From stapp@thsrv.lbl.gov Mon Feb 16 14:26:56 1998
Date: Mon, 16 Feb 1998 14:24:20 -0800 (PST)
From: Henry Stapp
To: Bill Unruh
Cc: JLFinkelstein@lbl.gov, mermin@msc.cornell.edu, RGRIF@cmu.edu,
peres@photon.technion.ac.il
Subject: Re: Reply to Unruh's letter to Finkelstein
Dear Bill, Feb 16, 1998
This is a reply to your letter of Feb 13.
On Fri, 13 Feb 1998, Bill Unruh wrote:
> I will interleave my reply with yours.
> >
> > REPLY
> >
> > Dear Bill, February 12, 1998
> >
> > Thanks for sending to me a copy of your letter to Jerry Finkelstein.
> >
> > Since it raises questions as to what my statement S means he thought
> > I should answer it.
> >
> > Schwinger has taught us how to formulate causality questions in
> > relativistic
> > quantum field theory, which is the proper theory for these questions.
>
> I agree, but also think it is irrelevant.
> >
> > Applying that formalism to our case, we set up the original Hardy
> > state, and
> > adjust the Lagrangian so that R2 is measured in region R.
>
>
> >
> > Then one can consider, in field theory, the case where the initial state
> > is kept fixed, but the Lagrangian is changed only in region R, so that
> > R1 is measured in region R instead of R2. In relativistic field theories
> > this sort of change produces no change in the state outside V+(R),
>
> No, it produces no change to the FIELDS outside this region, It says
> nothing whatsoever about the state, or changes to the state. A state is
> a global property in quantum field theories, not local. The fields are
> local, but they are the physical quantities which the states say
> something about.
>
You are using the Heisenberg picture. I was using
Schwinger's deformable space-like surface, upon which the Schoedinger
picture state is defined.
But the idea is the same: it is to impose changes in the Lagrangian to
implement changes in experimental set-ups: e.g., one can, by introducing
a small electric field, deflect the particles into "the other"
apparatus. But no expectation value changes outside the forward light-cone
of the region where the Lagrangian was changed.
> > the union of the forward light-cones with apexes in R. The condition
> > "If R1, instead of R2, is performed" means this kind of change in which
> > the state at early times is left the same and the Lagrangian is changed
> > only in region R in this way. The assumption that the choices made by
> > the experimenters are to be treated as free variables justifies the idea
> > that one can consider the effects of changing the Lagrangian in this
> > special way.
>
> No, your statements are also statements about the outcomes of
> experiments,
> not just the Lagrangians which describe the measurements.
> Ie, when you talk about L being measured and having the value + implying
> that R2 must have the value +, then you are talking about the outcome of
> measurements, not just the physical setup of the experiments.
>
One can indeed "talk about" outcomes of measurements. But the question
that I am addressing here is the one raised by Finkelstein:
What does the condition "If R1, instead of R2, were to be performed"
mean?
I am specifying here that this condition means just what it
usually means in the field theoretic studies of causality, namely a
change in an experimental set-up. This set-up is imagined to be under
the control of an experimenter who imposes his will by changing the
Lagrangian in a small region. But nothing else that is under the control
of experimenters is changed. This includes the preparation of the initial
state.
What outcomes Nature chooses to deliver under these various condition
that the experimenters have set up is something that we can THEN
"talk about".
> >
> > Statement S is:
> >
> > If R2 is performed in region R and the outcome there is +
> > then if R1, instead of R2, were to be performed
> > then the outcome there would be -.
> >
> > The "meaning" of this statement (as contrasted to the "truth"
> > of this statement) is independent of everything outside region R,
> > apart from the fact that all conditions outside R that are under the
> > nominal control of experimenters, namely the preparation of the initial
> > state, and the experimental conditions in L, are left unchanged, just as
> > in the usual relativistic field-theoretic treatment of causality
> > conditions.
>
> If this is meaning of the statement S, then it is false.
> I do not
> believe that you have any basis on which to make this assertion.
> It was
> in attempting to come up with a meaning for S which could possibly be
> true, or be a valid inference that I supplied the meaning I did. I could
> have just assumed that you were making an invalid inference and left
> everything there. However, I believe that in arguing one should try to
> be as generous as possible, and choose that meaning, from amongst may,
> which might have a chance of making the opponents statements true.
