meekerdb wrote:
On 3/17/2015 2:50 PM, Bruce Kellett wrote:
Bruno Marchal wrote:
To be sure, I have to meditate more on some of Sean Carroll saying
about how to interpret stationary states in quantum mechanics, too.
This is one of the more interesting questions Sean raises and I am not
sure I have fully understood his answer to the main problem.
The point is that any quantum state can be expanded in terms of any
arbitrary basis in Hilbert space. The stationary state he refers to is
time independent in the basis in which it is expressed, but there are
always other, time-dependent, bases within which the state could be
expanded. Take a part of the state in such a time-dependent basis and
use it as a clock. Correlations between this internal 'clock' and the
rest of the state make the overall system time-dependent, where time
is defined by the internal 'clock'.
This is how time is though to originate in the whole universe. The
'wave function of everything', as given by the Wheeler-DeWitt
equation, is time independent. But that does not stop time development
within the state according to internally defined clocks.
Carroll had an argument against this in his lecture, but it is not in
his paper, and I didn't really grasp what he was on about.
As I understood it, an internally defined clock requires that there be
expansion of spacetime so that the clock can be an out-of-equilibrium
device. In the limit the de Sitter transistions to Minkowski spacetime
and everything is in equilibrium and there can be no clock.
Brent
I see. So that is related to his contention that even in de Sitter
space, the Gibbons-Hawking radiation is in thermal equilibrium and so
does not fluctuate -- does not even have thermal fluctuations. He agrees
that if you put a low entropy, out-of-equilibrium, detector in de Sitter
space, it will see the Gibbons-Hawking flux. But without this there are
no fluctuations.
I think that a bit more argument might be required here. Certainly, a
clock is an out-of-equilibrium device, but I though Boltzmann thermal
fluctuations even in the Gibbons-Hawking case could produce a local
entropy minimum that could last long enough to function as a detector/clock?
Bruce
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