but not to me actually. I am too orthodox for that. You see really the
definition of orthodox is how you're going to spend your time, how you're
willing to spend your time, (laughter) Bohm, by the time he finished his
book, I'm sure had strong inclinations not to be orthodox. But he remained,
orthodox until he finished his book. He then became heterodox because he then
began spending his time trying to make a different theory. Well, I never
spent my time being unorthodox, (laughter) Well, uh, what was I saying?
You were trying to say there is no difficulty.
: Well, I was saying the difficulty it really raises is not this one. It
tempts a person to think that there must
be hidden parameters, by George
(uneasy chuckle in the audience) Because, if you can find out the position or
the coordinate, at the same time that you're on one side of the room and the
particle is on the other side of the room, you can make either of these
measurements on something that you have separated from the particle.
: Dr. Furry, some of our group would like you to say over again what
you said about the cards before
the card trick you played on us.
: Oh, I'll play the card trick in a moment.
: That is exactly on this line.
: If I could do that, the feeling is that, by George, that particle over
there really has a position because I can find it out, if I choose. It also
really has a momentum because I can find that out, if I choose, without
touching the particle, or without coming near it. Since it really has both,
and since quantum mechanics does not allow it really to have both, the theory
must be incomplete. But there must be a better theory which contains both as
real properties of the particle. Now the danger is the hidden parameters,
because they are not visible in quantum mechanics.
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: How about hidden parameters and your card game?
: The card game has the hidden parameters in it because, by George,
the cards are classical objects.
Band: Would you explain that card trick for this audience?
: Well, I explained it pretty fully before when I talked in terms of
ordinary playing cards, but now I'll explain it better by providing two decks
of cards. All of one pile of cards look the same on the back. Half of them
have a red spot on the front side and half of them have a black spot on the
front side. Now the other pile of cards is just like it, except they look
the same on the back, but half of them have a blue spot on the front, and
half of them have a yellow spot on the front. And the spots are good size,
you see, so if I tear a card into two halves I'll have part of the spot on
each half. So now I have two boxes. Each box has two envelopes, a right-
hand envelope, and a left-hand envelope. And now I have Mr. X to do this bit
of service for us. Mr. X takes a card from the red-black pile. He can
select one or draw it an random. I don't care. He takes a card, tears it in
two and puts half of it in the right-hand envelope of each box. He takes a
card, from the blue-yellow pile, tears it in two and puts half of it into
the left-hand envelope in each of the two boxes. I mean half in the left-
hand envelope of one box and half in the left envelope of the other. And then
one box is mailed to Chicago. How this is a classical experiment, you see so
far. I mean it corresponds to a classical situation, because now I can open
this one at my leisure. I can now open both envelopes at my leisure. But
these boxes correspond a little more closely to quantum mechanics than that,
because each of these boxes is rigged with a little charge of incendiary
explosive alongside of each envelope. And each charge is rigged, in such a
way that it will explode and burn up its envelope
instantly if the other envelope is removed. That means you can't measure
one if you measure the other. Now that's true of both boxes. Now if I look
at this box to find out if it's red or black, I'm forever deprived of
looking into the box to see if it's blue or yellow, and vice versa. That's
also true of the other box which is now in Chicago. Of course, in the
meantime, Mr. X has jumped off of the top of a building or out of a window
or something. He just corresponds to interaction. (laughter) He just
corresponds to the interaction which existed only from time zero up to
capital T. So we now have this situation - we don't really need to look at
either one of them, in fact. We don't need to look at the right-hand
envelope in the Chicago box to find out whether it has red or black in it,
if you look at this one. If you look at this one, you'll know it will be
the other half of the same card, the same for the blue or yellow. If you do
pull out the same one in both boxes, you'll find the same answer. You'll
find that they match. If you want to get a complete measurement, you look at
one envelope in one box, and the other envelope in the other. But that
doesn't have anything to do with this illustration. Now the point I made in
discussing this box thing this morning, was that there is no transmission of
a signal faster than light or anything like that. Well, if I look at this,
say the right-hand envelope, and find red or black, then I can at once say
what the same one is in Chicago. The transmission all happens when the box
is taken to Chicago. There's nothing about sending a signal, sending
information or a signal. We know it just because we know the way these
boxes were prepared. The fact that the box was actually prepared in this
way is now brought into play, and the same holds true for
back to the slightly dirty cracks about sending signals faster than light and
so on. I do not think there is anything and I do not believe there is
anything in this theory. (He pounds the table)
: I don't believe it either, of course. That's one way to speak
It is not right.
And I agree, all through the illustration of the box, for in
quantum mechanics we say the particle has a wave function and it may be a
perfectly natural way of keeping a record. The information we have about
it is due to the notebook that we kept on all that happens, you see.