>
> I also realised that you were trying to interpret S as you did above,
> and part of my purpose was to state that this is an invalid inference,
> and that something close to SF was the only inference which I saw as
> having the possibility of being a correct inference. (Ie, I did not
> simply assume that you meant SF. I argued that if your inference was to
> have a possiblity of being correct then SF was the strongest inference
> you were entitled to draw, and that your interpretation of S went too
> far.)
I believe that you are conflating "meaning" and "proof".
Of course, the PROOF depends on the MEANING. But the proof depends also on
the CONDITIONS under which the statement is claimed to be true. I do not
claim that L2=>S is true unconditionally: I claim only that it is true
under the conditions QT and LOC1.
You are completely correct in saying that in the PROOF that L2=>S, under
conditions LOC1 and QT, I do make use of the fact that the outcome of
L2 remains +: Yes, in that PROOF I do indeed "talk about" outcomes.
But it is the condition LOC1 that imposes the needed invariance
of this outcome of L2 under the change from R2 to R1.
This invariace does indeed play a crucial role in PROVING
the truth of L2=>S under the conditions LOC1 and QT.
So your intuition about the importance of keeping both L2
AND the outcome + fixed in order to PROVE L2=>S is certainly
correct. But this invariance need not come from a modification
of my MEANING of S: it can, and in fact *does*, come, instead, from the
condition LOC1.
> The whole point of the paper was to point out that your meaning of S
> makes it an invalid inference.
Your whole point rests, therefore, on your implicit claim that I cannot
put the needed invariance property of the outcome of L2 into the condition
LOC1, instead of into the MEANING of the statement S itself.
However, MY statement S does NOT impose any condition on outcomes in
region L: that is how I have defined it. Your argument that my
claimed result cannot be proved using my definition is incorrect, because
I can in principle, and in fact do, get the needed invariance of the
outcome in L NOT from my definition of S, but rather from my condition
LOC1.
Of course, LOC1, QT, L2 and the MEANING of S all get intertwined in the
PROOF of S under the condition LOC1 and QT and L2.
But neither LOC1 nor QT nor L2 is entwined in the MEANING of S:
the conditions that DEFINE whether or not S is true do not depend
upon whether it is L1 or L2 that is performed in L, or on which
outcome occurs in region L, or on whether the outcome in
L depends on which experiment is performed in R, or on whether
the predictions of quantum theory are correct or not.
The PROOF of the truth of "(LOC1 and QT and LS)=>S" depends
on the invariance of the outcome + (of L2) under change R2-->R1.
But no attempt is being made to replace L2 by L1 in the PROOF.
Rather it it is argued *on other grounds* that if LOC1 and QT are
in fact true, so that S is in fact true if the experimenter in region
L, which lies later than R, chooses at the last minute to perform L2,
then S must be true also if that later free choice goes the other
way: What is true about things that may or may not occur today cannot
depend upon what will be freely decided only tomorrow.
Of course, I do agree that this locality condition is probably false.
But its failure would involve "some sort" of influence of the
free choice to be made in L on the truth of a statement whose
truth or falsity depends, by definition, only on possible events that
must occur, if they do occur at all, in the earlier region R.
The essential point is that in logic there may be many quite different
conditions under which some statement S can be proved. The meaning of a
statement must therefore not be conflated with the conditions
under which it can be proved to be true, or with the intermediate steps in
some particular proof that it is true: the MEANING should be free standing.
For example, what it MEANS for Fermat's Last Theorem to be true was well
defined *before*, and independenly of *whether*, it could be PROVED to be
true from certain axioms.
Likewise, I have given a definition of the MEANING of S that stands alone:
the MEANING of S does not depend on the conditions LOC1, QT, and L2 under
which S can be proved to be true. And this meaning of S does not involve
any outcome in region L.
The bottom line is that the configuration of conceivably possible
outcomes whose occurrences or non-occurrences DEFINE whether statement S
is true or false are all confined to region R. Hence if, under the
accepted-as-valid conditions LOC1 and QT, S is true if the later free
choice by the experimenter in L is to perform L2, but is false under the
condition that the later free choice is to perform L1, then that
configuration in R must depend in some way on that choice in L.
I re-emphasize that what is involved here is certainly NOT an effort to
extend the PROOF of the truth S from the case in which L2 in performed
to the case in which L1 is performed: no such extension is possible or
contemplated. The the claim is only that if S is TRUE if L2 is performed
but false if L1 is performed then, by virtue of what it MEANS ,by
definition, for S to be true, there must be some sort of influence
backward in time.