From: terry@asl.dl.nec.com
Subject: temporally undecided states (was: hidden variables)
Originator: terry@aslss01
Organization: (Speaking only for myself)
Date: Sat, 2 Jan 1993 05:57:43 GMT

In article <461@mtnmath.UUCP> paul@mtnmath.UUCP (Paul Budnik) writes:

> ... I believe there is a serious problem with the current QM model when
> you start asking what happens in the time domain in tests of Bell's
> inequality... At what time does QM predict that one will see a change in
> probability of joint detections as a result of changing the angles between
> polarizers? QM does not make a clear prediction about this.

You are correct;  QM does not (to my knowledge at least) make any statements
about the "timing" of such things.  But more subtly, QM implies that such
questions have no real physical significance -- that is, they do not lead to
any testable predictions.  If you try to "find" the order of events though
any kind of direct testing, poof! -- the very act of trying to force such
timing issues to be physically meaningful causes the events to cease to be
quantum in nature.

This reminds me of a promise I made a long time ago to post an oddball way
of interpreting such QM "timing" issues.  So why not give it now?

				Cheers,
				Terry Bollinger

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                  TEMPORALLY UNDECIDED QUANTUM STATES
                    Terry B. Bollinger   1993-01-01


SPOOKY ACTION AT A SPACETIME DISTANCE

In his writings John bell uses the adjective "instantaneous" to describe the
non-local, "spooky action at a distance" effects predicted by standard QM.
However, special relativity does quirky things to terms such as instantaneous,
since in relativity there is no such thing as events that are separated in the
purely spacelike fashion implied by term such as "instantaneous."  The problem
is that there will always be inertial frames from which such nominally
simultaneous events will be separated in both space and time.

This simple observation leads to the inference that whenever "spooky action
across spacelike separations" are discussed in QM, what is really being
discussed are "spooky actions across _spacetime_ separations."  By selecting
the right inertial frame, you can always arrange an interpretation by which
one or the other of two correlated detection events may affects the other
one through a spooky influence both across space _and_ backwards in time.

You may of course simply choose to disallow this class of interpretations
as meaningless.  However, I can't see that the backwards-in-time versions
are any better -- or worse -- than the forward-in-time and instantaneous
versions.  All involve superluminal "influence" across spacelike distances,
and all are subject to cases where a reasonable looking forward-in-time
interpretatioon by one observer will appear to another observer as having
been a backwards-in-time interpretation.

Now my suggestion at this point is really a simple one.  Since backwards-in-
time interpretations appear to be inherent in Bell type correlated events,
why not bite the bullet and go all the way with them?

That is, why not just say that the "influence" of detecting one member of
a correlated QM pair goes _all the way_ back in time and simply changes
the originating event itself?

In this interpretation the "altered" event then unfolds much as if it were
a genuinely local phenomenom after all.  In particular, the correlation
between the two branches "disappears" and the other event simply becomes
a quite ordinary _local_ wavefunction that carries all the information
along with it through time, until it is detected at some future point:

            TIME -->               _   - (1st detection)
                           _   -                / (past "created")
      (pair production)-   _ <-----------------'
                               -   _---------------------------.
                                       -   _     (past unfolds  | "locally")
                                               -   _            V
                                                       - (2nd detection)

One obvious advantage of such diagrams over diagrams that try to show
"spookies" traveling across spacelike separations is that these V diagams
are relativistically invariant, while the spacelike spookies are not.

You are, however, left with a residual uncertainty about the _direction_ of
the spooky arrows, at least in case where neither of the events falls within
the future light cone of the other.  The direction of the V-shaped spooky
path cannot be determined in such a case, since you can always select a new
intertial frame to make either one of the detections "first."

One rather simple tact for taking care of this ambiguity is to treat the V
spooky in the same way that photon and electron interactions are treated in
Feynman diagrams -- that is, you simply define the V spooky as some sort of
"interaction" between the two (three!) points in space time and declare the
direction to be irrelevant.  Surprisingly, this works.  The rules of QM for
determining correlated events ensure that no matter which event you pick as
being "first," the resulting wavefunctions will make consistent predictions
about event distributions at the "second" detector.

I suspect that all of that could be converted into an odd but interesting
"simplification" of the way the QM wavefunctions for correlated events are
set up and manipulated.  Rather than being fed a "detection" to produce the
new wavefunction, the original correlated wavefunction would be fed a specific
V spooky or "interaction" that would symmetrical result in a pair of local
(or at least more local) wavefunctions for the two detectable quantities.
I haven't really played around with this yet, but may give it a try just to
see if an orderly, useful formalism can be derived.

