Beyond the God Particle (34 page)

This is called “time-reversal symmetry.” But just as parity seemed to be a symmetry until we encountered the weak interactions, we might ask, “Is time reversal a fundamental symmetry of nature and therefore valid for the elementary particles?” Does the world through the time mirror have the same laws of physics as does ours? Or like parity, is it a broken symmetry?

The answer is that the weak interactions, which violate parity, also violate time-reversal invariance at a much weaker level. To see this, we need yet another mirror—the antiparticle mirror.

CPT

We have already noted that mirror symmetry, designated by “P” for parity, is not a valid symmetry when it comes to processes involving the weak forces. Furthermore, as we have seen, there exists yet another discrete symmetry operation, called “T,” which reverses the flow of time, that is, we can replace t → –t in all of our physics equations, swap initial conditions with final ones, and get the same consistent results.
¹⁹

Yet another symmetry now arises given the existence of antimatter: it consists of replacing all particles by antiparticles in any given reaction. This is called C or “charge conjugation.” This symmetry would imply that there is an analogy to Alice's mirror called an antiparticle mirror. When Alice falls through her parlor mirror, P, she enters the world in which all parities are reversed (all “lefts” become “rights” and vice versa). When Alice falls through the “antiparticle mirror,” C, all the particles of all matter are turned into antiparticles and vice versa. We have seen that the laws of physics are slightly different through the parlor mirror—parity is a broken symmetry. So, naturally we ask, are the laws of physics the same through the antiparticle mirror? For example, would anti-hydrogen, consisting of an antiproton and an antielectron (positron) have the same identical properties, e.g., energy levels, sizes of the electron orbitals, decay rates, and spectrum, as does the ordinary hydrogen atom?

If C is a valid symmetry, then an antiparticle must behave in every respect identically to its particle counterpart, provided we replace every particle by its antiparticle in any given process. But this makes no reference to the spins of the particles, which have to do with P. In the pion decay,
the produced muon always has positive helicity, i.e., it is always produced as an L particle (negative helicity) in the weak interaction, but its mass flips it into R (positive helicity) so the process can occur and conserve angular momentum. If we perform a C operation on this process, we get the antiparticle process,
π
⁺
→
μ
⁺
v
⁰
, where all particles are now replaced by antiparticles, but the spins all stay the same (we went through the C mirror, not the P mirror). Therefore, the helicity of the anti-muon in the antiparticle process would still be positive, or R (spin is still aligned with direction of motion).

In 1957, shortly after the overthrow of P, the symmetry C was tested directly through experiment. When the experiment was performed, the helicity of the anti-muon in pion decay was
not R
, rather it was
found to be L
. Therefore, the symmetry C is also violated, together with P in weak interactions, such as the decay of pions and muons.

The reason is not hard to see if you remember Dirac's sea. You'll recall that the L part of the muon couples to the weak interactions, while R does not. But antiparticles are holes, representing the absence of negative-energy particles in the Dirac sea. So, we would expect that if L has –1 weak charge, a hole would have +1 weak charge. But a hole is
the absence of L and must therefore be R
. So, for antiparticles we would expect that the R anti-muon couples to W bosons while the L anti-muon (the absence of R, which had weak charge 0) does not. Don't worry if you find this a bit confusing—it is, and it requires some practice to get it straight, and maybe a Tylenol
^®
afterward. But it turns out that it would be hard to have it otherwise; when we reverse particle with antiparticle we naturally reverse parities.

So, naturally, there arose the conjecture that, perhaps, if we simultaneously reflect in a parlor mirror, P, and then go through the antiparticle mirror, C, i.e., change particle to antiparticle, that this combined symmetry may be exact in nature. The combined symmetry operation is called “CP.” Upon performing CP to the negatively charged
left-handed
muon, we get a positively charged
right-handed
anti-muon. In the pion decay,
π
⁺
→
μ
⁺
v
⁰
, the produced muon is indeed left-handed, so CP has turned out to be a symmetry of the pion decay. We now seemed to have deeper symmetry, which connected space reflections with the identity of particle and antiparticle. In summary, CP symmetry says: Jump through Alice's parlor mirror, which reverses parities, P, then jump through the antiparticle mirror, which changes all particles to antiparticles, C (the order is immaterial, CP is equivalent to PC), and we seem to get back to a world equivalent to our own.

But—the world is often much more enigmatic than humans are led to believe. In 1964, in a beautiful and extremely well-executed experiment involving some other interesting particles called neutral K-mesons (again, this is an accelerator-based experiment where “intensity,” or many, many produced K's, is more important than high energy), it was shown that CP i
s not conserved
, that is,
CP is also not a symmetry
. The physics of weak forces is
not invariant
under the combined operations C and P. If you go through the P mirror and the C mirror, you do not come home, but rather you end up in a world with different properties than our own.
²⁰

The details of the origin of this breakdown of the symmetry, CP, has come to define a frontier of physics for the past 50 years. There remain
many unanswered questions, such as “Do neutrinos in their peculiar flavor oscillations interactions also display a violation of CP symmetry?” (See the
next chapter
.) We still do not know how this will play out, but we have since learned that if CP were indeed a perfect symmetry of nature, our universe would be so totally different that we, our solar system, stars, and galaxies, would probably not exist. Nor would you be reading this book. So, it's a good thing for us that CP as a symmetry of nature is actually violated.

