Transcript Structure of the atom - University of Houston

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
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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 subatomic 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 …
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We can predict the final value from
the initial value without knowledge
of “transaction” details
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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
Now,
Albert!
Hey! That
was my idea!
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
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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.
Should an object and its
reflection follow the same
physical laws?
Until you realize that
your right hand is
your mirror
image’s left hand!
What is so special about
Right Handedness?
A particle’s ‘spin’ direction
can be defined
in a right-handed
sense.
Experiments have shown that
‘handedness’ is not always
symmetric
The primary sense of the
beta rays here is lefthanded; 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 antimatter!
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
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Energy = mc2 + kinetic energy
Momentum = m0v/ (1 - v2/c2)
Angular momentum
Electric charge
Some not-so Familiar
Quantities
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Baryon number (number of quarks
minus number of anti-quarks)
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Lepton number (number of e- mu- tauand 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
Gold
foil
Radium
Lead collimator
Zinc sulfide screens
After The Discovery of Subatomic Particles
The Rutherford Experiment
“… 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.”
Sir Ernest Rutherford, quoted in The
Discovery of Subatomic Particles
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/mirr
ormovie.html
•The Discovery of Subatomic Particles, Steven
Weinberg
•Six Not so Easy Pieces, Richard Feynman
The players:
Our friends, the particles
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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)
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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 ???