Well, it's especially appropriate that a discussion of CP violation and matter-antimatter

asymmetry take place at this time because it was just 50 years ago this summer that Carl Anderson identified, discovered the compositeron, this first example of antimatter. It was published in September of 1932.

This first identification was made in cosmic rays in a cloud chamber that was immersed in a magnetic field. And it's interesting that the principal experimental problem that Anderson faced in convincing himself in the community that he had positrons and not

simply electrons traveling in the reverse direction. Of course, in the intervening years, we've become so used to the idea of simply turning vectors around and making E minuses, E pluses,

that it's hard to adjust to the fact that his principal experimental problem was what we now take for granted. Well, somewhat earlier, Dirac had proposed his famous equation in which antimatter is intrinsic.

But it appears that the theoretical developments in the experimental discovery were entirely disconnected. It's one of the many remarkable coincidences in physics that these experimental and theoretical developments should occur almost simultaneously.

Of course, it took a bit of time to completely adjust to the notion of antimatter. But we're now all very sophisticated and recognize that antimatter, completely symmetric with matter, is just a natural consequence of joining special relativity and quantum mechanics.

But I trust Professor Dirac will not object if I go back and quote what he had to say about matter and antimatter on the occasion of his Nobel Prize. And I quote here, if we accept the view of complete symmetry

between positive and negative electric charge so far as concerns the fundamental laws of nature, one must regard it rather as an accident that the Earth, presumably the whole solar system, contains a preponderance of negative electrons and positive protons. It is quite possible that for some of the stars,

it is the other way about, the stars being built on mainly positrons and negative protons. In fact, there may be half the stars of each kind. The two kinds of stars would both show exactly the same spectra, and there'd be no way of distinguishing them by the present astronomical methods.

Well, I will come back to this. We've had some economists in our midst or economists here yesterday. And of course, with economists present, why physicists always feel that they somehow have to justify themselves on economic grounds. And we all know the list of things

that physicists have done. You go recite the list of all the instruments in the hospital and concluding with the computer-aided tomography machines, the CAT scans. And we turn to transistors and computers.

There's one spin-off that had not occurred to me before. I wrote this down, and that is, there's this whole industry of science fiction. And surely, that industry would not be nearly as prosperous as it is if it weren't

for the idea of antimatter. So well, during this period, when the notion of complete symmetry between matter and antimatter was developing, the idea that all interactions were invariant

under spatial reflections were also being firmly embedded. And as you know, Wigner proposed a symmetry to explain spectroscopic rules, in particular, those of LaPorte and Russell. And then, following that, Li and Yang

proposed that series of tests to see if the puzzle created by the tau and theta particles was indeed a manifestation of the failure of parity symmetry in the weak interactions. And as you all know, it was found that not only parity was violated, but also matter-antimatter asymmetry.

But still, the CAT landed on its feet in the end, because it appeared that the total failure of parity was totally compensated by a corresponding failure in the charge conjugation, and that all interactions

in the end appeared symmetric under spacious inversion and matter-antimatter interchange. Well, it's now been 18 years since my colleagues Cronin, Turley, and Christensen discovered that the world is not completely symmetric under CP. This is a small, but nonetheless unmistakable

violation of CP in the system of neutral k mesons. But again, it's been found that the CP violation appears to be totally compensated by a failure of time reversal, preserving the general idea of CPT symmetry.

So let me now turn to a discussion of the k meson system, and for that, I will use this machine. These famous particles, first invented by Gell-Mann and Pais,

based on the observation that through the weak interactions, the particle, the k0, and the k0 bar were coupled. There are these common decay modes. And correspondingly, when we talk about k mesons, everyone has this elegant two-state system of quantum mechanics. The coefficients in these equations

comprise the so-called mass decay matrix. Under CPT symmetry, the diagonal elements, the a's and the b's, are equal. But under CP symmetry, the off-diagonal elements of the matrix are equal.

Now, assuming for the moment CPT symmetry, then the mass eigenstates are simply the long-lived neutral k, which I can write as p k0 minus q k0 bar, appropriately normalized, and the short-lived animal, this. Now, it's clear that with CPT symmetry,

the amplitude for decay of the k0 and k0 bar must be the same. So one could not have a decay of the kl to pi plus pi minus, for example, unless p was different from q, with the amplitudes for decay the same.

Well, what was observed, as you all know, was a finite decay of the kl to pi plus pi minus. In fact, the ratio of the rate of the kl to pi plus pi minus and the ks to pi plus pi minus is a very small number, about 1 in 200,000.

