> Unruh on Stapp's Comment.
>
> Stapp claims in this comment that I am wrong to argue that he makes any
> hidden reality assumptions in his proof. Unfortunately, this comment
> simply reinforces my belief that he does do so. The key is his
> characterization of SRi as bing true "in the actual world" which he
> repeats numerous times. His locality assumption LOC2 is predicated on
> the statement that if SR is a statement which is true , and as he
> emphasis in this comment, "is true in the actual world", and this
> statement can be shown to be true if only L2 is assumed to be measured
> at L, then it should also be true if L1 were measured at L instead.
>
> The problem is that SR is on the face of it not a statement about the
> real or actual world at all.
In modal logic statements can, under appropriate conditions, be true
"in the actual world W" even though they are "about" hypothetical worlds
W' that differ from W. I explain this in the new text.
> Rather it is a statement containing a
> counter-factual substitution of a measurement of R1 for the assumed
> measurement of R2 in the actual world. Now a counter-factual statement
> by definition cannot be a statement about the actual world.
> It is a statement about a relation between the actual world and a
> hypothetical world, a relation not true about reality but about the
> predictions of a theory.
>
Nevertheless, SR is a statement that is true "in the actual world W".
> In my original paper I studied some cases in which SR could be argued
> to be true of the real world. These were however crucially predicated
> not only on the fact that L2 was measured, but also that L2 had value
> c. It is only in this case that SR can be claimed to be true of the
> real world. Under the von Neumann measurement process, L2 having value
> c can be taken to imply that taken to be a measurement of R1 having
> value f. However, this interpretation of SR crucially assumes that 'L2
> has value c' is true of the real world as it is that which is being
> interpreted as implying that R1 has value f.
To prove SR it is necessary to prove something only under the condition
that R2+ holds in the real world W, and one has the von Neumann chain that
leads from g=R2+ to c=L2+.
> But in the absence of an
> actual measurement of R1, and in the absence of a reality assumption
> (that the measurement of R1 by L2 reveals the actual real value of R1,
> a value which can be regarded as true even if no measurement of any
> kind is made) the statement that "R1 has value f" is a shorthand (under
> the von Neumann procedure) for the statement that "L2 has value c" and
> " the state is correlated in a certain way between L2 and R1".
>
> However, Stapp needs more than this. He needs that R1 has value f is in
> itself a true statement about the world
What world? Certainly not the real world!
> (given that R2 has value g)
> independent of the value of L2.
I need that the outcome of R1 will be f=R1- in every hypothetical world
W' in which R1, instead of the real R2, is performed in R, and in which
the outcome IN REGION L is the same as in the real world W, in which
R2 is performed in region R, and outcome R2+ appears in R, and L2 is
performed in region L.
> The statement SR must be a true
> statement about reality, about the "actual world".
SR is "about" hypothetical worlds W': it is NOT about the actual world.
But SR it is true IN the actual/real world. (See the added text)
> He requires that the
> existence of the value of the measurement of L2 can be used as a proof
> of the truth of this statement
I require, in the proof of SR, that outcome L2+ appears in region L, under
the stated condition (Hardy and L2 and R2 and R2+), and that, as asserted
by assumption LOC1, a change in the later region R of the experimenter's
free choice will not disturb what has already really appeared to the
observers in the the earlier region L.
> but that the truth or falsity of this
> statement SR be logically independent of the value of L2.
> This the von Neumann measurement interpretation does not give him.
>
The von Neumann argument allows L2+ to be DEDUCED from the stated
premises "Hardy and L2 and R2 and R2+. Then the assumption LOC1
allows this crucial result L2+ to be carried over to the
relevant hypothetical worlds W', in which R1 is performed.
> I do not know of any other sense in which the statement SR can be made
> to be true of the real world.
I do not use the concept "true OF the the real world".
The counterfactual statement SR is true IN the real world W (See added
text). But SR is not ABOUT the physical world.
> As a counter-factual statement it is by
> definition not a statement about the real world, but rather about the
> theory. With SR a statement about the theoretical relation between
> hypothetical worlds, the locality requirement LOC2 loses all
> compulsion.
The proof shows that a certain combination of theoretical
ideas, formulated as precisely stated assumptions, leads to a logical
contradiction. Thus any proposed theoretical framework in which all
these ideas hold is ruled out. The type of theoretical framework
that is under consideration is one in which the actual world is assumed
to be imbedded in a set of "possible worlds" that all satisfy the rules of
quantum theory.
The assumption LOC2 is the assumption most likely to fail: certainly
there is no "compulsion" for it to be true. But you yourself said of LOC2
that if line 5 were true "then I would agree that this requirement would
be reasonable."
If we imagine that the "free choice" assumption really
does correspond in some way to the possibility that these choices could go
either way, then these locality assumptions, although about theoretical
possibilities, do allow us to imagine that we are talking about
connections between possibilities that could have been realities.
It is only within that general theoretical framework that these locality
assumption can express the idea that there is no backward-in-time
influence of any kind.
> It is only with the additional hypothesis, which Stapp
> appears to reinforce in this comment that he is making, that SR, though
> on the face of it a counter-factual statement, is also a statement
> about reality, that his LOC2 can claim to be a compelling statement
> about the local nature of reality.
>
I am not making any claim that SR is "about reality"; SR is a statement
ABOUT hypothetical worlds W'. It is true IN the actual world W defined
by HARDY+L2+R2+R2+, under the condition that assumption LOC1 is valid.
The "physical" significance of these theoretical statements does
not follow from any claim that SR is ABOUT the one real world W.
The rationale for the locality conditions arises from the idea that the
"free choices" assumption means that these choices could have gone either
way. But then these theoretical alternative possibilities can be imagined
to be possibilities that could have been realities: the free choices are
construed to be locally made choices between alternative possible
realities.
> Thus, SR can be interpreted as a statement about reality only by being
> a shorthand for a statement which involves things both on the left and
> on the right (in which case the condition of LOC2, that SR - actually
> and not just syntactically - involve only things on the right, is
> false), by incorporating a reality assumption about unmeasured
> properties. Otherwise it is counter-factual statement which is not
> about the actual world but about the theoretical relation between
> hypothetical worlds, in which case LOC2 looses its compulsion as a
> reasonable locality requirement.
>
The theoretical statements provide a basis for formulating theoretical
locality requirements because the ``free choice'' assumption allows one to
imagine that these theoretical possibilities could have been the realities
if the experimenters had chosen differently. Of course, only
possibilities specified by possible actions and resulting experiences
of the experimenter/observers are under consideration here. Then one can
speak in the usual way about the influence of locally made human choices
upon features of the worlds that would emerge from these choices.
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