that it? This is really a very great conceptual difficulty. The
conserved quantities can be measured. There's a great deal that
can be said about it, but let me not go too much into it.
It is easy enough to say that there is a measurement. A really
phenomenological theory, however, would not only say that there is
such a measurement, but it would tell how you carry it out. It would
say, "If you want to measure this quantity, order such and such screws
from so and so, and put things together this and that way."
For this reason, Heisenberg in '43, I believe, proposed to base
everything on the collision matrix. In other words, to admit that
Hermitian operators are not really measurable, in general. In fact,
they are not measurable. But what is measurable is only the momentum,
and the character of a particle — whether it's a proton or electron
or whatever it is. Well, not so many other particles do exist in this
sense in which Heisenberg postulated it. The momentum is a conserved
quantity, once the two systems separated, and therefore it is not
necessary to measure it at one cut. You can measure it, so to say,
at leisure. And the practical measurements, either with Professor
Furry's grading or with the old fashioned systems, are measurements
essentially of this nature — when it is smeared — well, when the
measurement occupies a space time volume.
Let me put down, therefore, the second criticism and its
elimination, namely "realistic". One wants to make the theory
realistic and not to demand things which you evidently can't do.
Now this leads one to the idea of the collision matrix. You note
that both these theories have been put forward by Heisenberg. This
one was not put forward because he wanted a relativistic requirement
to be satisfied for measurements, but this one was. You recognize here
the two great modern directions of quantum mechanics: the theory of
the collision matrix and its direct calculation by means of dispersion
relations, and the theory of the fields. We have to struggle along
It happens also, that they relieve the two fundamental problems
of the theory of measurement which come at once to mind. The unfortu-
nate thing is, of course, that neither of them relieves all
requirements entirely. If I go back to my three criteria — whether
it is relativistically invariant and so on — well, the theory of
collision matrix and of dispersion relations is relativistically
invariant. The relativistic requirement is satisfied and there is no
problem with it.
Well, it is also sufficiently realistic.
However, if we ask whether it is enough, whether it is possible
to reduce every physical problem to a problem of collision - and
calculate every physical problem by means of the collision matrix-
I think we have to say that it is probably not the case. As a matter
of fact, there is a good deal of discussion on this. And not very
ago even I belonged to the school which hoped that it would be enough.
it I think it was Källen who convinced me that it is not really
Fundamentally it is not enough because the world is constantly
in a collision with us, and there is a constant interaction between
matter. Unless we make it the purpose of physics to describe only
certain carefully made experiments, but not more than that, we
can't get along entirely with just the collision matrix. It is not
true that everything is only a collision. The world continues. For
instance, a gas constantly exerts a pressure on the wall. There
are many similar examples which show that it is not really possible
reduce everything to a collision. And it is not true that the
collision matrix really solves all problems. There are in this world
other things of interest in addition to collisions.
So you see, these two eliminate many of the difficulties and,
of course, that is why they are so attractive. But neither of them
seems to eliminate all the difficulties together.
Now you probably also realize that there is a considerable
discussion, let me call it, among the physicists, "Which is the more
promising field?" It is almost true, unfortunately, that there is
nobody who is entirely impartial between these two directions of work.
Some of us believe that the field theories will give the solution of
the problem — and I could point, even in this audience, to protagonists
of that point of view. I could also find people who believe that the
collision matrix approach will be the ultimately fruitful one. Perhaps
it is good, for this reason, to emphasize that they are really working
very closely together and the conflict between the two points of view
is not so very strong. As a matter of fact, when it turned out that
the collision matrix hypothesis was in gross conflict with the field
theory hypothesis — you remember, with the Mandelstam representation
— the collision matrix people, who swore up to that time by the
Mandelstam representation, dropped it most underemoniously and
returned to the field theory representation.
Now in one sense, I am practically through with what I wanted to
say. But I would like to return to that question which I mentioned
to you (and which, of course, is a little naive) about the "homo
To what degree can we hope that our knowledge will also be
ultimately supported in its details by science. I think we should
realize that when we thought that this can be done for physics alone,
we were a little too proud of our knowledge and of our discipline.
