On Thursday, January 16, 2020 at 4:45:41 PM UTC-7, Brent wrote:
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> On 1/16/2020 3:17 PM, Alan Grayson wrote:
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> 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]> wrote:
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>> >> 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. *
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>
> "Dark energy" is a place-holder name for whatever is responsible for the 
> accelerating expansion of the universe.  So it could be curvature (i.e. 
> just an intrinsic constant of spacetime) or it could be a quantum field 
> that would have a corresponding particle that we could look for.  And what 
> would be puzzling about Carroll having a different opinion than what is 
> "generally thought" when it is a completely unsettled empirical question on 
> which experts may be expected to have different theories.  In fact there 
> isn't any "generally thought" consensus, and science doesn't go by 
> consensus anyway.  What puzzles me is that you spend so much time writing 
> to these email lists when your level of understanding would be improved a 
> lot more by reading a book, e.g. David Mahon's "Relativity Demystified" or 
> Robert Wald's "General Relativity" or "Gravity" by Jim Hartle or even Vic's 
> "Comprehensible Cosmos".
>
> Brent
>

*Sure, it's a placeholder; everyone knows that. And AFAIK, curvature isn't 
a constant of space-time. It's a tensor field value that changes, depending 
on location and time. In any event, most professional comments about 
expansion do NOT claim that curvature causes expansion. Carroll seems to be 
an outlier and I was asking for a window into his opinion. Isn't that 
obvious? I am not going by any consensus here.  AG*

>
> *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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