On 1/30/2020 5:29 PM, Alan Grayson wrote:


On Thursday, January 30, 2020 at 5:09:56 PM UTC-7, Brent wrote:



    On 1/30/2020 12:45 PM, Alan Grayson wrote:

    That's not it. I think the two observers, one in a galaxy far
    removed and one here, would read the same CMBR "time", regardless
    of the distant galaxy's speed of recession.  But relativity says
    otherwise. This is what puzzles me. AG

    Ask yourself /*when*/ do they read the same time.

    Brent


I don't know if this helps. Since the temperature of the CMBR is the same everywhere, at any time t,

You're missing the point.  "At any time t" is /defined/ as when the CMB has a certain temperature.  It's the same everywhere at time t, because that's how we defined t.  Our model (FLRW) says the expansion is uniform, so that's the same proper time from the Big Bang.  But it's not the time that photons we're seeing now left the distant galaxy; the photons we would use to read a distant clock and see that it runs slow.

we can in principle determine if the two measurements are simultaneous or not. AG

In relativity, simultaneity is not an objective property.  It's motion and coordinate dependent.  So think of t as just one of four numbers, (t x y z) used to label a spacetime event.  Then we choose our labeling system to make our equations look simple.  But the labels don't have physical significance.

Brent


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