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Surely the may knowledge is acquired in general, - and the working
of the mind, - cannot be understood only by never having paid the
slightest attention to the question, how the mind works and how, in
particular, knowledge is acquired. I think a hope for a really
integrated knowledge - and for an absence of these very unpleasant
difficulties, or a reconciliation to this somewhat unpleasant fact of
the absence of an absolute reality — this cannot come as long as we worry
only how electrons, protons, and physical objects behave. It would be
unreasonable to expect that, just as it was unreasonable to expect that
we understand the behavior of protons and electrons only by studying
Science has taught us that in order to understand something we must
devote a great deal of careful thinking and detailed thinking to the
subject in question.
This brings me to the last point which I want to make. Namely, that
all this teaches us a great deal of humility as to the power of physics
itself. It also gives us a good deal of interest in the other sciences,
in particular to the general question, "How is it that knowledge and
understanding is acquired either by ourselves, or - well, when we were
children?" Or, "How is it acquired by other animals?"
It is perhaps not just a mere accident and coincidence that very
great strides are made not by us, but by other sciences in these
directions, and that surprising new results and new recognitions are
gained in those fields. I think an integration of more than physics
will be needed before we can arrive at a balanced and more encompassing
view of the world, rather than the one which we derive from the ephemeral
necessities of present day physics, which say that only probability
connections between subsequent observations are meaningful, without
really telling us at all anything about the character of observations.
Thank you very much.
Conference - October 1-5, 1962
TUES: A.M. -1-
Tuesday morning, October 2
One of the Observers:
Gentlemen, at the session we called before this meeting, we had a
question session, and we wanted to ask a question very pertinent
to this point. Shall we ask the question now?
says: "Yes, let's have the question."
Is it not true that a measurement will take a finite time
and the measurement could influence previous possible results?
Dr. Aharonov has some ideas on this and maybe Dr. Rosen could
fit right in here. If you make two instantaneous measurements,
they may overlap because they take a finite time.
measurements which could be carried out in a very short interval of time.
There are others which may require a long interval of
you have a period in which there is interaction taking place
precise about the state of the object.
says: Could I add something at this point? There was a
time when I thought to solve this paradox in the case of measurement
of position and momentum in the following way:
TUES: A.M. -2-
- 2 -
One of the difficulties of the Einstein-Podolsky-Rosen paradox is the
fact that the collapse of the wave function of the far away particle
occurs instantaneously (immediately when the measurement is done on the
first particle). Now consider the case of the state where p
. One finds that in relativistic theories it must take a
period ?t in order to measure the momentum to the accuracy rp = h/crt .
this period x
becomes uncertain since v
)/m is not certain. The hope was then that perhaps by the time a
measurement of momentum is possible, a measurement of position will not
be possible anymore. But it is clearly seen that the two periods of
time are different and therefore the relativistic aspect of the paradox
Conference - October 1-5, 1962
Tuesday Morning, October 2
speaking. I want to make a few rather standard remarks
about my ideas of measurement. I'm very glad that yesterday we
heard the lectures of Professor Furry and Professor Wigner
because the first one provided the basis for what I want to say,
and the second one considered some difficulties which would
otherwise take too long to discuss. Here I want to emphasize the
following point, one which I
mechanics deals with probabilities, and when we talk about
or a large number of measurements. It seems to me that the only
satisfactory way to define the probability of something
then in such and such percent of the cases we get such and
number of systems at the same time. In other words, we always
deal with ensembles. Professor Furry discussed the idea of a
Gibbs ensemble, but 1 want to go further and say that we have
an ensemble in every case, whether we have a pure state or a
mixture. Now this may be just a matter of words, but I'd like
to use this idea and introduce names.
An incoherent ensemble is what Professor Furry called yesterday a
mixed state, and a coherent ensemble is what he called a pure state.
If we carry out a measurement on a single system, then in general,
we don't know what the result of that measurement
of the various results. There are exceptions of course. There may be
a state which is an eigenstate of the observable, in which
distinguish between the single system and the ensemble, but in
general we do have to. Perhaps again this is just a matter of words,
but I'd like to put it this way. When we are dealing with
we write down equations. The idea of introducing probability
amplitudes is, of course, strange from the classical point of
few words about the classical interpretation of quantum mechanics.
Now I want to make several remarks about measurement. The whole
question of measurement is a very complicated topic because
easier to discuss, but sometimes somebody really should go into
dent observables whose operators commute with one another, and in
this case, if the measurement has been carried out exactly,
approximate measurement, a measurement which has some error in
to require analysis. We should distinguish, of course, between
the ensemble to which the system belongs before the measurement,
ensemble into which it has gone. This brings up the question of
reduction of the wave packet, which is the great mystery in this
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