It looks like an enormously small effect indeed in amplitude terms. However, it's about 2 tenths of a percent. Emphasize precision, which some of these quantities have been measured by noting that the phase

angle of this amplitude has been measured to slightly more than 1 degree. But whether one considers this number small or not depends on how you feel about the fine structure constant, because the magnitude of the ratio of these amplitudes is just about equal to alpha over pi, which itself is 2.32

times 10 to the minus 3. Now, this amplitude could have two contributions, one from the mass decay matrix that I've already discussed. And also, as I've indicated, even if p was equal to q

if those off-diagonal elements were identical, it would still be possible for there to be CP violation, simply if the decay amplitudes of k0 and k0 bar differed in phase. And one that normally allows for the possibility of CP

violation in the decay amplitudes by adding this extra parameter here, epsilon prime. Well, it turns out that at the moment, all of the evidence is that at least 98% or 99% of the effect is in the mass decay matrix. But as we will see later, it's of extreme interest now as to just how much might be in this epsilon prime.

Stating it another way, the CP violation is the difference of the two vectors.

The amplitude of the k0 going to k0 bar might be indicated like so. The reverse process, k0 bar back to k0, differs by this small amount, which is at an angle, as I've indicated, of about 45 degrees. And in terms of the length of each of the vectors,

is about 0.9 times 10 to the minus 2. Another way of phrasing it is that the difference of those off-diagonal elements in the mass decay matrix is about 10 to the minus 8 electron volts. Another manifestation of the CP violation, and the effect being the mass decay matrix,

comes from looking at the lepton decay modes of the k0 and k0 bar. The k0 can decay to e plus pi minus neutrino, and the k0 bar to e minus pi plus neutrino. The fact that it's just the k0 that decays to positrons,

and the k0 bar that decays to negative electrons is a consequence of a so-called delta s, delta q rule, which in turn is just a manifestation of the fact that the k0 is composed of an anti-strange quark and a down quark.

And there's only one way one can draw such a diagram involving the w's, and that is this one. You cannot get a negative electron coming out of such a diagram. But independent of any such argument, the delta s, delta q rule has been tested

to about the 1% level. Because of this fact that the k0s can decay only to positrons, and the k0 bars only to negative electrons, and the fact that p is different from q leads then to a charge asymmetry,

difference of the number of positrons from the decay of the long live neutral k's compared to the sum, which is obviously magnitude of p squared minus q squared over the sum, which is just two times the real part of epsilon to a high degree of approximation. Now, this charge asymmetry experimentally, as you see,

is about 3 tenths of a percent measured with an error of something of the order of 5% in the case of the electron, and for cases where the mu is substituting for the electron, somewhat larger error with the numbers being

the same within the error. Well, what are the consequences? First of all, I said that the eigenstates that I've drawn out I assume CPT invariance.

What if one does not assume CPT invariance? It turns out that if you make that assumption, the phase angle difference between p squared and q squared, or I should say the phase angle of eta plus minus independent of p squared and q squared, that phase angle should be something of the order of 135 degrees instead of the 45 degrees

that's observed. So clearly, CPT to quite a high degree of accuracy is experimentally confirmed. And therefore, it must be CP and time reversal invariance that is violated.

But asking the question, these results, what limit does this put on the equality of masses of k0 and k0 bar, we come up with the following. Namely, we've already seen that the effect is about 10 to the minus 8th electron volts.

If I say that because of other arguments, I set a limit of about 10 to the minus 9 electron volts on the difference of the diagonal elements. That compared to the mass of the k0 is about 2 times 10 to the minus 18th. That is, one knows the mass of the k0 and the k0 bar are identical to about two parts in 10 to the minus 18th.

Now, yesterday, I seized on a statement of Professor Schawlow, which I've written down here. And I'm being a little unfair, but I can only say here that he's looking at the wrong particle when

he makes a statement that nobody measures anything to one part in 10 to the 17th. Of course, he was referring to absolute numbers. And I will correct my unfairness. One of the very interesting, to me, very interesting aspects of the neutral k system

is what it can tell us about the gravitational interaction. Question is one of strong universality, and that is whether different objects, in this case, particle and any particle, behave the same in the gravitational field. And if they differ by kappa, then what

limits does this system place on kappa? Now, if one is discussing the gravitational potential of just the Earth, where the k has a potential on the surface of the Earth of about 3 tenths of an electron volt, then kappa must be less than about 10 to the minus 10th. If we're discussing the solar system,

it should be around 10 to the minus kappa is less than 10 to the minus 11. If it's a galaxy we're discussing, then that limit is around 10 to the minus 13th. Now, you can argue, well, mesons are composites of particles, anti-particles, quarks and anti-quarks.

But I remind you that the mass of the strange quark differs from that of the down quark by something of the order of 125 MeV. What are the principal ramifications and consequences, then, of this asymmetry between matter and anti-matter?

