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Re: [Phys-l] Violation of CP Invariance, C asymmetry, and baryon asymmetry of...




In a message dated 12/15/2007 4:21:33 P.M. Eastern Standard Time,
Faraday321@aol.com writes:

Violation of CP Invariance, C asymmetry, and baryon asymmetry of the
Universe.
In 1966 Andrei Sakharov wrote a landmark paper which addressed the problem
of the matter-anti matter asymmetry in our Universe. While certain details
of
Sakharov’s proposal are outdated based on more current particle physics
understanding, I think it is still very instructive to take a look at
Sakharov’s
proposal. Beside the general interest this paper holds I am also writing
about this to relate Sakharov’s basic idea to the proposals made by Bob
Klauber
in his paper “Mechanism for Vanishing Zero Point Energy.” (Astro –
ph/0309679)
and the energy – time symmetries identified in my earlier post which I
assert relates to both Sakharov’s and Bob Klauber’s paper.
The problem of why of the Universe we live in apparently has an asymmetry
of
matter and anti matter is a long standing question in cosmology and
particle
physics. The Swedish Physicists Alfven and Klein had proposed that there
existed some mechanism which separates the matter and anti-matter in the
early
Universe. However, this proposal doesn’t fare well either in fundamental
particle physics theory or in our astronomical observations. There is no
observational evidence for anti-galaxies, and given the relatively frequent
collisions
observed between galaxies there should be some evidence. Also, there is no
accepted mechanism to separate matter and anti matter in the early
Universe.
In addition , the discovery of CP violation by Christenson, Cronin, Fitch,
and Turley in 1964 does provide a mechanism for matter-anti matter
asymmetry.
This discovery served as the inspiration for Sakharov’s paper.
The basic approach used in Sakharov’s paper is based on M.A Markov proposal
of a hypothetical massive scalar field, called the Maximom field. The
quanta
for this field were spin zero Maximom particles which were postulated to
have
an invariant mass equal to the Planck mass.
In his paper, Sakharov proposes a new conserved charge, which he called
N_c
N_c = 3*n_b –n_mu
Where N_c is the fundamental charge conserved in the Universe, n_b is the
baryon number and n_mu is based on the muon family lepton number.
For the proton and neutron n_b =3 with the sign changing for anti protons
and anti neutrons. The value of 3 is based on the quark proposal of
Gell-Mann
and Zweig.
n_mu equals + 1 for muons and muon neutrinos. (He defined muon neutrinos as
mu_0 particles.)
So we get
Anti muons
Muon(+) and Muon(0) n_mu= -1 N_c =1
Muons
Muon(-) and Muon(0) n_mu =1 N_c = -1
For baryons
P & N n_b = +1 N_c =3
Anti Baryons
Pbar * Nbar n_b =-1 N_c =-3
We can see from this that N_c is close to the concept of a B-L charge which
is the fundamentally conserved charge in SU (5) symmetry.
The N_c charge carried by the Maximom scalar particle is zero. However,
like
the photon which couples to electric charges the Maximom would couple to
N_c
charge. However, the mass of the Maximom quanta would make this new force
unobservable in the Universe. The Maximom particle is proposed to have
two
decay channels.
M= 3*q (+) + Muon (-) + 2*Muon (0) N_c= 3*1 -3*1 =0
M= 3*q (-) + Muon (+) +2 *Muon (0) N_c=3*1-3*1=0
Based on CP violation the first decay channel would be favored in any
Universe with the same arrow of time we have in our own Universe. However,
for a
time revered mirror Universe the second decay channel would be favored.
However, from a dynamic point of view three conditions would need to be
true
to generate the observed matter-anti-matter asymmetry we see in the
Universe
today. These are the three well known Sakharov conditions.
They are;
1. That Baryon number is not a conserved quantity. It can start out
zero but end up positive (as it apparently does).
2. CP symmetry must be violated -- even though in most processes it
almost never is.
3. That the universe went through a stage of non-equilibrium.
Note that none of these conditions by itself is sufficient. They all need
to
exist in order to explain the matter anti-matter imbalance.
The first of these conditions is what grand unified theories provide -- the
