encountered a puzzlethey could not resolve. They had been bom-barding an Uranium sample with neutrons,hoping that bumping lots of neutrons into alarge nucleus as Uranium would prompt thenucleus to become extra radioactive. Indeedthey found radioactivity, but they also foundsubstantial amounts of Barium, a lighter el-ement (see figure 3.1). No matter how hardthey tried, they could not get the Barium toseparate from the radioactive components in their experiments. Hahn wrote thefollowing letter to Meitner:

Dear Lise,... There is something about the ”Radium isotopes” that is so re-markable that for now we are only telling you... Perhaps you cansuggest some fantastic explanation ... If there us anything you couldpropose that you could publish, than it would still in a way be workby the three of us!Otto Hahn

Around Christmas time that year, Meitner met her nephew Robert Frisch,also a physicist, in a small village on the on the West coast of Sweden. Duringbreakfast they discussed Hahn’s letter, and Meitner suggested that the Uranium

2The extremely long life time of Uranium makes it a useful in dating the age of the earth.

31

Figure 3.1: The periodic table of elements. Uranium splits into Barium andKrypton. According to the table, which of these two elements is heavier?

might had broken into two pieces, and that the extra amount of Barium wasjust one of the remnants. The idea seemed totally absurd. A Uranium nucleusconsists out more than two hundred protons and neutrons, all tied togetherwith an extremely strong force, know as the strong nuclear force or strongforce3. (You will learn more about the strong force in the last lecture.) Thenucleus had been unchanged for millions of years, untouched. It could have beenconceivable that the neutron would have knocked off a small fragment, but itseemed ludicrous that a single neutron could completely break such an extremelytightly bound object, with a size over 200 times the size of the neutron. Whatcould possibly supply the necessary energy to achieve such a dramatic act? Youcan compare it with throwing a small stone at a big rock. The rock will noteven move, let alone break into two parts.

They finished breakfast and went for a walk in the snow. According to thestate of the art models of the nucleus at that time, the nucleus was to be thoughof as a liquid drop, rather than as a collection rigid balls glued together. Forour purposes we can think of it as a balloon filled with water. A balloon withonly a small amount of water is very stable and does not break easily, howevera very full balloon I have do handle with care, if I don’t want to end up wet.

Maybe something similar was going on with the Uranium nucleus? Meitnerand Frisch sat down on a tree trunk in the forest and took out their pencilsand paper. The strong nuclear force holds the nucleus together while the elec-

3If it would not be for the strong nuclear force, the nucleus would be blasted appear by theelectrostatic repulsion of the positively charged protons. This means that the nuclear forcemust be many times stronger than the electromagnetic force.

32

trostatic force wants to push it apart. They figured that the interplay betweenboth forces could make the nucleus unstable, in which case it would becomerestless, oscillating back and forth. If it at some point would oscillate a littleto much, it is not inconceivable that it would break apart. For a simulation,check the ”fission.avi” movie file in the Sakai resources folder. So if the nucleuswas already on the brink of breaking before it got hit by a neutron, maybe theadditional neutron could tip the balance and make the nucleus so unstable thatit had to split. In the snowy Swedish forest, Meitner and Frisch computed theenergy that would be released. (The positively charged protons where now splitover two smaller nuclei, which allowed them to be farther apart. So the electricenergy is the nuclei is reduced, and transferred into kinetic energy.) Moreoverthey noticed that the sum of the masses of the two decay products was lessthan the mass of the original Uranium nucleus. Meitner knew about Einstein’sE = mc2 formula, and they so could compute how much energy had to be as-sociated with the difference in mass. It all fitted like a glove. Inspired by theanaloguous concept in biology, they labelled their discovery fission.

A nucleus splitting into two smaller nuclei is called nuclear fission.When fission occurs, energy is always released. Fission can eitheroccur spontaneously, or after a nucleus captured a neutron and be-comes unstable by doing so. Fission only occurs for very heavyelements like Uranium or Plutonium.

The nucleus was open. Meitner and Frisch had understood how you couldbreak a nucleus apart and in the process convert a tiny bit of its mass into atremendous amount of energy. Smacking them together at high speed had failedover and over again, but if you took a highly ”jiggly” nucleus like Uranium andjust added a single neutron to tip the balance, the nucleus would eventually justcrack itself if you waited long enough. This explosion powered itself.

Any other time the developments following this discovery would have hap-pened more slowly. But now the greatest war ever was about the break outand furious race between the competing nations began to be the first to releasethe power of E = mc2 on a large scale. The center of gravity of contemporaryphysics had been in Germany for more than half a century, while Americantheoretical physics was almost non-existing and most other European countrieswhere quickly overwhelmed by Germany. It is thus no surprise that the GermanNazi regime was the first to notice the destructive potential of E = mc2, andstarted investing large amounts of resources in what had to become the mostpowerful bomb ever made.

3.3 Germany

At the time of the discovery of fission, Einstein was already the most famousscientist in the world. However the anti-Jewish climate in Germany had forcedhim to flee to the United States, where he took up a position in the Institute ofAdvanced Study in Princeton. Einstein had heard about Meitner’s results and

33

understood the possible consequences. Moreover colleagues who had fled fromGermany more recently, had informed him of the more than average interest thatthe Nazi regime was displaying in the splitting of nuclei. These developmentsdeeply worried him, and brought him to write the following letter to PresidentRoosevelt:

F.D. RooseveltPresident of the United StatesWhite HouseWashington, D.C.Sir:Some recent work ... which has been communicated to me in manuscript,leads me to expect that the element Uranium may be turned into anew and important source of energy in the immediate future. Certainaspects of the situation which has arisen seem to call for watchfulnessand, if necessary, quick action on the part of the administration...This new phenomenon would ... lead to the construction of bombs... A single bomb of this type, carried by boat and exploded in a port,might well destroy the whole port together with some of its surround-ing territory....Yours very trulyAlbert Einstein

The answer from Roosevelt was short and simple:

The White HouseWashingtonOctober 19th, 1939My dear Professor,I want to thank you for your recent letter and the most interestingand important enclosure. I found this data of such import that Ihave convened a board...... Please accept my sincere thanks.Very sincerely yours,Franklin Roosevelt

When an administrator assures you that ”a board has been convened” for a”most interesting and important enclosure”, you know you have been brushedoff, and Einstein’s fame was probably the only reason why he received an answerin the first place. Unsurprisingly, the administration did nothing. In April1940, Meitner’s nephew Robert Frisch had succeeded in convincing the Britishauthorities of the feasibility of the bomb, and a top secret report was sent tothe US. Also this report was locked in the safe of a senior administrator and didnot see the daylight until several years later.

In the meanwhile, the attitude of the German administration was completelydifferent. They felt no need to dwell in the past, as it had only brought themeconomic hardship and humiliation after world war I. In contrast to the Amer-ican administration, they were eager to try new ideas and technologies if they

34

could be of use to them in their conquest. They had the labs and the skilledpersonal to undertake this endeavor. In particular, they had the perfect manto lead the project. Werner Heisenberg was already one of the most impor-tant physicists of his time: young, brilliant and very renowned for his workon quantum mechanics. But almost the project was jeopardized before it hadeven started: Heisenberg was arrested by the secret police for collaborating withJewish physicists like Einstein and others, and was about to be send off to aconcentration camp. However the Nazi‘s realized their mistake in time: Heisen-berg was released and put in charge of developing the German atomic bomb.

Werner Heisenberg1901-1976

Heisenberg is most famous forhis key contributions to

quantum mechanics and hisefforts towards the German

nuclear program during worldwar II. After the war he

remained on of the leadingscientists in Germany.

Although Meitner and Frisch had shownhow to split Uranium, to road to an ac-tual atomic4 bomb was still long. The en-ergy released in a single splitting is still rela-tively small from a macroscopic point of view-Hahn’s lab never exploded- and one thusneeds to arrange a large amount of Uraniumnuclei to split simultaneously. This could beachieved through a chain reaction: When-ever a Uranium nucleus splits, it does not justbreak into two lighter elements, but also typ-ically emits a few extra neutrons in the pro-cess. If these extra neutrons could get cap-tured by another Uranium nucleus, they couldtrigger fission in that one as well, resultingin even more neutrons. If only the neutronscould hit the Uranium very efficiently, a mas-sive chain reaction would occur where all theUranium would split at almost the same in-stance, releasing a vast amount of energy in avery short period of time. You can find a nicesimulation here. For a video simulating a chain reaction with pingpong ballsand mousetraps, click here.

Say a single Uranium nucleus emits two neutrons, all of which weassume all would get captured by another nucleus. If we start withone fission reaction, we can thus trigger 2 new reactions. Each ofthese in their turn trigger 2 more reactions, leading to a total of4 reactions. How many reactions will there by after 3 such steps?What about after 5 and 10 steps?

Heisenberg reasoned that if you would just stack sufficiently purified Ura-nium, this sort of chain reaction would have to occur. The experiment was built,

4Note that the name is ”atomic bomb” is very misleading. The electrons play hardly anyrole; it is really the nucleus that gets split. Term ”nuclear bomb” would be more accurate,but ”atomic bomb” stuck for historic reasons.

35

and... nothing happened. The reason lies in the enormous amount of emptyspace in the atoms. Recall that the nucleus is only a tiny little speck in thecore of the atom, which consists almost entirely of empty space. So it is not sosurprising that the majority of the neutrons would just sail through, withoutever hitting a nucleus at all! This means that one either needs a large amountof very dense Uranium, or a smaller, but very pure sample, to prevent othernuclei from absorbing the precious neutrons. This is usually indicated by theconcept of critical mass:

The critical mass is the smallest amount of Uranium needed for asustained nuclear chain reaction. The critical mass depends uponthe density, the shape, the enrichment, the purity, the temperature,and the surroundings of the sample.

So if you don’t achieve critical mass, no chain reaction happens. This iswhat occurred in Heisenberg’s experiment. One of the reasons was that theneutrons emitted in the rapture of the Uranium nucleus are traveling relativelyfast; they just race past the Uranium without ever noticing it. If it would bepossible to slow the neutrons down they would be more likely to interact witha nucleus. It was already known at the time that neutrons could be sloweddown by sending them through water. The reason is that the neutrons willbump into the Hydrogen atoms of the water, and loose some of their speedwith each collision. (The H in the chemical formula for water (H2O) stands forHydrogen. You can see a graphical representation of a water molecule in figure3.2.) Heisenberg and his team repeated the experiment, now surrounding theUranium with water. They now observed a few reactions in the core of theirUranium sample, but far insufficient to sustain the chain reaction. The majorityof the neutrons still moved too fast and just streamed out. They needed a bettermediator to slow down the neutrons.

Figure 3.2: Schematic representation of regular water (H2O, left) and heavywater (HDO, right). Red blobs represent Oxygen atoms, green blobs representprotons, and the blue blob stands for a neutron. Free flying neutrons scattermore efficiently with deuterium than with regular Hydrogen, because it is bigger.

36

The solution to the puzzle was something called heavy water. It is almostthe same as ordinary water, but has one additional neutron attached to one ofthe Hydrogen nuclei. A Hydrogen atom with an extra neutron is usually calledDeuterium. Because of the presence of this extra neutron, the neutrons fromthe fission reaction are more likely to bump into the Deuterium, and hence areslowed down more. Heisenberg and his team started using heavy water, andin the Spring of 1942 they achieved a breakthrough: for the first time moreneutrons poured out of their experiment than they had inserted. This was clearevidence that a chain reaction had been achieved, multiplying the amount ofneutrons at each step. All that was left to do was to perfect the design andmake the reaction more efficient, and Germany would have an atomic bomb atits disposal.

To complete out this final set of experiments, large amounts of heavy waterwere required. Heavy water is very sparse in nature (about one cup in eachswimming pool of regular water), and to carry out his experiments, Heisenbergneeded a large factory to purify the heavy water. Such a factory existed in Ve-mork (figure 3.3), Norway, at that time occupied by Germany. The Nazi regimestarted to produce large amounts of heavy water in Vemork, to be shipped toHeisenberg’s labs in mainland Germany. However in the meanwhile the Britishintelligence services had found out about Heisenberg’s successes, and also in theUS the administration started to take the atomic bomb seriously. Even so theprospects for the allied forces looked grim: Heisenberg had all the infrastructureand staff already in place, and more importantly, a two years head start. In themeanwhile the administration in the US had just started to get organized. TheGermans had to be sabotaged.

