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 Both force and acceleration change sign, so Newton's 2nd -F = -ma 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! Co 60 Nuclear spin electron Nuclear spin electron 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 proton antiproton 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.

b b B s 0 meson Anti-B s 0 meson Matter ↔ Antimatter 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.