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
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