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. 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 >
Since you can't measure anything in the NON-observable region, your argument fails. Moreover, the radius of a sphere is the same everywhere, so if we measure it via the CMBR, this is sufficient to calculate its total volume, including the NON-observable region. 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/53c8ffcd-9a9d-4ea8-9563-4177e41bb690%40googlegroups.com.
