Beyond the theory of everything · 2010-06-14 · 1 Beyond the theory of everything Professor A J Schofield Theoretical Physics Group The University of Birmingham TheLeverhulmeTrust

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Beyond the theory of everythingProfessor A J Schofield

Theoretical Physics GroupThe University of Birmingham

TheLeverhulm eTrust

I’d like to thank Professor Cruise for his kind words of introduction and to say how privileged I feel that the University to should reward me in this way. Many of you have travelled along way to be here this evening and I am honoured by your presence. I’d like to thank my father especially to whom I owe my initial interest in science and physics in particular. I sometimes wonder whether it was in an effort to understand what my father – a research physicist – was talking about that I my interest in physics began. I’m not sure I’ve made it yet! As well as thank you all for coming, I’d like to thank those funding my research. As well as the University of Birmingham, I am been supported by the Royal Society, my research students are funded by the Engineering and Physical Research council and I have a postdoc supported by the Leverhulme Trust.

When I asked what an Inaugural lecture was for I was told it was an opportunity to layout your stall of research interests and goals to the rest of the University and the community.

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I particularly welcome this opportunity to dispel a few myths that may have arisen about my research. Contrary to what you may have heard, I don’t perform the bulk of my research in local bars staring at the walls. Its not true that my research is only ever published along side articles of dubious scientific value.

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Neither is it true that I only publish in unreferreed journals. At least here I can set the record straight.

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Goal of Theoretical Physics

• Understanding the physical universe,

• with the language of mathematics,

• to make testable predictions.

What then is the goal of my research as a theoretical physicist? Well – as I see it I am trying to understand the workings of the physical universe. The way we do this is by trying to describe it in the language of mathematics and this is important because it allows us to make predictions and so test our understanding when compared with experiments.

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Influential Method: Reductionism

One of the most successful method we have adopted to do this is to break matter down to its most fundamental constituents. If we can understand how these behave then we can build up a picture of the whole. Its rather like using this diagram of the working parts of a car engine and figuring out how they behave together to make a car work. It’s a very old idea usually attributed to the Greeks – like Democritus here. It has been a remarkably successful program. In the next few view graphs I am going take you on the voyage of discovery that physicists have undertaken to identify the basic building blocks of the Universe and to work out how they behave. I want to show you how this has led to one of the key quests of modern theoretical physics namely the search for “The Theory of Everything” and I am going to tell you what physicists mean by that. But then, as my title somewhat ambitiously suggests, I want to take you beyond that and show you using aspects of my own research and those working in my field how we are discovering that this reductionistapproach of taking matter apart leaves something out – suggesting that there is fundamental physics beyond the theory of everything.

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Powers of one thousand!1 meter: human scale

1m 1mm 1 mµ 1nm 1pm 1fm 1am

Many of you will have seen the film or book called “Powers of Ten” by The office of Charles and Ray Eames” which inspires these next fre slides. Here is a speeded up version of the last few hundred years in our endeavours to uncover what the universe is ultimately made of. We begin with ourselves at roughly a meter or two in size (or in my daughters case when this was taken, exactly a meter). With each successive slide we will be zooming in by a factor of a thousand to discover what we are made of and how the universe works.

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Powers of one thousand1 mm = 0.001 meter: snowflake


We’ve now zoomed in by a factor of a thousand to the scale of a millimeter where we see the beauty of a snowflake.

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Powers of one thousand1 µm = 0.000001 meter: cells


A thousand times smaller than those snowflakes, we see the building blocks that we are made of. (These are red blood cells – a few millionths of a meter across). Transistors in a home computer are slightly smaller than this but around this scale marks the current limits of production technology.

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Powers of one thousand1 nm = 0.000000001 meter: atomic structure


A thousand times smaller still and we start to see the atoms themselves. We are looking at a scale of a billionth of a meter and are seeing atoms on the surface of silicon. In fact what you are seeing are clouds of electrons, the outermost part of the atom. There are about one hundred different sorts of atoms. Notice this regular array has some imperfections in it. This picture of atoms was taken here in the School of Physics by my colleagues in the nanophysics group where they are manipulating atoms. We now go a thousand times small again – inside the electrons clouds and we see…

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Powers of one thousand1 pm = 0.000000000001 meter: inside atoms


…nothing. This was Rutherfords famous discovery that most of the atom is empty space. We are inside the clouds of electrons which make up the outer limits of an atom, but the inner core (the nucleus) is still way smaller than this scale. This huge gap between the physics of the electrons in an atom and the nuclear core means that the fascinating physics of the nucleus is irrelevant to atomic electrons. As far as an electron is concerned, a nucleus is simply a dot with a positive charge attracting the electrons to it. This gap will be important later.

