I just gave you a full proof that as long as the expansion is uniform and expansion rate > 0, then it follows objects will sooner or later recess from each other at speed > c.
Le jeu. 12 sept. 2024, 10:07, Alan Grayson <[email protected]> a écrit : > > > On Thursday, September 12, 2024 at 12:31:21 AM UTC-6 Quentin Anciaux wrote: > > Le jeu. 12 sept. 2024, 01:24, Alan Grayson <[email protected]> a écrit : > > On Wednesday, September 11, 2024 at 4:44:43 PM UTC-6 Brent Meeker wrote: > > > > > On 9/11/2024 9:04 AM, Alan Grayson wrote: > > 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. > > > This is what you keep claiming, but have yet to offer a *mathematical > proof*. Try this; two galaxies on the equator of a sphere, with a > separation distance s, and the equator expanding as a function of its > radius r to simulate expansion. The recessional velocity is ds/dt, which > depends on dr/dt. If dr/dt is constant, so will be ds/dt, and the > recessional velocity is constant and cannot reach c or greater. What is > wrong with this proof, falsifying Hubble's law and your model? AGHHubble's > law says the recession velocity is proportional to the distance so ds/dt=Hs > whose solution is s=c*exp(Ht) So s is not constant and r is not constant. > What is constant is H=(1/s)*ds/dt. > > > *The phenomenon depends only on geometry, not on Hubble's law. Can you > prove it without Hubble's law? AG * > > > To explain this and prove the geometric progression using the expansion > analogy: > > Step-by-step proof of geometric progression: > > 1. Assumptions: > > Let’s assume each step adds points geometrically, meaning the number of > points between the two galaxies increases by a fixed ratio each time. > > Let’s also assume the speed of light corresponds to 300 points. This means > if the distance between the galaxies exceeds 300 points, their recession > velocity will be greater than the speed of light (c). > > > > 2. Geometric Progression Setup: In geometric progression, each new step > adds points at an increasing rate. For simplicity, assume that at each time > step, the number of points doubles. If we start with 2 points (the > galaxies), here’s how the number of points between them progresses: > > t0: 2 points (the galaxies themselves) > t1: 3 points (1 point between the galaxies) > t2: 5 points (3 points between the galaxies) > t3: 9 points (7 points between the galaxies) > t4: 17 points (15 points between the galaxies) > t5: 33 points (31 points between the galaxies) > t6: 65 points (63 points between the galaxies) > t7: 129 points (127 points between the galaxies) > t8: 257 points (255 points between the galaxies) > t9: 513 points (511 points between the galaxies) > > The number of points grows geometrically, roughly doubling at each step. > > > 3. Determine when recession velocity exceeds : We are assuming that when > the number of points between the galaxies exceeds 300 points, their > recession velocity will exceed the speed of light. > > From the progression: > > t8: 257 points (255 points between the galaxies) > t9: 513 points (511 points between the galaxies) > > At t8, the galaxies are separated by 255 points, which is still below the > speed of light. At t9, the number of points between the galaxies is 511, > which exceeds 300. Therefore, at t9, the recession velocity will exceed the > speed of light. > > > 4. Conclusion: Using this geometric progression model, we see that by t9, > the two galaxies will be receding faster than the speed of light because > the number of points (representing space) between them exceeds 300, the > threshold set for the speed of light > > > *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* > > > 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. > > * 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/d056136a-41f7-41c6-9c79-18d648ecfd4an%40googlegroups.com > <https://groups.google.com/d/msgid/everything-list/d056136a-41f7-41c6-9c79-18d648ecfd4an%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/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/93ce1b6e-0393-42eb-884f-d23dfccfb01cn%40googlegroups.com > <https://groups.google.com/d/msgid/everything-list/93ce1b6e-0393-42eb-884f-d23dfccfb01cn%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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