Length contraction in Special Relativity

[Alan Grayson]

For an observer moving toward a rod of some fixed length in a rest frame, the rod shrinks, but what happens when the observer is moving away from the rod, given that the gamma factor remains unchanged?

[Jesse Mazer]

Answer depends on whether you are talking about how the rod looks visually to them (in which case a receding rod appears contracted but an approaching rod appears elongated, see https://en.wikipedia.org/wiki/Terrell_rotation ) or if you are talking about how they assign coordinates to the rod in their own rest frame, using a system of rulers and clocks which are at rest and synchronized relative to themselves (like in the illustration at https://faraday.physics.utoronto.ca/GeneralInterest/Harrison/SpecRel/SpecRel.html#Exploring with synchronization based on the procedure described at https://en.wikipedia.org/wiki/Einstein_synchronisation ), which was what Einstein was concerned with in his original SR paper. In terms of the latter, if they measure the back end and front end of the moving rod simultaneously using their own clocks and rulers, they will always find the distance to be shrunk by the gamma factor regardless of whether it's moving towards or away from them.

On Sat, Sep 7, 2024 at 3:25 AM Alan Grayson <agrays...@gmail.com> wrote:

For an observer moving toward a rod of some fixed length in a rest frame, the rod shrinks, but what happens when the observer is moving away from the rod, given that the gamma factor remains unchanged?

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[Alan Grayson]

It's the approaching rod that is contracted, say the distance to the Andromeda galaxy as the observer is approaching it. But what if the observer is receding from Andromeda? How is the problem modeled in this situation, where the observer doesn't see the ends of some rod? Your second link might have the solution. AG

[Jesse Mazer]

Again, are you talking about visual contraction, or contraction in terms of simultaneous measurements of both ends in your reference frame? If the former the approaching rod appears elongated rather than contracted (it says so on the Terrell rotation page), if the latter then the rod is contracted by the gamma factor regardless of whether it's moving towards you or away from you (assuming that either way its velocity vector is parallel to the line between the two ends).

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[Alan Grayson]

AFAICT, the approaching rod is shortened. Possibly I don't understand your argument, but it directly contradicts my understanding of SR. AG

[Brent Meeker]

In everyday life, where all relative velocities are small compared to the speed of light, we can always assume that when light rays reach our eye simultaneously and there create the image of some object, they have also simultaneously left the object. This assumption is, of course, not justified any more, when the relative velocity between observer and object is comparable to the speed of light. Then, the light travel times have to be taken into account.

What a sphere and a cyclist would really look like at high speed is shown in Figures 2 and 3: A sphere (Figure 2a, at rest), when measured in accordance with Einstein's definition of simultaneity, is contracted into an ellipsoid (Figure 2b). But when looked at (Figure 2c) it appears perfectly circular, though rotated!



Given that already since Olaf Römer's observations of 1676 it has been known that light propagates at a finite speed, it would have been possible more than 300 years ago to conclude that objects moving at nearly the speed of light must look distorted. Surprisingly, no such conclusions have been drawn in the framework of classical physics. Figure 2d shows the classically (i. e. without length contraction) computed appearance of a fast moving sphere. It appears rotated and in addition stretched. The comparison of Figures 2c and Figure 2d reveals the effect of length contraction. It ensures (as can be proved generally) that a sphere with any speed and at any distance is always seen with a spherical outline. In light of this result one might nearly become philosophical. Fast moving objects can only be watched comfortably if the fly-by time is long enough. Their dimension must then be on the order of light seconds, i. e. they must be as large as stars. But stars because of gravitation are always spheres. The Lorentz transformation and with it our space-time structure are set up in such a way that stars always retain their shape whatever the speed of a racy spaceflight.

Figure 3 illustrates what Gamow's cyclist (Figure 3a, at rest) would really look like. Not length contracted (Figure 3b) as in Gamow's picture but essentially just rotated (Figure 3c). When looking sideways onto the cyclist moving at nearly the speed of light (the viewing direction is the same as in Figure 1), one sees his back side.

The issue of the visibility of length contraction was the starting point for investigations on the visual appearance of fast moving objects. Apart from a little noticed article by Anton Lampa [3] in 1924, the question was first examined by Roger Penrose [4] and James Terrell [5] in 1959.

Brent

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[Jesse Mazer]

I agreed the rod was shortened in terms of simultaneous measurements of both ends in the observer's rest frame, so presumably you are just talking about visual appearance here? Keep in mind that what you see visually at any given moment is a sum of events on the surface of your past light cone at that moment, events which can have occurred at different moments in your rest frame. In the case of a rod moving towards you, the light you are seeing from the back end must have been emitted at an earlier time (when the back end was further away) then the light you are seeing from the front end, assuming we measure the time both ends emitted those photons in your own rest frame.

A little numerical example: suppose the rod has a rest length of 10 light-seconds, but it is moving along your x-axis at 0.6c in your frame so it has a contracted length of 8 light-seconds in your frame. And suppose at a time coordinate of t=0 seconds, the back end of the rod was at x=100 light-seconds while the front was at x=92 light-seconds. At that moment, the back end emitted a photon which reached your position at the origin 100 seconds later, at t=100 seconds. Meanwhile at t=20 seconds, since the front of the rod is moving towards you at 0.6c it will have reached a position of x = 92 - 0.6*20 = 80 light-seconds. At that moment the front end emits a photon which naturally takes 80 seconds to reach you, so it also reaches your eyes at t=100 seconds. Thus at t=100 seconds you are seeing an image of the back end of the rod aligned with the x=100 light-seconds mark on your ruler, and an image of the front end aligned with the x=80 light-seconds mark on your ruler, meaning that visually the rod appears to be 20 light-seconds long, which is elongated compared to its rest length of 10 light-seconds.

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[John Clark]

On Sun, Sep 8, 2024 at 1:23 AM Brent Meeker <meeke...@gmail.com> wrote:

> Given that already since Olaf Römer's observations of 1676 it has been known that light propagates at a finite speed, it would have been possible more than 300 years ago to conclude that objects moving at nearly the speed of light must look distorted. Surprisingly, no such conclusions have been drawn in the framework of classical physics. 

True. They could also have concluded in 1676 that the universe must be a finite number of miles across, or created a finite number of years ago, or space itself must be expanding and so very distant stars must be moving away from us faster than the speed of light so the light from them will never reach us. I say that because if none of those three things were true then if you extended a line from you to any point on the sky it would eventually hit the center of a star, and so every point on the nighttime sky would be as bright as the sun. But that's not what we observe.

And as early as 1687 (maybe even earlier) when Isaac Newton published Principia Mathematica, all the mathematics needed to develop Special Relativity was there, all that was needed was to make the assumption that nothing can go faster than light, and that it's measured speed was always the same for all observers. I don't think Newton would've minded the idea that the universe contains a speed limit, he was after all very uncomfortable with the idea of action at a distance, but it would've probably taken a lot of convincing for him to believe that all observers would see light moving at exactly the same speed.

If I was talking to Newton I'd point out how odd it was that the concept of mass can be defined in two apparently unrelated ways, the amount of gravitational force the mass produces, and how difficult it is to change the velocity of that mass. And I'd ask him if he thought it was just a coincidence that those two things gave the same value and was the reason that heavy things and light things fell with the same speed in a gravitational field . And I'd mentioned the thought experiment about a man and a falling elevator and a man in an accelerating rocket.

As for General Relativity, I don't think anybody could've come up with that more than two or three decades before Einstein did, before that the mathematics just wasn't sufficient. 

  John K Clark    See what's on my new list at  Extropolis

jws

   

[Alan Grayson]

On Sunday, September 8, 2024 at 6:45:59 AM UTC-6 John Clark wrote:

On Sun, Sep 8, 2024 at 1:23 AM Brent Meeker <meeke...@gmail.com> wrote:

> Given that already since Olaf Römer's observations of 1676 it has been known that light propagates at a finite speed, it would have been possible more than 300 years ago to conclude that objects moving at nearly the speed of light must look distorted. Surprisingly, no such conclusions have been drawn in the framework of classical physics. 

True. They could also have concluded in 1676 that the universe must be a finite number of miles across, or created a finite number of years ago, or space itself must be expanding and so very distant stars must be moving away from us faster than the speed of light so the light from them will never reach us. I say that because if none of those three things were true then if you extended a line from you to any point on the sky it would eventually hit the center of a star, and so every point on the nighttime sky would be as bright as the sun. But that's not what we observe.

As for the unobservable part of the universe, moving away at faster than light speed, I conjecture that Inflation is the cause. So if we run the clock backward, they would eventually come back into view, showing that the whole universe is finite, and therefore cannot be flat (which implies spatially infinite). AG

I disagree with your final conclusion. Even if the universe is infinite, many stars that are directly in our line of sight, might be too faint to be seen, as is the case of nearby brown dwarf stars, which comprise 50% of stars in our relatively nearby neighborhood, but too faint to see. AG

[John Clark]

On Sun, Sep 8, 2024 at 9:13 PM Alan Grayson <agrays...@gmail.com> wrote:

>> if you extended a line from you to any point on the sky it would eventually hit the center of a star, and so every point on the nighttime sky would be as bright as the sun. But that's not what we observe.

> As for the unobservable part of the universe, moving away at faster than light speed, I conjecture that Inflation is the cause.

