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October 5, 1997\\
Professor William G.Unruh\\
Physics Department\\
University of British Columbia\\
unruh@physics.ubc.ca
Re: My proof of nonlocality (Amer. J. Physics, 65, 300-304, 1997)
Dear Bill,
We left the Max Born Symposium without resolving your reservations
concerning my proof of nonlocality.
As far as your formal objection is concerned, I believe that it does not
stand up. The point is that {\it as far as the results of the measurements
on the SAME side are concerned} we should have no locality requirement at all.
That is, if R2 were to be performed on the RHS and `g' were to appears there,
then {\it nothing at all} should be entailed by locality alone about what must
appear on that SAME side if, instead of R2, the measurement R1 were to be
chosen and performed there: changing what one does on one side certainly does
disturb things on THAT side, but, according to a certain idea of locality, it
should not disturb anything that happened earlier (and far away).
Thus if, as you have proposed, one were to add to the premise in line 1 of
my proof [line 1 is my first locality assumption, LOC1] the condition that
`g' occurs, and one were to insist on keeping this extra condition there, and
wanted to put in a corresponding statment on the conclusion side of that
line 1, as you suggested, then that extra statement on the conclusion side
of line 1 would have to be " e OR f ". For the locality assumption should
imply nothing at all about the outcome on the RHS if the measurement on
that SAME side were to be changed.
This condition, "e OR f", is empty (as it should be) because this condition
(e OR f) was already a precondition on the set up. Adding this extra
condition, "e OR f", does not disrupt the deduction of line 4.
And adding the extra condition (i.e., that `g' occurs) to the premise
in the locality assumption, as you proposed, and also to the conclusion side
of statement 2, as you proposed, does not disrupt the proof: all the steps
go through essentially as before.
But let me consider, then, your intuitive "feeling" that the proof {\it must}
be wrong because, according to your intuitions, the conclusion is
incorrect.
Your actual objection---which you were trying to fortify by showing how it
fit formally into (but disrupted) my proof---was to the fact that in line 1
(my LOC1) we KNOW that the premise condition `c' is true only by virtue
of the fact that we know (by assumption) the result `g'; but we can know that
`g' appears only if (as specified in the premise in line 1) we do perform R2.
But this condition that R2 be performed gets undone by the condition
"if, instead of R2, R1 is performed". So this counterfactual assumption
destroys the basis FOR KNOWING the truth of the condition `c'. Hence you
suggest that truth of `c' should not continue to hold under this
counterfactual condition, as line 1 (LOC1) demands.
On the other hand, the premise of this assumption, LOC1, is only that L2 and
R2 are performed and that `c' appears: it does not say anything about how we
come to know that `c' appears. The dependence on `g' comes in by just following
the rules of (modal) logic.
Although my argument conforms to the principles of modal logic, which have been
designed to capture the intuitive meanings that these words normally possess,
you can maintain that those rules fail to give the right meaning in this
quantum case: "correct" quantum thinking might be different from what the
logicians were striving to capture in the formalism of modal logic.
So I agree that we must look at the situation through our "quantum"
eyes, and not rely on "classical-think" logicians. (But it is, I think,
important that the proof `at least' conform to the rules of modal logic.
Modal logicians seem to regard this as a desiratum, so I do conform `at least'
to that desiratum, and am assured of a consistent set of logical rules. But
the question now, however, is the deeper one of whether these rules conform
correctly to "quantum-think".)
It is certainly true that the strict Copenhagen interpretation is
"knowledge based": it is epistemological rather that ontological.
(And I have, in my talk at the symposium, suggested that this knowledge-based
formulation be taken more seriously than the cautious founders of quantum
theory---eg. Bohr and Heisenberg, in particular---did.) The strict CI approach
is pragmatic: it recognizes that in practice our science is based on our
(human) knowledge, not on the real external world itself, which we can never
know with as much certainty as the experiences from which we infer the
existence and structure of the external (to our experiences) world. Within the
strict knowledge-based Copenhagen interpretation one might be justified in
saying that if our knowledge is changed then the physical reality is changed.
But there is another current within the Copenhagen interpretation.
It says that real events do actually occur out there at the devices: i.e.,
(in Heisenberg's words) the transition from `possible' to `actual' occurs when
the interaction between the observed system and the measuring device, and
hence the rest of the world, comes into play. This second current is
`weakly realistic' in the sense that it claims that there are real, actual
events `out there', even before anyone looks, and these events actualize
certain values that, in general, are not fixed before the event occurs.
I am examining, in my AJP paper, the possibility of maintaining this weak
quantum-type reality (which avers that certain physical quantum events are
real, along with the values that they actualize, but that the actualized values
are generally ill-defined before the events that actualize them occur), and
of maintaining also, together with this Heisenberg/Bohr weak quantum-type
reality, the locality idea that no effect of a `free choice' can occur outside
the forward light cone of the physical-interaction region associated with that
free choice. By `effect' I include (and in fact focus upon) effect at the
individual-event level: there is no problem with the effects at the
statistical level.
