The only shortcoming is you've confused things by assuming that theta is
an independent variable. Hubble's discovery that recession speed is
proportional to distance means that theta for any given galaxy is constant.
Brent
On 9/12/2024 1:07 AM, Alan Grayson wrote:
*But how do you know the separation distances are what you claim?
Again, you seem to be assuming what's needed for a proof. *
*
*
*I prefer this method. s = r * theta, where s is the arclength or
separation distance of two galaxies residing on a circle of radius r,
where theta is the angle subtended by s. Differentiating, ds/dt =
dr/dt * theta + r * d(theta)/dt. Even if the expansion rate, dr/dt, is
constant, the RHS is positive since the second term must be positive
based on the physical assumption that d(theta)/dt must be positive
(since the arclength s must be increasing as the universe expands).
So, eventually, ds/dt will exceed the velocity of light, the condition
that the galaxies will lose contact. Any flaws in this logic? AG*
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