An assault on the labs in mainland Germany or an assassination attempt onHeisenberg were both considered impossible, as they were too heavily protected.The British intelligence service decided that the weak spot was the heavy waterfactory in Vemork. A first attempt was made in 1942 by 30 British marines intwo glider airplanes. Both planes got caught in a snowstorm and crashed, thesurvivers were all found and executed by the German forces. A second attemptwas undertaken in February 1943 by small team of the Norwegian resistanceunder leadership of Knut Haukelid. They climbed the cliff on which the Vemorkfactory was constructed, evaded the guards and where able to detonate the mostimportant heavy water pipelines the factory. This courageous act slowed downthe German research with many more months, as the experiments could notcontinue without the heavy water.

3.4 America

In April 1943 the United States first got into the race with the opening ofthe research center in Los Alamos, New Mexico. The project was known un-der the code name ”Manhattan project” and was obviously classified as topsecret. The physicists working in Los Alamos where the top of the Americanphysics establishment at the time, plus a large amount of European refugees.

37

Figure 3.3: The Vemork heavy water factory in Norway in 1935.

Robert Oppenheimer1904-1967

”The father of the atomicbomb” remained a chief advisorto Washington D.C. on nuclearmatters, until he was strippedoff all of his responsibilities in

a communist witch hunt in1954. Nevertheless he stillmade several important

contributions to quantummechanics and nuclear physics,but never reached a status of

appreciation similar that of hisGerman counterpart

Heisenberg in Germany.

Traditionally many theoretically schooledphysicists where of Jewish descent, and manyof them had not waited for the war to breakout, and had already migrated to the US.Others followed soon when the war eventuallystarted. This massive brain-drain was one ofthe decisive factors that eventually would tipthe balance in favor of the US. In this sensethe Manhattan project was also the first largescale, ”international” collaboration of scien-tists on a common project.

This was an entirely new way of doing sci-ence, which was later named ”Big Science”.Today such very large collaborations, ”BigScience” collaborations are quite common inphysics, since certain experiments have be-come too large and expensive for a single na-tion to support. We will see some examples ofbig science in the last lecture of this module.

The man in charge of the scientific side ofthe Manhattan project was the New YorkerRobert Oppenheimer. Not only was he anexcellent physicist, he was also a master inreading other people’s desires and fears, a skillthat made him perfectly suitable to lead ateam of scientists with a wide variety of na-tionalities. Oppenheimer was able to bring the best physicists to Los Alamosand had them work in teams parallel towards a single goal. Their approach wasdifferent from the approach of their German counterparts: On the one hand

38

they tried to obtain as much highly purified Uranium as possible, similarly towhat the Germans had done. One of the problems with Uranium was that itwas very difficult to keep the chain reaction going long enough. It only workedif the Uranium was extremely pure, an extremely tedious thing to achieve. Thisis the same problem Heisenberg and his team ran into, and had solved to someextend using the heavy water. But Oppenheimer also had a second card toplay: A team in Washington had succeeded to transform Uranium into a new,even more powerful element: Plutonium. Plutonium is not plagued by the sameproblem as Uranium: it is much more explosive than Uranium. In fact, it istoo explosive. To trigger a Uranium bomb, you could take a clump of nearlycritical Uranium, and just shoot another piece of Uranium into it. Critical masswould be rapidly achieved, and the chain reaction would be started. This sim-ple method does not work for Plutonium. The reaction in Plutonium occursso fast, that all the Plutonium in the ”bullet” would have reacted away evenbefore it would reach the center of the big clump. Hence in most of the bigclump the chain reaction would reach critical mass and therefore never igniteat all. For this reason a different strategy was chosen for the Plutonium bomb.The idea was to surround a ball of nearly critical Plutonium with conventionalexplosives. If they could detonate these explosive all precisely at the same time,the Plutonium ball would implode and achieve critical density. If the explosionhappens sufficiently symmetric, the entire Plutonium ball would become criticalat exactly the same time, leading to a large chain reaction, which in its turn pro-vides the energy for the explosion. See figure 3.4 for a schematic representationof the two different mechanisms.

At the end of 1943 the Uranium purification had not yet been sufficient fora bomb, and neither had the Plutonium problem been solved, since it provedexceptionally difficult to get the explosion to work out sufficiently symmetrically.Moreover disturbing news came from Germany, as the Vemork factory had beenrepaired, and the heavy water production was higher than ever. In February1944, the Norwegian resistance reported that the entire stock of the Vemorkfactory was about the be shipped to Germany. Another sabotage attempt wouldbe exceedingly difficult. The Vermork factory was now very well protected,and so were the railroads along which the transport was supposed to occur.

Figure 3.4: Schematic representation of a Uranium bomb (left) and a Plutoniumbomb (right). The black circle represent the conventional explosives.

39

But there was one weak spot, as the transport had to pass over the deep lakeTinnsjo. If they could sink the ferry that carried the heavy water, it wouldbe impossible for the Germans to recover it. This posed Knut Haukelid andhis compatriots of the Norwegian resistance for a difficult dilemma: the ferrywas also the most important crossing for the workers of the factory and theirfamilies, and in order to destroy the heavy water, they would have to kill severaldozens of innocent Norwegians as well. The British intelligence service insistedon the importance of the operation, and the Norwegians decided to carry outthe operation regardless the price in human lives that would have to be paid.An insider in the factory managed to arrange that the transport would takeplace on a Sunday, so that the amount of innocent casualties would be minimal.Knut Haukelid’s bomb went off at 10:45AM, with 53 people on board of theship. The ship sunk immediately with on board the heavy water and over adozen passengers who had not managed to abandon the vessel in time. Thisfinal act of sabotage more or less ended the German prospects for an atomicbomb, although Heisenberg continued to work on it until he was arrested insmall town in the Alps by the US snatch squad that was send out to find him.

Figure 3.5: The city Nagasakibefore and after the nuclearstrike.

One year and 6 months after the sinking ofthe ferry on lake Tinnsjo, in August 1945, 50pounds of highly purified Uranium incased insomething looking like an oversized trashcanwas being prepared to be loaded on a B-29bomber. Oppenheimer’s team had collectedjust enough purified Uranium for a bomb.Moreover the Plutonium problem had beensolved, and more bombs of the Plutoniumtype were already under construction. Therewas a fair amount of doubt whether or not thebomb was to be used. Germany was defeatedand Japan’s forces were trapped in China,under high pressure of Russia’s Red Army,with American submarines blocking their re-treat to Japan. Japan’s industry was mostlyburned out, and American bombers had al-ready destroyed over 50 Japanese cities. Itseemed only a matter of time before Japanwould surrender. A demonstration in the Pa-cific Ocean was considered, but eventually the final verdict was to use the bombon a Japanese war plant surrounded with workers homes, without prior warning.

On August 6 1945 at 8:16 AM, at an altitude of 1900 feet above the townHiroshima, the final disastrous chain reaction began. The Uranium nulcei usedin the bomb were each more than 4.5 billion years old, their protons and neutronssqueezed together by a force far more powerful than anything mankind has everproduced. In a fraction of a second all these nuclei split almost simultaneously,converting each a small fraction of their mass into a vast amount of energy. Aflash several hundred times brighter than the sun appeared in the Japanese sky,

40

followed by a shockwave faster than the speed of sound, destroying anythingin its path. The death toll was estimated between 90000 and 150000 peoplein Hiroshima, and about 70000 in Nagasaki 3 days later. Roughly half of thecasualties fell on the day of the bombings, while the others died later due toinjuries or radiation poisoning. Japan surrendered 6 days after the bombing ofNagasaki.

3.5 Epilogue: reaching for the stars

Cicilia Payne 1900-1979

Cicilia Payne was the first toshow that the sun consistedmostly out of Hydrogen. As

had Meitner, Payne shesuffered from severe sexism

throughout her career, as hersupervisor first denied her

results and later tried to takecredit for them. Nevertheless

she was later appointed aschair of the Harvard

Astronomy department, as thefirst women ever to head a

department at Harvard.

In the last part of this chapter, we will morepeaceful applications of E = mc2, and learnabout the central role it plays in the universe,and our own very existence. In the early 20thcentury, physicists and astronomers were puz-zled about what could be the source of powerof the sun. The industrial revolution was wellunderway, and by now engineers were very fa-miliar with power sources such as coal andelectricity. The sun was know to emit anenormous amount of power, and had been do-ing this for billions of years without interrup-tion. None of the known fuels at the timewould come even close to delivering such aninconceivably large amount of energy. Af-ter what you have learned in this chapter,you can probably guess that E = mc2 mustbe involved one way or another. Maybe thesun continuously converts some of its massinto energy, using the giant conversion fac-tor c2 in its advantage? It turns out thatthis is indeed the case, although the mecha-nism through which this happens very differ-ent from the splitting of Uranium. The sunconsists roughly for 72% of Hydrogen, 27% ofHelium and about 2% of other elements. Thiswas first shown by the young EnglishwomanCecilia Payne, one of the first women to enter astronomy. Her results unambigu-ously showed that there was simply not enough Uranium in the sun providesits power through fission. The key realization is here that center of the sun issuch an extremely hot place, much hotter than anything on earth. Moreoverthe pressure is enormous. In these extreme circumstances, nuclei can collideand stick together, and hereby convert some of their mass to energy. In a sense,this is precisely the opposite process of fission.

Nuclear fusion is the process by which two or more atomic nucleijoin together, or ”fuse”, to form a single heavier nucleus. During

41

this process some of the mass of the fusing nuclei is converted toenergy.

The center of the sun is hot enough to fuse Hydrogen into Helium, a reactionthat delivers many times more energy that the fission of Uranium. Moreover,the sun use this reaction to burn 620 million tons of Hydrogen each second.This provides a gigantic amount of energy, compared to which the explosion ofan atomic bomb is just a small flickering. Since the sun is such an incrediblymassive object, it can easily sustain its wasteful lifestyle for billions of years.But at some point it inevitably runs out off fuel. At this point all the Hydrogenin the core has been converted into Helium. Since there is no more energy sourceto balance out the crushing force of gravity, the sun will start collapsing underits own weight. The pressure in the center of the sun rises, and at some pointthe sun is so hot and dense that it can start fusion Helium into heavier elementslike Carbon and Oxygen. Although the sun as found a new fuel, this will onlyextend its life for a several hundreds of thousands of years. Helium is not nearlyas good as a fuel as Hydrogen, and the sun needs to burn enormous amountsof it each second to withstand the gravitational pressure. In this phase the sunhas become what we call a red giant, as it has grown to between 20 and a 100times it size. As the sun is dying, she will gradually expel her outer layers, untilonly a small glowing core remains. The sun has become a white dwarf and willslowly fate away.

Figure 3.6: A picture of the fa-mous crab nebula. The glow-ing filaments are the remnantsof the outer layers of the starthat have been blasted away bythe supernova. At the center ofthe nebula lays a neutron star.

Cool. The sun is Helium factory. Maybeit produce some Oxygen and Carbon on theside, but where is all the other stuff comingfrom? What about Iron, Aluminium, Ura-nium, Gold and what not? Where do thoseelements come from? Well, it turns out thesun is a relatively small star. Small stars aregood Helium factories, but make the heav-ier stuff we’ll need a bigger factory. Thesefactories exist, we call the blue giants. Bluegiants are very large stars that are much hot-ter than the sun. Because they are so heavy,they need to burn much more Hydrogen tosupport their weight, and thus their lifetimesare much shorter than the lifetime of the sun.If they run out of Hydrogen and Helium, theycan produce heavier elements, in contrast tothe sun. But also these monster stars cannotextend their lives indefinetifly. The reason is of their doom is Iron. Iron is themost stable element in the universe, which means that fusing Iron into anotherelement actually costs energy. So after the star has its entire core into Iron, itis truelly doomed. It is in a desperate need for energy, but all that is has left isa core of useless Iron. The fat star now undergoes a violent implosion under its

42

own tremendous weight and forms an extremely dense neutron star5 or a blackhole. But in the process of collapsing at bounces back one last time, blastingaway its most outer layers in a gigantic explosion (see figure 3.6). Such an ex-plosion we call a supernova. Supernova’s are powerful enough to wipe their ownplanetary system and those of their neighbors. More importantly, a supernovais so hot that it has more then enough energy to be able to afford the cost offusing elements heavier than Iron. In other words, in a supernova turns energyinto mass, exactly the opposite of the processes that we had discussed so far!The wicked power of Uranium nuclei that destroyed Hiroshima had been lockedin there billions of years earlier by an explosion much more powerful than themost powerful bomb we could even conceive building. In practice, all the atomsin the universe heavier than Oxygen where fabricated in supernovas. Moreoverthese dying superstars are so friendly to immediately blast all these freshly pro-duced goodies into outer space, where they later can start clumping together toform planets, and, at least in one case, life. You, me and all the things we seearound us are literally made of the remnants of a dying star. This is, at leastin my opinion, the most fascinating and important legacy of E = mc2.