I'm not talking about inflation, just the normal everyday expansion of the universe, which has been known since the mid-1920s, means that stars  a finite distance away are moving away from us faster than the speed of light , and so the light from them will never reach us.  

> if we run the clock backward, they would eventually come back into view, 

Yes there are stars that we can see today that we won't be able to see tomorrow, 1 trillion years from now we won't be able to see any stars except those that are in the Milky Way because those stars are gravitationally bound together.  

> I disagree with your final conclusion. Even if the universe is infinite, many stars that are directly in our line of sight, might be too faint to be seen, as is the case of nearby brown dwarf stars, which comprise 50% of stars in our relatively nearby neighborhood, but too faint to see.

Sirius A is the brightest star in the sky but it has a companion, Sirius B, which is hotter and, because the light emitted of a hot object  is proportional to the size of the object and to the fourth power of the temperature, is much much brighter, and yet it is impossible to see unless you have a fairly large telescope. That is because although its light is very intense Sirius B is far smaller than Serious A. One has a diameter of about 1,000,000 miles while the other has a diameter of only 6800 miles, so even though it's very intense the total amount of light given off is much less than Sirius A. 

  John K Clark    See what's on my new list at  Extropolis

abc

[Jesse Mazer]

On Sun, Sep 8, 2024 at 9:13 PM Alan Grayson <agrays...@gmail.com> wrote:

On Sunday, September 8, 2024 at 6:45:59 AM UTC-6 John Clark wrote:

On Sun, Sep 8, 2024 at 1:23 AM Brent Meeker <meeke...@gmail.com> wrote:

> Given that already since Olaf Römer's observations of 1676 it has been known that light propagates at a finite speed, it would have been possible more than 300 years ago to conclude that objects moving at nearly the speed of light must look distorted. Surprisingly, no such conclusions have been drawn in the framework of classical physics. 

True. They could also have concluded in 1676 that the universe must be a finite number of miles across, or created a finite number of years ago, or space itself must be expanding and so very distant stars must be moving away from us faster than the speed of light so the light from them will never reach us. I say that because if none of those three things were true then if you extended a line from you to any point on the sky it would eventually hit the center of a star, and so every point on the nighttime sky would be as bright as the sun. But that's not what we observe.

As for the unobservable part of the universe, moving away at faster than light speed, I conjecture that Inflation is the cause. So if we run the clock backward, they would eventually come back into view, showing that the whole universe is finite, and therefore cannot be flat (which implies spatially infinite). AG

I disagree with your final conclusion. Even if the universe is infinite, many stars that are directly in our line of sight, might be too faint to be seen, as is the case of nearby brown dwarf stars, which comprise 50% of stars in our relatively nearby neighborhood, but too faint to see. AG

The idea of the sky being bright in an infinite universe which had been around forever is called Olber's paradox (see https://en.wikipedia.org/wiki/Olbers%27s_paradox ), even if all stars were brown dwarfs that would mean the sky should look as though we were enclosed in a spherical shell whose entire inner surface was at the same temperature (and emitting the same blackbody radiation) as the surface of a brown dwarf. The argument for the paradox is based on the assumption of a uniform density of stars, which means the mean number of stars at a given distance increases with the square of the distance, which exactly balances out the fact that intensity of light from any given star decreases by an inverse square law. Similarly if the Earth was enclosed in a non-reflective spherical shell with the same temperature as a brown dwarf surface, we would see the same thing regardless of whether the shell was only slightly larger than the radius of the Earth's atmosphere, or the radius was 100 billion or 100 googolplex light years (again assuming it was had been emitting the same radiation for an infinite time).

[Brent Meeker]

On 9/9/2024 12:51 PM, John Clark wrote:

On Sun, Sep 8, 2024 at 9:13 PM Alan Grayson <agrays...@gmail.com> wrote:

>> if you extended a line from you to any point on the sky it would eventually hit the center of a star, and so every point on the nighttime sky would be as bright as the sun. But that's not what we observe.

> As for the unobservable part of the universe, moving away at faster than light speed, I conjecture that Inflation is the cause.

I'm not talking about inflation, just the normal everyday expansion of the universe, which has been known since the mid-1920s, means that stars  a finite distance away are moving away from us faster than the speed of light , and so the light from them will never reach us.  

> if we run the clock backward, they would eventually come back into view, 

Yes there are stars that we can see today that we won't be able to see tomorrow, 1 trillion years from now we won't be able to see any stars except those that are in the Milky Way because those stars are gravitationally bound together. 

And not just the Milky Way but also Andromeda, with which we will have collided by then, plus several small galaxies that are part of the local group.  https://en.wikipedia.org/wiki/Local_Group

> I disagree with your final conclusion. Even if the universe is infinite, many stars that are directly in our line of sight, might be too faint to be seen, as is the case of nearby brown dwarf stars, which comprise 50% of stars in our relatively nearby neighborhood, but too faint to see.

Sirius A is the brightest star in the sky but it has a companion, Sirius B, which is hotter and, because the light emitted of a hot object  is proportional to the size of the object and to the fourth power of the temperature, is much much brighter, and yet it is impossible to see unless you have a fairly large telescope. That is because although its light is very intense Sirius B is far smaller than Serious A. One has a diameter of about 1,000,000 miles while the other has a diameter of only 6800 miles, so even though it's very intense the total amount of light given off is much less than Sirius A.

I think his idea is that there are dark bodies and so Olber's paradox is resolved by there being enough dark bodies to intercept you line-of-sight and create the dark background of space.  I don't believe it, but it could be true in a different universe.

Brent

[Alan Grayson]

On Monday, September 9, 2024 at 2:09:16 PM UTC-6 Brent Meeker wrote:

On 9/9/2024 12:51 PM, John Clark wrote:

On Sun, Sep 8, 2024 at 9:13 PM Alan Grayson <agrays...@gmail.com> wrote:

>> if you extended a line from you to any point on the sky it would eventually hit the center of a star, and so every point on the nighttime sky would be as bright as the sun. But that's not what we observe.

> As for the unobservable part of the universe, moving away at faster than light speed, I conjecture that Inflation is the cause.

I'm not talking about inflation, just the normal everyday expansion of the universe, which has been known since the mid-1920s, means that stars  a finite distance away are moving away from us faster than the speed of light , and so the light from them will never reach us.  

 

> if we run the clock backward, they would eventually come back into view, 

Yes there are stars that we can see today that we won't be able to see tomorrow, 1 trillion years from now we won't be able to see any stars except those that are in the Milky Way because those stars are gravitationally bound together. 

And not just the Milky Way but also Andromeda, with which we will have collided by then, plus several small galaxies that are part of the local group.  https://en.wikipedia.org/wiki/Local_Group

Although the rate of expansion of the universe appears to be increasing, is it increasing fast enough to cause galaxies in our local group to become part of the UNobservable universe?  Right now, the local rate of expansion is only about 70 km/s/mpsec. Can expansion alone increase that rate so much, that galaxies in our local group are receding faster than light speed, thus becoming out of sight from the perspective of the Milky Way? AG 

BTW, FWIW, I conjecture that the UNobservable universe came into being with Inflation. If so, it must have been initially finite in spatial extent, and thus can ever become flat, if flat means infinite in spatial extent. I sent this conjecture to some cosmologists who believe the global geometry of the universe is flat, but they show no interest. AG

[John Clark]

On Mon, Sep 9, 2024 at 9:54 PM Alan Grayson <agrays...@gmail.com> wrote:

> the rate of expansion of the universe appears to be increasing, 

Yes but even if the rate of expansion stopped increasing it would still be true that some galaxies we can see today we won't be able to see tomorrow. 

> is it increasing fast enough to cause galaxies in our local group to become part of the UNobservable universe?

 

We are already part of the unobservable universe to galaxies that we cannot see. None of the galaxies in the local group are moving away from us because the local group is gravitationally bound together, that is to say the mutual gravitational attraction between its members is strong enough to overcome the general expansion of the universe. But there are only about 80 galaxies in our local group, the three largest in order of size are Andromeda, the Milky Way and the Triangulum Galaxy. 77 are just dwarf galaxies.  Except for those, all the other galaxies in the universe are moving away from us.

 

 > I conjecture that the UNobservable universe came into being with Inflation. If so, it must have been initially finite in spatial extent

If the entire universe, observable plus unobservable, is infinite today then it must've been infinite even before inflation started, it must've been infinite from the first Planck Time Instant of its creation. I think most cosmologists would say that at the largest level space is curved into some unknown shape but inflation has flattened it out so much the curvature is too small to ever be detected.  

They used to say there was a strict relationship between the amount of mass/energy in the universe and its shape, if it was less than a certain figure it was positively curved like a sphere, if it was over that figured it was negatively curved like a saddle, and if it was EXACTLY at that figure it was flat; but after the discovery of Dark Energy things became a lot more complicated and they knew that simple relationship could not be true.   

By the way, there is some indication that Dark Energy is getting weaker and thus the acceleration of the universe is slowing down, but there's not enough evidence to claim a discovery and get a Nobel prize; it only has 3.9 sigma, enough to be very exciting but you need at least 5 sigma to claim a discovery. If that turns out to be true then all bets are off and we have no idea what the distant future will be like, for all we know after Dark Energy drops to zero it may turn negative and Dark Energy might start slowing down the expansion of the universe. Nobody knows.

