On 18 Mar 2015, at 04:34, Bruce Kellett wrote:
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?
It seems to me that if the marriage of general relativity and quantum
mechanics preserves unitarity and enough of the energy-time
uncertainty relation, we might go from an empty stationary universe to
a fully active, dynamical with high energy, seen internally, from a
change of base. The curvature of space might be base dependent. Feel
free to explain me this would not make sense. No way to avoid the
Boltzmann brains here, I think.
This might be predictable by computationalism (well understood of
course): below our sharable substitution level, we are confronted to
the competition of infinitely many "Boltzmann brain", but those are
"simply" the universal numbers(*) in arithmetic which realize "our
current states". Only the one with a linear bottom seems to have the
reasonable measure.
Consciousness cannot collapse the wave, but if comp gives the good
energy-time relation, consciousness, or the correct inference of local
consistency, might naturally be selected in the base where the Gibbons-
Hawking flux makes relative sense.
As I said, what I am just trying to explain, is that computationalism
makes the matter part of the mind-body problem *more* complex, perhaps
even insane/refuted; and it expands the idea of Everett on, not "just"
the universal Schroedinger wave, or the universal Heisenberg matrix,
but on the whole (sigma_1) arithmetic, through the self-observable of
all universal machines.
The physicists are still too much fuzzy on what is an observer. Once
admitted that the observer is Turing emulable at some level, we
multiply it into infinity, in infinitely many computations.
There is no sense to think that we might be in *a* Boltzmann Brain,
because the solidity that we can "see" results normally from the sum
on *all* Boltzmann Brains/universal numbers below our substitution
level.
It remains to be seen if the QM elimination of aberrant histories à-la
Feynman (phase randomization) remains valid in arithmetic, ... or
even in the correct marriage of QM and general relativity. Nice talk
by Sean to remind things are not trivial in physics too.
Bruno
(*) For a computable enumeration phi_i of the partial computable
functions,
u is said to be a universal number if, for all x and y, phi_u(<x, y>)
= phi_x(y). u is said to emulate x on y. It computes a universal
partial computable function. And <x,y> is some computable bijection
from NXN to N.
Note that the relation "phi_u(<x, y>) = phi_x(y)" is provably
equivalent with an arithmetical statement, and sigma_1 complete
theories can prove them when they are true.
A number is "Löbian" when it is universal, and it knows (in some
technical sense) that it/he/she is universal (then it will know also
that it is Löbian, and it will know the price, which is that it can be
deluded, lied, wrong, dead, inconsistent, crashed, in a loop, in a
dream, in infinitely many dream at once, etc).
Typical possible concrete (if that exists) universal numbers are
cells, brains, computers, interpreters of programming language,
apparent physical laws (more precisely their apparent rational
approximations), etc.
Bruce
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