On 1/19/2020 2:44 PM, Alan Grayson wrote:
On Sunday, January 19, 2020 at 11:52:18 AM UTC-7, Brent 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.
Brent
*But it could be HUGELY spherical and seem to be zero! *
That's right it COULD! But that's not the way to bet and just because
it could wrong doesn't make it an assumption. The whole theory of
general relativity not only could be wrong, we in fact know it must be
wrong at sufficiently short distances.
*The cases could be indistinguishable. What I want to know is this;
when you solve using the FLRW model, does it give exactly zero for the
curvature? TIA, AG
*
Solutions exist for all different curvatures.
Brent
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