Take-home points

• Mass and energy are two sides of the same coin. Under special circum-stances, mass can be converted into energy or visa versa. A tiny bit ofmass corresponds to a huge amount of energy.

• When nuclei split, a small fraction their mass is converted into energy.This can either occur naturally at a very slow rate (millions of years) orstimulated by adding one or more neutrons to the nucleus.

• When a Uranium nucleus splits, it releases a few additional neutrons,which can be used to split more nulcei. This can trigger a chain reactionif the density of pure Uranium is high enough.

• The manhattan project was the first example of ”Big Science”, a paradigmfor scientific research that is increasingly important today.

• Stars are so hot that they can fuse elements into new elements. Smallerstars produce the bulk of the light elements, while heavy elements areexclusively produced by very heavy stars.

Test your understanding!

• What are the components of the equation E = mc2 and what do theymean?

5You can best compare a neutron star with a giant nucleus with trillions of neutrons andno protons.

43

• How is it possible that a heavy nucleus that has been stable for millionsof years suddenly breaks apart when a single neutron is added?

• Describe the German and American efforts in constructing an atomicbomb. What are similarities/differences in their approach?

• What is the difference between Uranium and Plutonium? What are theadvantages/difficulties of each approach?

• If you look at figure 3.1, what is the most important difference betweenelements as Hydrogen and Helium on the one hand, and elements likeIron and Uranium on the other hand? What are the consequences ofthese differences for their nuclear properties?

• Which elements are formed in a star of the size of our sun? Can it produceUranium? Why (not)?

• All current nuclear reactors are based on fission, while reactors based onfusion have been in development for multiple decades now. Why do youthink is one so much more difficult than the other?

• If you were in charge of designing a fusion reactor, which element wouldyou pick as the element to be fused into a new element? Why? Can youthink of elements you would certainly not pick?

Additional references

• Most of the material in this chapter is based on a very accessible book byDavid Bodanis.

• There are plenty of nice videos about fission on youtube that you canexplore. I like this one in particular.

44

Chapter 4

Radioactivity (workshop)

In this class we will distinguish the concept of radiation from radioactivity, andlearn about the different types of radiation. You will get a sense for the relativerisk associated with each of these by performing some quantitative estimates.

4.1 Radiation

In popular culture, the terms of radiation and radioactivity are often inter-changed. Although they are related, for a good understanding it is essential toclearly separate both concepts. In this section we discuss radiation:

Radiation is the process of exchanging a particle or wave betweentwo objects, the emitter and the absorber. Radiation can occurin a many different forms and at very different energies. Radiationthat is sufficiently energetic to break apart atoms is called ionizingradiation. This type of radiation is most dangerous, since it candamage biological tissue or modify our DNA.

There are several types of radiation that you already know of: microwave radi-ation, radio wave radiation, UV radiation, infrared radiation, X-rays and mostnotably: light. These are all examples of electromagnetic radiation. Youwill learn more about electromagnetic radiation in module 3. So you see thatradiation is extremely common; you are literally permanently sitting an intensebath of radiation. In fact your body itself is continuously emitting infrared ra-diation. Off all the types of radiation mentioned above, X-rays are the mostenergetic, followed by UV-radiation and light. Only X-rays can be ionizing,although there are also health risks associated with long-term exposure to UVlight. We will discuss three other forms of ionizing radiation in the next section.

List as many sources of radiation (emitters) as you can, and rankthem according to their size and their intensity (amount of radiationthey emit). Is there generally a relation between the size of theemitter and its intensity? Can you explain this relation?

45

Sometimes radiation can be focussed (for example a laser), but most of thetime it spreads out in all directions evenly (like the radiation from a light bulb).In the case of the light bulb, you know that this implies that the intensity ofthe radiation that you receive diminishes if you move yourself further away fromthe source. This property generalizes to all types of radiation. Another obviousproperty of light is that you can block it by putting another absorber betweenyou and the emitter (for example a wall). This also generalizes to all othertypes of radiation, however some types of radiation are harder to block1 thanothers. X-rays can penetrate flesh and produce an image of the patient’s boneswhile regular light can’t. In summary, there are two ways to shield yourself fromradiation (ionizing or not):

1. Increase the distance between yourself and the emitter. This always works,but the effectiveness depends on the intensity of the emitter. The sun isvery far away, but we still receive a lot of its radiation because it has sucha high intensity.

2. Place another absorber between you and the emitter. The effectivenessdepends crucially on the type of radiation: For some types a piece of paperis enough, while others require thick wall of lead.

Before moving on towards radioactivity, I have one cautionary remark for youin terms of the terminology being used:

In the definition I wrote ”process of exchanging a particle or wave”, however we are dealing extremely small objects and thus the lawsof quantum mechanics must apply. Recall from chapter 1 that thelaws of quantum mechanics prescribe that any microscopic objectmust have the properties of both a wave and a particle, and that themanifestation of either the particle or wave properties depends onthe experiment that is performed. When we are call a microscopicobject ”particle” or ”wave”, we are usually referring to the modelthat is applicable in most experiments, but we need to keep in mindthat every ”particle” can also act as a wave and visa versa. Forexample: Light is usually categorized as a wave, since this picture issuitable to explain the well known diffraction and interference effectswe discussed in chapter 1. However there surely exist experiments2

in which light acts as a particle. Similarly atoms are usually labeledas particles, despite the fact that there also exist many experimentsin which atoms behave as waves. The naming conventions are largelyhistorical artifacts from the time before wave-particle duality wasdiscovered.

1A particularly fascinating form of radiation are neutrino’s. Neutrino‘s are emitted by thesum in enormous quantities and pass through the entire earth. As you read this billions ofneutrino’s are passing through your body. Although neutrino’s are very interesting, they areoutside the scope of this course. If you are interested you can find more information here.

2For example the photo-electric effect, which lead to the Nobel Prize for Einstein in 1921.

46

4.2 Radioactivity

We saw that radiation can have many different kinds of sources. Radioactivityis one special example of such a source

Radioactity is the process by which an atomic nucleus loses energyby emitting ionizing radiation. In the process the nucleus mighttransform into a nucleus corresponding to a different element. Notall nuclei can undergo this process. Nuclei that can are called ra-dioactive nulcei or unstable nuclei.

In other words, radioactivity is the process inside the nucleus that causes ionizingradiation to be emitted.

Radio waves used in radio communication have nothing to do withradioactivity and are harmless.

An important thing to remember is that each unstable nucleus can only decayonce.3 This means that if we start with a certain fixed amount of radioactivematerial and we wait long enough, all the nuclei will have decayed and no moreradioactive material would be left. So the easiest way to get rid of radioactivematerial is to simply wait. How long should we wait? This is quantified by thehalf-life time of the unstable nucleus.

The half-life time of a nulceus is the time after which on averagehalf of the nuclei that you started with will have decayed.

To understand half-life better, take a look at this interactive simulation. Thehalf-life time is a very important parameter that policy makers have to accountfor when making decisions on the processing of nuclear waste.

Now that the basic concepts have been introduced, we can take a closer lookat the kind radiation that is emitted by these unstable nuclei. There are manydifferent types of radiation from radioactivity, but the most important ones arecalled α, β and γ radiation:

• α radiation: Some very heavy nuclei can expel an entire Helium nucleus(also referred to as an α-particle). α particles are really the monster-trucks among the ionizing radiation: They are quite heavy and inflictmassive damage to the atom they collide with. Since they are big theyare likely to collide with other nuclei, and thus they can‘t penetrate verydeeply into the material. A piece of paper or your skin are enough tostop these particles. α-radiation external to the human body is thereforequite harmless, although the new nucleus that was created in the decayis often a β or γ emitter which are dangerous even outside the humanbody. On the other hand, if a sizable concentration of an α-emitter makes

3There are cascade decays known where the nucleus decays into another nucleus whichalso radioactive, which in then further decays. The cascade will stop whenever the daughternucleus is a stable nucleus.

47

its way into the body through inhalation or food it is very poisonous.The α-emitter 210Po was used in the murder of the Russian dissident andex-FSB officer Alexander V. Litvinenko in 2006.

• β radiation: We speak of β-radiation when a nucleus emits a single elec-tron. To stay with the traffic analogy, you can compare β-radiation witha motorcycle: Its impact upon collision is much less than for the monstertruck α particle, but since it is smaller, a motorcycle can weave throughtraffic much better. To stop β particles you typically need a layer of metalor several meters of air. β-radiation can therefore penetrate deep into thehuman body when a β-emitter in contact with the skin. β-emitters aresometimes used for cancer treatment. When a β-emitter is injected intothe tumor the resulting radiation can destroy the cancer cells surroundingthe emitter.

• γ radiation: γ radiation is electromagnetic radiation, just as light and X-rays, but more energetic. γ radiation is less ionizing than α or β radiation,but can penetrate materials more easily. You could compare γ radiationswith pedestrians. They can penetrate traffic much better than motorcyclesand trucks, and their impact upon collision is much smaller. However thedanger here is high intensity: although a collision with a single pedestrianmight cause little harm, this changes if you are overrun by a crowd of amillion pedestrians.

The properties of α, β and γ radiation are summarized in table 4.1. Fora nice video of a demonstration of the ionizing properties of α radiation, clickhere.

α radiation β radiation γ radiation

object emittedH4

e nucleus (2 pro-tons + 2neutrons)

1 electronelectromagneticwave

harmful very harmful quite harmfulharmful in largedosis

penetrationdepth

sheet of paper sheet of Aluminium several cm of Lead

typical lifetimes 1000 years or more hours to months less than a second

Table 4.1: Summary table of the properties of the most important types ofionizing radiation from nuclear decay.

Can you list at least 5 beneficial applications of radioactivity? Usethe internet.

48

4.3 Some examples

The rest of this section consists of a few problems that you should tackle insmall groups during class time. You can find the full set of instructions in thesakai resources folder. The problems are only repeated here for easier referencewhen you are studying for the exams.

4.3.1 Problem 1: Estimate your annual radiation dose

To estimate your yearly dose of radioactivity, complete the following questions:

1. Fill out the worksheet “background radiation“ (attached). You canfind a map with New Jersey’s radon levels here: http://www.city-data.com/radon-zones/New-Jersey/New-Jersey.html. To compute your yearlydose due to radon, you’ll need to convert the information on the map fromunits of pCi to mSv. The absolute amount of radiation is measured inpico-Curie (pCi), while mili-Sievert (mSv) takes into account the impactof particular kind of radiation on biological life. A continuous exposure ofa radon level of 1pCi

l corresponds roughly to 0.4 mSv

yr . In formulas this is

1pCi

l≈ 0.4

mSv

yr.

2. To interpret what you found, answer the following questions:

(a) How does your yearly dose compare to the dose of your fellow groupmembers? What is causing the difference?

(b) Compare your yearly dose with some of these examples http://en.

wikipedia.org/wiki/Sievert#Dose_examples. Is the dose you re-ceived last year high or low compared to some of these examples?(The notation mSv

a use on Wikipedia means the same as mSv

yr .)

49

(c) For example, how does the total dose you received last year compareto the total dose the received by people living close to the Fukushimaaccident?

Useful information:1 MSv= 1,000,000 Sv = 106 Sv1 kSv= 1000 Sv = 103 Sv1 mSv= 0.001 Sv = 10−3 Sv1 µSv= 0.000001 Sv = 10−6 Sv

Practical comment: We recommend that all members of the group calcu-late their own personal dose of radioactivity (because it’s fun and educational),but it suffices to hand in a single worksheet with the names of all the groupmembers on it. (You can just choose one group member’s worksheet to hand in.You will find that the answers are not all that different between various groupmembers.)

