Tim May wrote:

> On Monday, January 13, 2003, at 02:40  PM, Jesse Mazer wrote:
> > Tim May wrote:
> >
> ....
> As to why there is only a single past but multiple futures, this is
> implicit in the measurement process.  (I doubt you will find this
> convincing unless I expand on this.)
> Consider the "There will be a sea battle next year" proposition, the
> favorite of the Stoics and Aristotle.  Unknown at this time, and few
> prospects for computation. Determinism is not very supportable,
> especially at full detail.
> And yet the proposition "There was a sea battle at Jutland during World
> War II" is answerable. And all will agree on that answer.
> The future is not knowable, the past is not disputable.
> This arises with quantum measurements of course. Once a measurement is
> made--path of a photon, for example--all honest observers will report
> exactly the same thing. There simply is no basis for disputing the
> past, for Alice to say "I saw the photon travel through the left slit"
> but for Bob to say "I saw it travel through the right slit."
> (If I am wrong on this, please correct me ASAP!)
> Honest observers will report the same outcomes of measurements, whether
> those measurements are of photons in slits or sea battles...



This is not quite the case for QM: I mean either the unalterability of the
Past or the idea that "all honest observers will report the same thing" or
even that the future is not knowable.

On the first one must be careful because the alterability of the past does
not coincide at all with the notion of "many pasts". It is the same past
is presummably altered from the present and future. This is the conclusion
that comes out of several different considerations of the time-symmetry
of the Unitary Evolution Law. Aharonov and Vaidman developped an
approach to QM which is entirely equivalent to the current one but
emphasises this aspect of the formalism. Check their papers on the
2-vector formalism.  Alternatively Novikov's popular book  "The
River of Time" reaches the same conclusion by different means.

The second question comes up when you consider QM observers
in different relativistic frames: there are a good number of paradoxical
situations concerning the identification of collapsing events bearing on
the fact that wave-function collapse is not a relativistic invariant.
A lot of people since Wigner have showed that this is the case over
the years. The bibliography is too long for me to go over...

On the question of the unknowability of the future, that is again
a question of perspective: if you are a quantum system you DO know
all your future if you know your present! The Schrodinger equation
tells you so because it is entirely time-deterministic. Now this is
true for each photon: once emmitted it already "knows" in this very
precise sense where and when it will be absorbed!

That we do not know our future in the same way is our problem,
not Quantum Mechanics and presummably not a quantum mechanical one...

-Joao Leao


Joao Pedro Leao  :::  [EMAIL PROTECTED]
Harvard-Smithsonian Center for Astrophysics
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