I am glad that we found so much to agree upon. When I posted my reply, I
trembled in fear going against a relativist like you. :-) I would like a
clarification on a point, since it has been about 5 years since I last
studied GR or special relativity and have hardly thought of it since then,
preferring anthropology for the past couple of years.
At 12:23 PM 9/18/97 -0600, Don N Page wrote:
>
> Second, an infinite age for the universe does not imply the Eternal
>Return. I think Frank Tipler (who does do some sensible stuff --- I just
>corresponded with him yesterday about a paper he sent me on "Quantum
>Nonlocality Does Not Exist," which I almost entirely agree with, despite my
>disagreement with the conclusions of his rather awful book) is right in
>pointing out (in writings other than what was quoted) that in classical
general
>relativity the Eternal Return generically cannot occur, even if the
universe is
>infinite in time. Even if gravity did not exist, and one had just
>nongravitational field theory in Minkowski spacetime, the phase space is
>infinite, because of the infinite spatial volume, even at finite total energy,
>so one of Nietzche's assumptions would be wrong and there would generally not
>be any Eternal Return. Instead, fields would generically just disperse over
>time and could only be concentrated into a finite spatial region for a finite
>time.
>
I would agree that Nietzche's assumption would be violated by an infinite
universe. But Nietzche's assumption was that there was a finite amount of
energy, which would imply a finite space. As I recall, Minkowski space is
flat and thus not capable of a boundary. Is this correct? It may be that
Nietzche knew that it is easier to limit energy rather than space and thus
hid his problem inside of his assumption. Do any philosophers on this list
know if this would be the case?
> Although such a periodic quantum state would presumably not be generic
>(at least if the Hamiltonian has a continuous spectrum), if time really were
>well defined, and if our universe were asymptotically flat (say at distances
>beyond what we can see), so that it could have a finite energy, I know of no
>evidence that would rule out such a periodic quantum state composed purely of
>commensurate energy eigenstates. In fact, the energy superselection rule
would >allow it to be in a single energy eigenstate, as William K. Wootters
and I
>pointed out in "Evolution without Evolution: Dynamics Described by Stationary
>Observables," Phys. Rev. D27(12), 2885-2892 (1983). The period for the
quantum
>state could be arbitrary, possibly billions of years, or possibly a tiny
>fraction of a second. (Actually, the period could be long only if the state
>were a superposition of commensurate energy eigenstates with the least common
>divisor of the energy eigenvalues being an extremely tiny energy, but if the
>state were an energy eigenstate, its period would be h-bar divided by the
>energy. Taking the rest mass energy of the roughly 10^22 stars in the
>observable universe as a lower bound on the energy would give an upper
bound of
>the period for a single energy eigenstate as less than 10^{-103} seconds, a
>decimal point followed by 102 zeroes before the digit one!)
After a couple of readings I think I finally understand what you are
suggesting. Why is it not more likely that the universe has to be described
as a superposition of the states of the component particles rather than
having the entire mass of the univers be in a single state. I am expressing
this poorly. let me try again. The second suggestion appears to require the
many-world's hypothesis. Our universe be in one state, but other universes
are in another. It seems to me that since we can only really observe one
universe at the moment, that the eigenstate should be the superposition of
the states of the individual particles. I don't see how Christianity could
survive the confirmation of the many-world's hypothesis.
Furthermore in describing a system of particles don't we treat the system as
the superposition of the individual particle states? Why wouldn't the
universe be the same?
>... I see no reasons to accept Nietzsche's
>conclusions, "No ultimate purpose to life," "Progress is an illusion," and
"God
>could not exist." (I should admit that I haven't read his arguments of why I
>should accept them, but since for each universe compatible with our
>observations and experiences, I can imagine a periodic quantum universe that
>gives precisely the same observations and experiences, I can't see how the
>purpose, progress, and createdness would be any different for the periodic
>universe. I wish I could have tried this rebuttal on Nietzsche before he went
>into the insane asylum.)
Would the name Sisyphus mean anything? Eternally condemned by Zeus to push
the rock uphill each day only to have it fall back. What sort of purpose
would that serve? That is why I think the eternal return would lead to a
purposeless universe.
glenn
Foundation, Fall and Flood
http://www.isource.net/~grmorton/dmd.htm