4.3.2 Problem 2: Carbon dating

Carbon dating is a very important tool in archeological studies. Carbon-14 is a radioactive isotope of Carbon which is continuously being producedin the atmosphere by collisions of Nitrogen with cosmic radiation. Carbon-14 is a β emitter and has a half life time of 5730 years. In living organ-isms the amount of Carbon-14 is roughly constant, because their Carbon-14intake from the atmosphere roughly compensates for the amount of Carbon-14 nuclei that decay during the lifetime of the organism. When the organ-ism dies, its Carbon-14 supply is not replenished, and steadily decreases dueto the radioactive decay of the nuclei. By measuring how many nuclei areleft, researches can estimate how much times has elapsed between the deathof the organism and today. Download the radioactive dating game: http:

//phet.colorado.edu/en/simulation/radioactive-dating-game and solvethe questions in the “Radioactive dating game“ worksheet. If you like youcan learn more about Carbon dating here http://science.howstuffworks.

com/environmental/earth/geology/carbon-14.htm. (If you like, you can doone of your blog assignments about it.)

50

4.3.3 Problem 3: Cell phone radiation

This problem will help you estimate how much energy you absorb from theradiation from your cell phone. Remember that cell phones use radio waves,which are not ionizing and are unrelated to radioactivity. Answer the followingquestions:

1. The power output of a typical cell phone is no more than 2 W.

(a) Assuming that all this power is absorbed by your head, how muchenergy does your head absorb from a 5 minute phone call? Recall1W = 1 Joule/second.

(b) On a sunny day the power delivered by the sun on the earth’s surfaceis roughly 1200 W/m2.) How much energy does your head absorbfrom walking in the sun for three hours? Estimate the surface areaof your head to do calculate this. Recall that 1m2 = (100cm)2 =10000cm2 = 104cm2.

(c) How do your answers for (a) and (b) compare? Which one is largest?Is it a big difference?

2. A cellphone tower typically has a power output of a 100 W. The totalpower emitted by the tower gets distributed in all directions, so the power

51

in one particular direction ends up being much less. Assuming that thecell phone tower emits power in the same amount in all directions, thepower per surface area a certain distance from the tower is given by theformula

power

surface area=

total power output of the tower

4π distance2

(a) What is the power per surface area at a distance of 500 meters fromthe cell phone tower? Is this larger or smaller than the power persurface area delivered by the sun? (See part b of previous question).

This is about 108 times smaller than the power per surface area

delivered by the sun.

(b) If you are standing for three hours at a distance of 500 meters fromthe tower, what is the energy absorbed by your head during thattime? Use the estimate of the surface area of your head that youmade for part b of the previous problem.

(c) Which of the following leads to the greatest about of energy absorbedby your head?

• Use your cell phone for 5 minutes (answer part 1 (a))

• Walk in the sun for 3 hours (answer part 1 (b))

• Stand near a cell phone tower for 3 hours (answer part 2 (b))

Take-home points

• Radiation and Radioactivity are related but not the same thing.

• There are several different types of ionizing, with very different properties.Which one is most dangerous depends on the situation.

• You can not ”remove” radioactivity. All you can do is wait long enoughuntil all radioactive atoms have decayed.

52

Test your understanding!

• Distinguish clearly in your own words between radiation and radioactivity.

• What are examples of radiation? Which of your examples are harmfuland under what conditions are they harmful?

• If you cannot undo the radioactivity of a substance, what do people meanwhen discussing the clean-up of a radioactive site or substance?

• Why is the half-life time an important criterium when addressing environ-mental issues?

• Can you list at least 5 beneficial applications of radioactivity?

• Take the radioactivity quiz!

53

Chapter 5

The Fukushima disaster

In this lecture you will learn how a nuclear reactor works and what can go wrong.We will investigate in detail the Fukushima disaster and its consequences forthe environment.

5.1 Nuclear reactors

Nuclear reactors generate electricity in the same way as ordinary coal or petroleumplants do: They burn fuel to turn water into steam, which is than channeledthrough a set of turbines. The steam passing through the turbines makes themrotate, which generates electricity. After passing through the turbines, thesteam condenses to water and the whole process is repeated. This is process isillustrated in figure 5.1. The major difference with a conventional petroleum orcoal plant, is the type of fuel that is burned. In particular, nuclear plants arevastly more efficient that conventional plants. A typical nuclear plant willuse several tens of tons of fuel each year, while a coal plant consumes severalthousands of tons of coal a week. Here is a video of a gentlemen with a juicyBritish accent explaining the general setup of a nuclear power plant. (He doesn‘treally explain the nuclear aspect, but I will do so later in these notes.) If youprefer an animation instead, you can watch this one.

In figure 5.1 you can see a picture of an actual power plant. The large towersare needed to release the water vapor from the cooling circuit in the air. Asyou might guess, nuclear plants need huge amounts of cooling water, so theyare often constructed next to rivers or near the coast.

A common misconception, which is fueled by the scary cooling tow-ers, is that nuclear plants are very harmful for their immediate en-vironment. However in normal circumstances their are much lessharmful than plants that burn fossil fuels, as they only release steaminto the atmosphere, rather than the Carbon dioxide, dust and heavyelements released by plants burning fossil fuels. Just from the point

54

of view of global warming nuclear plants are very environmentallyfriendly in comparison to coal and oil consuming plants.

Figure 5.2: A picture of a nuclear powerplant. You can clearly see the cool-ing towers. The constructions with thespherical roofs contain the actual reac-tors.

Now lets take a closer look atthe reactor itself, in figures 5.3a and5.3b. In the center of the reactoryou’ll find the fuel rods, which con-tain the highly enriched Uranium orPlutonium. The idea of a nuclear re-actor is precisely the same as of theatomic bomb, which we discussed afew classes ago. To extract a mean-ingful amount of energy from the fis-sion process, it is essential to es-tablish a chain reaction, such thatthe neutrons emitted from the fis-sion of one nucleus trigger the fissionof the next set of nuclei. For theatomic bomb this chain reaction wasextremely rapid and violent, and allthe nuclei split in a fraction of sec-ond, delivering a gigantic amount ofenergy. This is possible because the chain reaction was made to be as efficientas possible: every splitting Uranium/Plutonium nucleus would induce the split-ting of 2 or 3 other nuclei. For peaceful power generation such a rapid chainreaction is of course undesirable. Instead you would want a fairly slow reaction,where on average the fission of each nucleus triggers the fission of about oneother nucleus. This is achieved by making use of control rods. These canbe raised and lowered in the reactor and consist out of a material that easilyabsorbs neutrons, usually Cadmium. By regulating the amount of rods, techni-cians can regulate the speed of the chain reaction: the more rods are inserted,the more neutrons are absorbed and the slower the reaction occurs. If all therods are inserted, the chain reaction will stop and the reactor is shut down. Youcan find an interactive simulation here. Click on the ”nuclear reactor” tab. Nowyou can fire neutrons in the reactor and play with the control rods yourself. Ifyou paid close attention during the last few lectures, you might wonder how thereaction is sustained in the first place, since the neutrons from the fission travelat high speed and tend to just sail past the other nuclei. (Remember that thevast majority of the volume of an atom is just empty space.) Heisenberg andhis crew solved this problem by slowing down the neutron using heavy water.Something similar happens in a nuclear reactor: the space between the fuelrods and the control rods in filled by a moderator, which has the exact samefunction as the heavy water in Heisenberg‘s experiments. Nowadays there areseveral other types of moderators besides heavy water that are commonly used,like Beryllium, Lithium or graphite.

55

Figure 5.1: Schematic representation of a nuclear reactor. The generator sup-plies power to the electricity grid. Credit: http://www.freeinfosociety.com/

(a) Picture of nuclear reactor. Thewhole reactor is submerged under wa-ter, which is used to both as a radiationshield and to cool the reactor. The blueshine is due to Cherenkov radiation, seetext.

(b) Schematic representation of the ac-tual nuclear reactor. Credit: EuropeanNuclear Society

56

Figure 5.3: Unlike its common repre-sentation in popular culture, radioactivematerials don’t glow. Certain materialscan produce blue Cherenkov light, butonly when submerged under water.

Before we move on to what can gowrong with nuclear reactors, I’d liketo tell you something about the fas-cinating blue shine on figure 5.3a. Incontrast to popular culture, nuclearreactors have a blue and not a greenshine. Why is that? We learned lastlecture that ionizing radiation is in-visible, and of course nuclear reac-tion can not be exception. The blueshine is a very interesting, indirect ef-fect, and only happens when certainradioactive materials are submergedin water. When a high speed neu-tron crashes in to a water molecule,it occasionally knocks off an electron,which will fly away with high speedas well. Sometimes the electron fliesaway so fast that it exceeds the speed by which light travels in water. 1 When acharged particle, like an electron, exceeds the speed of light in a certain medium,like water, it emits light of a certain color, in this case blue. This is called theCherenkov effect. A detailed treatment of the Cherenkov effect is beyond thescope of this course, but you can think of it as something very analogous to asupersonic aircraft traveling through the sound barrier. This results in a soundshockwave that we on the ground perceive as a loud bang. In case of Cherenkovradiation the blue light is analogous to the bang. Most importantly you shouldremember that the blue light is an indirect effect, caused by the high speedneutrons crashing into electrons, but by no means is it caused by ”radioactiveglow” or something along those lines. There is no such thing.

Finally, there are few important concepts that we need to introduce thatrelate to nuclear disasters. They appear often in the media, and it is importantthat you understand what they mean. The first concept is that of a nuclearmeltdown:

A nuclear meltdown or meltdown is a situation in which, forwhatever reason, the cooling of the nuclear fuel rods fails and thefuelrods melt. A meltdown can occur even after the the chain re-action is stopped, since the radioactive decay in the fuel rods keeps

1You might recall the famous speed limit of nature that nothing can ever travel faster thanthe speed of light. This speed limit refers to speed of light in vacuum. In a medium likewater, light travels slightly slower (because it constantly bumps into water molecules) and itis possible for particles to exceed this speed. However all objects are still bound to travelslower than the speed of light in vacuum, under any circumstances. There was some briefcontroversy last year about certain particles, called neutrino, who were measured to travelfaster than the speed of light in vacuum. In the meanwhile it became clear that there was amistake in this experiments, and also neutrino’s obey the fundamental speed limit, just likeanyone else. If you want you can read more about it here.

57

producing heat many years after the reactor has been shut down.The temperature during a meltdown can reach several thousand de-grees and the reactor core becomes the equivalent of extremely ra-dioactive lava. In the worst case scenario it can melt through thecontainment vessel and the reactor building, cause severe environ-mental problems.

An extreme case of a nuclear meltdown is sometimes referred to as the Chinasyndrome:

In the event of a complete nuclear meltdown, it has been theorizedthat the temperature of the the liquid reactor material would behigh enough to melt through the entire earth’s crust and end upon the other side of the world, hence the name China syndrome.This is however a misconception, as the radioactive lava would stopat the center of the earth. The China syndrome is the absolutenightmare scenario of all nuclear accidents, as the radioactive lavawould heavily contaminate the groundwater supplies of a very largearea.

You can watch a nice explanation of a nuclear meltdown and the China syn-drome in this video. Several partial meltdowns have occurred in history, both incommercial power plants (Chernobyl, Three Mile Island and Fukushima) and inmilitary applications (several nuclear submarines, both American and Russian).None of these incidents has let to the China syndrome.

5.2 55 reactors on the Ring of Fire

To understand the cause of the Fukushima disaster, we first need to take acloser look at the special geological location of Japan. Japan is located on whatgeologists call the pacific Ring of Fire, see figure 5.4. The pacific Ring ofFire is an area with increased geological activity (vulcanoes and earthquakes)at the edges of the basin of the Pacific Ocean. The reason for its existence istwofold:

• The earth’s crusts is not not monolithic, but consist out of several patches,which geologists refer to as tectonic plates. These tectonic plates canslide and move with respect to each other, which creates tension in theearths crust. When this tension is released, an earthquake occurs.

• The earth’s interior is hot and to some extend liquid due to the enormouspressure and the heat released from radioactive decays (mostly Uranium)in the earth’s core. This enormous source of heat drives the motion oftectonic plates, as shown in figure 5.5.

In practice this mechanism results in the ocean plate sliding under the conti-nental plate at its boundary, which results in vulcanic activity and earthquake,

58

Figure 5.4: The pacific ring of fire. Black lines are tectonic plate boundaries,red dots indicate vulcanoes and yellow dots indicate major earthquakes.

hence the name ”Ring of Fire”. It turns out that the ridge in the center ofthe Atlantic ocean creates crust faster than its counterpart in the pacific ocean.This causes a slow but steady squeezing of the pacific ocean plate. In 300million years the pacific ocean will have disappeared and America will havecollided with Japan, which will result in a enormous mountain range, like theHimalaya’s. (The Himalaya’s where created by the collision of the Euroazianand Indian tectonic plates.)