Dark Energy May Be Weakening, Major Astrophysics Study Finds

  John K Clark    See what's on my new list at  Extropolis

ba0

 

[Alan Grayson]

On Tuesday, September 10, 2024 at 6:32:37 AM UTC-6 John Clark wrote:

On Mon, Sep 9, 2024 at 9:54 PM Alan Grayson <agrays...@gmail.com> wrote:

> the rate of expansion of the universe appears to be increasing, 

Yes but even if the rate of expansion stopped increasing it would still be true that some galaxies we can see today we won't be able to see tomorrow. 

But you haven't explained WHY that is the case. AG 

> is it increasing fast enough to cause galaxies in our local group to become part of the UNobservable universe?

 

We are already part of the unobservable universe to galaxies that we cannot see. None of the galaxies in the local group are moving away from us because the local group is gravitationally bound together, that is to say the mutual gravitational attraction between its members is strong enough to overcome the general expansion of the universe. But there are only about 80 galaxies in our local group, the three largest in order of size are Andromeda, the Milky Way and the Triangulum Galaxy. 77 are just dwarf galaxies.  Except for those, all the other galaxies in the universe are moving away from us.

 

 > I conjecture that the UNobservable universe came into being with Inflation. If so, it must have been initially finite in spatial extent

If the entire universe, observable plus unobservable, is infinite today then it must've been infinite even before inflation started, it must've been infinite from the first Planck Time Instant of its creation. I think most cosmologists would say that at the largest level space is curved into some unknown shape but inflation has flattened it out so much the curvature is too small to ever be detected.  

You're assuming what I'd like to see argued. Guth says Inflation started at t = 10^-35 seconds and the universe was around the size of a proton. I think the huge expansion created the unobserved region since space must have expanded greater than the speed of light. AG 

[Quentin Anciaux]

Le mar. 10 sept. 2024, 15:43, Alan Grayson <agrays...@gmail.com> a écrit :

On Tuesday, September 10, 2024 at 6:32:37 AM UTC-6 John Clark wrote:

On Mon, Sep 9, 2024 at 9:54 PM Alan Grayson <agrays...@gmail.com> wrote:

> the rate of expansion of the universe appears to be increasing, 

Yes but even if the rate of expansion stopped increasing it would still be true that some galaxies we can see today we won't be able to see tomorrow. 

But you haven't explained WHY that is the case. AG 

> is it increasing fast enough to cause galaxies in our local group to become part of the UNobservable universe?

 

We are already part of the unobservable universe to galaxies that we cannot see. None of the galaxies in the local group are moving away from us because the local group is gravitationally bound together, that is to say the mutual gravitational attraction between its members is strong enough to overcome the general expansion of the universe. But there are only about 80 galaxies in our local group, the three largest in order of size are Andromeda, the Milky Way and the Triangulum Galaxy. 77 are just dwarf galaxies.  Except for those, all the other galaxies in the universe are moving away from us.

 

 > I conjecture that the UNobservable universe came into being with Inflation. If so, it must have been initially finite in spatial extent

If the entire universe, observable plus unobservable, is infinite today then it must've been infinite even before inflation started, it must've been infinite from the first Planck Time Instant of its creation. I think most cosmologists would say that at the largest level space is curved into some unknown shape but inflation has flattened it out so much the curvature is too small to ever be detected.  

You're assuming what I'd like to see argued. Guth says Inflation started at t = 10^-35 seconds and the universe was around the size of a proton.

The actual observable universe was the size of a proton, for all we know it could be infinite in size at that rime, but the region of our observable universe was at that time the size of a proton... inflation maybe eternal and stopped only in our region.

I think the huge expansion created the unobserved region since space must have expanded greater than the speed of light. AG 

They used to say there was a strict relationship between the amount of mass/energy in the universe and its shape, if it was less than a certain figure it was positively curved like a sphere, if it was over that figured it was negatively curved like a saddle, and if it was EXACTLY at that figure it was flat; but after the discovery of Dark Energy things became a lot more complicated and they knew that simple relationship could not be true.   

By the way, there is some indication that Dark Energy is getting weaker and thus the acceleration of the universe is slowing down, but there's not enough evidence to claim a discovery and get a Nobel prize; it only has 3.9 sigma, enough to be very exciting but you need at least 5 sigma to claim a discovery. If that turns out to be true then all bets are off and we have no idea what the distant future will be like, for all we know after Dark Energy drops to zero it may turn negative and Dark Energy might start slowing down the expansion of the universe. Nobody knows.

Dark Energy May Be Weakening, Major Astrophysics Study Finds

  John K Clark    See what's on my new list at  Extropolis

ba0

 

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[John Clark]

On Tue, Sep 10, 2024 at 9:43 AM Alan Grayson <agrays...@gmail.com> wrote:

>> even if the rate of expansion stopped increasing it would still be true that some galaxies we can see today we won't be able to see tomorrow. 

> But you haven't explained WHY that is the case. AG 

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.

>> If the entire universe, observable plus unobservable, is infinite today then it must've been infinite even before inflation started, it must've been infinite from the first Planck Time Instant of its creation. I think most cosmologists would say that at the largest level space is curved into some unknown shape but inflation has flattened it out so much the curvature is too small to ever be detected.  

> You're assuming what I'd like to see argued.

In the above what specifically do you think I'm assuming?  

 

> Guth says Inflation started at t = 10^-35 seconds and the universe was around the size of a proton.

I'm certain Guth meant the size of the OBSERVABLE universe was the size of a proton at 10^-35 seconds. But if the entire universe, observable plus unobservable, is infinite now then it must've been infinite then. Nobody knows if the universe is finite or infinite.   

> I think the huge expansion created the unobserved region since space must have expanded greater than the speed of light. AG 

During inflation the universe expanded VASTLY faster than the speed of light, but even without inflation we still wouldn't be able to see things further than 13.8 billion light years away for obvious reasons.  

 John K Clark    See what's on my new list at  Extropolis

RRO

[Alan Grayson]

On Tuesday, September 10, 2024 at 10:41:22 AM UTC-6 John Clark wrote:

On Tue, Sep 10, 2024 at 9:43 AM Alan Grayson <agrays...@gmail.com> wrote:

>> even if the rate of expansion stopped increasing it would still be true that some galaxies we can see today we won't be able to see tomorrow. 

> But you haven't explained WHY that is the case. AG 

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. Why should galaxies now in our view, disappear? AG

>> If the entire universe, observable plus unobservable, is infinite today then it must've been infinite even before inflation started, it must've been infinite from the first Planck Time Instant of its creation. I think most cosmologists would say that at the largest level space is curved into some unknown shape but inflation has flattened it out so much the curvature is too small to ever be detected.  

> You're assuming what I'd like to see argued.

In the above what specifically do you think I'm assuming?  

You're assuming the universe today is infinite, which is what I don't believe, since it started very small and Guth doesn't say it was infinite in the past. AG 

 

> Guth says Inflation started at t = 10^-35 seconds and the universe was around the size of a proton.

I'm certain Guth meant the size of the OBSERVABLE universe was the size of a proton at 10^-35 seconds. But if the entire universe, observable plus unobservable, is infinite now then it must've been infinite then. Nobody knows if the universe is finite or infinite. 

That's what you don't know! AFAICT, Hubble's law applies to the past, not to the future, plus you don't know what Guth meant. AG   

[John Clark]

On Tue, Sep 10, 2024 at 3:57 PM Alan Grayson <agrays...@gmail.com> 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?!  

John K Clark    See what's on my new list at  Extropolis

hwt

[Alan Grayson]

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 

[Quentin Anciaux]

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 

John K Clark    See what's on my new list at  Extropolis

hwt

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[Alan Grayson]

On Tuesday, September 10, 2024 at 3:50:08 PM UTC-6 Quentin Anciaux wrote:

Le mar. 10 sept. 2024, 23:19, Alan Grayson <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 

That's the conventional wisdom but what is the physical mechanism? Hubble discovered that the universe was expanding faster in the past, than in the present.  Now its rate of expansion is much slower, allowing us to see many distant galaxies. What is the physical mechanism that will cause its present expansion rate to increase to greater than c, so distant galaxies will be beyond our field of view? AG

[Quentin Anciaux]

Le mer. 11 sept. 2024, 00:06, Alan Grayson <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 

That's the conventional wisdom but what is the physical mechanism? Hubble discovered that the universe was expanding faster in the past, than in the present.  Now its rate of expansion is much slower, allowing us to see many distant galaxies. What is the physical mechanism that will cause its present expansion rate to increase to greater than c

The expansion rate can still be the same or even slow down that my explanationis still valid,  no need for the *expansion rate* to change for current objects near the horizon to soon recess at more than c.

, so distant galaxies will be beyond our field of view? AG

John K Clark    See what's on my new list at  Extropolis

hwt

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[Alan Grayson]

On Tuesday, September 10, 2024 at 10:51:22 PM UTC-6 Quentin Anciaux wrote:

Le mer. 11 sept. 2024, 00:06, Alan Grayson <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 

That's the conventional wisdom but what is the physical mechanism? Hubble discovered that the universe was expanding faster in the past, than in the present.  Now its rate of expansion is much slower, allowing us to see many distant galaxies. What is the physical mechanism that will cause its present expansion rate to increase to greater than c

The expansion rate can still be the same or even slow down that my explanationis still valid,  no need for the *expansion rate* to change for current objects near the horizon to soon recess at more than c.