If an event that actualizes a value, either `c' OR `d', really occurs
in region L at the earlier time $t_L$ then the value actualized by this
event in L cannot (according to the relativistic notion of locality that is
under scrutiny here) depend on which choice, R1 OR R2, is made in R at a later
time.
If the value actualized by L2 is `d', then (according to the rules of QT, which
are accepted as valid) if R2 is performed in R the result there cannot be `g'.
So if R2 were to be performed in R and `g' were to appear there, then the
predictions of QT would ensure that that if L2 had been performed earlier in L
the result there must have been `c'.
But then weak quantum realism (that the physical events do occur, and
actualize certain values) together with the locality idea (that what occurs
outside the appropriate forward light cone associated with a free choice
can be assumed to be independent of which free choice is made) means that
whatever did occur (e.g., `c') at the earlier time if one choice (e.g., R2)
is made later can be assumed to have occurred at that earlier time
also if the other choice (e.g.,R1) were to be made at the later time.
What we later come to {\it know} is a consequence of what we later look for,
and of what occurred already earlier. The fact that "we cannot know" (in this
way) about the earlier result in L "if we do the wrong experiment" does not
disturb the earlier result itself, provided we accept weak quantum realism
(as Bohr and Heisenberg apparently did) and the proposed locality idea. For if
the earlier event in L actually did occur, and, was some fixed event
independently of which choice, R1 OR R2, is to be made later far away in R,
then the value actualized in L at that earlier timeshould be independent of
what knowledge we later acquire about it. Failing to do a certain later
measurement does not disturb the result actualized earlier: it can disturb
{\it the knowledge about} that earlier fixed result that is available in R
at the later time $t_R$, but changing what we can {\it know} later about
the earlier event does not, according to the normal idea of locality that
LOC1 formalizes, change what actually happened at the earlier time.
So if one grants (as Bohr and Heisenberg apparently did, and as most
practicing physicists probably do) that these physical events do actually
occur, and that they do fix/determine corresponding values, then a natural
LOC assumption is that the course of the earlier events does not depend of
what information is gleaned from later experiments. Rather the earlier events
place conditions upon what can occur later, under the various conditions that
might be set up later, and hence upon what we can know later. But what we
can or do learn from the later measurements does not, according to this
natural notion of locality, act back upon and disturb what occurred earlier.
This is what LOC1, in the framework of ordinary modal logic, asserts.
LOC1 may, of course, be wrong: indeed, at least one of the plausible-sounding
assumptions MUST be wrong.
But if LOC1 is wrong then there there must be a breakdown of the notion
that what is actualized outside the forward light cone associated with a
free choice can be assumed to be independent of which choice is made.
And this notion of locality is formulated within the framework provided
by the weak quantum reality apparently endorsed by both Bohr and Heisenberg
in their later years.
It is important, I believe, to distinguish this line of argument from that
of Bell, and those such as Shimony, Clauser, and the others who have followed
Bell's lead. Those other arguments depend upon Einstein reality/locality.
The Einstein reality/locality condition was originally set up to prove
the incompleteness of quantum theory: i.e., to prove the need for hidden
variables. Bell accepted, as an hypothesis, the conclusion of EPR that
QT was incomplete, in the sense that there were hidden variables that
determined the results of both the performed and unperformed experiments.
I have not made any such hidden-variable assumption: the structure of
the proof is such that a value is claimed only under the condition that
the experiement that actualizes that value is performed.
Orthodox quantum thinking denies the existence of such hidden variables.
EPR gave an argument for their existence. But that argument is based upon
the (in my opinion) indefensible Einstein reality/locality criterion.
The Einstein reality/locality condition says, in effect, that IF the results
`obtainable' from a set of mutually incompatible measurements performed far away
(and space-like separated) from a certain spacetime region R, would (if they
could all be performed) allow one to determine the results of several
different measurements in that region R, THEN all of those results (values)
really exist in nature, even if these different measurements in that region R
also are mutually incompatible. This assumption would mean that quantum theory
is incomplete.
This Einstein reality/locality assumption is much stronger than the weak
quantum realism idea that I use, which is is compatible with the idea that
quantum theory is complete. Weak quantum realism asserts that the values
are actualized by the experiments that actually measure them, with only the
tendencies or propensities for specific outcome specified by the quantum
formalism existing before the measurement/actualization event occurs.
The objection that can quite rightly be raised against Bell-type
arguments as a proof of nonlocality, namely that those arguments rest of the
dubious and contrary to quantum-think assumption of Einstein reality/locality,
do not apply to my proof: my proof rests on the much weaker
Heisenberg/Bohr weak quantum realism, and a natural idea of locality
that can be formulated within the framework provided by Heisenberg/Bohr
weak quantum realism.
Best regards,
Henry
hpstapp@lbl.gov\\
http://www-physics.lbl.gov/\~stapp/stappfiles.html
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