On the other hand, Japan has the highest amount of nuclear reactors persurface area of any nation in the world. So why did they decide to construct 55nuclear reactors right on one of the most geologically active areas in the world?

After World War II the study of geology really took off. At the time therewere two competing theories about the dynamics of the earth. The traditionalview was that the earth was slowly cooling and shrinking, which causes ripplesand trenches to occur, like for a dried prune. The alternative was the wacky the-ory of drifting tectonic plates. Gradually more and more evidence was collectedin favor of the latter theory, and in the 1970’s the latter was accepted by mostof the geologists in the United States. However it took the Japanese scientificcommunity until the 1980’s to settle the question, while most of Japan’s reac-tors were constructed in the 70’s. If the theory of tectonic motion would havecaught on earlier, it is unlikely that Japan would have constructed 55 reactorson one of the most seismically active spots on the planet.

Why did it take the Japanese science community so long to adopt the correcttheory? This is due to a sociological phenomenon that has occurred several timesin the history of science. Paradigms often shift when everyone is convinced ofthe new idea, but occasionally an older generation of influential scientists is not

59

Figure 5.5: The heat at the earth‘s core drives the motion of the tectonic plates.New crust is created at the center of the ocean, pushing the existing crust tothe boundary‘s, where it slides underneath the continental plate. This slidingoccurs not smoothly but with abrupt shocks, which we call earthquakes.

ready to accept a radical idea and they stick to the well established paradigmthat has worked well for them throughout their careers. Since these peopleoften make decisions in terms of hiring or promoting younger colleagues, theirvision can have a large impact on what direction the field is moving into. (Evenscientists need to eat you know.) A common cliche is that certain paradigmsonly change one retirement or funeral at a time.

Why am I bringing this up, while it is only marginally related to the topicof this lecture? I think it is important to take lessons from the past, and seehow we can better avoid potentially disastrous policies based on erroneouslyinterpreted scientific data. The Japanese problem is certainly not the only ex-ample in history: In the 1940’s an unschooled former peasant called Lysenkopersuaded Sovjet leaders that genetics was just a product of Western propa-ganda, and that agriculture according to good-old communist principles wouldyield superior results. It set back Sovjet agriculture for decades, until the studyof genetics was finally taken serious in the 60’s. Other examples we find in theUnited States, even as we speak. Important scientific paradigms like evolutionand global warming are continuously under attack, attacks which are driven by adesire to stick with a traditional, more comfortable, paradigm. The experimen-tal and theoretical evidence is overwhelming in the case of evolution, and veryconvincing in the case of global warming. A relatively new feature in the debateis that the discussion has been displaced to a large extend from the scientific fo-rum to the political forum. (In particular on evolution the case has been closeda long time ago among scientists.) This results in policies being made based onideology rather than scientific data. Policies which greatly impact our environ-

60

ment and the way we educate the future generations of US citizens. Eventuallythe scientific truth will prevail, however your children and grandchildren willhold us accountable for the damage done by this sort of delay...

5.3 The Fukushima disaster

Figure 5.6: A picture of a spentfuel pool.

On March 11th 2011 at 2:46pm, about 300hundred miles of the Okhotsk plate snappedupwards. As a result the island Honshumoved 8 feet closer to the United Statesand about 250 miles of Japanese coastlinedropped roughly two feet. The earthquake it-self lasted 6 minutes and the energy releasedwas about 600 millions times the energy re-leased in the Hiroshima bombing. Tokyo’sskyscrapers swayed back and forth for min-utes as you can see in this video, and it isthanks to the impressive skills of the Japaneseengineers that these earthquake proof build-ings survived the quake, saving thousands oflives. However worst was yet to come, as ahuge tsunami was kickstarted by the quake.Tsunami warnings were issued promptly af-ter the first shocks by the Japan Metreolog-ical Agency, allowing many the opportunityto seek higher ground. About 30 minutes af-ter the quake the first tsunamis arrived at theJapanese shoreline, causing imens amounts ofdestruction. At some places the waves ex-ceeded 3 stories in height.

The Fukushima Daishi nuclear plant contained 6 nuclear reactors, ofwhich only reactors 1, 2 and 3 where in use at the time of the earthquake. theother reactors where shut down prior to the earthquake for maintenance andupgrades. In addition to the active reactors, each reactor building also containa spent fuel pool. As the name suggest this is a pool of water in which usedup fuel rods are cooled down until they are cold enough for further processing.An picture of a spent fuel pool is shown in figure 5.6. As for the active parts ofthe reactors, these spent fuel pools need a constant flow of cold water to keepthe temperature of the fuel rods under control.

The March 11th earthquake triggered a disastrous sequence of events in thisfacility:

• March 11th 2011, 2:46 pm: The earthquake struck the plant andall control rods in the reactors in operation where fully lowered downautomatically by the emergency system, which immediately stopped the

61

nuclear chain reaction. So far so good. However the quake also knockedout an electrical power station 6 miles from Fukushima Daishi. This powerstation supplied the pumps of the plants cooling system with the necessarypower. Even after the chain reaction is been brought to a end, the nuclearfuel remains extremely hot for a very long time because of the radioactivedecay of its elements, and it is essential that it remains continuously cooledby circulating cold water over the fuel. Now that the power station wasknocked out, the plants 13 giant diesel generators automatically took over,supplying the pumps with the power to continue cooling the fuel rods.

• March 11th 2011, 3:01 pm: The first tsunami arrived and spilledover the 17 feet high seawall protecting the plant, flooding most of theinfrastructure. The salt water destroyed 12 out of the 13 emergency dieselgenerators. The third emergency system kicked in, where power for thepumps was provided by emergency batteries, which are designed to last12 hours. As an added complication, the meters that were supposed tomeasure the water flow into the reactor where damaged as well, and theengineers had no means of knowing whether the pumps and the batterieswere doing what they were supposed to be doing.

• March 11th 2011, 7:30 pm: The Japanese government called for anuclear emergency and installed a 3 kilometer evacuation zone around theplant. Less the 24 hours later the evacuation zone was extended to 20kilometers.

• March 12th 2011: morning The emergency batteries had now certainlydied, and power had not been restored. The water cooling the reactorwas no longer being refreshed and started evaporating rapidly, filling thecontainment building with radioactive steam.

This does not mean that the water itself had become radioac-tive. It means the steam was mixed with radioactive elements,evaporated from the fuel rods themselves. The water vapor insuch a situation is thus not radioactive itself, but it can carryradioactive elements along with it over long distances when it isreleased.

As time went on, pressure continued to build up, in particular in reactor1. Even worse, the temperature was now high enough to break the bondsfor the water molecules and to induce the chemical reaction

2H2O → 2H2 +O2

as shown in figure 5.7. This is a very dangerous situation, since a mixtureof Hydrogen H2 and Oxygen (O2) gas is an extremely explosive combi-nation. The operator of the plant, TEPCO (Tokyo Electric and PowerCompany) started venting the radioactive steam from reactor 1 into theair. This was a clear choice for the lesser of two evils.

62

Figure 5.7: At high temperature, H2O bonds can break, resulting in the forma-tion of Hydrogen (H2) gas and Oxygen (O2) gas, a very explosive mixture.

• March 12th 2011, 3:30 pm: The venting of the radioactive steamproved too little and too late. A Hydrogen explosion destroyed the outerbuilding of reactor 1, releasing large amounts of radioactive materials intothe air. The reactor core appears to have remained intact at this time.

This was certainly NOT a nuclear explosion, as was the case inHiroshima and Nagasaki.

Reactor 1 had undergone a meltdown, and it became clear later the ra-dioactive lava had melted through the containment vessel and part of theconcrete casing. In the meanwhile the situation at reactors 2 and 3 re-mained critical, since also these reactors underwent a partial meltdown.

• March 13th 2011, morning: The Japanese government ordered Tepcoto cool the reactors using sea water. This was a desperate measure, sincethe sea water would not only permanently damage the reactors, but moreimportantly, it would be contaminated in the process. About 500m3 ofcontaminated water would leak back into the soil or the sea on a dailybasis, until a permanent solution would be found.

• March 14th, morning: Another Hydrogen explosion blew away mostof the roof and the walls of the building containing reactor 3, as hadhappened for reactor 1 a few days earlier.

• March 16th, about 6 am: Yet another Hydrogen explosion destroyspart of the top floor of the building containing reactor 4. Recall thatreactor 4 had been shut down for maintenance prior the earthquake, butHydrogen gas originating from reactor 3 had been piling up in the build-ing of reactor 4 through a shared air conditioning vent. This placed theengineers for yet another problem: it was critical that the spent fuel inthe spent fuel ponts, present in all reactors, remained submerged under

63

Figure 5.8: Special high pressure cement truck spraying water directly into thespent fuel pool of reactor 4. Source: Reuters

water. The plumbing that is supposed to continuously replace hot waterwith cold water was no longer functioning, and the water that was readilyevaporating due to the heat produced by the spent fuel rods. Moreoverthe roofs of reactors 1,2,3 and 4 where now either damaged or destroyed,and if the water levels in the pond would drop below the level of the fuelrods, large amounts of highly radioactive waste (in particular radioactiveCesium and Iodine) would be in open contact with the air. This couldhave resulted in highly radioactive waste being carried by the wind overa distance of more than 20 kilometer. Certain types of radioactive wasteremain radioactive for about 10 000 years. Helicopters and firetrucks wereused to spray water over the buildings, in an attempt to refill the spentfuel pools. The most efficient method proved to spray water directly intothe spent fuel pools through a long hose and from special trucks, whichare intended for pumping concrete to high levels in construction works,see figure 5.8. This effort succeeded to some extend, as spent fuel rods arebelieve to have been remained submerged by water for most of the time.

• Summer 2012: Closed circuit cooling systems had been restored, remov-ing the need to contaminate sea water to cool the reactors and to refill thespent fuel pools.

• December 2012: Reactors 1,2 and 3 were brought to a cold shutdown,which means in practice that no there is little further risk for a furthermelting of the reactor core. Nevertheless the situation remains critical as,one needs to prevent further nuclear spill as much as possible. In par-ticular, some experts are concerned about the stability of the building of

64

reactor 4. A collapse of this building would have disastrous consequencesfor the spent fuel pool in this facility.

5.4 Aftermath

6 employees of the Tepco died during the disaster or during the attempts to getthe plant under control. None of these deaths is shown to be directly related toradiation poisoning. No far no deaths have been linked directly to the radiation,although several elderly persons died from the effect of having to evacuate.Japanese instated an evacuation zone of 30 km around the plant, where nobodyis supposed to be living. It is likely that this region will remain uninhabitablefor decades. The reason for this no-man zone is the radioactive fall-out whichis particularly high the closer you get to the Fukushima plant:

Radioactive fall-out or fall-out are the radioactive dust particlesthat are blown into the air when a nuclear incident occurs. The tinydust particles get carried by the wind and can travel for long dis-tances, sometimes even across the globe. When it rains they comedown to the soil, and can be a health hazard when their concentra-tion is sufficiently high.

The fall-out of the Fukushima disaster has been measured all across theglobe, including in America, South Africa and Australia.

This does not mean that the Fukushima disaster imposes an im-mediate health hazard for people living in the United States. Theradiation dose you might get from the Fukushima fall-out is neg-ligible compared to your normal annual radiation dose, which youcomputed last class.

The dangers from direct irradiation are usually not significant, except forpeople working for an extended period of time in regions with very high radiationlevels, like the emergency workers and technicians who stabilized the Fukushimaplant, and it is likely that many of them will suffer health problems in the future.When the radiation doses are lower, external irradiation is not the main concern.The reason is that most radiation, in particular α and β can be stopped by air,clothes or skin. Moreover the dust particles get more and more diluted overtime, which should result in lower radiation levels.

What is much more worrisome, is the potential contamination of the foodchain. There are two reasons for this:

• When radioactive particles are inside the human body, there is no shield-ing and even α and β particles can now easily damage biological tissue.Moreover the radiation is guaranteed to hit a target when the emitter isinside the body, while for emitters external to the body the majority ofthe radiation will just go into the air or earth.

65

Figure 5.9: Diagram illustrating the accumulation of contaminants in the foodchain.