You haven't explained anything. You're just repeating what you've heard or read. A long time ago Brent explained it as a purely geometric result of the expansion, but now I tend to doubt that explanation. Specifically, if a galaxy now relatively close and visible but due to the expansion moves, say, into a region where the recessional velocity HAD BEEN some multiple of its recessional velocity when relatively near the Milky Way, why does its recessional velocity increase? AG 

[Quentin Anciaux]

Le mer. 11 sept. 2024, 07:39, Alan Grayson <agrays...@gmail.com> a écrit :

On Tuesday, September 10, 2024 at 10:51:22 PM UTC-6 Quentin Anciaux wrote:

Le mer. 11 sept. 2024, 00:06, Alan Grayson <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 

That's the conventional wisdom but what is the physical mechanism? Hubble discovered that the universe was expanding faster in the past, than in the present.  Now its rate of expansion is much slower, allowing us to see many distant galaxies. What is the physical mechanism that will cause its present expansion rate to increase to greater than c

The expansion rate can still be the same or even slow down that my explanationis still valid,  no need for the *expansion rate* to change for current objects near the horizon to soon recess at more than c.

You haven't explained anything. You're just repeating what you've heard or read. A long time ago Brent explained it as a purely geometric result of the expansion, but now I tend to doubt that explanation. Specifically, if a galaxy now relatively close and visible but due to the expansion moves, say, into a region where the recessional velocity HAD BEEN some multiple of its recessional velocity when relatively near the Milky Way, why does its recessional velocity increase? AG 

Because expansion is everywhere the same, take the inflated balloon example, any two points are receeding faster from each other as the balloon inflate at a constant rate, and again it's not the objects that are going at +c, but the space between those objects that expand.

, so distant galaxies will be beyond our field of view? AG

John K Clark    See what's on my new list at  Extropolis

hwt

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[Quentin Anciaux]

To be clearer, imagine you have points drawn on the surface of a balloon. As you inflate the balloon, the distance between two points increases, even though the points themselves aren't moving across the surface of the balloon. The farther apart the points are initially, the faster they seem to be moving away from each other as the balloon inflates. Similarly, in the universe, the farther away a galaxy is, the faster its recession velocity, but this velocity is due to the expansion of space itself, not because the galaxy is moving through space.

Quentin 

[Alan Grayson]

On Wednesday, September 11, 2024 at 12:41:56 AM UTC-6 Quentin Anciaux wrote:

To be clearer, imagine you have points drawn on the surface of a balloon. As you inflate the balloon, the distance between two points increases, even though the points themselves aren't moving across the surface of the balloon. The farther apart the points are initially, the faster they seem to be moving away from each other as the balloon inflates. Similarly, in the universe, the farther away a galaxy is, the faster its recession velocity, but this velocity is due to the expansion of space itself, not because the galaxy is moving through space.

Quentin 

 

If we imagine two separated galaxies on the equator of an expanding sphere, the distance between them increases as the sphere expands. But the light from either will reach the other, unless the distance is increasing faster than c. How does your model guarantee that the distance is increasing faster than c? AG 

[Quentin Anciaux]

Le mer. 11 sept. 2024, 09:14, Alan Grayson <agrays...@gmail.com> a écrit :

On Wednesday, September 11, 2024 at 12:41:56 AM UTC-6 Quentin Anciaux wrote:

To be clearer, imagine you have points drawn on the surface of a balloon. As you inflate the balloon, the distance between two points increases, even though the points themselves aren't moving across the surface of the balloon. The farther apart the points are initially, the faster they seem to be moving away from each other as the balloon inflates. Similarly, in the universe, the farther away a galaxy is, the faster its recession velocity, but this velocity is due to the expansion of space itself, not because the galaxy is moving through space.

Quentin 

 

If we imagine two separated galaxies on the equator of an expanding sphere, the distance between them increases as the sphere expands. But the light from either will reach the other, unless the distance is increasing faster than c. How does your model guarantee that the distance is increasing faster than c? AG 

Because the expansion is continuous  as long as expansion rate is > 0, sooner or later distant object will receed faster than c.

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/c7f0e3dc-ede1-4df6-9690-b3ddec26d0fdn%40googlegroups.com.

[Quentin Anciaux]

Chatgpt:

The reason distant objects eventually recede faster than the speed of light (c) is due to the continuous and large-scale expansion of the universe. As long as the expansion rate is positive (which it is, and even accelerating due to dark energy), the space between us and sufficiently distant objects will eventually increase faster than c. This isn't because these galaxies are moving through space faster than light, but because the space between us and them is expanding at such a rate.

In cosmology, we describe the expansion of the universe in terms of the Hubble parameter. For any galaxy at a distance greater than a certain threshold (the "Hubble distance"), the expansion of space itself causes the galaxy's recessional velocity to exceed the speed of light. This is a result of general relativity and the way space expands, and it doesn’t violate any physical laws because it’s the space itself that’s expanding, not the motion of objects through space.

So, the model guarantees that distant objects will eventually recede faster than c simply because the expansion rate is continuous and increasing with distance. The farther a galaxy is, the faster it appears to move away due to the expansion of the space between us.

Hubble's law: The farther away a galaxy is, the faster it appears to recede from us. For galaxies beyond a certain distance, this speed will exceed the speed of light.

No violation of special relativity: It’s important to note that no object is moving through space faster than light; it’s the expansion of space itself that causes this apparent superluminal recession.

Observable consequences: Once a galaxy is receding faster than the speed of light, its light can no longer reach us, which is why we eventually lose sight of galaxies beyond the observable universe.

[Alan Grayson]

On Wednesday, September 11, 2024 at 1:20:49 AM UTC-6 Quentin Anciaux wrote:

Le mer. 11 sept. 2024, 09:14, Alan Grayson <agrays...@gmail.com> a écrit :

On Wednesday, September 11, 2024 at 12:41:56 AM UTC-6 Quentin Anciaux wrote:

To be clearer, imagine you have points drawn on the surface of a balloon. As you inflate the balloon, the distance between two points increases, even though the points themselves aren't moving across the surface of the balloon. The farther apart the points are initially, the faster they seem to be moving away from each other as the balloon inflates. Similarly, in the universe, the farther away a galaxy is, the faster its recession velocity, but this velocity is due to the expansion of space itself, not because the galaxy is moving through space.

Quentin 

 

If we imagine two separated galaxies on the equator of an expanding sphere, the distance between them increases as the sphere expands. But the light from either will reach the other, unless the distance is increasing faster than c. How does your model guarantee that the distance is increasing faster than c? AG 

Because the expansion is continuous  as long as expansion rate is > 0, sooner or later distant object will receed faster than c.

If the rate of expansion is, say, fixed, the distance between galaxies keeps increasing, but the distance between them isn't increasing faster than c. It just takes light longer time to cover the separation distance. AG 

[Alan Grayson]

On Wednesday, September 11, 2024 at 1:26:13 AM UTC-6 Quentin Anciaux wrote:

Chatgpt:

The reason distant objects eventually recede faster than the speed of light (c) is due to the continuous and large-scale expansion of the universe. As long as the expansion rate is positive (which it is, and even accelerating due to dark energy), the space between us and sufficiently distant objects will eventually increase faster than c. This isn't because these galaxies are moving through space faster than light, but because the space between us and them is expanding at such a rate.

Can you prove this mathematically based on geometry? AG 

[Alan Grayson]

On Tuesday, September 10, 2024 at 3:50:08 PM UTC-6 Quentin Anciaux wrote:

Le mar. 10 sept. 2024, 23:19, Alan Grayson <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 

That's your claim, but, like I wrote, if say, the rate of expansion is fixed, the separation distance isn't increasing faster than c. It's just increasing. AG 

[Quentin Anciaux]

1. Hubble's Law

Hubble's Law provides a linear relationship between the recession velocity of a galaxy and its distance from us. The equation is:

v = H_0 \times d

Where:

 is the recession velocity of the galaxy (the rate at which it moves away from us due to the expansion of space),

 is the galaxy’s distance from us,

 is the Hubble constant (the current rate of expansion of the universe).

2. Speed of Light Threshold

To determine when a galaxy's recession velocity exceeds the speed of light , we can rearrange Hubble's Law to find the critical distance at which this occurs:

v = c \implies H_0 \times d = c

Solving for :

d = \frac{c}{H_0}

This distance, known as the Hubble distance, is the point beyond which galaxies recede from us faster than the speed of light due to the expansion of space. For a typical value of around 70 km/s/Mpc, this distance is approximately 14 billion light-years.

3. Superluminal Recession Beyond the Hubble Distance

When a galaxy is located at a distance greater than the Hubble distance , its recession velocity exceeds the speed of light. However, this does not violate special relativity because the galaxy isn't moving through space faster than light—the space between us and the galaxy is expanding.

4. General Relativity and Expanding Space

The framework of general relativity allows for the expansion of space itself, where two points in space can recede from each other faster than the speed of light without breaking the laws of physics. The light emitted by such galaxies can never reach us if the space between us continues to expand faster than the light can travel.

Conclusion:

Mathematically, based on Hubble's Law, any object at a distance greater than will recede faster than the speed of light due to the continuous expansion of the universe. This superluminal recession is a natural consequence of the geometry of expanding space and does not require any change in the local speed of light.

This shows, geometrically and mathematically, that the distance between two galaxies can increase faster than the speed of light if they are separated by more than the Hubble distance. This is guaranteed by the continuous nature of the expansion as described by Hubble’s Law.

