CONCLUDING REMARKS
V. F, Weisskopf
CERN, Genève
I am here to perform an impossible task. I am
supposed to summarize this Conference that has been
summarized by Rapporteurs during the last three
days and I am supposed to do it in one hour. The
simplest thing to do would be to say, " Look boys,
you have done fine (with some exceptions !); just go
ahead that way and in two years at the next Con-
ference we will have much better results That
would be the easy way out but it is too short. So
what can I do? I have to look at the highlights of
this Conference and try to give you my personal ideas
about them. Evidently many of you will disagree
with me on my choice and would emphasize other
items. But this is unavoidable.
In fact the task is not so difficult. In particular,
if one looks back at the situation as it was in 1960,
when one runs through the last Rochester Conference
Report, one can really see how much has happened.
At that time there were no isobars, no Y's, no omegas,
no p's, no rç's, except in the heads of a few theorists.
The cross-sections were flat as a desert and the particle
distributions were barren as a phase space. Since
then a new world has been created; you see peaks
and valleys everywhere, resonances have grown all
over the scale; a new world has emerged. It is a
pleasure to summarize a Conference in which this
new world has been reported for the first time.
Many new facts have been found in the last two
years. Let me put those facts in three groups. The
first group are the phenomena connected with high-
energy scattering, the ones where 5->oc. Here one
can distinguish between two general groups of find-
ings. One (a) is the fact that the cross-sections become
constant and equal for certain groups of particle
pairs. It is what one calls the Pomeranchuk limit.
This was already known or guessed at two years ago.
The second group (b) contains really new facts and
that is the discovery of the shrinking diffraction peak.
It is the fact that the nucléon at very high energies
gets more diffuse and larger as far as scattering with
strongly interacting particles is concerned. This is
certainly a remarkable insight into the behaviour of
elementary particles; it is unexpected and new, and
opens up completely new vistas. It implies, in some
ways, the absence of a core. One would have thought
that at high energies the innermost hard core of the
nucléon would appear. No, it seems that the nucléon
only becomes more diffused.
These results were obtained from scattering experi-
ments of nucléons by nucléons or pions by nucléons.
It is interesting to compare them with the results of
experiments with electron scattering. Two years ago
there was talk about finding a hard core by this
method: a peak of distribution at the centre of the
nucléon. Now we have heard reports on the distribu-
tion of charge and magnetism of the nucléon that
reveal to us that, in all probability, there is no inner
peak to be seen in these distributions either; but this
is by no means certain. It would be very interesting
if there were such an inner core in certain effects and not
in others, but so far the results are not conclusive.
We will have to wait for the next Conference to find
out how actually the charge and magnetic distribution
of the nucléon will turn out to be. The question is
whether, in the language of dispersion theory, there is
a sum over a few masses or whether there will be a
constant term in the momentum distribution; the
latter of course would mean a hard core.
The second group of phenomena are the isobars.
Here again we can group them into two parts, (a) are
what I would call the boson families. This is, for
example, the eight-group of the n, q, K and K particles.
Here, I think, one can be satisfied by the discovery
of the rf particle with spin and isotopic spin zero,
that fitted so well into that group of pions; it was
sorely missed before and now here it is - we now face
930 Plenary session XIII
a very nice round family of bosons which fills all the simple
quantum numbers which one might expect from a system of a nucléon
and its antiparticle in an S-state. This is not the only boson
family; we have another with strangeness different from zero, the
co and the p and now the K* and K*. It is not clear to what group
they belong. The second group (b) of isobars includes the baryons,
excited or not. There was a lot of excitement about numerous
baryons of different kinds, as we have heard in many of our talks.
Let us start with the eight " ground states neutron, proton, sigma,
lambda and Xi. On top of these eight ground states a system of
excited states of the pion field seems to appear. (It is perhaps
questionable whether one should call the 1° a ground state in this
respect, but this is irrelevant.) Again we find almost all the
simple quantum numbers represented in our list of excited states,
but we do not yet know what this means. It will be most interesting
to see how this list of excited states of baryons develops. There
are good reasons to believe that it will not go on like, say, the
excited states of the hydrogen atom. There are indications that the
list of those excited states is limited, such as the fact that the
pion-nucleon cross-sections seem to be pretty flat at several GeV
and also the indirect evidence, reported by Peters, which is found
with high-energy cosmic rays.
The third category of new facts are the weak interactions. Here,
of course, (a) first of all, most surprising (or less so to some
theorists) and most exciting, is the discovery of the existence of
two neutrinos. This now well-established fact opens up a new field
of research, neutrino physics, which will be in the centre of
interest for many years to come. The second group (b) includes the
increasing amount of evidence that the muon is equal to the
electron in all its properties, apart from its mass. The third
group (c) comprises a number of unexpected pieces of information,
details about the nature of the weak interaction, such as strong
indications that AS # AQ, and that the isotopic spin changes by
more than y2. Nobody knows what will be the situation in two years
from now, but it certainly seems that there is a problem here.