• The concentration of contaminants in larger animals products, like largefish, can be high, even if the concentration in the surroundings is low.When animals and humans take in certain radioactive elements like ra-dioactive Srontium and Iodine, certain organs collect these elements andprevent them from being excreted. (I will explain this better shortly.)This means that over time, the body collects more and more radioactivesubstance. This is not necessarily a problem a priori, if the concentrationis low. But consider the following: A small fish collects a small amountof contaminants over some period of time, after which its get eaten bya larger fish. The larger fish eat multiple small fish, which each carry asmall amount of contaminants. So the slightly larger fish de facto col-lects multiple small pockets of contaminants, that now accumulate in itsbody. When this fish in its turn gets eaten by an even bigger fish, thatbigger fish will collect even more contaminants. This process is illustratedin figure 5.9 and is shown to work for other contaminants as well. Onewidespread example of this is the presence of Mercury in large fish liketuna. In summary, the dose of radioactivity in certain animal productscan greatly exceed the dose you would naively expect from radiation levelsin its environment. This promises to be a particularly difficult problem inJapan, since the Japanese’s diet heavily relies on fish and large amountsof radioactive elements were leaked to the sea in a desperate attempt tocool the reactors with sea water.

As we mentioned, radioactivity is most dangerous when the elements aretaken up by the human body. Two such elements are Iodine 131 and Srontium90:

• The human body needs a certain amount of Iodine, in particular chil-dren. One of the functions of our thyroid is to stock up on Iodine, butthe thyroid does not distinguish between radioactive and non-radioactiveIodine. If it stocks up too much radioactive Iodine this can cause thy-roid cancer. After the Chernobyl disaster, a sharp rise in thyroid cancers

66

was observed, in particular with young people. (Thankfully the survivalrate for thyroid cancer is rather high when treated properly.) One canprotect oneself against radioactive Iodine by taking Iodine tablets, whichsaturated the thyroid with Iodine, leaving no room for radioactive Iodine.The radioactive Iodine will then just be excreted by the body.

• Strontium does it destructive job in a different fashion. Srontium is justone row below Calcium in the periodic table of elements, and thus hasvery similar chemical properties as Calcium. When radioactive Srontiumenters the body, it is possible that it the body will mistake it for Calciumand incorporate it in its bones. The Srontium then decays and radiatesthe bone marrow, which can lead to leukemia. It has a half life time of 29years and there is no way to neutralize the effect of Srontium once it hasentered the body. Bone marrow transplantations to fight the leukemia areoften the only solution.

The long term impact of the Fukushima disaster on the health of the Japaneseis still highly uncertain. Much will depend on how the government will continueto react to the disaster. The Japanese now need a strict screening of their foodintake, in particular fish, and good education and training for the whole popula-tion on how to best protect themselves from the effects of radioactive pollution.Furthermore they will have to continue to monitor radiation in and close to theexisting safety perimeter, and if necessary expand it.

You should keep in mind that the radiation levels in the currentsafety perimeter are not of a magnitude that would make you dropdeath in week if you entered the zone. These safety perimeters areintended to protect people from long term exposure. For example,there are now tourist tours that can take you to the old Chernobylreactor. A young person can probably live for as long as a yearor more in the Chernobyl ”death zone” without suffering any ma-jor health effects. However there is no good data on the effect ofthis kind of radiation doses over a time span of multiple decades,which is why permanently living in these safety perimeters is highlydiscouraged or forbidden.

Despite all environmental consequences for Japan and its population, thedisaster had also a few positive effects. The world wide attention for nuclearsafety has certainly increased, and many countries are reevaluating their reac-tors, strengthening security measures and closing down their oldest reactors. Inparticular China, which has 27 new reactors under construction, is likely to slowdown the pace of their nuclear ambitions in favor of more and better trainingof engineers and operators. Germany on the other hand has expressed the am-bitious to close all of its power plants in the long run, to reform the electricalgrid and to become the first industrial nation to rely mostly on renewable en-ergy. These developments are good news for both opponents and supporters ofnuclear energy.

67

5.5 Other incidents with nuclear reactors

For the sake of completeness, we briefly discuss the two other major incidentsthat have so far occurred with commercial nuclear plants.

Three Mile Island

The Three Mile Island nuclear reactor is located at the Susquehanna River,10 miles North of Harrisburg, Pennsylvania. On March 28th 1979 at 4 am,a small inlet valve for cooling liquid on one of its reactors failed, leading to atemperature rise inside the unit. The automatic emergency system immediatelylowered the control rods, shutting down the chain reaction. A sequence of othersafety mechanisms kicked in to provide extra cooling for the reactor, but wereeach aborted both through human errors and mechanical defects. The fuel rodsstarted to melt and Hydrogen gas continued to built up, which let to a Hydrogenexplosion in the afternoon. The explosion damaged the reactor building but notto containment vessel. The latter fact is what prevented a complete meltdown.The reactor was brought to a cold shutdown two weeks after the incident. Inprocess of the explosion, radioactive materials were released in the air and inthe Susquehanna river. To this day, their effect on the local population remainslargely unknown.

Chernobyl

The Chernobyl nuclear reactor is located about 80 miles North of Kiev. OnApril 26th 1986, sovjet engineers performed a test on the reactor in an attemptto improve its emergency system. A sequence of multiple human errors in com-bination with flaws in the design of the reactor, caused the temperature in thereactor to rise to very high levels, resulting in a partial meltdown and a seriesof explosions. The explosions destroyed the containment building and damagedthe reactor vessel. The radioactive fall-out from the accident was more than200 times the fall-out from the Hiroshima and Nagasaki bombs combined, andradiation spikes over 10 000 the normal value were measured as far as Scotland.At least 30 emergency workers died from acute radiation poisoning in the weeksafter the disaster. The number of indirect deaths due to cancers caused radi-ation poisoning is heavily under debate, but estimates range from thousandsto more than a hundred thousand. At this time the rate of Thyroid cancer inUkraine is still 20 times higher than before the accident. A safety perimeterextending over 19 miles around the facility is still in effect, which virtually un-inhabited. The area is estimated to not to be safe for human life for another20 000 years. Although the full aftermath of the Fukushima disaster is notyet known, the Chernobyl accident is likely to remain most devastating nuclearaccident in history.

68

Take-home points

• Working principle of nuclear reactors

• The concept of a nuclear meltdown and the China syndrome

• The ring of fire and why it is the reason for earthquakes in Japan

• The concept and use of a spent fuel pool, and why it is important tocarefully maintain it.

• Major health hazards after the disaster for the surrounding populationand how to protect oneself against them.

Test your understanding!

• Explain to a friend how a nuclear power plant works, in your own words.

• Why was the Fukushima power plant constructed so close to the sea?

• Why is meltdown still a threat if the chain reactions have been stopped?

• Why did they use firetrucks to spray water on the reactors and the spentfuel pool?

• Why is the amount of radioactive material in animal products often muchhigher than the amount found in the environment?

• What are the major differences between the Fukushima disaster and theChernobyl disaster?

Resources

• http:www.world-nuclear.orginfofukushima accident inf129.html

• ”Fukushima Meltdown” by Takashi Hirose. This book contains valuableinformation, but requires a cautious read. The author takes a very strong,often emotional stand against nuclear energy, and I found several of hisarguments to be highly misleading or even incorrect.

• ”Fukushima: Nuclear Disaster on the Ring of Fire” - Bill Sargent, shortand concise description of the sequence of events and nicely written. Ifinished it in one evening.

69

Chapter 6

Introduction to modernparticle physics

In this final lecture we will explore the frontier of our current understanding ofthe world of the small, as we attempt to answer the question: What is reallythe smallest of all things?

6.1 The forces of nature

To understand this deep question we first need to answer a simpler question:What are the forces of Nature? Naively, a force is precisely what you think itis: It is an interaction between two objects, usually after which one or both ofthe objects changes its motion. The list of examples is endless: you can exerta force on a crate, and if you’re strong enough it will move. The harder youhit a tennis ball, the higher your chances to hit an ace (provided you knowhow to aim). If you drop your coffee mug, the earth will attract it and thefloor will eventually exert a force on it, causing it to shatter. The light in yourroom is working because there is a force that pushes electrons to move throughthe wiring in your house, which results in an electric current. The examples acountless, and I hope it is not to hard to convince you that everything that yousee happening around you is caused by a force of some sort.

Now I am telling you that we so far only discovered four different forces, ofwhich you only experience two in your daily life. Que? Four forces? But whatabout the huge diversity in forces that we experience everyday? Can they allbe reduced to just two forces? Yes, they can:

So far, physicists have discovered four fundamental forces and allother forces we know of can be ultimately traced back to a one ora combination of these four forces. The four fundamental forces aregravity, the electromagnetic force, the strong force and theweak force.

70

The most familiar of these is probably gravity. You already have a goodintuitive understanding1 of what gravity does on the distances scales importantto us: Here on earth it ensures that stuff falls down and not up and it makes theearth orbit around the sun and the moon around the earth. As you probablyknow, the gravitational force that the moon exerts on the ocean is responsible forthe tides. The second force that we encounter everyday is the electromagneticforce. Objects can carry an electric charge, which can either be positive ornegative. Same sign charges repel while opposite charges attract. The magneticforce is very closely related to this electric force, which is why they are consideredas one and a same force, which we denote by the the term electromagnetic force.You are probably most familiar with the electromagnetic force in terms of alsorts of applications involving electricity. However the electromagnetic force alsorules the world on the level atoms and molecules. All2 of chemistry is determinedby the electromagnetic force. If you are pushing a box, what really happens isthat the electrons in your hands repel the electrons in the box, allowing you toexert a force on the box. (In this sense you never really ”touch” the box; thereis always a tiny distance between the electrons in your hands and the electronsin your box.)

Come up with some examples of forces that you encountered at homeor on your way to school today, and try to understand how they areultimately caused by either the electromagnetic or the gravitationalforce. Post your example on the Sakai discussion board.

I told you before that we know of four fundamental forces, but so far we onlydiscussed two. The other two forces are the strong force and the weak force.The names seem perhaps somewhat silly, but describe the forces really well:The strong force is the strongest force we have discovered so far, while theweak force is weaker than the strong force and the electromagnetic force, butstill stronger than gravity. So why don‘t we notice these forces in daily life,especially since the strong force is much stronger than the others? This isbecause the strong and the weak forces are fundamentally different from gravityand the electromagnetic force: they only work on very short distances, smallerthan the size of the nucleus of an atom. Yet they are very important to us, inparticular the strong force. You learned already in lecture 3 that the nucleusof an atom consist out of a collection of protons and neutrons. Protons havepositive electric charge and neutrons are neutral, so why don’t the protonsrepel each other, causing a catastrophe where every nucleus would fall apartimmediately, only leaving Hydrogen? (No more Carbon and Oxygen, elementsthat are dear to our hearts.) Turns out, the strong force saves the day. At shortdistances it is stronger than the electromagnetic force. It attracts the protonskeeping the nucleus together.

1Interestingly, of all forces gravity is the one that is least understood at very short distances.Our best attempt so far is what we call string theory.

2In the interest of full disclosure, there are a few exceptions where the strong and theweak nuclear force have very small effects on atomic physics and chemistry, but gravity nevermatters.

71

force action range strength force particle(compared toEM force)

strong attractive only inside nucleus 102 gluon

electromagnetic attractive andrepulsive

long 1 photon

weak attractive andrepulsive

inside proton 10−4 W and Z boson

gravity attractive only long 10−38 graviton

Table 6.1: Overview of the most important properties of the four fundamentalforces.

From what you just learned about the strong and electromagneticforces, why do you think are there no nuclei with, say a thousandprotons?

As is the strong force, the weak force is also short ranged but much weaker.The weak force is what facilitates β decay. It enables the process in which aneutron decays into a proton, and electron and a neutrino:

n0 → p+ + e− + ν0

When this happens inside a nucleus, the proton stays inside but the electronand the neutrino fly out, a process we call β decay. (The neutrino is neutral andonly interacts through the weak force and gravity. Because both interactionsare so weak, this particle can fly straight through the earth without interactingat all.) The properties of all four forces are summarized in table 6.1.

One thing that might surprise you that I labeled gravity as extremelyweak, while it appears such a dominant force in daily life. Howeveryou should keep in mind that the earth, the sun and the moonare really big objects. When we decide to jump, a tiny splash ofchemical energy (electric force!) in our legs proves to be sufficient toovercome the gravitational attraction of the entire earth. This mustmean that the gravity is an extraordinarily feeble force! Nobodyknows why gravity is so feeble in comparison to the other 3 forces,and it is one of the greatest remaining mysteries in physics today.