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/efc374c4-d738-4fb1-998d-ebf238e48d95n%40googlegroups.com.

[Quentin Anciaux]

Le mer. 11 sept. 2024, 09:42, Alan Grayson <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 

That's your claim, but, like I wrote, if say, the rate of expansion is fixed, the separation distance isn't increasing faster than c. It's just increasing. AG 

Just take the balloon example, it's a perfect explanation,  any two points receed faster from each other as the balloon inflates. 

John K Clark    See what's on my new list at  Extropolis

hwt

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[Alan Grayson]

On Tuesday, September 10, 2024 at 3:50:08 PM UTC-6 Quentin Anciaux wrote:

Le mar. 10 sept. 2024, 23:19, Alan Grayson <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 

Because Inflation hugely accelerated the initial expansion, much much greater than c, what Hubble discovered is that the rate of expansion increases as we go backward in time, but is slower today. AG

[Quentin Anciaux]

Le mer. 11 sept. 2024, 09:51, Alan Grayson <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 

Because Inflation hugely accelerated the initial expansion, much much greater than c, what Hubble discovered is that the rate of expansion increases as we go backward in time, but is slower today. AG

As long as the expansion rate is > 0, sooner or later distant objects will receed faster than c, inflation is not needed for that, see the balloon analogy. 

John K Clark    See what's on my new list at  Extropolis

hwt

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[Alan Grayson]

On Wednesday, September 11, 2024 at 1:44:39 AM UTC-6 Quentin Anciaux wrote:

Le mer. 11 sept. 2024, 09:42, Alan Grayson <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 

That's your claim, but, like I wrote, if say, the rate of expansion is fixed, the separation distance isn't increasing faster than c. It's just increasing. AG 

Just take the balloon example, it's a perfect explanation,  any two points receed faster from each other as the balloon inflates. 

If the rate of expansion is fixed, the distance along some equator containing two separated galaxies increases linearly as a function of the radial distance, s. So I don't see what you claim your model proves.  AG 

[Quentin Anciaux]

Le mer. 11 sept. 2024, 09:56, Alan Grayson <agrays...@gmail.com> a écrit :

On Wednesday, September 11, 2024 at 1:44:39 AM UTC-6 Quentin Anciaux wrote:

Le mer. 11 sept. 2024, 09:42, Alan Grayson <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 

That's your claim, but, like I wrote, if say, the rate of expansion is fixed, the separation distance isn't increasing faster than c. It's just increasing. AG 

Just take the balloon example, it's a perfect explanation,  any two points receed faster from each other as the balloon inflates. 

If the rate of expansion is fixed, the distance along some equator containing two separated galaxies increases linearly as a function of the radial distance, s. So I don't see what you claim your model proves.  AG 

You're correct that, with a fixed rate of expansion, the distance between two galaxies increases linearly as a function of time. However, the key point is that recession velocity depends on the distance between the galaxies.

Using the balloon analogy: imagine two points on an inflating balloon. Even if the balloon expands at a constant rate, the farther apart the points are, the faster they move away from each other. This means the rate at which the distance between the two points increases is proportional to how far apart they are. So, as the distance between galaxies grows, their recession velocity increases.

In an expanding universe, the same thing happens: even if the expansion rate is constant, galaxies that are farther apart recede faster. At large enough distances (like beyond the Hubble radius), the recession velocity will exceed the speed of light because the space between the galaxies is expanding faster.

So, while the distance may increase linearly with time, the recession velocity still increases with distance, and at sufficiently large distances, it exceeds . This is how galaxies beyond a certain distance can recede faster than the speed of light, even with a constant rate of expansion.

John K Clark    See what's on my new list at  Extropolis

hwt

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[Alan Grayson]

On Tuesday, September 10, 2024 at 3:50:08 PM UTC-6 Quentin Anciaux wrote:

Le mar. 10 sept. 2024, 23:19, Alan Grayson <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 

Prove it, if you can. I see the separation distance increasing linearly as the radius of the sphere expands, so light can reach either galaxy, from either galaxy. AG 

[Alan Grayson]

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 <agrays...@gmail.com> 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. 

That's because the initial rate of expansion was HUGE due to inflation, and we're just seeing the velocities increasing as we look back in time. But if you're right, you should be able to prove it mathematically from the geometry. Can you that? AG 

[Quentin Anciaux]

Le mer. 11 sept. 2024, 10:08, Alan Grayson <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 

Prove it, if you can. I see the separation distance increasing linearly as the radius of the sphere expands, so light can reach either galaxy, from either galaxy. AG 

To address your point about the linear increase in distance, here's how distant galaxies can still recede faster than the speed of light, even with constant expansion:

1. Hubble’s Law:

Hubble’s Law shows that the recession velocity (v) of a galaxy depends on its distance (d) from us:

v = H0 * d

Where H0 is the expansion rate. This means that as the distance increases, the recession velocity increases proportionally.

2. Linear increase in distance:

You're right that, with a constant expansion rate, the distance between two galaxies increases linearly with time. However, because recession velocity depends on distance, the farther apart two galaxies are, the faster they recede from each other. So, even if the distance grows linearly, the recession velocity grows proportionally with distance.

3. Hubble Distance:

The key point is the Hubble distance:

d_H = c / H0

At distances greater than this, the recession velocity exceeds the speed of light (c). This doesn't violate relativity, as it's the space between galaxies that expands faster than c, not the galaxies moving through space.

4. Analogy of the balloon:

Think of two points on the surface of an inflating balloon. As the balloon expands at a constant rate, the distance between the points increases linearly. However, if the points are far enough apart, they will move away from each other faster than a closer pair of points. Similarly, in the universe, even though the expansion rate is constant, galaxies farther apart recede faster due to their increasing distance.

5. Why light can’t reach us:

For galaxies beyond the Hubble distance, the space between us expands faster than light, meaning their light can never reach us. This is why galaxies eventually move out of our observable universe.

In summary, even with a linear increase in distance due to constant expansion, the recession velocity increases with distance, and for sufficiently distant galaxies, this velocity eventually exceeds c.

John K Clark    See what's on my new list at  Extropolis

hwt

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[Brent Meeker]

On 9/11/2024 1:02 AM, Quentin Anciaux wrote:

Le mer. 11 sept. 2024, 09:56, Alan Grayson <agrays...@gmail.com> a écrit :

On Wednesday, September 11, 2024 at 1:44:39 AM UTC-6 Quentin Anciaux wrote:

Le mer. 11 sept. 2024, 09:42, Alan Grayson <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 

That's your claim, but, like I wrote, if say, the rate of expansion is fixed, the separation distance isn't increasing faster than c. It's just increasing. AG 

Just take the balloon example, it's a perfect explanation,  any two points receed faster from each other as the balloon inflates. 

If the rate of expansion is fixed, the distance along some equator containing two separated galaxies increases linearly as a function of the radial distance, s.

No, the distance between two galaxies carried by the Hubble expansion increases exponentially.

The problem, AG, is that you put no effort at all into understanding or researching your on your own.

Brent

So I don't see what you claim your model proves.  AG 

You're correct that, with a fixed rate of expansion, the distance between two galaxies increases linearly as a function of time. However, the key point is that recession velocity depends on the distance between the galaxies.

Using the balloon analogy: imagine two points on an inflating balloon. Even if the balloon expands at a constant rate, the farther apart the points are, the faster they move away from each other. This means the rate at which the distance between the two points increases is proportional to how far apart they are. So, as the distance between galaxies grows, their recession velocity increases.

In an expanding universe, the same thing happens: even if the expansion rate is constant, galaxies that are farther apart recede faster. At large enough distances (like beyond the Hubble radius), the recession velocity will exceed the speed of light because the space between the galaxies is expanding faster.

So, while the distance may increase linearly with time, the recession velocity still increases with distance, and at sufficiently large distances, it exceeds . This is how galaxies beyond a certain distance can recede faster than the speed of light, even with a constant rate of expansion.

John K Clark    See what's on my new list at  Extropolis

hwt

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[Alan Grayson]

On Wednesday, September 11, 2024 at 2:17:10 AM UTC-6 Quentin Anciaux wrote:

Le mer. 11 sept. 2024, 10:08, Alan Grayson <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 

Prove it, if you can. I see the separation distance increasing linearly as the radius of the sphere expands, so light can reach either galaxy, from either galaxy. AG 

To address your point about the linear increase in distance, here's how distant galaxies can still recede faster than the speed of light, even with constant expansion:

1. Hubble’s Law:

Hubble’s Law shows that the recession velocity (v) of a galaxy depends on its distance (d) from us:

v = H0 * d

Where H0 is the expansion rate. This means that as the distance increases, the recession velocity increases proportionally.

But that's because Hubble is looking backward in time, when recessional velocity was much greater than today, but slowing down after Inflation. AG

2. Linear increase in distance:

You're right that, with a constant expansion rate, the distance between two galaxies increases linearly with time. However, because recession velocity depends on distance, the farther apart two galaxies are, the faster they recede from each other. So, even if the distance grows linearly, the recession velocity grows proportionally with distance.

Again, that's your conclusion using Hubble's law, when looking backward in time. If separated galaxies on a sphere are separated at a rate greater than c, you should be able to prove it mathematically, based on geometry, without relying on Hubble's law. AG

3. Hubble Distance:

The key point is the Hubble distance:

d_H = c / H0

At distances greater than this, the recession velocity exceeds the speed of light (c). This doesn't violate relativity, as it's the space between galaxies that expands faster than c, not the galaxies moving through space.

