From Eternity to Here (26 page)

So you’d like to make a collection of kaons and antikaons, and keep track as they oscillate back and forth into each other. If time-reversal invariance is violated, we would expect one process to take just a bit longer sthan the other; as a result, on average your collection would have a bit more kaons than antikaons, or vice versa. Unfortunately, the particles themselves don’t come with little labels telling us which kind they are. They do, however, eventually decay into other particles entirely—the kaon decays into a negatively charged pion, an antielectron, and a neutrino, while the antikaon decays into a positively charged pion, an electron, and an antineutrino. If you measure how often one kind of decay happens compared to the other kind, you can figure out whether the original particle spends more time as a kaon than an antikaon.

Even though the theoretical predictions had been established for a while, this experiment wasn’t actually carried out until 1998, by the CPLEAR experiment at the CERN laboratory in Geneva, Switzerland.
¹¹⁹
They found that their beam of particles, after oscillating back and forth between kaons and antikaons, decayed slightly more frequently (about 2/3 of 1 percent) like a kaon than like an antikaon; the oscillating beam was spending slightly more time as kaons than as antikaons. In other words, the process of going from a kaon to an antikaon took slightly longer than the time-reversed process of going from an antikaon to a kaon. Time reversal is
not
a symmetry of elementary particle physics in the real world.

At least, not “naïve” time reversal, as I defined it above. Is it possible to include some additional transformations that preserve some kind of time-reversal invariance in the world of elementary particles? Indeed it is, and that’s worth discussing.

THREE REFLECTIONS OF NATURE

When you dig deeply into the guts of how particle physics works, it turns out that there are three different kinds of possible symmetries that involve “inverting” a physical property, each of which is denoted by a capital letter. We have time reversal
T
, which exchanges past and future. We also have parity
P
, which exchanges right and left. We discussed parity in the context of our checkerboard worlds, but it’s just as relevant to three-dimensional space in the real world. Finally, we have “charge conjugation”
C
, which is a fancy name for the process of exchanging particles with their antiparticles. The transformations
C
,
P
, and
T
all have the property that when you repeat them twice in a row you simply return to the state you started with.

In principle, we could imagine a set of laws of physics that were invariant under each of these three transformations separately. Indeed, the real world superficially looks that way, as long as you don’t probe it too carefully (for example, by studying decays of neutral kaons). If we made an anti-hydrogen atom by combining an anti-proton with an antielectron, it would have almost exactly the same properties as an ordinary hydrogen atom—except that, if it were to touch an ordinary hydrogen atom, they would mutually annihilate into radiation. So
C
seems at first blush like a good symmetry, and likewise for
P
and
T
.

It therefore came as quite a surprise in the 1950s when one of these transformations—parity—was shown
not
to be a symmetry of nature, largely through the efforts of three Chinese-born American physicists: Tsung-Dao Lee, Chen Ning Yang, and Chien-Shiung Wu. The idea of parity violation had been floating around for a while, suggested by various people but never really taken seriously. In physics, credit accrues not just to someone who makes an offhand suggestion, but to someone who takes that suggestion seriously enough to put in the work and turn it into a respectable theory or a decisive experiment. In the case of parity violation, it was Lee and Yang who sat down and performed a careful analysis of the problem. They discovered that there was ample experimental evidence that electromagnetism and the strong nuclear force both were invariant under
P
, but that the question was open as far as the weak nuclear force was concerned.

Lee and Yang also suggested a number of ways that one could search for parity violation in the weak interactions. They finally convinced Wu, who was an exper imentalist specializing in the weak interactions and Lee’s colleague at Columbia, that this was a project worth tackling. She recruited physicists at the National Bureau of Standards to join her in performing an experiment on cobalt-60 atoms in magnetic fields at very low temperatures.

As they designed the experiment, Wu became convinced of the project’s fundamental importance. In a later recollection, she explained vividly what it is like to be caught up in the excitement of a crucial moment in science:

Following Professor Lee’s visit, I began to think things through. This was a golden opportunity for a beta-decay physicist to perform a crucial test, and how could I let it pass?—That Spring, my husband, Chia-Liu Yuan, and I had planned to attend a conference in Geneva and then proceed to the Far East. Both of us had left China in 1936, exactly twenty years earlier. Our passages were booked on the Queen Elizabeth before I suddenly realized that I had to do the experiment immediately, before the rest of the Physics Community recognized the importance of this experiment and did it first. So I asked Chia-Liu to let me stay and go without me.

As soon as the Spring semester ended in the last part of May, I started work in earnest in preparing for the experiment. In the middle of September, I finally went to Washington, D.C., for my first meeting with Dr. Ambler. . . . Between experimental runs in Washington, I had to dash back to Columbia for teaching and other research activities. On Christmas eve, I returned to New York on the last train; the airport was closed because of heavy snow. There I told Professor Lee that the observed asymmetry was reproducible and huge. The asymmetry parameter was nearly -1. Professor Lee said that this was very good. This result is just what one should expect for a two-component theory of the neutrino.
¹²⁰

Your spouse and a return to your childhood home will have to wait—Science is calling! Lee and Yang were awarded the Nobel Prize in Physics in 1957; Wu should have been included among the winners, but she wasn’t.

