On Wednesday, September 25, 2002, at 10:09 AM, Wei Dai wrote:

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> On Tue, Sep 24, 2002 at 03:20:54PM +0200, Bruno Marchal wrote:
>> I mentioned Deutsch for his account of time in term of parallel
>> universes.
>> I don't remember if Deutsch deduced this explicitly from relativity.
>> (I lend his book so I cannot verify now).
>> I was just doing the following caricatural reasoning:
>> General Relativity (GR): gravitation = space-time curvature
>> Quantum mechanics (QM): forces should be quantized (and unified
>> through
>> symmetry/broken-symmetry)
>> Now GR + QM gives: space-time itself should be quantized. A MWI view
>> of this
>> doesn't give many minkowski worlds, but something more like a
>> discrete minkowski multiverse.
>
> Is there a paper or book that describes this discrete minkowski
> multiverse
> in more detail?
Several of the papers by Rafael Sorkin, Carlo Rovelli, Chris Isham,
Fotini Markopoulou, John Baez, and others discuss "causal sets" as a
model of spacetime.
For example, picking just one of them,
arXiv:gr-qc/9910005 v 1 2 October 1999 C.J. Isham, J. Butterfield,
"Some Possible Roles for Topos Theory in Quantum Theory and Quantum
Gravity."
Here's one small part to provide some of the flavor:
"By a causal set we mean a partially-ordered set P whose elements
represent spacetime points in a discrete, non-continuum model, in which
p <= q, with p, q elements of P, means that q lies in the causal future
of p.....
"The set P is a natural base category for the presheaf of Hilbert
spaces in which...."
(etc.)
I talked about these issues in my article several weeks about time as a
lattice of partially-ordered events.
Now, whether time and space are "really" continuous or discrete (at
some very small scale, presumably near the Planck scale) is not
terribly important for this analysis. Just as both QM and relativity
are usually involved with events (measurements, clocks, light flashes,
etc.), and just as much of the traditional "causal analysis" of
everyday events (a la Pearl) is of discrete, chunked events, the causal
set model is very generally applicable.
And again I have no choice but to recommend Lee Smolin's "Three Roads
to Quantum Gravity" as a good introduction to the ideas of the authors
named above.
--Tim May