CP violation tells us that a particle and an antiparticle do behave in slightly different ways. In fact, CP violation is a prerequisite to explaining yet another enigmatic question: “Why does the universe seem to contain only matter and no antimatter?” If we go back to the initial instants of the big bang, when the universe was extremely hot (hotter than any energy scale ever probed in the lab), cosmological theory would predict equal abundances of matter and antimatter. However, with CP violation, some ultra-heavy-matter particles could have decayed slightly differently than their antiparticle counterparts. This miniscule asymmetry could have favored, at the end of the decay sequence, the production of a slight excess of the normal matter (hydrogen) over the antimatter (anti-hydrogen). Then, as the universe cooled, and all the remaining matter and antimatter annihilated each other, this slight mismatched excess of matter remained. The slight mismatched excess of matter is us and everything we see in the universe.

The problem is that, while we need CP violation to explain the fact that the universe contains matter and no antimatter, we don't think we have yet discovered
the
particular CP-violating interactions
that produce this effect. The CP-violation effect, first seen in neutral K-mesons, now seen in other particle decays, remains an intriguing hint of much more to come, but it cannot explain the matter–antimatter asymmetry. This issue is being studied aggressively around the world. And the answer may ultimately come from the lowly neutrino, if indeed neutrinos display CP violation. The devil is in the details. We have reached the frontier—we don't know the answer to this question.

DOES ANY COMBINATION OF MIRRORS TAKE US HOME?

Alice now has three mirrors to jump though. There's her parlor mirror, which flipped parities, P. There's the time-reversed mirror, T, which runs
things backward in time, and there's the antiparticle mirror, C, which flips all matter into antimatter. Is there a sequence of mirrors we can jump through that will get us back home to the same world in which we live?

Quantum mechanics makes probabilistic predictions for the outcome of events. When we flip a “fair” coin, we have equal probability of getting heads or tails. But even with an “unfair” coin, the sum of the probabilities of getting heads or tails in a coin flip is one—the sum of all probabilities that anything should happen must add to one, or else we are not able to talk meaningfully about probability—the quantum theory would fall apart if this were not so. What would it mean that the probability of heads in a coin flip is 2/3, while tails is also 2/3? How can the total probability be 4/3?

It turns out that it is a theoretically necessary condition in quantum mechanics that, if we want the total probability of all possible outcomes for a given process to add to one, then the combined operations of CPT must indeed be an exact symmetry. If we combine C, P, and T, at least at the present level of experimental sensitivity, we do appear to have an exact symmetry of the world, CPT. There has been no experimental evidence of CPT violation, and many people consider it to be very unlikely. So—if Alice jumps through the C mirror, then the P mirror, then the T mirror (in any order), she gets back home!

If CPT failed as a symmetry, then over time probability would not be conserved. This undermines the notion of probability in quantum theory, and we would have to significantly modify it. That is, the probability for anything to happen under any circumstances would either exceed or be less than one! Nevertheless, we must ask, if the violation of CPT were very, very tiny, would we have noticed? It is, after all, an experimental question.

Let's step back and reflect on the situation. There are many questions we do not have answers to. The devil is always in the details, and physics is an experimental science. And, if there's one thing we have should have learned from history by now: rare processes, processes that may probe up to a 100 times or more beyond the LHC, may lead us to new physics. New discoveries could radically change our entire view of nature may be lying just beyond our current reach.

According to our modern scientific version of “genesis,” the universe emerged from a plasma of the elementary constituents of matter: quarks, leptons, gauge bosons, and perhaps many other hitherto undiscovered particles furiously swarming about at extreme temperatures and pressures in an embryonic warped and twisted space and time. Space itself exploded, driven by the raw energy of the constituents of the universe, as described by the equations of Einstein's general theory of relativity. As the universe and its constituent plasma expanded, it cooled and condensed, ultimately transforming itself into a uniform gas of hydrogen, some helium, and relic particles of electromagnetic radiation, neutrinos, and some unknown(s) that are referred to as “dark matter.” Primordial quantum fluctuations in the density of these relic particles may have been transmitted, through gravity, to the hydrogen gas cloud, leading to its collapse, and the formation of the galaxies and the first “protostars” of the early universe. These monstrous stars were the parents of all the later heavy elements, the planets, and the solar systems to come, including our own sun.

All the atoms heavier than helium, such as carbon, oxygen, nitrogen, sulfur, silicon, iron, etc.—the stuff of our own solar system, rocks, and our solid and wet planet; the stuff of life itself—were created within the gigantic protostars. The heavy elements were cooked by the process of nuclear fusion, within their cores, bound by immense gravitation, deep within these super-massive stars. These heavy atoms became the raw ingredients of the modern universe, without which there would be no structure. Eventually, by the parentage of the protostars, the sun and planets formed, and the special conditions on Earth led to the subtle and gradual evolution of life and of human beings. The true scientific story of our heritage is richer than any fables, and it is more mysterious and bizarre in its reality.