Looking backward in time, you get a result which follows from an initially HUGE expansion greater than c, and then a slowing down due to gravity. But using Hubble's law leads to a questionable result going forward IMO. AG 

[Alan Grayson]

On Wednesday, September 11, 2024 at 2:31:53 AM UTC-6 Brent Meeker wrote:

On 9/11/2024 1:02 AM, Quentin Anciaux wrote:

Le mer. 11 sept. 2024, 09:56, Alan Grayson <agrays...@gmail.com> a écrit :

On Wednesday, September 11, 2024 at 1:44:39 AM UTC-6 Quentin Anciaux wrote:

Le mer. 11 sept. 2024, 09:42, Alan Grayson <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 

That's your claim, but, like I wrote, if say, the rate of expansion is fixed, the separation distance isn't increasing faster than c. It's just increasing. AG 

Just take the balloon example, it's a perfect explanation,  any two points receed faster from each other as the balloon inflates. 

If the rate of expansion is fixed, the distance along some equator containing two separated galaxies increases linearly as a function of the radial distance, s.

No, the distance between two galaxies carried by the Hubble expansion increases exponentially.

The problem, AG, is that you put no effort at all into understanding or researching your on your own.

Thanks for nothing. Have you googled "chakra"? AG

[Brent Meeker]

On 9/11/2024 1:16 AM, Quentin Anciaux wrote:

Le mer. 11 sept. 2024, 10:08, Alan Grayson <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 

Prove it, if you can. I see the separation distance increasing linearly as the radius of the sphere expands, so light can reach either galaxy, from either galaxy. AG 

To address your point about the linear increase in distance, here's how distant galaxies can still recede faster than the speed of light, even with constant expansion:

1. Hubble’s Law:

Hubble’s Law shows that the recession velocity (v) of a galaxy depends on its distance (d) from us:

v = H0 * d

Where H0 is the expansion rate. This means that as the distance increases, the recession velocity increases proportionally.

No.  Note that v is just ddot = H*d  So it's a differential equation with solution d=c*exp(Ht) where c is the distance at time zero.

Brent

2. Linear increase in distance:

You're right that, with a constant expansion rate, the distance between two galaxies increases linearly with time. However, because recession velocity depends on distance, the farther apart two galaxies are, the faster they recede from each other. So, even if the distance grows linearly, the recession velocity grows proportionally with distance.

3. Hubble Distance:

The key point is the Hubble distance:

d_H = c / H0

At distances greater than this, the recession velocity exceeds the speed of light (c). This doesn't violate relativity, as it's the space between galaxies that expands faster than c, not the galaxies moving through space.

4. Analogy of the balloon:

Think of two points on the surface of an inflating balloon. As the balloon expands at a constant rate, the distance between the points increases linearly. However, if the points are far enough apart, they will move away from each other faster than a closer pair of points. Similarly, in the universe, even though the expansion rate is constant, galaxies farther apart recede faster due to their increasing distance.

5. Why light can’t reach us:

For galaxies beyond the Hubble distance, the space between us expands faster than light, meaning their light can never reach us. This is why galaxies eventually move out of our observable universe.

In summary, even with a linear increase in distance due to constant expansion, the recession velocity increases with distance, and for sufficiently distant galaxies, this velocity eventually exceeds c.

John K Clark    See what's on my new list at  Extropolis

hwt

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[Quentin Anciaux]

Le mer. 11 sept. 2024, 10:31, Brent Meeker <meeke...@gmail.com> a écrit :

On 9/11/2024 1:02 AM, Quentin Anciaux wrote:

Le mer. 11 sept. 2024, 09:56, Alan Grayson <agrays...@gmail.com> a écrit :

On Wednesday, September 11, 2024 at 1:44:39 AM UTC-6 Quentin Anciaux wrote:

Le mer. 11 sept. 2024, 09:42, Alan Grayson <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 

That's your claim, but, like I wrote, if say, the rate of expansion is fixed, the separation distance isn't increasing faster than c. It's just increasing. AG 

Just take the balloon example, it's a perfect explanation,  any two points receed faster from each other as the balloon inflates. 

If the rate of expansion is fixed, the distance along some equator containing two separated galaxies increases linearly as a function of the radial distance, s.

No, the distance between two galaxies carried by the Hubble expansion increases exponentially.

It's because the expansion rate is going faster.... but even if it was linear, as long as it is > 0, there will be objects receeding faster than c.

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/84d50e17-bd0c-417f-b3f6-cfcb3c87741d%40gmail.com.

[Quentin Anciaux]

Imagine the universe like a balloon that you’re inflating. 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.

3. Hubble Distance:

The key point is the Hubble distance:

d_H = c / H0

At distances greater than this, the recession velocity exceeds the speed of light (c). This doesn't violate relativity, as it's the space between galaxies that expands faster than c, not the galaxies moving through space.

Looking backward in time, you get a result which follows from an initially HUGE expansion greater than c, and then a slowing down due to gravity. But using Hubble's law leads to a questionable result going forward IMO. AG 

4. Analogy of the balloon:

Think of two points on the surface of an inflating balloon. As the balloon expands at a constant rate, the distance between the points increases linearly. However, if the points are far enough apart, they will move away from each other faster than a closer pair of points. Similarly, in the universe, even though the expansion rate is constant, galaxies farther apart recede faster due to their increasing distance.

5. Why light can’t reach us:

For galaxies beyond the Hubble distance, the space between us expands faster than light, meaning their light can never reach us. This is why galaxies eventually move out of our observable universe.

In summary, even with a linear increase in distance due to constant expansion, the recession velocity increases with distance, and for sufficiently distant galaxies, this velocity eventually exceeds c.

John K Clark    See what's on my new list at  Extropolis

hwt

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[Quentin Anciaux]

Balloon analogy:

Not a coincidence, but a geometric consequence:

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 same rules in different contexts:

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). This type of expansion naturally leads to a proportional relationship between velocity and distance, as described by Hubble’s law

3. Hubble Distance:

The key point is the Hubble distance:

d_H = c / H0

At distances greater than this, the recession velocity exceeds the speed of light (c). This doesn't violate relativity, as it's the space between galaxies that expands faster than c, not the galaxies moving through space.

Looking backward in time, you get a result which follows from an initially HUGE expansion greater than c, and then a slowing down due to gravity. But using Hubble's law leads to a questionable result going forward IMO. AG 

4. Analogy of the balloon:

Think of two points on the surface of an inflating balloon. As the balloon expands at a constant rate, the distance between the points increases linearly. However, if the points are far enough apart, they will move away from each other faster than a closer pair of points. Similarly, in the universe, even though the expansion rate is constant, galaxies farther apart recede faster due to their increasing distance.

5. Why light can’t reach us:

For galaxies beyond the Hubble distance, the space between us expands faster than light, meaning their light can never reach us. This is why galaxies eventually move out of our observable universe.

In summary, even with a linear increase in distance due to constant expansion, the recession velocity increases with distance, and for sufficiently distant galaxies, this velocity eventually exceeds c.

John K Clark    See what's on my new list at  Extropolis

hwt

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[Alan Grayson]

On Tuesday, September 10, 2024 at 3:50:08 PM UTC-6 Quentin Anciaux wrote:

Le mar. 10 sept. 2024, 23:19, Alan Grayson <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 

[Quentin Anciaux]

Le mer. 11 sept. 2024, 11:23, Alan Grayson <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 <agrays...@gmail.com> 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.

John K Clark    See what's on my new list at  Extropolis

hwt

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[Alan Grayson]

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 <agrays...@gmail.com> 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. 

I conjecture that the Unobservable universe came into being with Inflation, and thus the entire universe was, and remains finite. I see no way to prove this conjecture, but it seems like a plausible scenario. AG 

 

> Hubble's law applies to the past, not to the future,

What the hell?!  

[Alan Grayson]

On Wednesday, September 11, 2024 at 3:26:01 AM UTC-6 Quentin Anciaux wrote:

Le mer. 11 sept. 2024, 11:23, Alan Grayson <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 

[Quentin Anciaux]

Le mer. 11 sept. 2024, 11:49, Alan Grayson <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 <agrays...@gmail.com> 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.

John K Clark    See what's on my new list at  Extropolis

hwt

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[Alan Grayson]

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

[Quentin Anciaux]

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

hwt

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[Quentin Anciaux]

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 

[Quentin Anciaux]

Example with points:

At t0:

. .

At t1:

. . .

At t2:

. . . . .

At t3:

. . . . . . .

At each step, more and more "space" is being added uniformly between the two initial points. This represents the expansion of space between two galaxies. Even if each added "piece" of space is infinitesimally small, over time, the total expansion will eventually exceed the speed of light because the space between the points is continuously expanding.

The key idea is that even if the space is expanding at a constant rate, the total distance between two points increases over time. The farther apart they are, the faster they recede from each other. Eventually, the distance grows so large that the rate at which they recede exceeds c.

[John Clark]

Alan Grayson <agrays...@gmail.com> wrote:

> 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?

What the hell?  

> 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 

What the hell? Quentin gave the correct answer to both of your questions: 

> "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". 

