Reply to Jonathan Oppenheim:>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.
But what IS "quantum mechanics in and of itself"? The Schroedinger
equation and formal transition amplitudes are certainly insufficient
to describe measurements.
Several good textbooks discuss the irreversible nature of
measurements. Paul Davies' book of 1974/77 contains a chapter on Time
Asymmetry in Quantum Mechanics. In the third and fourth edition of my
book, the chapter on the Quantum Mechanical Arrow of Time contains a
section on The Time Arrow in Various Interpretations of Quantum
Theory (see www.time-direction.de), where I have discussed (and
criticized) Aharonov's concept of postselection.
Freeman Dyson probably refers to the irreversible transition from
potentiality to actuality used in the Copenhagen interpretation. For
example, Pauli once declared that "the occurrence of a definite
electron position is a CREATION outside the laws of nature". In the
theory of decoherence, the click in the counter is instead described
by the "irreversibly" arising entanglement (an effect that has been
observed, as Serge Haroche will probably tell us), based on the
Schroedinger equation AND on a time-asymmetric environment. No
measurement can be regarded as complete if it remains reversible.
However, if the state is (irrerversibly) CHANGED in a measurement,
you cannot postSELECT it any more.
What has this all to do with John Wheeler? John has always been
open-minded to accept both the Copenhagen and the Everett
interpretation (see his article with Max Tegmark in the Scientific
American of March 2001). It sounds contradictary, but he may be
right: the former may now be understood within the latter, by means
of decoherence, as a very useful pragmatic or phenomenological
approach -- though not as a conceptually consistent and fundamental
one!
>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.
In contrast to a measurement apparatus, the universe does not have an
environment. So in principle it may indeed possess a time-symmetric
final condition (with a big crunch), but this leads to serious
consistency problems in any deterministic theory. In quantum theory,
cosmic time reversal symmetry would require decoherence to be
replaced by recoherence during recontraction of the universe, or
Everett branching to be replaced by recombination of branches.
Measurements would thus be undone during the contraction phase.
In section 5.3 of my book, I have discussed the proposals by
Gell-Mann and Hartle, Davies and Twamley, and a related paper by
Craig, but added further quantum arguments for consistency. While our
universe would remain transparent for classical light, thus carrying
its information content even beyond the turning point of the cosmic
expansion (as Davies and Twamley argue), the information capacity of
QED is limited by its photon aspect (or the finite size of Planck
phase space cells in another language). This and other quantum
effects (occurring at the turning of the tide) may undermine their
objections. Only the Everett universe as a whole can be symmetric in
quantum theory -- not its individual quasi-classical branches. In
(effective) quantum gravity the consistency problem is further
relaxed, since big bang and big crunch would become identical
according to the time-less Wheeler-DeWitt equation.
Dieter Zeh
--------------------------------------------------------------
H. Dieter Zeh Phone: (+49)6223 74097
Gaiberger Str. 38 Fax: (+49)6223 74098
D69151 Waldhilsbach e-mail: zeh@urz.uni-heidelberg.de
Germany
See also:www.zeh-hd.de(or www.time-direction.de)
_________________________________________________
End note added by Paul Davies:
I think a key point here, implicit in what Dieter Zeh writes, is that the
wave function for the universe as a whole can be unitary (time-symmetric)
even if most individual Everett branches are not, so that some branches
start out in a low-entropy state and end in a high-entropy state. Others
start with high entropy and end with low entropy. A very few start at low
entropy and end at low entropy, as in the time-reversing models of Wheeler
("turning of the tide"), Gold, etc.
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