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On 2016-04-25 17:38, John Clark wrote:<br>
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<div class="gmail_default"
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style="font-family:arial,sans-serif">On Mon, Apr 25, 2016
William Flynn Wallace </span><span dir="ltr"
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moz-do-not-send="true" href="mailto:foozler83@gmail.com"
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style="font-family:arial,sans-serif"> wrote:</span><br>
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In the standard general relativity view there is a
patch of spacetime there, with its own properties
(curvature).</span></div>
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<div class="gmail_default"><font size="4"><font
face="arial, helvetica, sans-serif"></font>If
"real" means something that's invariant then curved
spacetime is not real because it looks different for
different observers.</font></div>
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Nope. I was using curvature here to denote the metric tensor (or, if
you want to go deep, the Riemann tensor). Tensor equations are
observer-invariant. So while you might measure using a different
coordinate system from me and get different numbers, there is a
simple rescaling between our results. In particular, the line
element ds^2=g_ij dx_1 dx_2 will have the same length for us no
matter how we move and reparametrize. Geodesic curves for one
observer are geodesics for all others.<br>
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In general relativity spacetime is pretty much ontologically
primary: it is all about some Riemannian manifold, described by its
metric. How observers see things is irrelevant: the structure is
still the same manifold and metric. <br>
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<pre class="moz-signature" cols="72">--
Anders Sandberg
Future of Humanity Institute
Oxford Martin School
Oxford University</pre>
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