Example with points,we add one point uniformely at each steps: At t0: . . At t1: . . . At t2: . . . . . At t3: . . . . . . .
At each steps more and more point are added between the two initial points, at one time the expanded added space will be greater than c. Even if at each steps you add an infinitesimal piece and not a full point that will still occurs, but will take longer. Quentin Le mer. 11 sept. 2024, 13:05, Quentin Anciaux <[email protected]> a écrit : > > > Le mer. 11 sept. 2024, 12:53, Alan Grayson <[email protected]> a > écrit : > >> >> >> On Wednesday, September 11, 2024 at 4:33:51 AM UTC-6 Quentin Anciaux >> wrote: >> >> >> >> Le mer. 11 sept. 2024, 11:49, Alan Grayson <[email protected]> a >> écrit : >> >> >> >> On Wednesday, September 11, 2024 at 3:26:01 AM UTC-6 Quentin Anciaux >> wrote: >> >> >> >> Le mer. 11 sept. 2024, 11:23, Alan Grayson <[email protected]> a >> écrit : >> >> >> >> On Tuesday, September 10, 2024 at 3:50:08 PM UTC-6 Quentin Anciaux wrote: >> >> >> >> Le mar. 10 sept. 2024, 23:19, Alan Grayson <[email protected]> a >> écrit : >> >> >> >> On Tuesday, September 10, 2024 at 2:19:42 PM UTC-6 John Clark wrote: >> >> On Tue, Sep 10, 2024 at 3:57 PM Alan Grayson <[email protected]> wrote: >> >> >> *>> Even if you ignore Dark Energy and postulate that the Hubble constant >> really is constant, every object a megaparsec away (3.26 million >> light-years) is moving away from us at about 70 kilometers per second. So >> if you try to look at objects a sufficiently large number of megaparsec >> away you will fail to find any because they are moving away from us faster >> than the speed of light.* >> >> >> >* That was in the past. At present, the universe is expanding at about >> 70 km/sec.* >> >> >> *Galaxies are receding from the Earth at 70 km/sec for EACH megaparsec >> distant from Earth they are. The further from Earth they are, the faster >> they are moving away from us, so if they are far enough away they will be >> moving faster than the speed of light away from us. * >> >> *> You're assuming the universe today is infinite,* >> >> >> *NO! I said IF the entire universe is infinite today then it was always >> infinite, and IF it was finite 10^-35 seconds after the Big Bang then it's >> still finite today. I also said nobody knows if the entire universe is >> infinite or finite. * >> >> >> *>* *Hubble's law applies to the past, not to the future,* >> >> >> *What the hell?! * >> >> >> *How about an intelligent reply? Obviously, if the universe is infinite >> today, it was always infinite. But that's what I am questioning. For >> galaxies to fall out of view, they have to moving at greater than c. Now >> they aren't receding that fast. How will they start moving that fast? >> You're applying Hubble's law without thinking what it says. Just because a >> galaxy is now receding at less than c, how will continued expansion >> increase that speed to greater than c? AG * >> >> >> The farther they are the faster they are receding from you, so as they >> continue to get farther away they receed faster from you till the point >> they receed faster than c and go out of your horizon. >> >> Quentin >> >> >> Instead of preaching the Gospel, why don't you try to justify Brent's >> equation to prove your point, if you can. I see the distance separation >> along the equator for two separated galaxies as linear as the radius of the >> sphere expands. Brent uses Hubble's law, but the proof of what you claim >> shouldn't depend on Hubble, but just the geometry. AG >> >> >> I did multiple times with the balloon analogy which is purely >> geometrical, see previous answers. >> >> >> I don't think so. You just asserted it. AG >> >> >> The equation that links distance and recession velocity in both cases >> comes from the same geometric principles of uniform expansion in space. The >> proportionality between distance and velocity is a natural consequence of >> how expansion works, whether it’s on a 2D surface like a balloon or in 3D >> space like our universe. >> >> The expansion of the balloon and the universe follow similar dynamics >> because, in both cases, the expansion is homogeneous (the same everywhere) >> and isotropic (the same in all directions). >> >> If you mark two points close to each other on the balloon and start >> inflating it, those two points will move apart slowly. However, if you mark >> two points farther