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Powers of one thousand1 fm = 0.000000000000001 meter: the nucleus


Now to the nucleus itself – and we see that even this has structure: protons and neutrons, and they too are not fundamental but are made up of quarks in constant motion.

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Powers of one thousand1 am = 0.000000000000000001 meter: W,Z particles


And this is the limit of where experimental physics has got to in its quest for the smallest constituents of matter. This picture is an aerial view of the microscope we use to see a billion billionth of a meter – it’s a huge particle accelerator at CERN in Switzerland run by an international community of physicists including colleagues at the University Birmingham. 27km in circumference – Lake Geneva in the background.

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What have we learnt?• Indivisible particles:

– electron, quarks …• Which feel forces:

– gravity

“Nothing yet … How about you Newton?”

So that is where experimental physics has taken us inwards and we can summarize what we’ve discovered. We have found some particles which can’t be split apart –they are fundamental: things like the electrons. These fundamental particles experience the universe through forces which push and pull them in response to the movement of other particles. Some of these forces are familiar to us: gravity for example. Perhaps surprisingly gravity is by far the weakest of the forces – it requires a planet sized amount of matter before it exerts much effect.

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– gravity– magnetism

Magnetism – also known since ancient times aligns compass needles with the north pole.

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– gravity– magnetism– electricity

Electricity – here an experiment which demonstrates how like electrical charges repel. This persons hair has got an excess of electrons which in their struggle to move apart from each other push his hair apart too.

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– gravity– magnetism– electricity– weak nuclear force

Then come two other forces which are not so obvious in everyday life because they are confined to within the nucleus of the atom. Self illuminating signs like these one use a bye-product of the weak nuclear force to operate.

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– gravity– magnetism– electricity– weak nuclear force– strong nuclear force

The strong nuclear force is what holds the nucleus together against the electric repulsion of its constituents (which are positively charged).

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– gravity– magnetism– electricity– weak nuclear force– strong nuclear force

} electromagnetism -Maxwell } Electroweak –

Weinberg, Salam & Glashow

But one of the key discoveries we have made is that these forces are not all independent of each other. Maxwell in the 19th century was able to combine electricity and magnetism into a single theory. Einstein showed that whether you experience magnetism or electrical forces is just a matter of relativity. Modern telecommunications relies on this piece of theoretical physics. Almost a century later in the 1960s a further unification was made – the weak nuclear force and electromagnetism are both facets of the same force. This is an even more astonishing piece of theoretical physics because these two forces have very different apparent characters: electricity and magnetism and long ranged influencing all the particles around us. While the weak nuclear force only exists on the smallest measurable lengths: - the puzzle of how they are connected was solved in the mid 1960s and the predictions of this theory we shown to be true in the early 1980s in that particle accelerator I showed early and the Birmingham team played a key role in the experiment.As you can see we are starting a trend here – perhaps all these forces could be shown to be different aspects of the same force – one that combines the electro weak force, the strong nuclear force and even gravity into a single theory perhaps accounting for the fundamental particles too.

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“The theory of everything”Unifying all the particles and forces into a single theory

It is this quest that has become a kind of Holy Grail for theoretical physicists – to produce a theory which combines all known forces and fundamental particles into a single equation: The theory of Everything.

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“The theory of everything”Unifying all the particles and forces into a single theory

String theory (1990s)

Supergravity (1980s)

M-theory (2000s) ?

It’s a quest that many theoretical physics groups worldwide are working on. Many mathematical theories are being put together – the most promising candidate theories change over the years with exotic names like “supergravity” and “string theory” – which is what the picture is meant to represent - and now “M-theory” (no one seems to know what the M stands for!). It may be possible to test out these candidate theories in bigger particle accelerators, but the place where they really will come into their own is – as far again on our powers of 1000 journal as we covered in going from the human length scale down to the current experimental limits.

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Is “The theory of everything” the end of theoretical physics?

“Dreams of a final theory” – Weinberg (1994)

“Is the end of theoretical physics in sight?”Inaugural Lecture of Prof Stephen Hawking (1980)

– 50-50 chance that it would be in 20 years.

– Mountaineering after Everest climbed.

However, if we discover “The theory of everything” that unifies all the fundamental particles and forces: then isn’t this the end of theoretical physics. Won’t our job have been done? Well some very eminent theoretical physicists have thought so. Weinberg – one of the architects of unified theory as suggested it in his book “Dreams of a final theory”. It has been most strongly argued in another inaugural lecture: Stephen Hawking, entitled his inaugural lecture “Is the end of theoretical physics in sight?”Somewhat to the surprise of his audience he concluded basically that it was. He even put a timescale on it. It was an even bet that it would happen in the next 20 years. He said that theoretical physics after the discovery of the theory of everything would be like mountaineering after Everest was conquered.