Alan, that is something they would teach you on the very first day of an astronomy 101 class if you hadn't already learned it in high school, which makes your previous two questions even more bizarre. You should have at least a little understanding of the basics of classical physics before you start worrying about the subtleties of the metric tensor in General Relativity. 

> Hubble discovered that the universe was expanding faster in the past, than in the present. 

No it did not. If you're talking about cosmic inflation, that is a hypothesis that immediately after the Big Bang for about 10^-35 seconds the universe expanded at an exponential rate; the idea seems reasonable but it has not been proven. What we know for sure is that Hubble (the man not the telescope) discovered in the 1920s that the universe is expanding, and thanks to a group of astronomers in 1997 we know that for unknown reasons the universe's expansion is accelerating. So what we know for sure is that in the past the universe was expanding *SLOWER* than it is now.  

Very recently there have been some tentative indications that the rate of change of acceleration (the official technical term for that is "jerk") of the universe is not zero but is negative. In other words the universe *might* be decelerating, but of course even if it turns out to be true that doesn't mean the expansion of the universe is slowing down, although that might happen eventually if the deceleration continues for long enough, if it continues for long enough the universe might even start to collapse, but nobody knows if it will because nobody knows what the hell Dark Energy is.

  John K Clark    See what's on my new list at  Extropolis

smt

[Alan Grayson]

On Wednesday, September 11, 2024 at 4:33:51 AM UTC-6 Quentin Anciaux wrote:

Le mer. 11 sept. 2024, 11:49, Alan Grayson <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 <agrays...@gmail.com> 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? AG

[Quentin Anciaux]

I did multiple times and gave an example with points... up to you to read it.

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

hwt

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[Alan Grayson]

On Wednesday, September 11, 2024 at 7:49:22 AM UTC-6 John Clark wrote:

Alan Grayson <agrays...@gmail.com> wrote:

> 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?

What the hell?  

> 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 

What the hell? Quentin gave the correct answer to both of your questions: 

> "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". 

Alan, that is something they would teach you on the very first day of an astronomy 101 class if you hadn't already learned it in high school, which makes your previous two questions even more bizarre. You should have at least a little understanding of the basics of classical physics before you start worrying about the subtleties of the metric tensor in General Relativity. 

That's not a proof, just a statement of what he believes. Didn't you ever learn what a mathematical proof is? AG 

[Quentin Anciaux]

Example with points:

At t0:

. .

At t1:

. . .

At t2:

. . . . .

At t3:

. . . . . . .

At each step, more and more "space" is being added uniformly between the two initial points. This represents the expansion of space between two galaxies. Even if each added "piece" of space is infinitesimally small, over time, the total expansion will eventually exceed the speed of light because the space between the points is continuously expanding.

The key idea is that even if the space is expanding at a constant rate, the total distance between two points increases over time. The farther apart they are, the faster they recede from each other. Eventually, the distance grows so large that the rate at which they recede exceeds c.

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

hwt

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[Alan Grayson]

You and Clark have no clue what a mathematical proof is. You're just stating what you believe, which might be true, but hardly qualifies as a proof of concept. AG 

[Quentin Anciaux]

🤣🤣🤣 ok figure out by yourself then... you're doing religion, not trying to understand your mistake.

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

hwt

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[Alan Grayson]

This is what Brent told me years ago and I accepted it. Now I am not so sure. In your case, just above, you seem to be conflating increasing distance between galaxies, with their recessional RATE. No matter how great is the distance, unless the recessional rate exceeds c, the galaxies remain in contact. I gave you a mathematical challenge, but you failed to see my point, or argue directly against it. BTW, I can't see your points above on my computer. AG 

[Alan Grayson]

On Wednesday, September 11, 2024 at 4:33:51 AM UTC-6 Quentin Anciaux wrote:

Le mer. 11 sept. 2024, 11:49, Alan Grayson <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 <agrays...@gmail.com> 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.

You don't seem to understand what a proof is. What you write is what you believe, which might be correct, but clearly is not a proof of concept. AG 

[Quentin Anciaux]

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/6e3debe7-8fa4-49a3-ad52-36d271103c2dn%40googlegroups.com.

[Alan Grayson]

On Wednesday, September 11, 2024 at 4:33:51 AM UTC-6 Quentin Anciaux wrote:

Le mer. 11 sept. 2024, 11:49, Alan Grayson <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 <agrays...@gmail.com> 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 <agrays...@gmail.com> 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.

But when will you PROVE it? This is just a statement of what you believe; not a mathematical proof that the recessional velocity is greater than c, which is the condition for non-contact. Clark is in the same bag. He has no clue what a proof is. I do. I have two degrees in mathematics. Did you like Brent's "proof"? Do you understand it? Listen; the fact that the distance between galaxies increases with expansion is INSUFFICIENT by itself to PROVE loss of contact. You must show that the rate of distance increases faster than light speed. You reiterate your conclusion, but haven't proven anything. AG

[Alan Grayson]

If anyone is doing religion, it's you! I am just asking for a proof that the rate of separation becomes greater than c as the expansion continues, but you just keep repeating what you believe, and consider this a proof of concept. It's NOT! AG 

[Brent Meeker]

Hubble'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.

C'mon AG put some effort into understanding.

Brent

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

hwt

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[Alan Grayson]

 The phenomenon depends only on geometry, not on Hubble's law. Can you prove it without Hubble's law? That's what I'm looking for. AG 

C'mon AG put some effort into understanding.

 Have you googled "chakra"? They're part of your body, but TOTALLY UNCONSCIOUS! AG

[Brent Meeker]

On 9/11/2024 4:24 PM, Alan Grayson wrote:

On Wednesday, September 11, 2024 at 4:44:43 PM UTC-6 Brent Meeker wrote:

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

What the hell?  Do you think things are proven from nothing.  You've apparently never proven a theorem in you life.  "The phenomena" of  maximum observable distance is a consequence of Hubble's law, which  is an empirical observation...not an axiom of Euclid.

Brent

 

C'mon AG put some effort into understanding.

 Have you googled "chakra"? They're part of your body, but TOTALLY UNCONSCIOUS! AG

Brent

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

hwt

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[Brent Meeker]

So are my toenails.

Brent

[Alan Grayson]

The proof depends on the geometry of expanding circles or spheres (far from "nothing"). AG 

[Alan Grayson]

And so is what allows you to think. AG 

 When a superior person hears of the Tao,

She diligently puts it into practice.

When an average person hears of the Tao,

he believes half of it, and doubts the other half.

When a foolish person hears of the Tao,

he laughs out loud at the very idea.

If he didn’t laugh,

it wouldn’t be the Tao.

[Alan Grayson]

You make light of what's unconscious, but take note; you're unconscious of what allows you to think, speak, and reason.  AG

[Quentin Anciaux]

Le jeu. 12 sept. 2024, 01:24, Alan Grayson <agrays...@gmail.com> a écrit :

On Wednesday, September 11, 2024 at 4:44:43 PM UTC-6 Brent Meeker wrote:

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

C'mon AG put some effort into understanding.

 Have you googled "chakra"? They're part of your body, but TOTALLY UNCONSCIOUS! AG

Brent

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

hwt

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[Quentin Anciaux]

Le jeu. 12 sept. 2024, 09:27, Alan Grayson <agrays...@gmail.com> a écrit :

But how do you know the separation distances are what you claim?

Expansion is uniform means it happens at every space point, even if at each steps what is added is infinitesimally small, conclusion follows, it will just take more "steps".

Try this. s = r  * theta, where s is arclength between two galaxies, r is the radius of some circle on which two galaxies are situated, and theta is the angle subtended by s. Then ds/dt = dr/dt * (theta) + r * d(theta)/dt.   ds/dt is the recessional velocity.  dr/dt is the rate of expansion. The terms on the RHS are both positive and increasing even if dr/dt is constant since r is increasing, while d(theta)/dt is also increasing as the galaxies separate. So eventually ds/dt will exceed the velocity of light as long as r is increasing. Any flaws in my logic? AG

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[Quentin Anciaux]

Let's go through the same reasoning but now adding only 1/10 of a point at each step.

At each step, 0.1 points are added uniformly, but not multiplied—it’s a cumulative addition. 

At t0, we start with 2 points (the two galaxies).

At each step, we add 0.1 points to the previous total, increasing the distance progressively.

Progression of Points:

t0: 2 points (galaxies themselves)

t1: 2.1 points (0.1 points added)

t2: 2.3 points (0.2 points added)

t3: 2.6 points (0.3 points added)

t4: 3.0 points (0.4 points added)

t5: 3.5 points (0.5 points added)

t6: 4.1 points (0.6 points added)

...

Steps to exceed 300 points:

1. At , we start with 2 points.

2. At each step, we add 0.1 points cumulatively to the total.

To find when the total number of points between the galaxies exceeds 300 points:

Initial points: 2

Points needed to exceed: 300

So, the difference is:

300 - 2 = 298 points

At each step, we are adding 0.1 points. Therefore, the number of steps required to reach 300 points is:

Steps = 298 / 0.1 = 2980 steps

t0: 2 points

t1: 2.1 points

t2: 2.3 points

t3: 2.6 points

t4: 3.0 points

t5: 3.5 points

...

t2980: 300 points (recession velocity exceeds speed of light)

Conclusion:

After 2980 steps, with 0.1 points added at each step, the total number of points between the galaxies will exceed 300, and their recession velocity will be greater than the speed of light.

[Alan Grayson]

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

[Quentin Anciaux]

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.

