Conservation Laws, Symmetry and Particle Physics

Modified from Dr. Allen I. Mincer’s webcast from NYU

Jan ‘05

A bit of motivation

SJS science teacher Harry Portwood encourages his

students to ask “How do you know that?”

He hopes that they will get in the habit of asking that question in

all matters of science.

Game Plan

Our task must be defined We must discover the rules of this game we

play: Symmetries and conservation laws We need some practice before we play the

game: Measurement of particle interactions Let’s play! Experiments to do

Our task: Explain the structure and properties of the sub-atomic world.

Unfortunately, we don’t ever get to see any of these things!

This is starting to sound like its going to be hard…

However, nature plays by some very consistent rules

If we discover the rules, our task simplifies (?) to the

reconstruction of what has happened based upon what we

observed.Example: coin exchanges

A quantity that does not change is sometimes called an ‘invariant’ (fancy word alert)

Transactions that have an invariant in the face of a

change of time, place, order, etc,

have the property known as symmetry.

Richard Feynman quotes Prof. Hermann Weyl:

“a thing is symmetrical if one can subject it to a certain

operation, and it appears exactly the same after the operation.”

Different types of transactions have different invariants?

Does that mean there are different types of symmetries?

Hmm…. If we observe an invariance, can we deduce a

specific symmetry?

But what does any of this have to do with Physics?

It’s time for that story…

Have you ever heard of one of the most important, yet mostly unknown, female mathematicians of the 20th century?

Emmy Noether (1882-1935):

• Educated as a language teacher, but she preferred mathematics • Granted permission in 1907 to study mathematics under Hilbert, Klein, Minkowski.• Became a lecturer in mathematics in Vienna, 1913 • Granted faculty status at Gottingen in 1919

Noether’s Theorem (1915):

For every continuous symmetry in nature,

there is a corresponding

conservation law.

Every conservation law has a corresponding

symmetry.

Conservation Laws! At last, some physics …

We can predict the final value from the initial value without knowledge of “transaction” details

Doing many experiments and seeing what is conserved gives information about the “transactions” even if details are not known

Come to think of it, we also know some symmetries:

Snowflakes are symmetric under 60 degree rotations, but this is a discrete symmetry, rather than a continuous symmetry.

Einstein included some of Noether’s work with invariants in his 1916 General Relativity Paper

Hey! That was my idea!Now,

Albert!

Noether’s Theorem, derived from Classical Mechanics, emerged intact from the ‘Quantum Mechanical Revolution’

Now, Werner!

It’s the one thing I’m

certain of!

So when we observe symmetries in nature, Noether tells us to look for a conservation law – a big payoff:

At last we found the rules of the game… and by applying conservation laws, we can reduce the number of possible interpretations of our experiments!

Or given a conservation law, we can use symmetry principles to predict the unobservable!

Pi=Pf

There must be some unseen collision

products!

Example: linear momentum and

total mechanical energy

KE = ½ mv2 for each object in system PE depends on position of each object p = mv for each object KE and p may be summed over the entire system

If our system is symmetric with respect to time, mechanical energy will be conserved

If our system is symmetric with respect to position, momentum is conserved.

If our system is symmetric with respect to rotation, angular momentum is conserved.

There is also symmetry of reflections – ‘parity’

The Marx brothers do an early experiment with parity.

Until you realize that your right hand is your mirror image’s left hand!

Should an object and its reflection follow the same physical laws?

What is so special about Right Handedness?

A particle’s ‘spin’ directioncan be definedin a right-handed sense.

Experiments have shown that ‘handedness’ is not always symmetric

The primary sense of the beta rays here is left-handed; its mirror image is right-handed.

This form of radioactive does not conserve parity.

And this particular asymmetry led to an understanding of a key reason why we can exist!

Our universe is a ‘weak left-hander,’ resulting (thankfully) in a preference for matter over anti-matter!

Enough theory:

Let’s play some ball!

Conservation laws assure us that the interaction still must play by the established rules.

Conservation Laws are obeyed!

Some Familiar Conserved Quantities

Energy = mc2 + kinetic energy Momentum = m0v/ (1 - v2/c2) Angular momentum Electric charge

Some not-so Familiar Quantities

Baryon number (number of quarks minus number of anti-quarks)

Lepton number (number of e- mu- tau- and neutrinos minus anti-particles)

Another type of scattering measurement

If we shoot a sufficient number of particles at a target, we can

determine its size (area) by counting the number of hits

and misses.

Larger data volumes provide better results!

The Rutherford Experiment

From: The Discovery of Subatomic Particles by Steven Weinberg

The Rutherford Experiment

After The Discovery of Subatomic Particles

RadiumLead collimator

Gold foil

Zinc sulfide screens

The Rutherford Experiment

Sir Ernest Rutherford, quoted in The Discovery of Subatomic Particles

“… the chance of an alpha particle being scattered backwards was very

small. …

It was almost as incredible as if you fired a 15-inch shell

at a piece of tissue paper and it came back and hit you.”

A momentary distraction for those who love powerpoints…

Enough theory …

Sources

•Dr. Allen Mincer, NYU Physics Dept.•Harry Portwood, St. John’s School•Symmetry and the Beautiful Universe, Leon Lederman•http://www.emmynoether.org•http://www.eftaylor.com•http://xroads.virginia.edu/~MA01/Cober/marx/mirrormovie.html

•The Discovery of Subatomic Particles, Steven Weinberg•Six Not so Easy Pieces, Richard Feynman

The players: Our friends, the particles

Atom = nucleus + electrons Nucleus = protons +

neutrons Neutrons, protons and hosts

of other particles now known to be made of quarks!

Leptons And of course, anti-matter

(but we’ll save that for another day).

The interactions (forces)

Gravity (How small can we make Newton’s apple?)

Electromagnetic force (like charges repel, etc)

Strong nuclear force (keeps nuclear protons from repelling each other)

Weak nuclear force (radioactive decay)

??? Higgs Boson ???