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But could we be missing something?

Is there fundamental physics beyond the theory of everything?

But all of this rather assumes that our method of discovery – namely taking things apart, reductionism – tells us all that we need to know. Could it be that we might miss something in this approach? I don’t simply mean miss how to exploit our theory for technology. Could it miss fundamental principles which underpin the way the universe works? Is there fundamental physics that lies “Beyond the theory of everything”. In the rest of this lecture I will argue that this method does miss fundamental physics. We don’t yet have “the theory of everything” for the whole universe. But I will draw my arguments from my area of my research where we do a single equation which unifies the particles and forces. I like to call it “The theory of almost everything” .

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The theory of almost everything!

• Particles: electrons and nuclei• Forces: electric and magnetic• Rules: quantum mechanics } UNIFIED: (1926)

The Schrödinger equationThe theory of almost everything

1020 1010 100 10-10 10-20| {z }

z }| {

What I currently work on concerns the properties matter starting from atoms upwards. Remember the empty space inside the atom: As I showed earlier, to the electrons around the atom, the nucleus appears like a single point of charge. Now if you were taking the car apart to find out how it works you have to decide when to stop. Having used a screwdriver and spanner to get the engine in pieces, it would be foolish to start using a hacksaw. You would get smaller pieces but they would not help in understanding the workings of the engine. If we want to understand how the matter around us behaves, to start from the physics that operates inside of the nucleus is like cutting the flywheel in half – its much better to treat it as the point of charge that the electrons see. So we will treat the nucleus as a fundamental particle. At the other end of the scale I will ignore the effects of gravity – there too there is a similar gap before gravity becomes apparent. So providing I limit myself to these ranges of scales – from atoms to people – I have a self contained set of working ingredients. They are the particles, negatively charged electrons and positively charge nuclei, which feel electromagnetic forces and obey certain mathematical rules (called quantum theory). These ingredients were unified in a single theory in 1926 called Schrödinger's equation. It won’t tell me how the sun works for example, but it is the theory of everything that you see in this room for example. It should describe most of chemistry and pretty much all of biology. It is the theory of almost everything.

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The theory of almost everything

It may sound like living on cloud 8, but having the theory of almost everything that we can write down on the black board should at least give us an indication of whether the reductionist method has left anything out – for at least the almost everything that it should describe.

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Having taken matter apart…

…its much harder to put it back together!

However, we have a problem even with this – our theory of almost everything. You see having taken matter apart to find is basic building blocks, we now need to put it back together again with out theory and that turns out to be much harder. We can put one or two electrons and nuclei together and understand that, but in a real material we have far-far more than that and none of our current mathematical tools are able to help.

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Like chess: knowing the rules is child’s play

… but that doesn’t make you a grand master!

Instead of mountaineering after Everest, its more like playing chess having just been told the rules. While in principle you may know how to play the game you are still a long way off being a grand master.

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Why not just use a computer?

• Chess 8x8, 32 pieces: yet no computer can “solve” chess.

• Needs a strategy – what does a good move look like.

But if we can’t immediately use the rules to understand the behaviour of electrons, perhaps we could get a computer to do it – after all they are excellent at following rules. Well the reason we can’t is the same as the reason that a computer will never play an unbeatable game of chess. You may know that Kasparov has managed to secure a draw with Deep Junior in a recent competition of computer versus human, but have you ever wondered why there is any hope for humanity at all in such a contest. After all surely a computer could just check out every single possible move through to completion of the game so that there is no surprise that a grand master could spring. Shouldn’t it be like noughts and crosses for us where essentially you can keep every possible game in your head so guarantee never to be beaten? Well the number of possible chess games is estimated as 1 with 40 zeros following it. Even if you could store each game on a water molecule you would need all the ice in Antarctica to do it. It isn’t going to happen soon! Instead Deep Junior develops strategies to identify promising moves. If that is the case for just 32 pieces on a small board, how much more limited will computers be for solving the behaviour of the large collection of numbers of electrons and their nuclei. To use a computer for that you too will need strategies.

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Beyond the theory of almost everything -Emergence

• New principles seem to govern collections of particles – not apparent for isolated ones.

“More is different”Phil Anderson (Nobel Laureate)

It seems that matter too develops its own strategies in solving the theory of almost everything. However these strategies often seem to bear little resemblance to our “Theory of almost everything”. This happens so frequently that we’ve coined a word for it “emergence”. Emergence is when new principles appear to govern collections of particles that are not apparent for particles in isolation. Emergence is what reductionism leaves out because More is different. I want to flesh this out with three examples of emergence.

