On Thursday, September 12, 2024 at 5:47:27 PM UTC-6 Brent Meeker wrote: That's backwards. theta represents a fixed point on the expanding balloon universe so dtheta/dt=0 and all the change is in r the scale of the universe. Assuming expansion is constant means dr/dt=Hr where H is Hubble's *observed* constant.
Brent IMO, theta represents the angular displacement along the arc connecting two galaxies, where one is assumed as fixed, the other receding. I don't see what backwards about this. When we discussed this ages ago, I recall your argument that the increasing recessional velocity was purely a geometric consequence. This continues to be my view. Consequently, there is no need to appeal to Hubble's law. AG On 9/12/2024 4:12 AM, Alan Grayson wrote: *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* *If the parameter r captures size of the universe, and if we assume it's expansion is constant, then dr/dt = 0 and the first term when differentiating s is zero. So the increase of ds/dt is completely captured in the second term. AG* You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/6093db62-898d-4a67-9c90-08b3467bf31bn%40googlegroups.com <https://groups.google.com/d/msgid/everything-list/6093db62-898d-4a67-9c90-08b3467bf31bn%40googlegroups.com?utm_medium=email&utm_source=footer> . -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/893aa7bf-dd6f-4da9-8c89-9a515cf78832n%40googlegroups.com <https://groups.google.com/d/msgid/everything-list/893aa7bf-dd6f-4da9-8c89-9a515cf78832n%40googlegroups.com?utm_medium=email&utm_source=footer> . -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/cd404351-6389-4503-a443-bd53469fed4cn%40googlegroups.com.
