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Article #4573

Space-time IS a semi-Riemannian manifold (?)

#4573
From: John C. Baez
Date: Mon, 05 Oct 1992 05:28
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matmcinn@nuscc.nus.sg (Mcinnes B T (Dr)) writes:

>No. It isn't unanswerable. If the word "existence" has any meaning at a
>all, then time exists. I am amazed at all this talk of time being
>"defined" by clocks, at people who speak of spacetime as a "model", at
>talk of "temporal" phenomena by people who doubt that time exists.
>Spacetime is not "modelled" by semi-riemannian manifolds, it IS such a
>manifold.

I am awed by your certainty.  Many of the best researchers in quantum
gravity would dearly like to know whether spacetime is a
semi-riemannian manifold.  What info do you have that they don't? 
Barring seances with Einstein's ghost, I would prefer to say
"spacetime is well modelled by a semi-riemannian manifold on
sufficiently large distance scales."  

On the other hand, I agree that the idea of time being "defined" by
clocks is essentially a cop-out unless one has a good theory of what
counts as a clock and why cesium clocks are regarded as "better"
clocks than baloney sandwiches.  (In other words, although I am of an
operationalist bent, I don't think one can weasel out of the issue of
time simply by defining time to be that which is measured by that
which we build to measure time.)

As for whether time "exists," until someone lays out their precise
definition of "exists" I will use my everyday sloppy one, according to
which time, numbers, baloney sandwiches and societies all exist, even
though they are very different sorts of things.   
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Path: arc1-ca.pugleaf.net!sparky!uunet!snorkelwacker.mit.edu!galois!riesz!jbaez
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Space-time IS a semi-Riemannian manifold (?)
Message-ID: <1992Oct5.052820.12186@galois.mit.edu>
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Organization: MIT Department of Mathematics, Cambridge, MA
Date: Mon, 5 Oct 92 05:28:20 GMT
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