apart, they will move away from each other much more >> quickly as the balloon expands. >> >> In the same way, in the universe, the farther away a galaxy is, the more >> space there is between us and that galaxy. Since each portion of space is >> expanding, more distant galaxies experience the cumulative effect of the >> expansion over several portions of space. This means that for a galaxy at a >> great distance, the total expansion of space is larger, which results in a >> higher recession velocity. >> >> >> *Consider this model; two separated galaxies on an expanding equator with >> separation distance s, and expanding circumference with radius r. The >> recessional or separation velocity is ds/dt. And ds/dt depends on dr/dt. >> How can ds/dt be > c, unless dr/dt becomes large. IOW, the recessional >> velocity seems to depend on the rate of expansion. It won't automatically >> become > c unless the rate of expansion exceeds some large value. AG* >> > > You’re right that the separation velocity (ds/dt) depends on the rate of > expansion of the circumference (dr/dt), but the key idea is that even with > a constant expansion rate, the separation velocity between two points on > the expanding equator (or in the universe) will eventually exceed the speed > of light (c) because the recession velocity grows proportionally with the > distance. > > Let’s break this down: > > 1. Expansion Rate and Distance: > > For a uniformly expanding circumference, the rate of expansion (dr/dt) is > constant. However, the distance (s) between two points on the equator > increases as the radius (r) increases. The relationship between the > separation velocity (ds/dt) and the expansion rate (dr/dt) is proportional > to how far apart the two points are. > > ds/dt = H0 * s > > Where: > > H0 is the expansion rate (or dr/dt). > > s is the distance between two galaxies on the expanding equator. > > > As the distance (s) increases, even with a constant H0, the separation > velocity (ds/dt) increases proportionally. Over large distances, this > proportionality means that ds/dt can exceed c, even if H0 (the rate of > expansion) remains relatively moderate. > > 2. Superluminal Recession: > > The reason this happens is that the recession velocity depends not just on > the rate of expansion (H0), but on the cumulative distance between the two > points. As distance increases, the velocity at which two points recede from > each other grows proportionally. Eventually, this velocity will surpass c > because the space between the galaxies is expanding, not because they are > moving through space faster than light. > > 3. Analogy to the Universe: > > In the universe, even though the expansion rate (H0) is constant or even > slowing, galaxies that are far enough apart will have a recession velocity > greater than c simply due to the large distance between them. The same > principle applies to your model of galaxies on the expanding equator. > > Conclusion: > > The recession velocity (ds/dt) can exceed c without requiring dr/dt to > become extremely large. Instead, this happens because the separation > velocity grows proportionally with the distance between galaxies. Over > sufficiently large distances, this leads to superluminal recession, even > with a constant or moderate expansion rate. > > > * John* K Clark See what's on my new list at Extropolis >> <https://groups.google.com/g/extropolis> >> >> hwt >> >> >> -- >> 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/5485c7a2-a527-448a-b337-3c8c60466d73n%40googlegroups.com >> <https://groups.google.com/d/msgid/everything-list/5485c7a2-a527-448a-b337-3c8c60466d73n%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/c6b38b12-78d8-4245-a011-1f5fd04cf8b0n%40googlegroups.com >> <https://groups.google.com/d/msgid/everything-list/c6b38b12-78d8-4245-a011-1f5fd04cf8b0n%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/b0006226-f930-437b-8df8-c258118625d3n%40googlegroups.com >> <https://groups.google.com/d/msgid/everything-list/b0006226-f930-437b-8df8-c258118625d3n%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/1bc4811c-f814-4f1f-befe-533c899bc3ben%40googlegroups.com >> <https://groups.google.com/d/msgid/everything-list/1bc4811c-f814-4f1f-befe-533c899bc3ben%40googlegroups.com?utm_medium=email&utm_source=footer> >> . >> > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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