On Tuesday, January 28, 2020 at 5:44:52 AM UTC-7, John Clark wrote: > > On Mon, Jan 27, 2020 at 8:54 PM Alan Grayson <[email protected] > <javascript:>> wrote: > > >> We know for a fact time runs slower relative to us for an observer in >>> a distant galaxy because we can see the redshift, the decrease in >>> frequency, of light that comes from there. But if clocks ran slower for >>> them but lengths did not also contract for them then they would observe a >>> different speed of light then we do. But we also know for a fact from other >>> experiments that the speed of light is the one true constant for everyone >>> everywhere, the observed speed of light does not depend on the speed of the >>> observer or on the speed of the source producing the light. So why are you >>> "not sure it is applicable in this situation"? >> >> >> *> Simple.* > > > Yes your answer is very simple, but that word has more than one meaning. > > * > **Because length contraction, say of a rod, depends on comparing >> measurement of the rod's length as observed in two frames of reference, >> moving wrt each other. In this case, we're making a measurement of the >> CMBR to determine curvature. AG* > > > I'm not talking about Euclidean curvature! I'm trying to show you the > volume in a expanding sphere can be infinite. An observer in a distant > galaxy using a clock and a meter stick can measure the speed of light. We > know for a fact his clock runs slower than our clock (we know this from the > redshift). So if his meter stick is not shorter than our meter stick (from > relativistic length contraction) then he would measure a different speed > for light than we do. But we know all observers measure the same speed for > light. Therefore he must experience both time dilation *AND* length > contraction. >
*For the observer situated in a distant galaxy, his clock does not dilate, and his length does not contract. Rather, that's how it appears for an observer far from that galaxy, moving away with some relative speed. Moreover, if that galaxy is in the non-observable region wrt to the distant observer "measuring" time and length, no measurements are possible. And even if the impossible measurement could be made, those galaxies would NOT shrink in length to zero, presumably allowing for infinite volume, since the expansion has been going on for finite time, 13.8 BY. AG* So regardless of what the local geometry is, on a large scale the geometry > of our universe must be hyperbolic; and the same would be true for any > universe that was expanding and had a finite speed of causality. > > >>> *would just mean that the estimate without it would be too large, >>>> but not infinite. AG * >>> >>> >>> >> Neither Einstein's theory or anything else in physics says length >>> contraction, time dilation, and mass increase discontinuously stops at some >>> point short of the speed of light, they don't suddenly stop increasing, >>> they increase continuously up to the speed of light. >>> >> >> >> *> I haven't stated anything about discontinuities. They don't exist in >> this situation. AG* >> > > OK fine, but if there are no discontinuities then as galaxies get more and > more distant from us the clocks in them can run arbitrarily slower than > ours from time dilation. And galaxies can be arbitrarily thin from length > contraction. And so you could fit a arbitrarily large number of galaxies in > a arbitrarily small volume of space. And so globally the universe must > follow the rules of hyperbolic geometry not those of Euclid. And so there > is nothing to prevent the volume of a sphere from being infinite if it is > expanding and does what Einstein says. > > John K Clark > -- 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/1ef1ef1c-48fa-496d-aeeb-caa7c08ee8b4%40googlegroups.com.
