On Thursday, September 12, 2024 at 2:40:56 AM UTC-6 Quentin Anciaux wrote:
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. What was the justification for the geometric progression? I made no such assumption in my "proof". Not absolutely sure it's correct, but it seems to show the velocity of separation continues as the universe expands. We more or less already knew that. AG 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]. 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