Hubble's Law

[Alan Grayson]

I finally was able to identify and resolve my confusion about Hubble's Law. First, let's use a geometric model to establish that the recessional velocity of distant galaxies increases as the universe expands. For convenience, assume the universe is spherically shaped and uniformly expanding, and consider two galaxies at distances of one and ten billion light years removed from our own. As r, the radius of the universe increases linearly, so will the separation distances of these remote galaxies, since the arc distances to these galaxies, if they placed e.g, on the equator, will also increase linearly. So in some unit of time, if say the rate of increase is 10%, the closer galaxy will recede by 10% of 1 billion light years, or 100 milllion light years, whereas the most distant galaxy will recede 1 billion light years in the same time duration. So clearly, in an expanding universe, more distant galaxies will recede faster than nearer galaxies.

Let's now consider the light emitted from these galaxies. The light reaching us left those galaxies 1 and 10 billion years ago respectively. If their red shifts represent their recessional velocities when the light was emitted, it would imply that in the early universe those galalaxies were receding very rapidly, the farther away in time they are, that is the more distant they are, the more rapidly they must be receding. But this contradicts the geometric model, wherein we have inferentially proven the opposite; that in early times, those galaxies were receding with decreasing velocity as their separation distances from us was decreasing. So what the hell is going on? 

The answer is that although the light emitted from those galaxies was emitted in the distant past, the expansion of the universe distorted those emissions as they propagated in our direction. That is, the red shifts observed were caused by the expansion of the universe, and therefore represents the current red shifts of those receding galaxies. 

AG

[Brent Meeker]

On 8/7/2025 10:17 PM, Alan Grayson wrote:

I finally was able to identify and resolve my confusion about Hubble's Law. First, let's use a geometric model to establish that the recessional velocity of distant galaxies increases as the universe expands. For convenience, assume the universe is spherically shaped and uniformly expanding, and consider two galaxies at distances of one and ten billion light years removed from our own. As r, the radius of the universe increases linearly, so will the separation distances of these remote galaxies, since the arc distances to these galaxies, if they placed e.g, on the equator, will also increase linearly. So in some unit of time, if say the rate of increase is 10%, the closer galaxy will recede by 10% of 1 billion light years, or 100 milllion light years, whereas the most distant galaxy will recede 1 billion light years in the same time duration. So clearly, in an expanding universe, more distant galaxies will recede faster than nearer galaxies.

Let's now consider the light emitted from these galaxies. The light reaching us left those galaxies 1 and 10 billion years ago respectively. If their red shifts represent their recessional velocities when the light was emitted, it would imply that in the early universe those galalaxies were receding very rapidly, the farther away in time they are, that is the more distant they are, the more rapidly they must be receding. 

Why not phrase this as the equally true statement, "The more distant they are the more rapidly we must be receding.", which is then consistent with your first paragraph?

Anyway, I'm glad you resolved it to your own satisfaction.

Brent

[Alan Grayson]

On Friday, August 8, 2025 at 2:10:19 PM UTC-6 Brent Meeker wrote:

On 8/7/2025 10:17 PM, Alan Grayson wrote:

I finally was able to identify and resolve my confusion about Hubble's Law. First, let's use a geometric model to establish that the recessional velocity of distant galaxies increases as the universe expands. For convenience, assume the universe is spherically shaped and uniformly expanding, and consider two galaxies at distances of one and ten billion light years removed from our own. As r, the radius of the universe increases linearly, so will the separation distances of these remote galaxies, since the arc distances to these galaxies, if they placed e.g, on the equator, will also increase linearly. So in some unit of time, if say the rate of increase is 10%, the closer galaxy will recede by 10% of 1 billion light years, or 100 milllion light years, whereas the most distant galaxy will recede 1 billion light years in the same time duration. So clearly, in an expanding universe, more distant galaxies will recede faster than nearer galaxies.

Let's now consider the light emitted from these galaxies. The light reaching us left those galaxies 1 and 10 billion years ago respectively. If their red shifts represent their recessional velocities when the light was emitted, it would imply that in the early universe those galalaxies were receding very rapidly, the farther away in time they are, that is the more distant they are, the more rapidly they must be receding. 

Why not phrase this as the equally true statement, "The more distant they are the more rapidly we must be receding.", which is then consistent with your first paragraph?

Anyway, I'm glad you resolved it to your own satisfaction.

Brent

Thanks for your kind thought, but unfortunately I am still confused. I think the geometric model is conclusive; the more distant a galaxy is, the more rapid is its recessional velocity, which is Hubble's Law. Moreover, considering the red shifts of two galaxies of different distances, from the pov of time moving forward, there is slowing of recessional velocity due to gravity (ignoring the speed up discovered in 1998). But my problem arises when I consider time flowing backward, where in remote times the recessional velocity inferred from the red shift is huge. Clark seems to be of two minds on this; he has stated that in very early times, after the manifestation of the CMB of course, the galaxies were very close and receding from each other slowly; and once recently he stated the opposite. What, IYO, is going on the very early universe wrt recessional velocities, and why? TY, AG 

[Brent Meeker]

On 8/8/2025 8:38 PM, Alan Grayson wrote:

