**Stephen Paul King** (*stephenk1@home.com*)

*Thu, 02 Dec 1999 13:08:58 -0500*

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On 28 Nov 1999 21:03:27 -0800, in sci.physics.research

toby@ugcs.caltech.edu (Toby Bartels) wrote:

*>Zachary Uram <zu22@andrew.cmu.edu> wrote:
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*>
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*>>http://plato.stanford.edu/entries/spacetime-holearg/
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*>
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*>The paragraph at the end of section 4 is unconvincing.
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*>See <http://math.ucr.edu/home/baez/physics/energy_gr.html>
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*>for reasons why gravitational energy is not really energy.
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*>Thus, it's no problem to let the spacetime substantivalist
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*>have spacetime be the manifold together with the metric.
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*>
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*>Now, when the web page first mentioned general covariance,
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*>I realised that a manifold with fields on it
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*>could not be a mathematical representation of reality;
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*>rather, we would need to use isomorphism classes.
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*>The paper eventually formulates this as Leibniz equivalence.
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*>I'm all for that.
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*>
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*>But the site never justifies its assumption
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*>that Leibniz equivalence is incompatible with spacetime substantivalism.
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*>If reality is the tuple (M,g,O1,O2,...,On),
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*>the spacetime substantavilist identifies (M,g) with spacetime.
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*>However, reality is actually isomorphism classes of such tuples.
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*>But this doesn't leave the substantivalist without a spacetime!
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*>On the contrary, the substantivalist may identify spacetime
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*>with isomorphism classes of pairs of the form (M,g).
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*>
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*>It's possible that the authors make the implicit assumption
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*>that any part of physical reality
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*>must have, as its mathematical representation,
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*>a subset of the mathematical representation of all reality.
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*>This is untenable; a table exists in reality,
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*>yet it is not a subset of (M,g,O1,O2,...,On),
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*>much less of its isomorphism class.
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*>A table is a complicated function of the Oi.
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*>Yet it is real; how much more so spacetime,
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*>whose mathematical representation is a quite simple function
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*>of the mathematical representation of all reality.
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*>
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*>I think it's important to defeat the hole argument in this way,
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*>because I'm *not* a spacetime substantivalist,
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*>and I want my claim to have physical meaning.
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*>In GR, spacetime certainly is real, but GR is wrong,
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*>and it is my faith that the correct theory of quantum gravity
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*>will find that spacetime doesn't exist independently of its contents.
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*>This is a very different state of affairs from GR,
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*>despite what the cited web page tries to argue.
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*>
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*>
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*>-- Toby
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*> toby@ugcs.caltech.edu
*

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