nonconservation of baryon number. While this is consistent with the
standard
model, a mechanism that can actually change baryon number is needed. This
is
what grand unified theories do in supposing there are interactions which
can
convert quarks to leptons.
CP symmetry is short for "charge-parity" symmetry. This is composed of two
other discrete symmetries. The first is charge conjugation symmetry (C) --
the
exchange of particles with antiparticles. (The fact of baryon number not
being conserved implies a violation of charge conjugation symmetry, which
is
basically the symmetry between matter and antimatter.) The second symmetry
is
parity (P) -- also known as handedness -- the exchange of right and left.
This
is manifested in the direction of motion of a particle compared with its
direction of spin.
The fact that CP symmetry can be violated (though it very seldom is) is a
well-established observational fact as related above. The mechanism behind
it,
however, is still mysterious. Grand unified theories don't shed any light
on
this puzzle.
There is one more important type of discrete symmetry -- time reversal
symmetry (T) -- change in the direction of time. And there is a very
fundamental
theorem -- the CPT theorem -- which says that when all three symmetries (C,
P,
and T) are applied to a process, the final result must be the same. Suppose
then that any two symmetries are applied to a process and the result is not
the same. Then the combination of the two symmetries is violated, and hence
the third symmetry as applied to the process must also be violated so that t
he
final result will not change. It follows from the theorem, then, that a
violation of CP symmetry implies a violation of time reversal symmetry as
well. So
another way of stating Sakharov's second condition is that it must be
possible to violate time reversal symmetry. In other words, the "arrow of
time"
must make a distinction between past and future. It has very recently been
verified directly that there are processes where this occurs.
The third of Sakharov's conditions – non –equilibrium is necessary so that
reactions which proceed in one direction are unable to reverse themselves
and
become undone by proceeding with equal probability in the other direction.
This is basically guaranteed by conditions of rapid expansion and cooling
early
in the history of the big bang together with together with the existence of
massive particles.
What it amounts to is that reactions which took place at a certain stage
cannot be undone, because the temperature decreases too rapidly (so that
certain
reactions become much less likely or impossible), and because the
interacting
particles move apart rapidly along with the expansion of the universe (so
that they become much less likely to interact). In other words, the effects
of
certain particle reactions become "frozen in" as the universe expands and
cools. The effects cannot be undone.
In his paper, Sakharov does propose that matter –antimatter symmetry is
preserved in a larger Biverse. He writes
“We can visualize that neutral spinless Maximoms (or photons) are produced
at t<0 from contracting matter having an excess of anti quarks, that pass
over
the other at the instant that t=0 when the density is infinite, and decay
with an excess of quarks when t>0, realizing total CPT symmetry of the
Universe. All the phenomena at t<0 are assumed in this hypothesis to CPT
reflections
of the phenomena at t>0. “
End quote
This is of course the Biverse idea which Lawrence and Bruce view rather
negatively.
Nevertheless there is other theoretical support for the Biverse proposal.
The Hawking Hartle no boundary proposal also predicts the existence of CPT
reversed histories as states of the wave function of the Universe. Hawking
writes;
“Another feature of the wave function that is worth remarking on is that it
is real. This means that, in the oscillating region, the WKB ansatz is
C*(exp
(-iS) +exp (-iS)). One can regard the first term as representing an
expanding
Universe and the second as a contracting Universe. More generally if the
wave function represents some history of the Universe; it also represents
the
CPT image of that history.”
“Because the no boundary quantum state is CPT invariant there will be
histories of the Universe that are the CPT reverses of that described above.