The case in which the future light cone of one event includes the second
detection event is interesting, since it does provide a definite direction
to the V spooky.  I do not know whether the same statement about symmetry
of QM predictions holds in that case or not.


TEMPORALLY UNDECIDED QUANTUM STATES

Actually, I would phrase all of the above a bit differently.  Rather than
saying that the influence "goes back into the past," I would say that the
past for that particular set of correlated events _never existed at all_
until the detection event "forced" a past to come into existence.  You may
recognize this as just an extension of some fairly standard quantum concepts,
in particular the idea of superimposed states.  But in this case I'm saying
that the entire _history_ of the correlated events is a set of superimposed
states, and that those states are "isolated" from the normal (entropic) time
flow of the universe at large until a detection of some sort forces them to
"re-integrate" and display a distinct, meaningful past history.

This emphasis on superimposed past histories, or what I've called "temporally
undecided quantum states," also helps to explain why such a curious view of
QM _does not_ lead to causality violations.

Quite the contrary:  I'm rather certain an interpretation such as the one
I've just given means that _no_ amount of manipulation of QM will ever lead
to a mechanism for sending causality-violating information superluminally or
(equivalently) into the past.  (By "causality-violating" information I mean
information that changes the known past of the universe.)


WHY CAUSALITY IS NOT VIOLATED

While the idea of changing an event that may have occurred many years ago
and making it "local" fairly well screams "Causality violation! Causality
violation!", there is a great Catch-22 in all this:  The moment you attempt
to "extract" any data about future events from the superimposed histories,
the quantum behavior that allows such future-to-past information transfers
will simply disappear -- and you will be left with nothing but dull, ordinary
non-QM behavior that is firmly embedded in ordinary, unidirectional, entropic
time flow.

Thus the irony is that while this interpretion does imply monstrously large
violations of the ordinary concept of unidirectional time flow (with events
happening now "spookily influencing" quantum events originated years or even
billions of years in the past), the only time you are permitted to do such a
thing is when it is _guaranteed_ that that earlier event has had _no influence
whatsoever_ on the unfolding of the rest of the universe during that same time
period.  You are not so much changing the past in this kind of view as you are
"bringing it into existence" and re-integrating it with the time flow of the
rest of the universe.


QUANTIFICATION

While I firmly believe that the interpretation that I just gave is an example
of an "operationally equivalent" understanding of QM (that is, that it leads
to no differences in the predictions of QM), I also suspect that following up
on it seriously could lead to some interesting differences in how QM is
expressed mathematically.

In particular, the sort of taking-relativity-to-an-extreme concept that some
regions of the universe simply don't _have_ meaningful histories until the
are subjected to detection should lead to some interesting differences in
how time is expressed and quantified.  Detection would mean not just finding
a new "state," but going back and creating a new "history" by which that
state came to be.

For simple problems such quantification should be trivial, because the
"history" of (for example) two correlated spins will be very sparse and
should look just a lot like the process of "updating" the wavefunction to
make it local.  The interpretation does change, however; the newly "local"
wavefuntion is viewed to have existed _all along_ as the wavefunction of
the other detection event.

However, for more complex histories in which there are multiple quantum
events related to each other in some way, the "creation" of a "past" for
the set of particles involve could become non-trivial.  I would be this bold
at least:  I would assert that for such rather complex cases the idea of a
superimposed histories interpretation might lead to some interesting insights
and perhaps simplifications of the calculations.  Certainly the reliance of
QED on integrals of possible histories to derive its results would seem to
indicate that a similar formulation of QM for larger-scale, Bell-style
problems might not be such a bad way to go.

Finally, the idea of quantification using V spookies as "interactions"
between events could be very interesting and a lot of fun to play around
with, and would represent a more drastic departure form the usual models.


REFERENCES, PLEASE?

All of the above is off-the-cuff, so any references to similar ideas in QM
would be very much appreciated.  I have seen at least one very brief (and
derisive) reference to the changing-the-past concept in a Scientific American
article on Bell's Inequality back, oh, about 1982, but have never run across
anything similar since.  (I had already played around with the idea before
seeing the Scientific American reference.  For that matter I had also played
around with my version of "there is really only one electron in the universe"
back in the same time period, and was quite annoyed when I found out that
some guy named Wheeler had beaten me to it.  Sigh.)

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