On 1/22/2020 7:40 AM, Bruno Marchal wrote:
On 19 Jan 2020, at 19:52, 'Brent Meeker' via Everything List
<[email protected]
<mailto:[email protected]>> wrote:
On 1/18/2020 11:58 PM, Alan Grayson wrote:
On Sunday, January 19, 2020 at 12:18:54 AM UTC-7, Brent wrote:
On 1/18/2020 10:56 PM, Alan Grayson wrote:
I don't claim anything except that GR has solutions for a
cosmos in which space is flat and, in that solution, space
is infinite and empirically it appears that space is flat.
*Measurements don't establish it's flat, as I previously
argued. And, as you previously stated, the sign of k, the
parameter in GR intimately associated with curvature, is folded
into the initial conditions. But since the initial conditions
are really unknown, or are speculative, you can assume initial
conditions which satisfy your bias, in this case FLAT. AG *
No. It's not an assumption. Empirically the universe appears
flat, which (assuming the FLRW model) implies it was always
flat. It is not a question of assuming an initial condition, it
is inferring the initial condition from present measurements of k.
*This seems to modify what you wrote a few day ago. In any event,
"empirically" means "measurement", and one cannot measure the
curvature as exactly zero, which is what you need to empirically
establish flatness. The measurements are very close to zero, but not
zero. AG*
When you measure something and it is so close to zero as to be
indistinguishable from zero, then taking it to be zero is not an
assumption.
Locally.
No. Even taking it to be flat globally is more than an assumption, it
is an inductive inference. I know that as a (deductive) logician you
deprecated inductive inference...nevertheless as Sean Carroll quipped,
"All human knowledge has come from studying the shadows on the cave wall."
Brent
Be careful, you might be cited by some platists! (Those defending that
the Earth is flat!).
Bruno
Brent
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