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/93ce1b6e-0393-42eb-884f-d23dfccfb01cn%40googlegroups.com.

[Quentin Anciaux]

Le jeu. 12 sept. 2024, 11:53, Alan Grayson <agrays...@gmail.com> a écrit :

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".

As explained multiple times and in the quote you made, expansion is uniform and happens at every point in space.

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 

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[Alan Grayson]

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 to increase as the universe expands, so eventually it will be > c.  AG

[Alan Grayson]

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

If the parameter r captures size of the universe, and if we assume it's expansion is constant, then dr/dt = 0 and the first term when differentiating s is zero.  So the increase of ds/dt is completely captured in the second term. AG

[Brent Meeker]

The only shortcoming is you've confused things by assuming that theta is an independent variable.  Hubble's discovery that recession speed is proportional to distance means that theta for any given galaxy is constant.

Brent

[Brent Meeker]

That's backwards.  theta represents a fixed point on the expanding balloon universe so dtheta/dt=0 and all the change is in r the scale of the universe.  Assuming expansion is constant means dr/dt=Hr where H is Hubble's observed constant.

Brent

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[Alan Grayson]

On Thursday, September 12, 2024 at 5:47:27 PM UTC-6 Brent Meeker wrote:

That's backwards.  theta represents a fixed point on the expanding balloon universe so dtheta/dt=0 and all the change is in r the scale of the universe.  Assuming expansion is constant means dr/dt=Hr where H is Hubble's observed constant.

Brent

IMO, theta represents the angular displacement along the arc connecting two galaxies, where one is assumed as fixed, the other receding. I don't see what backwards about this. When we discussed this ages ago, I recall your argument that the increasing recessional velocity was purely a geometric consequence. This continues to be my view. Consequently, there is no need to appeal to Hubble's law. AG

[Alan Grayson]

On Thursday, September 12, 2024 at 3:55:45 AM UTC-6 Quentin Anciaux wrote:

Le jeu. 12 sept. 2024, 11:53, Alan Grayson <agrays...@gmail.com> a écrit :

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".

As explained multiple times and in the quote you made, expansion is uniform and happens at every point in space.

What bothers me about your method is that you assume a geometric increase in the separation distance, when, IMO, that's the variable that must be calculated (which I did). So no matter how many times you affirm your proof as valid, I can't agree. AG 

[Brent Meeker]

You wrote, "... 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)"  The arclength is increasing but the arcangle, theta, is not.

I argued that the recession is not due to a force but simply due to the expansion of space.

Brent

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[Brent Meeker]

You didn't calculate the expansion parameter, which is the Hubble constant.  It's an observed value.

Brent

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[Alan Grayson]

On Thursday, September 12, 2024 at 11:00:21 PM UTC-6 Brent Meeker wrote:

On 9/12/2024 9:21 PM, Alan Grayson wrote:

On Thursday, September 12, 2024 at 3:55:45 AM UTC-6 Quentin Anciaux wrote:

Le jeu. 12 sept. 2024, 11:53, Alan Grayson <agrays...@gmail.com> a écrit :

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".

As explained multiple times and in the quote you made, expansion is uniform and happens at every point in space.

What bothers me about your method is that you assume a geometric increase in the separation distance, when, IMO, that's the variable that must be calculated (which I did). So no matter how many times you affirm your proof as valid, I can't agree. AG

You didn't calculate the expansion parameter, which is the Hubble constant.  It's an observed value.

Brent

Why must I do that, when I just want to show that eventually the recessional velocity exceeds c? Also, I don't see why theta is fixed, when the end of the arc defines the position of the receding galaxy. AG

[Quentin Anciaux]

Why uniform expansion implies exponential growth

Uniform expansion does not necessarily mean that the sphere grows linearly. In fact, uniform expansion implies that the proportion of growth remains constant at every moment, which is the definition of exponential growth. If the distance between the points increases proportionally to the current distance, then we obtain exponential expansion, as seen in the example you provided.

In this case, adding one extra point between each point at every step illustrates the phenomenon of exponential expansion: at every moment, the total distance increases in proportion to the existing distance.

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[Alan Grayson]

On Thursday, September 12, 2024 at 11:07:49 PM UTC-6 Alan Grayson wrote:

On Thursday, September 12, 2024 at 11:00:21 PM UTC-6 Brent Meeker wrote:

On 9/12/2024 9:21 PM, Alan Grayson wrote:

On Thursday, September 12, 2024 at 3:55:45 AM UTC-6 Quentin Anciaux wrote:

Le jeu. 12 sept. 2024, 11:53, Alan Grayson <agrays...@gmail.com> a écrit :

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".

As explained multiple times and in the quote you made, expansion is uniform and happens at every point in space.

What bothers me about your method is that you assume a geometric increase in the separation distance, when, IMO, that's the variable that must be calculated (which I did). So no matter how many times you affirm your proof as valid, I can't agree. AG

You didn't calculate the expansion parameter, which is the Hubble constant.  It's an observed value.

Brent

Why must I do that, when I just want to show that eventually the recessional velocity exceeds c? Also, I don't see why theta is fixed, when the end of the arc defines the position of the receding galaxy. AG

Now I am not sure I proved the recessional velocity is greater than c, after some time has passed. If the sphere is expanding, then the distance between any two fixed points on the sphere will increase as time passes. But that was obvious due to the expansion. What's wrong, if anything? AG

[Alan Grayson]

On Friday, September 13, 2024 at 4:06:49 AM UTC-6 Alan Grayson wrote:

On Thursday, September 12, 2024 at 11:07:49 PM UTC-6 Alan Grayson wrote:

On Thursday, September 12, 2024 at 11:00:21 PM UTC-6 Brent Meeker wrote:

On 9/12/2024 9:21 PM, Alan Grayson wrote:

On Thursday, September 12, 2024 at 3:55:45 AM UTC-6 Quentin Anciaux wrote:

Le jeu. 12 sept. 2024, 11:53, Alan Grayson <agrays...@gmail.com> a écrit :

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".

As explained multiple times and in the quote you made, expansion is uniform and happens at every point in space.

What bothers me about your method is that you assume a geometric increase in the separation distance, when, IMO, that's the variable that must be calculated (which I did). So no matter how many times you affirm your proof as valid, I can't agree. AG

You didn't calculate the expansion parameter, which is the Hubble constant.  It's an observed value.

Brent

Why must I do that, when I just want to show that eventually the recessional velocity exceeds c? Also, I don't see why theta is fixed, when the end of the arc defines the position of the receding galaxy. AG

Now I am not sure I proved the recessional velocity is greater than c, after some time has passed. If the sphere is expanding, then the distance between any two fixed points on the sphere will increase as time passes. But that was obvious due to the expansion. What's wrong, if anything? AG

Now I see the light. We've been struggling to prove that a receding galaxy will fall out of view if the universe is expanding, but all the so-called "proofs" fail, but for different reasons. What Quentin offers is not a proof. He's just repeating a result done by someone else, using mathematics, which he believes (and might be true). Brent is mistaken in his apparent belief that the proof of concept requires appeal to Hubble's law. This is also mistaken IMO since the result to be proven depends exclusively on the geometry of an expanding sphere. Finally, my proof also fails, since it's obvious that the arclength, s,  between two galaxies on an expanding  sphere, will obviously increase as the sphere expands. That is, ds/dt will obviously be positive since the arclength is increasing. IOW, a constantly increasing arclength s, assuming a uniformly expanding sphere, necessarily yields ds/dt > 0, but it does NOT demonstrate that the velocity of the receding galaxy eventually increases to be greater than c. When I have the energy, I will calculate the second time derivative of the arclength, s, hopefully to demonstrate, that for a uniformly expanding sphere, the four terms of the second derivative of s, imply a positive acceleration. This will establish that eventually the receding galaxy will pass out of view for the observer on the assumed stationary galaxy. Comments welcome. AG

[Brent Meeker]

On 9/12/2024 10:07 PM, Alan Grayson wrote:

On Thursday, September 12, 2024 at 11:00:21 PM UTC-6 Brent Meeker wrote:

On 9/12/2024 9:21 PM, Alan Grayson wrote:

On Thursday, September 12, 2024 at 3:55:45 AM UTC-6 Quentin Anciaux wrote:

Le jeu. 12 sept. 2024, 11:53, Alan Grayson <agrays...@gmail.com> a écrit :

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".

As explained multiple times and in the quote you made, expansion is uniform and happens at every point in space.

What bothers me about your method is that you assume a geometric increase in the separation distance, when, IMO, that's the variable that must be calculated (which I did). So no matter how many times you affirm your proof as valid, I can't agree. AG

You didn't calculate the expansion parameter, which is the Hubble constant.  It's an observed value.

Brent

Why must I do that, when I just want to show that eventually the recessional velocity exceeds c? Also, I don't see why theta is fixed, when the end of the arc defines the position of the receding galaxy. AG

How do you think you're going to  show that a velocity exceeds c without having a variable with the dimensions of velocity?  If you don't see why theta is fixed you don't even understand the problem.

Brent

[Alan Grayson]

I calculated ds/dt which, last I heard, is velocity. I must calculate an acceleration which is positive to show velocity eventually gets > c. Hubble's law confirms that the solution just involves geometry, it doesn't prove it. As for theta, I told you why it isn't constant. I don't recall any rebuttal from you; just your claim. AG