[time 1084] Re: WWW: the Hole Argument

Stephen Paul King (stephenk1@home.com)
Thu, 02 Dec 1999 13:08:58 -0500

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

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