Finally we should understand precisely how a force does its job. If you thinkabout it, it’s all quite mysterious. The sun is millions of miles away from us, butwe are still subject to its gravitational pull. There appears to be some sort ofaction at a distance going on. If the sun would suddenly disappear, how wouldwe know that immediately when it happens, or is there some time in betweenfor the signal to travel over here? It turns out the latter option is the correctone. When an object exerts a force on another object, the object must emit aforce particle or force carrier that is absorbed by the second object:

72

A force particle or force carrier are special particles that arecontinuously exchanged between objects that attract or repel eachother. Each force has one or more force particles associated with it,see table 6.1.

You can compare the mechanism of force particles with two skaters facing eachother, where one is holding a ball. If the skater with the ball throws it to theother scatter, both will move backwards a little bit, as if they repel each other.If they would do so a million times a second and if the ball would be invisible,you would conclude that there is force that repelling both skaters, as if theywere electrically charged. See figure 6.1 for an illustration.

(a) Analogy with skaters (b) Feynman diagram

Figure 6.1: The mechanism of force particles illustrated with the skater analogy(left). The diagram on the right represent two electrons scattering off eachother; in the process they exchange a photon. This type of diagrams is calledFeynman diagrams.

Even force particles can not travel faster than the speed of light invacuum3. This means that there is always a tiny bit delay and nospooky ”instantaneous action at a distance”. If I put two magnets ona table, and move one, the other will move almost instantaneously,but in reality there is a tiny bit of delay, since the second magnetneeds to wait for the photons of the first magnet to arrive before it”knows” that the first magnet has been moved.

Here is a nice video reviewing the four fundamental forces.

6.2 The lego box of the universe

We discussed the forces of nature, but what is ”stuff” (We will further referto is as matter) made off? We already learned that protons and neutrons are

3This video will teach you a cool experiment to measure the speed of light with yourmicrowave at home.

73

”glued” together by the strong force to form a nucleus. (Hence the name ”gluon”for the force particle of the strong force). Nuclei combine with electrons to formatoms and atoms in their turn combine to form molecules. For a long time itwas thought that protons, neutrons and electrons were the most fundamentalbuilding blocks of all matter. Today we know now that protons and neutronsare composite particles themselves. As far as we can tell today, this is notthe case for electrons. Protons and neutrons are each constructed out of threesmaller particles, which we call quarks4. Inside a proton we find different typesof quarks: 2 up-quarks which carry electric charge +2/3 and 1 down-quarkwith electric charge -1/3, for a total charge of +1.

If I tell you that a neutron also consists out of 3 quarks, can youfigure out how many of each kind? (Remember the neutron is elec-trically neutral.)

The two up quarks would therefore certainly repel each other, if it were not forthe strong force which ties them together. See figure 6.2 for an illustration. Thestrong force acts here as a set of enormously strong springs spanned between thequark: the further you try to pull the quarks apart, the harder they will attracteach other. This is why protons are such incredibly stable objects. If you pumpa huge amount of energy into a proton with a collider (see section 6.4) you canin fact rip one or more quarks out of the proton, but now the lonely quark willimmediately steal on or more quarks from its environment to form a new boundstate. We can therefore never observe ”naked” up and down quarks.

So our new lego box consists of the up-quark, the down-quark,the electron and this weird little neutrino. The neutrino does not appearimmediately useful, but the other three guys are sufficient to build up all thematter that we know off and even a whole zoo of other composite particles.(These other particles are all highly unstable, and decay rapidly into protons,neutrons and electrons.)

If you have ever read Dan Brown’s ”Angels and Demons”, you might recallthe existence of these mysterious things called anti-particles. I have beena bit glib in my discussion Nature’s lego box, ignoring anti-particles so far.Nevertheless they are important, and I wrote a couple paragraphs about them.

Every particle has an anti-particle, with precisely the same massbut opposite electric charge. When a particle and anti-particle meetthey annihilate into energy. When this happens, their mass is en-tirely converted into energy. (E = mc2 at work!) The opposite canhappen as well: given enough energy in a certain place, a particle-antiparticle pair can spontaneously appear.

Use E = mc2 to calculate how much energy is needed to createa electron- anti-electron pair. The mass of an electron is approxi-mately 10−30 kg. Compare this energy with the useful energy con-

4In particle physics, we have a long tradition of giving very silly names to importantparticles. Nobody knows why.

74

Figure 6.2: A schematic representationof the structure of a proton. The squig-gly lines represent the continuous ex-change of strong force particles, whichwe call gluons.

Figure 6.3: The lego set of the universe,with the up-quark, the down-quark, theelectron and the neutrino.

tent of a can of soda. (Indicated on the can in cal’s.) Don’t forgetto convert your answer to the correct units.

The existence of antiparticles is an interesting consequence from merging Ein-stein’s theory of special relativity (in particular E = mc2) with quantum me-chanics. It was first theoretically predicted by Dirac in 1928 and the first anti-electrons, also called positrons, were conclusively observed by Anderson in 1932.

In contrast to what is suggested in ”Angels and Demons”, antipar-ticles are not mysterious anymore. We have know about them sincethe 30’s and they are completely understood. There are even wellestablished medical applications that make use of anti-particles, likePositron Emission Tomography (PET scans).

6.3 What’s all the extra stuff for?

We have all the lego blocks we need to build up all of the matter around us;the electron, the up-quark and the down-quark all have a clear role in Nature’smasterpiece. You could be a little bit puzzled by the weird neutrino particle,whose use is not immediately clear from what we have discussed so far. Butbesides this minor point, it appears that our job is done and that we havereduced all of matter to a surprisingly simple set of only 3(!) fundamentalbuilding blocks. This is not crazy at all, and corresponds to the common attitude

75

among physicists in the early 19th century5. However in 1936 another discoveryby Anderson shook the foundations of this worldview. He found yet anotherfundamental particle, which was named the muon. Even more surprisingly, themuon had precisely the same properties as the electron, except that is was about200 times heavier. The community was deeply confused. It just didn’t fit inanywhere. The confusion was nicely summarized by a quote of Nobel laureateI. Rabi:

Who ordered that? - I Rabi

It didn’t stop with the muon, a whole host of other fundamental particles wasdiscovered in the decades following Anderson’s discovery. The last fundamentalparticle that was discovered (prior to last years discovery of the Higgs boson,which I’ll discuss shortly) was the top quark in 1995 in the Fermi National Lab(Illinois, USA). It was found that each of the pieces in our lego box (up-quark,down-quark, electron and neutrino) had precisely three copies. The only dif-ference between a particle and its copies is its mass, all the other propertiesare identical. For this reason they are grouped into families or generations.By now, there is good indirect evidence that there is no fourth family. Whydid nature choose 3 families, while strictly speaking only 1 family was needed?Why 3 and not 4 or 5? Why do they differ in mass? We don’t know. This isone of the most fascinating open problems in particle physics.

So let’s summarize: we had 4 fundamental forces, with each their corre-sponding force particle. (Usually we leave out gravity when discussing particlephysics, because we haven’t discovered the graviton yet and because gravity isso weak that for particle physics it is always negligible anyways.) This leavesus with 4 particles: The photon, the gluon, the W and Z boson. (The weakforce has two force particles.) As for matter, we found 3 copies of our lego boxwhich contained 4 particles, which makes 12 in total. All together this makes16 fundamental particles. This set of particles and the laws that prescribe theirinteractions is what we call the standard model of particle physics (figure 6.4).

If there are so many other particles, why are they not part of theLego set we discussed earlier? Why are there no nuclei build out oftop and bottom quarks, instead of up and down quarks. The answeris that all these extra matter particles are all highly unstable: theydecay almost immediately into up and down quarks, or electrons.This is why they don’t freely occur in Nature. If we want them, wehave to make them ourselves in a collider. (see section 6.4)

Until recently there was one major gap in the standard model: The laws thatprescribe the way all the particles of the standard model interact with one an-other are simply inconsistent without the existence of at least one extra particle.

5I apologize for another misleading account of history. In reality the muon was discoveredbefore the up and down quark, but it was definitively true people where shocked by thediscovery of the muon. You could totally do the job of building the known universe withprotons, neutrons and electrons, and nobody expected the muon.

76

Figure 6.4: Standard model of particle physics. The 3 families of quarks areshown in orange. Their names are up, down, charm, strange, bottom and topquark. The force particles are given in purple. The electron has two additionalcopies, named the muon and the tau particle, which each comes with their ownneutrino. The electron, the muon, the tau and their corresponding neutrino’sare commonly referred to as Leptons. In the center of the diagram you see theHiggs boson, which plays a central role in the standard model (see text).

The simplest candidate for this particle is the famous Higgs boson. The Higgsboson was first proposed in the ’60 by several physicists, among whom PeterHiggs, but it was only in July 2012 when the ATLAS and CMS experiments ofthe European lab CERN announced the discovery of this new particle. Sincethe discovery is so recent, many of its properties are still uncertain at this time.Higgs boson plays a central role in the standard model, since it is an essentialcomponent of the mechanism that provided masses for all the particles. In anutshell, this works as follows: Quantum mechanics prescribes that the Higgsboson must come with a field, which we conveniently call the Higgs field. TheHiggs field is invisible to us, but extends over all of space. When particles movethrough space, they always have to move through the Higgs field, which makesthem sort of sluggish, which we perceive as them being massive. You can com-pare it with pushing a wheelbarrow over a very muddy field. The mud (Higgs

77

field) provides an extra resistance for the motion of the wheelbarrow (particle).If you wouldn’t know about the mud, you would conclude that wheelbarrow isjust very heavy. Unfortunately we don’t have time for a more in depth treat-ment of the Higgs boson and its implications, but I encourage you to explorethe topic further in one of your blog assignments.

The discovery of the Higgs boson was a great triumph for the standard model,but even beyond this one measurement it has been confirmed by experiment overand over again to an astonishing precision. Yet several open questions remain,which we will discuss in the last part of this lecture.

6.4 The Large Hadron Collider (LHC)

All the information conveyed to you in the couple pages you just read was col-lected in over 50 years of careful experiments, which have grown to a tremendoussize and complexity. The vast majority of these experiments have been colliderexperiments. We learned already that the most interesting particles are highlyunstable, so we can’t just scoop them up from the floor but we need to makethem first. This is what colliders are: particle factories. The principle is sim-ple. In a nuclear bomb or power plant, E = mc2 a tiny spec of mass convertsinto energy. A collider does precisely the opposite: It converts a tremendousamount of energy into mass, hereby creating new particles for us to study. Itdoes so by accelerating particles as close to the speed of light as possible, so thateach particle acquires a huge amount of kinetic energy. This is accomplishedby applying very large electric fields, which push the particles to ever higherspeeds.

Do you think all particles are suitable for being accelerated in acollider? Which ones are (not)?

Figure 6.5: A particle splash in the AT-LAS experiment. Different colors cor-respond to different types of particles.

There are two types of particleaccelerators: circular acceleratorsand linear accelerators. Circu-lar accelerators have the advantagethat the beam of particles can makemany revolutions around the circle,and speed up even more with eachrevolution. In a circular collider twobeams of particles always travel in op-posite direction. After both beamshave reached the desired energy, theyare allowed to collide head on in toa massive splash of thousands of par-ticles, all created through E = mc2.(For an example of what such a splashlooks like, see figure 6.5). The splash

78

is then recorded a by set of sophisti-cated particle detectors and converted into information on the path, the energy,the electric charge and the mass of each particle that traveled through thesedetectors. A large team of experimental physicists then analyses this data, andtries to dig out yet unknown particles from millions of splashes. A tremendoustask.

Here are some famous colliders:

• The Stanford Linear Accelerator Center (SLAC), operational since1966, is the largest linear collider in the world. Today it is no longerpowerful enough to keep up with more modern, circular accelerators, butit is still used to study (bio)chemical processes.

• The Tevatron in Fermi National lab (Illinois) is the largest and mostpowerful accelerator in the US. The Tevatron was completed in 1983 anddiscovered the top quark in 1995. It was permanently shut down in July2012, and will be the last major collider on US soil in the foreseeablefuture.

• The construction of the Superconducting Super Collider (SSC) startedin 1991 in the vicinity of Waxahachie, Texas but was cancelled in 1993by US congress due to budget reasons. The collider was designed witha circumference of 54 miles, and would still have been the world’s mostpowerful accelerator today. By the time of its cancellation, much of the in-frastructure and roughly 14 miles of tunnel had already been completed.Today the complex is deserted and the tunnel flooded, which give theaccelerated its nickname ”Deserton”.