These three groups of new facts should give a very rough sketch
of what has happened in these two years. I certainly have left out
many new observations but I think that the ones I left out can be
fitted into these groups. It is a long list for two years of
research.
Perhaps I should also add at this point an item that has not
been mentioned at this Conference at all, and that is the
non-existence of magnetic monopoles. In spite of big efforts at the
two big machines, Brook-haven and here, no magnetic monopole was
discovered, and this pretty much excludes the existence of this
thing, if its mass is of the order of a proton mass and not much
higher.
These are the facts, but do we understand them? This Conference
was an experimental conference, most of the interesting and
exciting things have happened in experimental sessions. I hope that
my theoretical friends are not too mad at me if I say this. True
enough, they also worked hard and came up with many fascinating
ideas. Well, what is the theoretical situation ? What do we
understand and what do we not understand ? I would be exaggerating
if I said that we do not understand anything, as it has been said
very often. First of all, we do understand how to talk about
particles : this is a remarkable fact. It means we know what
particles are and what quantum numbers mean. Particles exist, we
ascribe them a charge, an isotopic spin, strangeness, parity,
statistics and so on. These concepts of quantum numbers for free
particles have stood against the flood of new discoveries and stood
like a rock. Not only this, the concept of antiparticles and the
validity of this concept in the way it was conceived in relativists
quantum mechanics has also stood up. We can speak of particles,
but, even more, we know how to describe particles and we know how
to describe a scattering event—an event where particles A and B
come in and particles C and D go out. We can introduce, in other
words, a scattering matrix for the description of this phenomenon.
We know what it means to say that the scattering matrix must have
certain properties such as unitarity (no particle can be created
out of nothing), causality (the signal cannnot come out before
another signal comes in), and so on. Because of our complete
understanding of the antiparticle concept—the time charge
conjugated form of the particle—we can also establish connections
and understand connections between different parts of the
scattering matrix. These are the so-called crossing relations
between different reactions, for example between A+B = C+D and A+C
= B+D. They lead to the requirement of analyticity in the
scattering matrix.
Conclusions 931
But what about the interaction process that causes the
scattering? Here we still have to use old concepts which we do not
know how to handle. What are the old concepts ? They are the
concepts of field theory. We introduce a Hamiltonian and an
interaction. To say that field theory does not work is perhaps too
strong a statement. Perhaps we do not know how to make use of it.
These two things need not be the same—they might be the same. What
is the trouble with field theory ? First of all, it diverges. That
can be overcome in some cases. Secondly, we are unable to solve its
equations, in particular when there is strong interaction, as is
the case in the nuclear field. We are able to deal with field
theory in the electromagnetic case where one can expand in the
coupling parameter. In nuclear problems, however, we are not
allowed to use expansion methods because of the strong interaction
and therefore we do not know how to handle it. What do we do in
this case ? We were looking— I mean the theorists were looking —
for a new language to talk about the phenomena. Dispersion theory
is such a new language. One tries to incorporate into such a new
language features which we understand and those which we do not
understand, but of which we know that they must play an important
rôle. There is one term in this new language that has been used so
often in this Conference and that is the term " Regge poles " or "
Regge trajectory ". It is an analogy taken from the Schrodinger
theory of potentials which is a strong interaction theory but a
non-relativistic one, without antiparticles. It is really no good
for our purpose but at least we can learn something about strong
interactions, about cases where one cannot expand in the coupling
parameter. We use these terms—this language—by way of an analogy,
we hope that the situation has some common features with our simple
example. This analogy has made certain things very much more
understandable, in particular our first group of facts (the
asymptotic scattering properties) seem to be more plausible when
using that language. This in itself is already a remarkable
achievement, and represents a proof of the versatility and
usefulness of the language of Regge poles. It is useful, but is it
also truthful ? I would like to mention here a comparison that was
made in our Saturday discussion with the band structure of solid
state physics. The band structure idea in solid state physics is
one of the most useful concepts in physics,
although it is a very bad approximation. We know, however, why
the bad features of that approximation do not disturb its
usefulness. Is the situation similar in the case of Regge poles and
their rôle in strong interactions ? We do not know. There were many
papers at this Conference which tried to show that the Regge pole
language is somehow contained in field theory. They were
interesting and, as Drell said, " By now the Regge pole type of
behaviour seems totally unavoidable ". But they were not conclusive
because, whenever one does a calculation in field theory, one must
leave out as much as one puts in. Certainly the concept of the
Regge poles and trajectories is a surprisingly simple concept
within the strong interaction picture. It might perhaps only remain
a way of speaking, which incorporates some of the essential
features and leaves out other equally important ones (in parallel
with the band structure of solids). The apparent simplicity and
validity of this concept might, however, also indicate that we face
here the vague outlines of a new principle governing strong
interactions. This, I think, is the hope of some of our colleagues
who also are encouraged by the fact that the most important of
those trajectories, —the so-called Pomeranchuk pole-trajectory—has
the maximum strength that a Regge pole can assume without getting
into trouble with fundamental principles. Hence the question still
remains: is the concept of Regge poles a useful analogy or a new
principle ? Or will it be forgotten in a few years ?
