Discrete Symmetry(i.e. ,parity, charge and time symmetry) , P-symmetry , CP-Symmetry and CPT-symmetry

1. Journey Of CPT Symmetry
Journey Of CPT Symmetry
By Mahender Shah

2. Emmy
Noether
• Emmy Noether
had a lasting
impact on her
colleagues and
students in the
fields of
mathematics and
physics.
• Noether linked two
important
concepts in
physics:
conservation laws
and symmetries.
• She resolved a
nagging puzzle in
Albert Einstein’s
newfound theory of
gravity, the general
theory of relativity.
• Unbreakable rules:
The laws of physics
are symmetric in
space, time and
rotation. According to
Noether’s theorem,
those symmetries
suggest that
momentum, energy
and angular
momentum are
conserved.

4. What do we mean by a symmetry?
A symmetry is a change of something that leaves the physical description of the system
unchanged.
Physical laws are unchanged if time or any of the space coordinates is shifted by a
constant amount.
Why is the relationship between conservation laws and symmetries important?
It allows for other conservation laws to be formulated.
This is the first link between symmetries and conserved quantities. It is true even in
classical mechanics, and also true in quantum mechanics and field theories.

5. There are many types of symmetry here, we will restrict ourselves to Discrete Symmetry:
1. Charge Conjugation Symmetry(C):– changing particles into anti-particles.
2. Time Symmetry(T) :– changing the direction of time.
3. Parity Symmetry(P):– reversing the direction of each of the three spatial coordinates.
The changes in symmetry properties can be thought of as "mirrors" in which some
property of the nucleus (space, time, or charge) is reflected or reversed. A real mirror
reflection provides a concrete example of this because mirror reflection reverses the
space direction perpendicular to the plane of the mirror.

6. 1. Charge Conjugation Symmetry(C):
It involves replacing every particle in a system by the corresponding antiparticle.
For every elementary particle, there is a corresponding antiparticle that is its exact opposite. For
example, the electron, with electric charge -1 ,it has an antiparticle ,the positron, with charge +1.
Bring an electron and a positron together, and they can totally annihilate each other, producing two
photons. The net charge was zero, and we know that photons have no charge.
All particles have antiparticles. Protons have antiprotons, neutrons have antineutrons, etc. Replacing
every particle in a system by its antiparticle produces almost the same physics.
You can create an antihydrogen atom out of an antiproton and a positron that seems to be have
just like a normal hydrogen atom does.

7. 2. Time Symmetry(T):
Inversion of the time coordinate is called “time reversal.”
That can be thought of as making a movie of a physical process and playing the movie back in
reverse. Now if you make a movie of a macroscopic process and play it backwards, the physics
will definitely not be right. For ex- moving of water from mountain to valley if we play it
backwards it just don’t any sense.
However, if you made a movie of the microscopic physics and played it backwards, it would
look fine.
For ex- take a full of particle where the wall and collision is elastic so that when we play it
backwards we can’t tell the difference between moving forward or moving backwards in time it
look the same.
The difference is really not well understood. But presumably it is related to that evil demon of
quantum mechanics, the collapse of the wave function and its equally evil macroscopic alter
ego, called the second law of thermodynamics.

8. 3. Parity Symmetry(P):
The parity operation (P) changes the direction (sign) of each of the spatial coordinates. Hence, it
changes the sign of momentum. Since spin is like angular momentum (the cross product of a
vector direction and a vector momentum, both of which change sign under the parity operation),
so the spin does not change direction under the parity operation.

9. What is Mirror World Like ?
Many of us grew up watching Doraemon . In that series there is a particular episode I
want talk to you about. In that episode Doraemon give Nobita , a gadget named ‘mirror
world’ which is pretty fascinating itself as what is mirror world made of , how it works
and many such unanswered questions.so today I want to give my presentation giving
scientific explanation to what mirror world is actually (in according to science) made of
and give the idea of how it is supposed to work.

10. Parity Violation
Parity conservation through parity symmetry or P-Symmetry was believed up until 1956 to be a
universal and fundamental law.
A concept characterized by the fact that any physical processes or
transformation and its mirror image yields similar products and occurs at the same rate. As
such, both
processes are said to be indistinguishable from one another on all scales, but have only been
tested in
electromagnetic interactions and not in the case of weak interaction, the force which governs
subatomic decay.
In 1956, P-Symmetry was tested experimentally on processes governed by the weak force in an
experiment on beta decay (a radioactive decay in which an electron is emitted by an atomic
nucleus)
on a cobalt-60 nucleus which proved that weak interactions do in effect violate the P-
Symmetry, that
depending on if they belong to the right or left-handed systems do not change according to
their
symmetrical projection. The parity violation in weak decay was experimentally observed by
Chien Wu.

13. C. S. Wu and her team found that when a specific nucleus was placed in a magnetic field, electrons
from the beta decay were preferentially emitted in the direction opposite that of the aligned angular
momentum of the nucleus. When it is possible to distinguish these two cases in a mirror, parity is not
conserved. As a result, the world we live in is distinguishable from its mirror image.
In other words, suppose you want to communicate with an alien civilization. The only way in
which you could tell them about the left-right of the universe is to ask them to observe the
decay of the Co-60 in a magnetic field. This is the only experiment by which they can solve the
left-right ambiguity.