• The Large Hadron Collider at the European Organization for NuclearResearch (CERN) in Geneva, Switzerland, is with its 17 mile circumfer-ence the largest and most powerful accelerator today. (Figure 6.6) TheLHC is the largest, and probably most complex machine ever build. Itwas build in collaboration between over 10000 scientists and engineersfrom over 100 countries. As such it is the biggest science project in his-tory, and the first one with truly global participation. In July 2012, CERNwas able to announce the long expected discovery of the Higgs boson.

Given that the LHC is so important today for the field of particle physics, Isay a few more things about its detectors and its operation. The LHC is buildentirely underground with a maximum depth of 175 meter. It has 4 detectors,which each are build for a specific purpose. The ATLAS and CMS detectors arethe largest and most important. The ATLAS experiment is 45 meters long, 25meters in diameter and weights 7000 metric tons. CMS is slightly smaller butheavier. Both experiments are build up in layers in a cylindrical shape aroundthe point where the particles collisions take place. Each layer is designed todetected a specific type of particle, to maximize the amount of information thatcan be recorded from the big particle splashes. The resolution of the detectors isstunning: The ATLAS pixel detector alone has over 80 million pixels, which are

79

(a) View from inside the tunnel of theLHC. During the operation of the LHCthe tunnel is closed due to high radia-tion levels.

(b) Aerial view of the Geneva area,with the ring of the LHC marked inwhite. The actual collider is deep un-derground. At the bottom of the pic-ture you see Geneva airport.

Figure 6.6: The Large Hadron Collider, at the European Organization for Nu-clear Research (CERN), in Geneva, Switzerland. The collider has a circumfer-ence of roughly 17 miles.

each have to be recorded by the electronics. Given that there are about 10 000particles collisions happening every second, this poses an enormous challengefor the electronics that have to process this enormous amount data at very highspeed. Such electronics did not exist at the time when the LHC was designed,and has been invented for this specific purpose. The total raw data outputof one experiment is roughly 1 petabyte per second, which is completely un-manageable with standard computing methods. The scientists and engineers atthese experiments have been pushing continuously on the frontiers of computerscience6, data filtering and data analysis to be able extract useful informationfrom this tremendous pile of data.

In July 2012, both ATLAS and CMS announced the discovery of the longexpected Higgs boson. Unfortunately we don’t have time to cover in more detailhow they did it, but it is surely a fascinating story, and I highly encourage youto research it more for one of your blog assignments.

6.5 Now what?

Despite the great successes of the standard model, there are still several openquestions that we would like to address:

• Is this really everything? Although we think there a no further fami-lies, maybe there are still other particles out there with totally differentproperties. Nature has surprised us before, and it might do so again...

6In 1990 the precursor of the World Wide Web was invented at CERN by Tim Berners-Lee,for the precise purpose of data management in particle physics experiments.

80

(a) Front view of the ATLAS detector.(b) View of the CMS detector when itwas still under construction.

Figure 6.7: The ATLAS and CMS detectors at the LHC in Geneva, Switzerland.

• Why are there precisely 3 families, and why are there families in the firstplace? Nature could have handed us a collection of totally random par-ticles, but instead we got a bunch of particles that nicely fit into a fewcategories. I remind you that this sort of thing happened before in Chem-istry: When Mendeljev first constructed his famous table of elements, hejust observed that all elements could be organized according to their chem-ical properties and that they nicely fitted in a nice pattern of rows andcolumns, but he had no clue about the origin of this pattern. Later it wasunderstood that all elements actually are composite particles, made upout of protons, neutrons and electrons, and the structure of Mendeljev’stable was explained. It is very compelling to think that there is some-thing similar going on in particle physics. We have yet to understand theprinciples behind the peculiar pattern of the standard model. Maybe thequarks and the leptons are composed out of smaller particles themselves?

• Are their really only 4 fundamental forces in Nature? Are there morethat we haven’t discovered yet? Are there less? We already have goodevidence that the weak force and the electromagnetic force are actuallyreally closely related. Could it be that they are in reality just to sides ofthe same coin and that we just haven‘t realized it yet? What about thestrong force and gravity? Interestingly there are already some hints thatthe strong force, the weak force and the electromagnetic force were oneand the same force immediately after the big bang. (see figure 6.8)

• Gravity is the only of the four forces that does appears not fit into thisframework. I already mentioned the peculiar feebleness of gravity, whichremains unexplained. On an even more fundamental level the special sta-tus of gravity is even more striking. Einstein’s theory of General Rela-tivity does a superb job modeling gravity on astronomical length scales,but as it is, it is fundamentally incompatible with quantum mechanics.This problem has been contemplated abundantly by theorists over the

81

Figure 6.8: In quantum mechanics, the strength of an interaction depends onthe energy. The early universe was extremely hot, and the strengths of variousinteractions was very different that they are today. When we calculate what thestrength of the weak, the strong and the electromagnetic energy would have beenright after the big bang, we find that the are almost equal. (The lines in the leftpanel almost meet at the same point.) However the agreement is not perfect. Inthe most popular extension of the standard model, called supersymmetry, theagreement is perfect (right panel). This magical agreement is very compellingsupport for the idea that these three forces all might stem from one motherforce.

past half a century and let to the development of string theory. Althoughstring theory is a very interesting and surprising field, it is still highly spec-ulative, because getting data is extremely challenging on the experimentalside. This is exactly because gravity is such an extremely weak force andthus extraordinarily hard to measure. We basically know nothing aboutgravity on distance scales shorter than a few tens of micrometers.

• If the standard model with the Higgs boson would be all there is in Nature,this would pose us for a big problem. Maybe ”problem” is not quite theright word. ”Discomfort” would be perhaps be better. Reason is that issuch a universe there would be giant coincidence lurking around to corner.The standard model is fully determined by roughly 20 constants of nature(the strengths of the force, the masses of the particles and a couple morethings). All these constants are independent of each other. To get theHiggs boson as light as it is, two of these constants have to cancel to anextreme precision of the 30’th digit behind the comma. Almost cancel,but not quite. This is what we call a tuning. It looks like someone tunedthe universe just right for us to be able to detect the Higgs boson. Itis just really weird and disturbing. Let me illustrate this better with anumerical example. Let’s say A and B are two constants of nature, andthat their difference has to be exactly 1 to get the Higgs mass to be the

82

one that we measured. Then A and B have to would be (for example)

A = 284723057381953729581047384017

B = 284723057381953729581047384016

A−B = 1

This sort of thing makes us suspect that there must be a reason why thesetwo parameters are almost equal to very high precision, but just not quiteequal. There are several proposals to extend the standard model thatwould solve this problem (at least partially). The most popular one issupersymmetry, which is just an extra symmetry that explains why Aand B are almost equal. It is also very appealing from the point of viewof the unification of the strong, the weak and the electromagnetic forceinto a single force. The problem with supersymmetry is that it predictsmany extra particles, particles that we haven’t found so far. Anotherproposal is that the universe could have hidden extra dimensions. Thenice thing about this idea is that it also explains to some extend whygravity is so feeble. Alas, no extra dimensions found so far. Finally theHiggs boson could be a composite particle, pretty much like the protonand the neutron. The LHC will teach us more about this possibility inthe years to come.

Of course, the tuning problem could be merely a mirage. Maybe theuniverse is tuned for some reason. An idea that has been going aroundalong those lines stems from the observation that if the Higgs mass wouldbe different by a lot, stars could not exist and neither would we. Perhapsthere are many universes, and we just live in the only one for which theHiggs mass is what it is by accident. Because we would not exist in auniverse where this is not the case, we should not be surprised that thereis this weird cancellation in our universe. This idea is called the anthropicprinciple. Personally I find it a somewhat ungratifying explanation, butit could certainly be true.

• As I mentioned, we just discovered the Higgs several months ago and haveyet to determine most of its properties in detail. Moreover, there couldcertainly be multiple Higgs. If so, what are their properties and theirprecise role in the clockwork of the universe? The LHC will answer thesequestions (at least partially) in the next few years.

• There is more matter than anti-matter in the universe, and we wouldlike to understand why this is the case. There are definitively good ideasaround, but none of them has gathered enough experimental support tobe convincing. We hope that the LHC and next generation of satelliteswill help us answer this question.

• Finally, there is the puzzle of dark matter and dark energy. Astronomicalobservations have taught us that only 4% of the energy content of theuniverse consists out of quarks, leptons, photon and neutrino’s; stuff we

83

think we understand. That is only a very small fraction of the entireuniverse! We know very very little about the other 96%. We do knowthat roughly 22% is probably made out of particles, particles that are notpart of the standard model. We call these undiscovered particles darkmatter. There might be multiple different kinds of dark matter; maybe

Figure 6.9: Energy content of the universe. Only 4% is given by stuff that weknow.

there is even a rich structure as there is for the standard model. We simplydon’t know. We try to corner dark matter with a variety of methods. Wetry to produce it directly in the LHC. We have very sensitive detectorsin labs very deep underground, that hope to detect dark matter particlesthat come to us from the universe. And we have satellites that hunt forindirect evidence for dark matter in the center of our galaxy. All thesemeasurements are getting better every day now, and there are alreadysome compelling hints today, although nothing conclusive yet. PersonallyI am pretty optimistic that we will learn much more about dark matterin the next decade or so.

The remaining 74% of the energy is occupied by something even moremysterious. We have almost no idea what it is, and therefore physicistscall it dark energy. The only thing we really know for sure about darkenergy, is that it is responsible for the acceleration in the expansion rateof the universe (Nobel Prize 2011). Whatever dark energy is, it is pushinggalaxies further apart from each other with an ever increasing speed. Thisis such a difficult problem, both experimentally and theoretically that Idoubt that we will get to understand dark energy in the next few decades,or even during our lifetimes.

You can find a nice, alternative summary of all these open questions on thewebsite of CERN.

84

Take-home points

• There are four fundamental forces in Nature: the electromagnetic force,gravity, the strong force and the weak force. The strong force and theweak force have only effects on the subatomic scale.

• Every fundamental force is carried over by the exchange of a force particle.

• All matter is build up out the up quark, the down quark and the electron.

• Nevertheless there are a whole zoo of other fundamental particles, whichare unstable. They form the standard model.

• We can make those particles by converting energy into mass through E =mc2. To do so we need a powerful particle accelerator.

• Much has been discovered in the last 50 years, but much is still unknown.

Test your understanding!

• Explain in your own words why gravity is so important for planets andgalaxies, despite the fact that is so much weaker than all the other forces.

• Count how many up-quarks, down-quarks and electrons there are in awater molecule (H2O). Use Mendeljev’s table to look up the amount ofprotons, neutrons and electrons in each element if needed.

• Name a peculiar feature of the standard model and explain why you thinkit is strange.

• What is the role of E = mc2 in a particle accelerator?

• Name 2 yet unsolved problems in particle physics and explain what theyare in your own words.

Resources

• A nice video. Note that the video was recorded prior to the discovery ofthe Higgs boson and prior to the start of the LHC

• A neat website.

• The website of CERN has very readable expositions on a variety of topicsdiscussed in this lecture.

• The particle adventure.

• A nice 5 minute video about the standard model, produced by CERN. Itwas recorder prior the discovery of the Higgs boson.

85

Epilogue

We have come at the end of our short exploration of the world of the small. I havetried to give you a taste of some important advances, ideas and applications. Byno means this was a comprehensive overview of the subject. (This is also truefor the course as a whole.) In a short three week module, one necessarily hasto make some choices, and many important topics were not covert at all. Wemerely scratched the surface of the fascinating subject of quantum mechanicsand did not touch on Einstein’s theory of special relativity. We did not discusshow atoms and molecules form, how they get their properties and eventuallyhow they form complex structures as DNA. (You’ll see some of this in module 4.)Neither have we talked about the microscopic structure of metals, insulators andsemi-conductors, which form the core of all developments in modern electronics.All these topics deserve a course by themselves. There are also many veryaccessible texts both online and in print, covering these topics for the generalpublic.

To finish up this module, I would like to emphasize that our quest for ananswer to the question:

What are the smallest building blocks of Nature?

is still unfinished and continues intenser than ever. Likewise, I hope that thiscourse could be a merely a starting point for you in your explorations of yourown interests, wherever they may take you.

Simon KnapenJanuary 7th 2013

86