However, intelligent beings in these histories would have the opposite
subjective
sense of time.”
End quote
“300 Hundred Years of Gravitation theory” edited by S.W Hawking and
W.Israel. 1987 Cambridge University Press.
Additional theoretical justification for the notion of a Biverse comes from
the inclusion of the true negative energy state solutions of the
relativistic
equations, the fundamental idea proposed in Bob Klauber’s paper and in a
proposal I made in 2002.
In my proposal I postulated the existence of four scalar fields.(based on
the full solution set of the Klein Gordon equation) I called these four
fields
, The Cosmon , the anti-Cosmon , the negative Cosmon and the negative
anti
Cosmon fields. These fields correspond to the four particle states I
outlined
in my post “The Beautiful Symmetries of Energy Flow and Time” and they
also
correspond to the particle states outlined in Bob Klauber’s paper.
Bob Klauber writes
“The absence of observed real supplemental particles may be conjectured as
being related to the fact that reversing the arrow of time in the
supplemental
solutions produces the traditional solutions. That may mean, with regard to
perception that real supplemental particles travel backward in time. Thus
one
might speculate that the Universe needed no initial energy from which to
begin, with equal amounts of traditional and supplemental particles
emerging
from nothing. From there, the real negative energy supplemental particles
traveled backward in time , and in the process created their own Universe,
which
would appear to any beings in that Universe to posses positive energy. Each
universe would have only one kind of particle, but virtual particles of
both
types. And this would result in the null vacuum or near null vacuum
cosmological
constants in both. In this scenario the act of creation itself would have
been the first and most fundamental symmetry breaking of nature’s laws.”
“Mechanism for Vanishing zero point Energy” Page 10.
It might helpful to look at this question in terms of the symmetries
outlines in my previous post. “The Beautiful Symmetries of Energy Flow and
Time”
I will use the muon as the example particle. (Since Sakharov uses this
lepton in his model)
We can draw a simple two dimensional space time diagram which I will
describe as space along the horizontal axis and time vertical.
Therefore we have
Quadrant 1--- muon (-) _L {+E +t}
Quadrant 2--- negative Muon (-) _R {-E +t}
Quadrant 3--- antimuon (+) _R {-E –t}
Quadrant 4 --- Negative antimuon (+) _L {+E –t}
The particle states in quadrant 1 and 3 are physical particles in our time
forward Universe but the particle states in Quadrant 2 & 4 are what Bob
Klauber calls supplemental states and are not physical particles in our
Universe.
The two operations outlined in my post “The Beautiful Symmetries of Energy
Flow and Time” can be represented by movement across one axis and along
another.
The P operation (space reflection) is represented by movement along the
space axis and across the time axis while the T operation (Time reflection)
is
represented by movement along the time axis and across the space axis.
Remember that Sakharov wrote;
“We can visualize that neutral spinless Maximoms (or photons) are produced
at t<0 from contracting matter having an excess of anti quarks, that pass
over
the other at the instant that t=0 when the density is infinite, and decay
with an excess of quarks when t>0, realizing total CPT symmetry of the
Universe. All the phenomena at t<0 are assumed in this hypothesis to CPT
reflections
of the phenomena at t>0. “
End quote
So let’s see how this works for our muon particle.
We have assumed that that the muon can take on four particle states. (The
unphysical states can only “exist” as virtual particles due the positivity
requirement of the Decoherence functional.)
So we have (~ means negative energy)
1) muon (-) _L {+E + t} Q1
2) ~ negative muon (-) _R Q2 {-E +t}
3) ~ anti muon (-) _R Q3 {-E –t} Reinterpret to {+E + t} = anti muon
(+) _R
4) negative anti muon (-) _L {+E –t} Reinterpret {-E +t} = ~ negative
anti muon.
Particle states 1 & 3 satisfy the positivity requirement and can be
measured
as real particles. Particle state 1 is selected by the arrow of time
associated with CP violation to predominant in the Maximom decay process in
our
Universe.
However, let’s look at these particle states from a reversed time
perspective which is how an observer in the time reversed Universe would
see these
states, though he would think his arrow of time is forward. We must do a
time
reflection.
1) muon (-) _L {+E + t} Q1 = [1>
T [1> = [4> = {+E –t}
2) ~ negative muon (-) _R Q2 {-E +t} = [2>
T [2> = [3> = {-E –t}
3) ~ anti muon (-) _R Q3 {-E –t} = [3>
T [3> = [2> = {-E +t}
4) negative anti muon (-) _L {+E –t} = [4>
T [4> = [1> = {+E +t}
So now in the time reversed Universe the unphysical states [2> & [4> become
the physical states [1> & [3>
This is exactly what Bob Klauber describes in his paper.
But because the CP arrow of time is reversed in the time reversed Universe
state [3> is selected to predominate in the time reversed Universe, thereby

demonstrating a CPT invariant Biverse.
Bob Zannelli











I should hasten to add , while I do assert the mathematical reasonableness
in this post and the previous related post, this of course constitutes no proof
whatsoever that nature worked this way in the early Universe. I should have
made this clear.

Bob Zannelli






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