A very similar situation exists when we try to talk about the
second group of phenomena: the isobars. Theorists also use
analogies here, they employ a language borrowed from other fields
of simpler quantum mechanics, a language which they try to
introduce because they do not see the real thing. They introduce
the concept of supermultiplets, for example, which is a group
theoretical concept well known from atomic physics, and they try to
see how far one comes in this field of facts with such analogies.
They sometimes get very far, for example when some of the mass
ratios come out right; sometimes they do not get anywhere when some
of the reaction probabilities are estimated. Again we face the
question : is this a useful analogy, a dead-end street or maybe a
new principle ? We do not know.
Some theorists go further than this. They try to explain the
facts which we face with a bold attempt at
932 Plenary session XIII
a new field theory. What I have in mind here is the work of the
groups of Heisenberg and Nambu, where it is tried to start with a
simple field equation and to see whether all these particles can be
created by one single field with an interaction. Of course, these
groups are up against the difficulties of field theory even in a
greater measure because they have set themselves a greater aim. In
this case also, what they are in fact doing is trying to find a
language. They introduce new concepts such as, for example, the
degenerate vacuum, in order to make it possible for a simple field
to give us all the variety of phenomena which we find. Now this is
an analogy taken from the experience we have had in the theory of
superconductivity ; again the question arises : is it an analogy or
perhaps a new principle or a step in the wrong direction ? We do
not know.
Finally, I come to the weak interactions. Here the theory is
really in the worst state. It is a completely open field. We
describe the weak interactions since Fermi by means of a 4-fermion
interaction. We know that a 4-fermion interaction is something that
can only be an analogy and cannot be the truth because it would
violate unitarity at high energy ; we would have no conservation of
particles. Here again one tries to introduce analogies to previous
experiences. One of these analogies is the introduction of an
intermediate boson in order to obtain the 4-fermion interaction as
the low energy limit of a Yukawa coupling. At present we just do
not know whether any analogy like this works at all, or whether it
is only an analogy or a new principle. The situation is very
confused. As Dr. Yang pointed out to me, we are running into
serious contradictions. On the one hand, we are attracted by the
analogy of a W particle; on the other hand, we are told by the
experimenters that AS is probably not equal to AQ. This will put us
in a difficult situation because it is hard to avoid AS = 2 in weak
interactions when there is an intermediate boson and at the same
time A S/A Q can have both signs. This is extremely hard to
reconcile with the K°x and K°2 mass difference. The smallness of
this difference definitely shows us that there is no AS = 2 direct
fermion interaction. The development of this problem promises to be
exciting. To be sure, there might be a trivial solution, namely
that the experimenters find after all that AS = A Q, But if it is
not so, it will be most interesting. Then a straight-forward
intermediate
boson is probably excluded and then the whole problem of weak
interactions is completely laid open.
To sum up the theoretical situation, let me show you the
following picture. Two explorers find a little pyramid-shaped
elevation in the desert sand. It says in the caption :
" This could be the discovery of the century. Depending, of
course, on how far down it goes."
The credit for this cartoon goes, of course, to the man who made
it and also to Dr. Salam who has it in his office.
Let me compare the situation in which we find ourselves with the
situation in atomic physics before 1924. This is a very tempting
comparison—in 1924 we learned so tremendously much—we hope to do
this soon again. There are, of course, obvious similarities : we
are facing a large amount of new and undigested phenomena. Sure
enough, the data at that time were accurate to the third decimal;
today some important data are based on a few events only. We do not
understand the meaning of what we observe. We are trying, not
without success, to introduce analogies and ways of speaking. Our
fathers or grandfathers did it too at that time. Let me mention a
few of their analogies. They singled out certain concepts in
classical mechanics that seemed to have special significance in the
quantum world. The action-integrals are an example, the adiabatic
principle is another. The correspondence principle was an extremely
useful language to talk about the new phenomena. Let me, not
without trepidation, compare the action-integrals with our Regge
poles. (Both use the letter / ! ) . Within the framework of
classical mechanics, the action-integral was a useful concept, but
not one which played a dominant rôle. In quantum mechanics, it
became a new principle and, by equalling it with an integer
multiple of h, it explained the hydrogen spectrum. The Regge pole
is a useful but not necessarily dominant concept in potential
theory and may be an important concept in field theory. Whether it
will play a similar rôle as the action-integral is still very
doubtful today. There is, however, a fundamental difference between
our situation and those bygone times. Today there is nothing
corresponding to the quantum phenomenon. At that time there were a
series of facts that were blatantly contradictory to classical
physics. Now
