On Thursday, January 16, 2020 at 2:02:22 PM UTC-7, John Clark wrote:
>
> On Thu, Jan 16, 2020 at 1:25 PM Alan Grayson <[email protected] 
> <javascript:>> wrote:
>
> >> as Sean Carroll says "*the manifestation of spacetime curvature is 
>>> simply the fact that space is expanding*".
>>
>>
>> *> If curvature is caused by energy and momentum in space-time, Carroll's 
>> statement doesn't make sense. AG*
>
>
> Has it ever occured to you that if a professor of physics at one of the 
> best universities in the world makes a statement about physics that makes 
> no sense to you it might not be because he is talking nonsense but because 
> you don't understand something? It makes no sense to you because you assume 
> spatial curvature and spacetime curvature mean the same thing. But you're 
> wrong, they don't. And they don't because the time dimension behaves in a 
> fundamentally different way than any of the 3 spatial dimensions do; more 
> specifically if you want to use Pythagoras theorem in space*TIME *(not to 
> be confused with space) to calculate a distance in space*TIME* then you 
> have to stick in a minus sign that Euclid and Pythagoras knew nothing about.
> I f
> John K Clark
>

*You're referring, of course, to the Lorentz metric with the minus sign. 
Yeah, I've heard of it -- used in pseudo Riemannian manifolds, and without 
it those space-time causal cones wouldn't make sense. But I read again and 
again that "curvature" of space-time is caused by the presence of 
mass/energy, so I find Carroll's comment puzzling. He seems to be saying 
that expansion is caused by curvature, when it's generally thought to be 
caused by dark energy. Also, as you know, I am not an enthusiast (to put it 
mildly) of the Many Worlds theory of Everett, but Carroll is. So I don't 
pray at the feet of physicists, even those from prestigious universities. 
AG*

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