Once it was established that the weak interactions violated parity, people soon noticed that the experiments seemed to be invariant if you combined a parity transformation with charge conjugation
C
, exchanging particles with antiparticles. Moreover, this seemed to be a prediction of the theoretical models that were popular at the time. Therefore, people who were surprised that
P
is violated in nature took some solace in the idea that combining
C
and
P
appeared to yield a good symmetry.

It doesn’t. In 1964, James Cronin and Val Fitch led a collaboration that studied our friend the neutral kaon. They found that the kaon decayed in a way that violated parity, and that the antikaon decayed in a way that violated parity slightly differently. In other words, the combined transformation of reversing parity and trading particles for antiparticles is
not
a symmetry of nature.
¹²¹
Cronin and Fitch were awarded the Nobel Prize in 1980.

At the end of the day, all of the would-be symmetries
C
,
P
, and
T
are violated in Nature, as well as any combination of two of them together. The obvious next step is to inquire about the combination of all three:
CPT
. In other words, if we take some process observed in nature, switch all the particles with their antiparticles, flip right with left, and run it backward in time, do we get a process that obeys the laws of physics? At this point, with everything else being violated, we might conclude that a stance of suspicion toward symmetries of this form is a healthy attitude, and guess that even
CPT
is violated.

Wrong again! (It’s good to be the one both asking and answering the questions.) As far as any experiment yet performed can tell,
CPT
is a perfectly good symmetry of Nature. And it’s more than that; under certain fairly reasonable assumptions about the laws of physics, you can
prove
that
CPT
must be a good symmetry—this result is known imaginatively as the “
CPT
Theorem.” Of course, even reasonable assumptions might be wrong, and neither experimentalists nor theorists have shied away from exploring the possibility of
CPT
violation. But as far as we can tell, this particular symmetry is holding up.

I argued previously that it was often necessary to fix up the operation of time reversal to obtain a transformation that was respected by nature. In the case of the Standard Model of particle physics, the requisite fixing-up involves adding charge conjugation and parity inversion to our time reversal. Most physicists find it more convenient to distinguish between the hypothetical world in which
C
,
P
, and
T
were all individually invariant, and the real world, in which only the combination
CPT
is invariant, and therefore proclaim that the real world is not invariant under time reversal. But it’s important to appreciate that there is a way to fix up time reversal so that it does appear to be a symmetry of Nature.

CONSERVATION OF INFORMATION

We’ve seen that “time reversal” involves not just reversing the evolution of a system, playing each state in the opposite order in time, but also doing some sort of transformation on the states at each time—maybe just reversing the momentum or flipping a row on our checkerboards, or maybe something more sophisticated like exchanging particles with antiparticles.

In that case, is
every
sensible set of laws of physics invariant under some form of “sophisticated time reversal”? Is it always possible to find some transformation on the states so that the time-reversed evolution obeys the laws of physics?

No. Our ability to successfully define “time reversal” so that some laws of physics are invariant under it depends on one other crucial assumption:
conservation of information
. This is simply the idea that two different states in the past always evolve into two distinct states in the future—they never evolve into the same state. If that’s true, we say that “information is conserved,” because knowledge of the future state is sufficient to figure out what the appropriate state in the past must have been. If that feature is respected by some laws of physics, the laws are
reversible
, and there will exist some (possibly complicated) transformations we can do to the states so that time-reversal invariance is respected.
¹²²

To see this idea in action, let’s return to checkerboard world. Checkerboard D, portrayed in Figure 39, looks fairly simple. There are some diagonal lines, and one vertical column of gray squares. But something interesting happens here that didn’t happen in any of our previous examples: The different lines of gray squares are “interacting” with one another. In particular, it would appear that diagonal lines can approach the vertical column from either the right or the left, but when they get there they simply come to an end.

Figure 39:
A checkerboard with irreversible dynamics. Information about the past is not preserved into the future.

That is a fairly simple rule and makes for a perfectly respectable set of “laws of physics.” But there is a radical difference between checkerboard D and our previous ones: This one is not reversible. The space of states is, as usual, just a list of white and gray squares along any one row, with the additional information that the square is part of a right-moving diagonal, a left-moving diagonal, or a vertical column. And given that information, we have no problem at all in evolving the state forward in time—we know exactly what the next row up will look like, and the row after that, and so on.

But if we are told the state along one row, we cannot evolve it
backward
in time. The diagonal lines would keep going, but from the time-reversed point of view, the vertical column could spit out diagonal lines at completely random intervals (corresponding, from the point of view portrayed in the figure, to a diagonal hitting the vertical column of grays and being absorbed). When we say that a physical process is irreversible, we mean that we cannot construct the past from knowledge of the current state, and this checkerboard is a perfect example of that.

In a situation like this, information is lost. Knowing the state at one time, we can’t be completely sure what the earlier states were. We have a space of states—a specification of a row of white and gray squares, with labels on the gray squares indicating whether they move up and to the right, up and to the left, or vertically. That space of states doesn’t change with time; every row is a member of the same space of states, and any possible state is allowed on any particular row. But the unusual feature of checkerboard D is that two different rows can evolve into the same row in the future. Once we get to that future state, the information of which past configurations got us there is irrevocably lost; the evolution is irreversible.