The fact, as we've seen, that the rate of k naught going to k naught bar differs from the reverse. These two vectors not only differ in magnitude, but phase, which, as we've seen, also says that interactions are not invariant. This fundamental interaction is not

invariant under time reversal. Well, we all know that time reversal is badly violated. Disorder is always increasing. Entropy is always increasing. But we also know that that's due to the boundary conditions. You start with a clean house, so you end up

with a dirty house. But here we have time reversal in non-invariance due to fundamental interactions, not boundary conditions. That is what is new and different from anything we've known before. This, then, can lead to anti-matter asymmetry

in the universe. And we can make a simple argument of the following kind. We've already seen, experimentally, that the decay of the long-life neutral k leads to an excess of positrons.

And it turns out, if one integrates proper equations governing the time dependence of the k0 and k0 bar, that equal numbers of k0 and k0 bar at t equals 0 will also produce an excess of positrons,

more positrons than electrons. But we already know that there is good reason for, at some level, coupling positrons and protons. You've learned that from Professor Weinberg this morning, correspondingly, electrons with anti-protons.

So with CP violations, since we've seen that the k0s and k0 bars produced in number leads to an excess of positrons, and with this kind of coupling, we would also be automatically led with the CP

violation of equal numbers of k0s and k0 bars producing an excess of protons over anti-protons. Of course, the difficulty is that the neutral k is not heavy enough to decay to nucleons. So I'm arguing only in principle here. In fact, the fact is, however, that there

are other mesons that have plenty of mass to decay to protons. In particular, the d0, the d0 bar, b0, b0 bar, and presumably it exists, the t0 and the t0 bar. All of these mesons produce neutral systems

that are completely analogous to the k system and are expected to show a CP violation, and in some cases, rather large. For example, large effects are expected in the case of the b0, b0 bar.

So with this identity and the fact that the existence of these objects means that independent of any particular model, one has a mechanism for producing an asymmetry of matter over anti-matter.

Now, most generally, this is discussed in terms of a heavy particle, as Professor Weinberg did earlier today. Here we have equated proton and e plus. And proton is just two up quarks and a down quark, of course.

So this is just the same thing written with one of the up quarks on the other side of the equation, which is then made equivalent to a lepto quark. A lepto quark then can decay to a u plus, an up plus, a down quark, or to a positron and an anti-up quark.

And a corresponding anti-heavy particle can go to the charge conjugate states. Now, back in 1967, Sakharov seized on CP violation right away. And this is pre-Grand Unified Theories. And he drew it all out.

He had the heavy lepto quark decaying appropriately. And, for example, the heavy lepto quark going to positron and u bar with an amplitude a, going to d plus u with an amplitude, relative amplitude,

of 1 minus a, choosing these as the only two decay channels for the purposes of symbolic arguments. By CPT, it's necessary that the total rate of the heavy lepto quark, total rate of decay, be the same as that of the anti-heavy particle.

On the other hand, these partial rates, the a and a bar, don't necessarily have to be equal. By CP violation, they can be different. The net result of all of this is that it can produce equal numbers of these heavy particles and, in their decay,

end up with a total baryon number, which is just the difference of a bar and a through CP violation in this particular channel. There's another essential ingredient to producing a baryon asymmetry in the universe, which

I have not mentioned yet. And that is that you have to guarantee that back reactions are not going to cancel out everything you've accomplished in these forward reactions. So one has to have a non-equilibrium situation prevailing.

Well, how does CP violation fit into any of the theoretical ideas that we have had described to us? First of all, the non-perturbative quantum chromodynamics has intrinsically a strong CP violation.

Characterizing that phenomena by parameter theta, the most natural value for theta is 1. However, to suppress the electric dipole moment of the neutron to an appropriate level, it's necessary that theta be less than 10 to the minus 8. This is still an awkward problem. I don't believe that anyone would

agree that it's been satisfactorily resolved. And what it has to do with the weak interactions is anyone's guess. Within the framework of the gauge models, there are two independent, not completely independent,

ideas that have been put forward. First of all, the Kobayashi-Maskawa six quark model, which extends the four quarks of Glashow and company to six quarks. And this model was actually proposed back in 1973

when we only knew of three quarks. Since then, two more quarks have been discovered. And as we have heard again and again now, a six quark is expected at any moment.

So this particular model has established some popularity. The essential point here is that it has space in it, an extra phase, which is CP violating. So it provides a very natural home for CP violation.

There is also an independent suggestion that the CP effect could be due to the exchange of Higgs particles, which were also mentioned by Professor Weinberg earlier. Indeed, he is one of the original proponents

of this particular idea. One of the reasons for resurgence of interest in this problem is that it turns out that these become eminently testable. And I will come back to that.

