Transcript www.bonner.rice.edu

Symmetries
You may not think about it, but you make assumptions every day
about symmetries.
If I do an experiment, then pick up my apparatus and move it over 1
m, you do not expect the results to change.
The laws of physics are invariant under translations in space.
If you do an experiment and then rotate your apparatus 90 degrees,
you do not expect the results to change.
The laws of physics are invariant to rotations in space.
If you do an experiment, wait an hour, and do it again, you do not
expect the results to change.
The laws of physics are invariant to translations in time.
Symmetries and conservation laws
There is a one-to-one correspondence between symmetries and
conservation laws, discovered in 1915 by Emmy Noether.
Emmy Noether was a German mathematician,
described by Einstein and Hilbert as the most
important woman in the history of mathematics.
After she received her PhD in mathematics, she
taught for seven years without pay at he Mathematical
Institute of Erlangen. But in 1915 she was invited by
Hilbert to join the mathematics faculty at the University
of Goettingen. Some of the faculty objected, and she
had to lecture for four years under Hilbert's name.
But she was eventually accepted onto the faculyt.
In 1933 she was dismissed from her position because
she was Jewish. She accepted a position at Bryn
Mawr College.
Symmetries and Conservation Laws
Symmetries of physical systems lead to conservation laws:
Symmetry under translations in space → conservation of linear momentum.
Symmetry under rotations in space → conservation of angular momentum.
Symmetry under translations in time → conservation of energy.
These are examples of continuous symmetries
Discrete symmetries
We can also define a discrete symmetry, the most well-known
example is parity.
The parity operation is the inversion of the coordinate
system:
x → -x
y → -y
z → -z
This operation is equivalent to reflection in a mirror followed
by 180 degree rotation.
Reflection about
y-axis
Rotate 180 degrees
about x axis
The parity operation is equivalent to reflection in a mirror
followed by 180 degree rotation.
Parity
To understand parity, imagine playing a game of pool and playing
a bank shot off the wall. If you watched the shot, or watched its
mirror reflection, could you tell the difference?
Mirror
Parity
The laws of classical physics are invariant under the parity
operation!
F=ma
-F = -ma
Both force and acceleration
change sign, so Newton's 2nd
law is unchanged.
The laws of electromagnetism are also unchanged.
In 1956 Lee and Yang, based on puzzles in meson decays,
suggested that parity might not be conserved in weak interactions.
C. N. Yang and T. D. Lee
Parity violation
Within a year, Madam Wu at Columbia demonstrated experimentally that beta
decay did not conserve parity—that is, a decay and its mirror image were not
identical!
Co60
electron
electron
Nuclear spin
Nuclear spin
Mirror
Discrete symmetry—charge conjugation
In particle physics we have another discrete symmetry that we use
often called charge conjugation.
This is the symmetry operation of matter ↔ antimatter
antiproton
proton
Do matter and antimatter behave the same way? NO! Within a year it was
also shown that the weak interaction distinguishes between matter and
antimatter.
Symmetries and the matter-antimatter
asymmetry of the universe
So why do we care? In 1968 Russian physicist Andrei Sakharov
showed that violation of these fundamental symmetries is a
necessary condition to generate the matter-antimatter
asymmetry of the universe.
Matter ↔ Antimatter
b
Anti-Bs0 meson
Bs0 meson
b
The Standard Model does have a mechanism to cause the violation of these
symmetries, but at a level way too small to account for the matter-antimatter
asymmetry of the universe.
What D0 found...
Matter and antimatter can change into each other, that we have known for 50 years.
But what we found was that the rate is in B mesons not the same in both directions.
And the difference is much larger (40x) than expected in the Standard Model.
This result has received a lot of
attention because it disagrees
with the SM by 3.2 standard
deviations, and also because it
relates to a 50 year old puzzle
that is central to the origin of
the universe.
Is this result enough to account for the matter-antimatter
asymmetry of the universe?
We don't know yet...but it is still a small effect.
There has been lots of press coverage...
A New Clue to Explain Existence
New York Times
Joe Lykken, a theorist at Fermilab, said, “So I would not say that
this announcement is the equivalent of seeing the face of God,
but it might turn out to be the toe of God.”
Is it right? Time will tell.
http://www-d0.fnal.gov/Run2Physics/top/public/CP_violation_evidence_DZero.html