On 1/19/2020 6:57 PM, Alan Grayson wrote:
On Sunday, January 19, 2020 at 4:46:41 PM UTC-7, Brent wrote: 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. *OK, but what value of curvature does the FLRW model give? AG *
All different ones, depending on what you assume about the cosmological constant, the state function of matter, etc.
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