Professor Schwinger has also proposed that the effect might lie in dions, that is electrically charged monopoles. One of the original suggestions seized on the fact that the effect that is measured in eta plus minus

is very close to the fine structure constant divided by pi. It's a terribly suggestive correlation. That is that the effect is electromagnetic. That seems to be completely ruled out now by the very relatively tight limits, at least tight limits for this argument on the electric dipole

moment of the neutron. So what are the consequences of these various theoretical models? What is really testable? Well, with Higgs exchange, as proposed originally

by Lee and Weinberg, the leading consequences are that one has milliwick effects throughout the weak interaction. The electric dipole moment of the neutron

should be in the range of 10 to the minus 24, 10 to the minus 25 e centimeters. Now, at the present moment, the accepted limit is 10 to the minus 24 e centimeters. So a small improvement in this measurement will begin to have a telling effect on this idea.

The experiments outside the neutral case system that have been done in the weak interactions have all been done essentially at the centi-weak level. And another factor of 10 is necessary in the accuracy of those experiments in order to begin to say something about whether there are milliwick

effects everywhere. But there is apparently a big problem with this model already, because it's been recently pointed out by Sanda and Deshpand, and later by Donahue, Hagelin, and Holstein, that in fact, the ratio

of epsilon prime over epsilon within the framework of this model, and some other assumptions that I won't go into here, should be of the order of 0.05. Now, in fact, the present experimental limit on this number is something like 0.02.

There are two ways one can get out of this immediately, though. One of them is that the theoretical prediction is apparently not as hard as one would really like. So there's some softness here. And in view of the difficulty of measuring

the epsilon prime component of the CP violation, there could be some softness in the present experimental number also. If one takes all that's known about the phases in the KM

model, Kibayashi-Maskawa model, then various people have made various predictions of what should be measured for epsilon prime over epsilon. And as I indicated, the current experimental number is a limit of about around 2%.

Now, new experiments could show something exceedingly interesting. And indeed, my colleague Cronin has just concluded taking data devoted to this problem in the last week or so. On the other hand, the effects within the framework

of this model in other sectors are really very small indeed. For example, the electric dipole moment of the neutron, which I have already indicated has been limited to around 10 to the minus 24 e centimeters, is predicted to be something of the order 10 to the minus 30th. 10 to the minus 24 represents a real tour de force

in experimental physics. Let me remind you that the magnetic dipole moment of the neutron is around 10 to the minus 14 e centimeters. So the present limit is already 10 orders of magnitude less than this number, which is rather easily measured,

of course. Well, these new experiments then promise to be able to distinguish between these principal ideas involving gauge theories.

But I think it's fair to say that we still do not know what the real source is. Even if it's found to lie within the extra phase that's available in the Kobayashi-Makawa model, the source of the violation is still a great unknown. It might find a natural home there,

but the real effect, the real cause, has yet to be determined. I would like to conclude by making a few remarks directed to the students here, a few remarks of a semi-philosophical nature

about the process of doing physics. At any one time, there are always plenty of people, fellow physicists, who will tell you that everything is understood and anything that follows is just a mopping up operation.

And in a certain sense, I feel that we're at a time like that now. But it just never happens that way. Every time we explore a new domain, we inevitably discover new phenomena

which require a major reordering of the old ideas or completely new theories to accommodate them. Who could possibly have guessed that the discovery of strange particles in the late 1940s would have led, in the following 15 years, to the discovery of parity and charge conjugation

violation and then the failure of CP, or that we would now be calling strangeness just another flavor. I would hope that I've left you with the feeling that, just to say it again, that we still know very little about the details of CP violation.

Time reversal violation is obviously touching on our knowledge of physics at the deepest level. What is the source? How does it operate? We've blithely written down relations between quarks and leptons.

And then we can ask, why does the electron have a charge 3, in terms of the quark, of course? And when will the electrons start to show structure? Just what are particles anyway? These little concentrations of energy that travel like waves.

And then when are we going to be able to provide the experimental control or the sometimes rampant speculations about the nature of the gravitational interaction? These are questions for your generation. And the answers you get will sometimes have nothing

to do with the questions. But that's what one does physics for. I've been doing experimental work for about 35 years. And in each point in time, proposed experiments, experiments that we've thought of,

have always seemed impossible. That's where you start from. We've always had to push the limit of the technology or exceed it just to achieve what we set out to do. But surprisingly often, then we've learned something that no one expected.

It's interesting that starting from a position where it seemed impossible, when it's all over and the data is understood, that which seemed impossible at the beginning now seems trivial. But that's true of everything in physics. It's either trivial or impossible.

And before you try, it's impossible. And after you've succeeded, it's trivial. You're, as students, at sort of the impossible stage now. But keep at it. Some parts of it will eventually seem trivial. And good luck to you.