The following comments have been received from Jonathan Oppenheim. I have
also added a comment of my own.Dieter Zeh wrote:
> In particular, I do not understand what postselection (required for Bill
> Unruh's symmetry arguments) means if there is no ensemble to select from.
I think Bill's argument is just that quantum mechanics itself says
nothing about a time direction, so in and of itself, it can't
yield an argument which says the past is different from the future.
Take for example an attempt to measure the momentum of a particle
at a particular place (the classic example being a very heavy atom
with a well defined energy spacing E). So if a photon excites
the atom, we can use E=pc to claim that we have measured the momentum
of the photon at a well defined location. Of course you have no idea
when the atom got excited or de-excited.
But the physical process of decays and excitations are time-symmetric.
Take an excited atom, evolve the wave function of the photon and atom
(and any decohering medium) well into the future. Then prepare this
wavefunction. Sure it is difficult but this is besides the point.
It is not that quantum mechanics is time asymmetric, it is that Dyson's
statements are time-asymmetric. He compares the statement "The atom
*decayed* at 9 a.m. yesterday" to "The atom has a *probability of
decaying* at 9 a.m. tomorrow." True, we can't find a wave function for an
atom and photon which decayed at 9 a.m. yesterday, but nor can we find one
for an atom and photon which will get excited at 9 am tomorrow. And while
we can find a wave function for a system which has a probability of
absorption or decay at 9 am tomorrow, we can also find a wave function
from the system which had a probability of decaying at 9 am yesterday
(but may also have decayed at some other time).
I.e., we ought to compare definite past results with results which will
occur with certainty in the future (or past amplitudes with future
amplitudes).
Or take the following rather silly case (which maybe is a bit
besides the point). I have a very small particle detector which sits at a
particular location (x=0 say). I prepare an ensemble with a well defined
p (but with enough dispersion so that it is located somewhere out at minus
infinity and traveling towards the origin). Then on half the ensemble I
measure p, and on half the ensemble I measure x using this particle
detector. The dispersion relation is then dxdp as small as I want. Can I
claim that I have prepared a state which in the future will violate the
laws of quantum mechanics? Okay, that example is very silly, but I think
it makes the point.
The argument applies to quantum cosmology as well. In deterministic
classical mechanics, one can give an initial condition which then implies
a (redundant) final condition (which people sometimes think of as having a
higher entropy).
In quantum mechanics, an initial condition (preparation), does not imply a
deterministic final condition (final result of measurement). Still for
some reason, people think of some initial wave function (even for the
universe where there is no measurer). Why then not consider a final wave
function? How can you justify an initial wave function
of the universe over a final wave function of the universe?
Yakir Aharonov has some rather bizarre models with final conditions,
and where entropy is seen to increase in both cases.
Final remark by Paul Davies: Gell-Mann and Hartle have formulated quantum
cosmology in an explicitly time-symmetric way, with matched initial and
final boundary conditions on the wave function. It was published in Physical
Origins of Time Asymmetry (ed. J.J. Halliwell et al, Cambridge University
Press, 1994) p 311. Together with Jason Twamley I published what I believe
are observational objections to this model: 'Time-symmetric cosmology and
the opacity of the future light cone' Class. Quantum Grav. 10 (1993), 931.
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=--=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
This email list is part of the Science & Ultimate Reality Symposium in honor
of John Archibald Wheeler, March 15-18, 2002 in Princeton, N.J. For more
information go to: http://www.metanexus.net/ultimate_reality. This list is
moderated by Paul Davies. Please feel free to forward these messages
to friends, colleagues, and students.
To subscribe, unsubscribe, or access the online archives, please go to:http://listserv.metanexus.net/metanexus/archives/wheeler.html.
This publication is hosted by Metanexus Online http://www.metanexus.net. The views expressed here do not necessarily reflect those of Metanexus or its sponsors.
Metanexus welcomes submissions between 1000 to 3000 words of essays and book reviews that seek to explore and interpret science and religion in original and insightful ways for a general educated audience. Previous columns give a good indication of the topical range and tone for acceptable essays. Please send all inquiries and submissions to . Metanexus consists of a number of topically focused forums (Anthropos, Bios, Cogito, Cosmos, Salus, Sophia, and Techne) and periodic HTML enriched composite digests from each of the lists.Copyright notice: Except when otherwise noted, articles may be forwarded, quoted, or republished in full with attribution to the author of the column and "Metanexus: The Online Forum on Religion and Science ". Republication for commercial purposes in print or electronic format requires the permission of the author. Copyright 1998, 1999, 2000, 2001, 2002, 2003, 2004 by Metanexus Institute.