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SuperconductivityDiscovered in 1911:

First theory breakthrough in 1957: still many open questions

Our first example is superconductivity. It turns out that knowing theory of almost everything was a positive hindrance to to the theoretical understanding of this phenomenon. Superconductivity was first discovered in 1911, the effect I am going to show you was found a little later. At room temperature this back solid is a metal, but immersing it in liquid nitrogen at –196 degrees C it becomes a new state of matter. It’s a remarkable phenomenon – one that first got me interested in my area of research. It was not until the late 1950’s that the first theoretical breakthrough came.

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Understanding took 40+ years!

• Why?– The rules had to be

broken.

I don’t have time to tell you the details of that theory – in fact there are still open questions about it – like are there any limits on the temperature necessary for superconductivity. Instead what I want to ask is why it took so long to be understood. The reason is that the starting point in superconductivity involves breaking 2 key rules in our theory of almost everything. You must allow electrons to attract each other – even though they have the same sign of charge and like charges repel. The other thing you must do is to allow electrons to appear and disappear. Now in time it was discovered how the rules of the theory of almost everything weren’t actually being broken – merely bent. But the theoretical breakthrough came from abandoning the theory of almost everything. Breaking these rules allows you to see that in a superconductor electromagnetism becomes a short range force: the magnetic field is pushed out of a superconductor because the fundamental rules of electromagnetism are changed in a superconductor. This is a hint as to how electricity and magnetism could be unified with a short range force (here is a way to make a long range force look short ranged).

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New particles can appear

If the rules can be bent, then we’ve also found new types of particle which appear in collections of electrons and nuclei but not present in the theory of almost everything. It is now possible to make wires which are a few atoms thick. On the left you can see it and magnified you can see that atoms – stylized on the right. Normally in a wire the electrons move all over the place rather like ants on a motorway they are too small to notice that the motorway has a particular direction. But with these atomic wires electrons can only move backwards and forwards along the wire. This restriction leads to the appearance of new particles. At the bottom you see electrons (the black arrows) and nuclei (the green atoms) interacting with the theory of almost everything rules. This is not a simulation – it’s a stylized view of what takes place. As the move about you might notice two disturbances moving backwards and forwards. I’ve coloured them to make them more obvious. These disturbances appear as new particles (one carrying magnetism and the other carrying charge). This is a rare case where we can solve our theory of almost everything and that’s how we find these new particles. One of my research students is currently developing an experiment to see these particles more clearly than has been done up until now.

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Fundamental particles may not be so fundamental!

So far you might be tempted to argue that its only because of your ignorance that this physics appears to be new. If you could do a better job with the theory of almost everything then you should surely have come up with superconductivity for example. This final experiment it a challenge to that idea – for here we see experiments where the fundamental unit of charge appears broken.

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Measuring lumps of electrical charge

I

V

Magneticfield

1

0 5Magnetic Field/T

1/21/3

1/41/5

2

1

345

There is a remarkable experiment where you can measure the charge on the electron. The experiment simply involves measuring an electrical voltage of some material in a magnet. As the strength of the magnet is increased, so does the voltage, but you find that steps appear in the voltage. These steps occur in very precise places such that there will be one half way up, one a third of the way up and a quarter and so on. It was later understood that this was measuring the charge of the electron and that you could count how many electrons were moving through the material by turning the fraction upside down.

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1

2

3

1/3

2/5

2/31

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4

0 5 10 15 20 25Magnetic Field/T

But keep increasing the magnetic field

Fractions of an electron?- isn’t that impossible?- like saying 1+1+1=1/3

RH/(h/e2)

Now the really bizarre thing that happened as people made better materials and higher magnetic fields suddenly a whole host of new steps appeared. I have now labelled them with the number of electrons and you see that many of them represent fractions of an electron. How can this be when an electron is indivisible – perhaps our interpretation of the experiment is wrong?

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Can this really be right?How much water in a raindrop? How much charge in the quantum

Hall effect?

50

60

70

80

90

100

0 0.5 1 1.5 2 2.5 3C

urre

nt n

oise

S (1

0-30

A2 H

z-1)

Total current (nA)

We really are seeing fractionsof an electrons charge.

Well you can do an independent check on the charge being carried in the experiment. The way you do it is rather like the following way of measuring how much rain there is in a raindrop. If you listen to the noise of rain falling on a tin roof and collect the rain at the same time, it turns out that you can work out the amount of rain in a single rain drop. Doing that same experiment at a step (say 1/3) you find that charge is indeed moving around in units of a fraction of an electron. Again this is physics that appears to be totally at odds with the theory of almost everthing which says that the electron is indivisble.

