Bill Unruh sent the following letter to Jerry Finkelstein:
> From: SMTP%"unruh@physics.ubc.ca" 11-FEB-1998 14:02:51.25
> To:JLFinkelstein@lbl.gov
> CC:hpstapp@lbl.gov
> Subj: Your Note "Yet another..."
> I agree with your characterisation of my meaning for your proposition S.
> The question I still have however, if you claim that Stapp disagrees
> with this explication of the meaning of S, is what does he actually mean
> by the statement. If you are saying that he means that in any possible
> hypothetical world R1 is measured, it must have the value - if in the
> real world R2 had value +, then this definition of the statment is
> clearly physically nonesense. In that hypothetical world the particle
> might not even have been put into a Hardy state. In fact the particle
> (or rather system, since Stapp has been at pains to dissociate the
> events from the existence of actual particles) might not even exist.
> Clearly in that hypothetical world there is absolutely no constraint
> on R1 because R2 was measured in the real world.
> The whole point to my paper was that the existence of L2=+ in both the
> hypothetical and the real world was crucial to the truth of the
> inference, whetehr L2 was later than or earlier than the R measurements.
> It is not sufficient to postulate only that L2 was measured but also
> that it had its particular value in allowing the inference to be drawn
> (R2=+=>R1=-) Ie, it is Stapp's dissociation of the value of L2 from the
> conditions of the inference that I believe is physically and logically
> wrong. (Logically because I can actually do the experiment in which I
> measure L2 and get a value of + for R1. Since I believe that the world
> enforces logic on me--ie that the outcomes of experiment cannot be
> directly contradictory to logic--this then implies that the real world
> cannot constrain the hypothetical world in the the way that Stapp seems
> to want.
>
> If the arguement that any realisation of the hypothetical world can
> never be the same as the true hypothetical that Stapp is discussing,
> then I feel he certainly needs to make clear what it is about that
> hypothetical world which makes it different from its realisation.
> To expand, you argue that in explicating the statement, you need to also
> list what the conditions are on the hypothetical world in comparison
> withthe real one such that the statement is believed to be true. Any
> such listing of conditions then should be applicable to a redoing of the
> experiment in which all of those conditions are met. Then the statement
> should be a statement not about a real world and a hypothetical one, but
> rather about two real worlds. Certainly in quantum mechanics, there is
> no difference between that real world which obeys all of the conditions
> and the hypothetical one. In hidden variable theories, the out is
> always that the conditionof all those hidden variables will be different
> in that attemped realisation from what it was in the hypothetical ( and
> that furthermore, no realisation is possible which has as condition that
> all of the hidden variables are exactly the same precisely because they
> are hidden). Thus if Stapp is talking about quantum mechanics, then
> there is no difference between the realisation and the hypothetical
> world. An in the realisation, there is a distinct difference in outcome
> between specifiying simply that L2 was measured and specifying also the
> outcome of that measurement (no matter when that measurement was
> perfomed.)
>
> Bill Unruh
> You are also correct that in writing my paper I was trying to give a
> meaning to the words of the syllogism which would make them not
> obviously wrong (a la your SF).
>
> PS Thank you for calling my atention to the various replies of Stapp, as
> I had not seen them.
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.
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),
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.
Statement S is:
If R2 is measured in region R and the outcome there is +
then if R1 were to be measured in region R, instead of R2,
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.
Now if, as you claim in your letter to Jerry, YOUR MEANING of S
is the the one called S_F by Finkelstein [quant-ph/9801011] then,
as Jerry pointed out, your meaning of S is not the meaning of the
statement S that occurs in my proof.
So your argument based on that differently defined S has no bearing
on my proof: if you want to analyse my proof then you must, of course,
use the meaning of S that occurs in my proof, not some different one that
you invent.
I take that observation---of the nonrelevance of your argument to
the validity of my proof---to be the point of Jerry's paper: you simply
are not using the relevant meaning of statement S!
You say: "The whole point of my paper was that the existence
of L2=+ in both the hypothetical and the real world was crucial to
the truth of the inference."
Well, EXISTENCE of L2=+ is perhaps crucial to the TRUTH of S.
But because of LOC1 and QT (the assumed validity of the predictions of
quantum theory) one does not, in the proof of L2=>S, need to
ASSUME that the outcome of L2 is +: that is the key point of my proof.
One needs to ASSUME, besides LOC1 and QT, only that L2 is performed, not
what its outcome is.
You say: "It is not sufficient to postulate only that L2
was measured .... in allowing the inference to be drawn"
Well, one needs, in addition, the postulates LOC1 and QT. But give these
one does NOT need to postulate L2=+: L2 alone is enough.
You claim that my deduction must by wrong "because I can actually
do the experiment in which I measure L2 and get a value of +
for R1." But that fact does not contradict my assertion that, given
LOC1 and QT,
L2=>[If R2^+ then R1/R2 -> -]
You have not put into your claim, about what you can do, all the other
conditions, and in particular the condition LOC1 and the condition
"If R2 is performed and the outcome is +".
To justify leaving out those condition you advance an argument like:
"If B could be false" then "A=> B" must be false.
But that is certainly not the case: B could be false under some conditions,
but true under the condition that A is true.
You are certainly making a tremendous logical error in arguing
that because one could do L2 and R1 and get + for R1, that this
same result must hold if LOC1 is imposed, and the condition
"R1 entails ..." is a counterfactual assertion conditional
on the fact that R2 is performed and the result is +.
The point, of course, is that if LOC1 is true, [i.e., if in ANALOGY to the
situation in quantum field theory, changing the Lagrangian in region R
has no effect on which OUTCOME appears in region L (which could
be earlier than region R)], then the mere condition that L2 be
performed, and that R2 is performed and gives +, is sufficient to
entail, given QT, that if the Lagrangian in R is changed, so that R1 is
performed there instead of R2, then the outcome in R must be -.
This is true both intuitively, given LOC1 and the Hardy predictions,
and formally by virtue of the first five lines of my proof.
Best regards, Henry
P.S. I emailed to you copies of all my replies to you except
possibly the last, which I assumed would be quickly sent to you by
The Physical Review.