16. Many desperate physicists tried to save the situation by appealing to CP invariance.
If the mirror in not only reversed spatial direction but also changed matter to antimatter, then the
experiment in front of the mirror would look just like its mirror image. Changing both C and P
preserves the symmetry and we call this CP symmetry. The separate violations of P symmetry and C
symmetry cancel to preserve CP symmetry. These symmetry violations arise only from the weak
interaction, not from the strong and electromagnetic interactions, and therefore shows up strongly
only in beta decay.
Charge-Parity(CP)

17. A more complex symmetrical
projection of our universe involves
parity (left-right inversion) and charge
conjugation (matter and antimatter).
This projection known as CP-
Symmetry is the product of two
transformations. So if parity involved
flipping the coordinates of a system
by their negatives, charge conjugation
involves replacing the particles with
their corresponding antiparticles
(opposite charge). Together, CP
operation means first taking the
mirror image of a system and then
replacing the particles of the system
with their antiparticles.

18. Violation of CP:
,In 1964, Cronin and Fitch looked at the outcomes of the
decay of neutral Kaons ,two particle species were found,
having apparently identical masses but very different
lifetimes. These particles have different decay modes. For
the sake of argument let us consider K0
s and K0
L as short
lived particle and long lived particle to be
.Now , K0
s has CP=+1 which is an even CP state which means
that it doesn’t change under combined CP transformation
and K0
L has CP=-1 which is odd CP state which its wave
function get multiplied by -1 on CP transformation.
If CP symmetry is conserved K0
s and K0
L should never
transformed into each other as that would break the
symmetry.
Cronin and Fitch performed a beam experiment in which
both type of neutral Kaons at the end of a 57 foot beamline
with detector at the end. Given the disparity of the lifetimes
of the two neutral Kaons species, we expect to see only the
K0
L at the end of the beam tube, but they found about 1 in
500 decays to be K0
s .
0 0

19. Implications of violation of CP Symmetry
This is because these experiments are seeking to answer a big question: Why are we here?
When the universe formed in the big bang 14 billion years ago, it should have generated matter
and antimatter in equal amounts. If nature treated both exactly the same way, matter and
antimatter would have annihilated each other, leaving nothing behind but energy.
And yet, our matter-dominated universe exists.
CP violation is essential to explain this imbalance. However, the amount of CP violation observed
in particle physics experiments so far is a million to a billion times too small.

21. Charge Parity and Time Symmetry
There are fundamental reasons for expecting that nature at a minimum has CPT symmetry–that
no asymmetries will be found after reversing charge, space, and time. Therefore, CP symmetry
implies T symmetry (or time-reversal invariance).
If CPT symmetry is to be preserved, the CP violation must be compensated by a violation of time
reversal invariance. Indeed later experiments with neutral Kaons systems showed direct T
violations, in the sense that certain reaction processes involving K mesons have a different
probability in the forward time direction from that in the reverse time direction .

22. Time Symmetry Violation:
When a pair of quarks are held
together by a strong force there
are two possible arrangement and
they can switch back and forth
between these two arrangement
via a weak nuclear force.
However switching in one
direction takes longer than
switching back.
So if we take a recoding of it and
play it backward it would look
different and hence time
symmetry is broken.

24. Electromagnetic Force
Strong Nuclear Force
Weak Nuclear Force

25. While describing
weak nuclear
force in violation
of discrete
symmetry
While describing
weak nuclear
force generally.

27. References
1. Websites
A) https://www.mdpi.com/2073-8994/8/11/114/htm
B) https://www.symmetrymagazine.org/article/charge-parity-violation
C) https://www.slideshare.net/wdconinc/holding-up-a-mirror-using-parity-to-test-the-standard-model-of-particle-physics
D) https://s3.cern.ch/inspire-prod-files-b/bea544508ff9e7ccef2b898088ad3a47
E) https://physicsworld.com/a/babar-makes-first-direct-measurement-of-time-reversal-violation/
F) http://hyperphysics.phy-
astr.gsu.edu/hbase/Particles/cpt.html#:~:text=After%20intense%20study%20over%20many,over%20antimatter%20in%2
0the%20universe
G) https://www.sciencenews.org/article/emmy-noether-theorem-legacy-physics-math
H) https://www.secretsofuniverse.in/ozma-problem/
I) http://www.eng.fsu.edu/~dommelen/quantum/style_a/physsym.html
J) https://www.mdpi.com/2073-8994/8/11/114/htm
2. You Tube Channels
A) This Particle Breaks Time Symmetry by Veritasium
B) Why the Weak Nuclear Force Ruins Everything by SciShow
C) PT symmetry and CP violation. Why energy and momentum are conserved? By Beyond Sci Fact
D) Kaons & CP Violation | Particle Physics by Pretty Much Physics
E) How to Tell Matter From Antimatter | CP Violation & The Ozma Problem by minutephysics
F) Our Antimatter, Mirrored, Time-Reversed Universe by PBS Space Time
G) What is Symmetry in Physics? - with Tara Shears by The Royal Institution