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Its very hard to see how a proper mathematical treatment can explain this starting with the theory of almost everything. Its like trying to make a structure out of these bricks that will go through the archway but not being allowed to break the bricks apart. Nevertheless it seems that what is impossible for an electron in isolation, becomes possible when you have the vast numbers of electrons and nuclei interacting together in a real material.

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Emergence: doesn’t care about the details of the theory of almost everything!

But there is something even more shocking than this. That is that the effects I am talking about don’t seem to care about the precise details of our Theory of AlmostEverything. You see we are seeing emergent phenomena like superconductivity, spin-charge separation and the fractional quantum Hall effect in real materials – and real materials aren’t nice. My branch of physics as often been called disparagingly “dirty physics”. That’s not to say material scientists aren’t doing a wonderful job of making clean materials - its just impossible to make things completely pure – the wrong nuclei will get into your experiment. Yet what we observe often doesn’t care about this. The steps in the quantum Hall effect are accurate to one part in a billion – all of this in a dirty experiment involving billions of particles. You see emergent phenomena transcend the details of “the theory of almost everything”.

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The electron may even be unstable

Okay – so now, to bring you right up to date with what I am doing now. I am looking for metals where the electron might not be stable. Our atomic wires are an example of this and what I want to do is to find other examples. The question is where to look.

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Quantum criticality: new emergenceKinetic Potential

Freedom Responsibility

Well the theory of almost everything tells us that electrons have to competing desires. One is to be free – moving independently but this can’t happen without them bumping into other electrons – and this is the second pressure on the electron – to stay as far apart from the others as it can. These two desires tend to fight it out in real materials.

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Quantum theory: opposites can coexist

Picasso:

“sad and happy”

However, the strange rules of quantum mechanics which govern the behaviour of electrons also allow two opposites to sometimes coexist.

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Schrödinger’s cat

Picasso

“sad and happy’’

?

A famous example of this is often cited as Schrödinger's cat. It can simultaneously be alive and dead in the quantum experiment. Its only when the cat is observed that its fate is decided one way or the other.

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Picasso

“sad and happy’’

Schrödinger’s cat

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Quantum critical points:a confused state of matter

Temperature

Anotherparameter

ordered disordered

Quantum critical point

Quantum critical region

The question of what happens when you tune a material to where the two opposing views are in balance at very low temperatures and then allow quantum mechanics to allow coexistence is one of the key questions I am looking at. We’ve recently discovered a way of producing this balance using a magnetic field and there is the first hint of a new type of emergence appearing there. Its also seems likely that this balancing act is going on in this material – a high temperature superconductor – but finding the definitive proof will require more research.

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Reductionism

Hawking’s view

1980: “The Theory of Everything” 20 years away

1998: 20 years away…from now!

Feb 2003: perhaps there is no “Theory of Everything?”

So to summarize reductionism suggests that we should view our universe in terms of extremes of length – going to the smallest length scales to find out what we are made of. So to bring you up to date on Hawking’s prediction. In his inaugural lecture he said that the theory of everything was 20 years away, in 1998 he stood by his prediction but the clock was to start now. More recently he has paralleled the quest for the theory of everything with Bertrand Russell’s failed hope of finding all the axioms of mathematics and argued that that might be no theory of everything.

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Simplest moleculesof Life ?

Beyond reductionism

1 2 3 4

The axis of complexity

The view I’ve come to is that Hawking need not worry. There is a new axis to be explored that is not measured by length, but the complexity of the materials we can make in bringing atoms together. What we find is in contrast to the complexity of the material, we find what reductionism has missed: new principles, new emergent physics often simple physical principles unrelated to the theory of the individual atoms. So while we may be struggling to climb Everest, eyes focussed on the top, and finding it recedes at each false summit – if we’d only turn round and look at the view, the bigger picture, we’d see that we are finding the principles may transcend the details of the microscopic theory. Principles Beyond the Theory of Everything.

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“We used to think that if we knew one we knew two because one and one are two.

“We are finding that we need to know a great deal more about ‘and’”.

Sir Arthur Stanley Eddington

I leave you with a quote from a famous physicist from the last century that sums up

what I’ve been saying. “We used to think that if we knew one we knew two because one and one are two. “We are finding that we need to know a great deal more about ‘and’”. That is exactly what I am doing in my research – thank you for your attention.

Documents

Beyond the theory of everything · 2010-06-14 · 1 Beyond the theory of everything Professor A J Schofield Theoretical Physics Group The University of Birmingham TheLeverhulmeTrust