: If you put a half-red in a left-hand box and the other half-red in
the other box
: Half of the card that came out of the red-black pile will go into
one of the two envelopes in each of the two boxes, and half of the card
that is blue or yellow will go into the other.
: How do you know the red half-card is in this box? How do you know that
the other half of that one isn't in the other box?
: (declares emphatically) It is!
: But why can't you pull that out?
: (exclaims) You can! If you check the same envelope in both boxes
you'll always get a consistent result. But you know from the way the thing
is set up the results will be consistent.
Oh, you keep them in the envelope No. 1, or the envelope No. 2, and
the other half of the card is in the corresponding envelope.
Right! If the little man does the job for us and then ceases to
exist. He took the card and tore it in two, put half of it in one box and
half in the other, in the proper envelopes. And for this reason, I know
what the color in one is if I look in the other, without needing to look in
the other. If I do look, I merely get a check.
: I think Dr. Soules has a question.
I was just going to ask, with regard to the paradox we're talking
about, is it well established that a state actually exists in which the red
: This, of course, is just a game. This is a classical example. I have
brought it as close to the quantum mechanics as possible with those charges of
incendiary. But it is not the proper quantum mechanical case. There really is
half of the red or black card and half of the blue or yellow card in the box
in Chicago. In the quantum mechanical case that would correspond to saying
that the particle that's now over on the other side of the room really has a
position and really has
a momentum, and I can find out what they are, one or
the other of them. And this is denied by wave mechanics, because there is no
wave mechanical state that has both precisely defined position and precisely
defined momentum. So it's precisely this. You see, in other words, this
classical thing I have reeks with the
the very dubious and unorthodox phase space of hidden parameters. And
Professor Wigner doesn't believe they exist and neither do I. We're orthodox
to that extent. Incidentally, the argument he gave last night for disproving
them — I deny that it's the von Neumann argument. I think if he rereads
chapter six, or whatever chapter it is, or maybe it's chapter four, he will
find that it's not the von Neumann argument. It is a better argument than the
von Neumann argument because it is not merely mathematical. But it's much more
convincing. (laughter) In fact, I think it is much more of a scourge of the
infidels (laughter) and I propose to call it the Wigner proof.
I remember in my elementary work having to work out certain
problems involving, let us say, a quadratic equation. I get two solutions.
Then the question is, are they both good or not? We substitute back and find
that one of them is an extraneous solution. It seems to me that there is a
certain parallel case here of a more sophisticated kind. We're simply saying
that quantum mechanics will give us a right or correct solution.
speak, is that which actually occurs. Whether it occurs during cognition, or
whether somehow or another we blame it on the process of measurement that
occurs, seems to be the debate. The basic thing seems to be pretty clear. It
is that quantum mechanics gives us multiple values, so to speak, and our
problem philosophically is, when do we pick the solution. We make it. We
: If you're positivistic minded enough, there is no problem, there
is no trouble. The logical positivists love this..
: The question is, really, what is it you do observe and how do we
: I think this morning we got even another viewpoint, which is that
even the observation doesn't determine which one we really have. Regardless
of whether we get the multiple valuedness, it continues on indefinitely.
: It depends also on whether we select out.
Yes it does. Now that is the point of view of Dr. Everett.
: Would you like to comment, Dr. Everett?
Yes. Well, what he said pretty much covers it.
Then we know that the angular momentum of one will be opposite to the angular
momentum of the other. After they have separated we can bring in the apparatus
for measuring the angular momentum on one of them. The other particles, being
far away, I don't think should be affected by it. So we can then measure the
component of angular momentum in the x direction. Or we can change the
apparatus around and measure the component of the angular momentum in the y
direction. In each case we will know what the angular momentum of the other
particle will be. The x and y components do not commute, so we get back
again the same paradox. The whole question, it seems to me, hinges on this:
How much reality are we going to attribute to the wave function? If the wave
function is merely a statement of our knowledge summarized in some way, well,
then, there is nothing wrong with saying that when we find out something about
one particle, then we can change the wave function in some way, so that we will
know something about the other particle. But if we're going to attribute
reality to the wave function, the situation is different. Then by doing
something to one particle and its wave function we change the wave function
for the other particle. We have a collapse of the wave function, if you like.
But that, I think, implies a kind of action-at-a-distance. We do something
here, and something else happens some place else instantaneously. This is not
kind of action that you can use to transmit signals
that the box
experiment with cards pretty well establishes
so there is no contradiction
with the theory of relativity. We do not transmit the signal faster than
light, but we can change the wave function all over the place instantaneously.
Of course, if it doesn't have reality instantaneously, because it doesn't
have reality imputed to it, then
I do not want to assert one or the
other. Let's see, there are two possibilities. Either it has reality, in
which case we are doing something, uh
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