On Friday, August 8, 2025 at 2:10:19 PM UTC-6 Brent Meeker wrote:

On 8/7/2025 10:17 PM, Alan Grayson wrote:

I finally was able to identify and resolve my confusion about Hubble's Law. First, let's use a geometric model to establish that the recessional velocity of distant galaxies increases as the universe expands. For convenience, assume the universe is spherically shaped and uniformly expanding, and consider two galaxies at distances of one and ten billion light years removed from our own. As r, the radius of the universe increases linearly, so will the separation distances of these remote galaxies, since the arc distances to these galaxies, if they placed e.g, on the equator, will also increase linearly. So in some unit of time, if say the rate of increase is 10%, the closer galaxy will recede by 10% of 1 billion light years, or 100 milllion light years, whereas the most distant galaxy will recede 1 billion light years in the same time duration. So clearly, in an expanding universe, more distant galaxies will recede faster than nearer galaxies.

Let's now consider the light emitted from these galaxies. The light reaching us left those galaxies 1 and 10 billion years ago respectively. If their red shifts represent their recessional velocities when the light was emitted, it would imply that in the early universe those galalaxies were receding very rapidly, the farther away in time they are, that is the more distant they are, the more rapidly they must be receding. 

Why not phrase this as the equally true statement, "The more distant they are the more rapidly we must be receding.", which is then consistent with your first paragraph?

Anyway, I'm glad you resolved it to your own satisfaction.

Brent

Thanks for your kind thought, but unfortunately I am still confused. I think the geometric model is conclusive; the more distant a galaxy is, the more rapid is its recessional velocity, which is Hubble's Law. Moreover, considering the red shifts of two galaxies of different distances, from the pov of time moving forward, there is slowing of recessional velocity due to gravity (ignoring the speed up discovered in 1998). But my problem arises when I consider time flowing backward, where in remote times the recessional velocity inferred from the red shift is huge. Clark seems to be of two minds on this; he has stated that in very early times, after the manifestation of the CMB of course, the galaxies were very close and receding from each other slowly; and once recently he stated the opposite. What, IYO, is going on the very early universe wrt recessional velocities, and why? TY, AG 

Which galaxies?  Galaxies that were close to each other were receding slowly.  Now that they're far from each other they are receding more rapidly.  This is a little different from Hubble's idea that obtained up until the '90s.  The early model was that the Big Bang provided an impetus and the galaxies flew apart while gradually slowing due to gravity.  So the furthest galaxies were furthest because they had been furthest and the universe had just uniformly expanded, rapidly at first but gradually slowing due to gravity.  But now it seems that the expansion has not been uniform and following an initial rapid expansion there was period of things just coasting apart followed by the current period of increasing expansion rate of space.  It's a matter of fitting models to the observations and observations have been reaching back further and further.  Keep in mind that "expansion rate of the universe" doesn't usually mean the recession rate of galaxies; it means a fitted Hubble parameter...like this:



https://science.psu.edu/news/great-space-coaster-expansion-universe-now-measured-era-dark-energy-takes-over

Brent

But this contradicts the geometric model, wherein we have inferentially proven the opposite; that in early times, those galaxies were receding with decreasing velocity as their separation distances from us was decreasing. So what the hell is going on? 

The answer is that although the light emitted from those galaxies was emitted in the distant past, the expansion of the universe distorted those emissions as they propagated in our direction. That is, the red shifts observed were caused by the expansion of the universe, and therefore represents the current red shifts of those receding galaxies. 

AG

--
You received this message because you are subscribed to the Google Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email to everything-li...@googlegroups.com.
To view this discussion visit https://groups.google.com/d/msgid/everything-list/f053be49-da62-4484-b6a0-3b8ab521ae2bn%40googlegroups.com.

[Alan Grayson]

On Friday, August 8, 2025 at 10:24:01 PM UTC-6 Brent Meeker wrote:

On 8/8/2025 8:38 PM, Alan Grayson wrote:

On Friday, August 8, 2025 at 2:10:19 PM UTC-6 Brent Meeker wrote:

On 8/7/2025 10:17 PM, Alan Grayson wrote:

I finally was able to identify and resolve my confusion about Hubble's Law. First, let's use a geometric model to establish that the recessional velocity of distant galaxies increases as the universe expands. For convenience, assume the universe is spherically shaped and uniformly expanding, and consider two galaxies at distances of one and ten billion light years removed from our own. As r, the radius of the universe increases linearly, so will the separation distances of these remote galaxies, since the arc distances to these galaxies, if they placed e.g, on the equator, will also increase linearly. So in some unit of time, if say the rate of increase is 10%, the closer galaxy will recede by 10% of 1 billion light years, or 100 milllion light years, whereas the most distant galaxy will recede 1 billion light years in the same time duration. So clearly, in an expanding universe, more distant galaxies will recede faster than nearer galaxies.

Let's now consider the light emitted from these galaxies. The light reaching us left those galaxies 1 and 10 billion years ago respectively. If their red shifts represent their recessional velocities when the light was emitted, it would imply that in the early universe those galalaxies were receding very rapidly, the farther away in time they are, that is the more distant they are, the more rapidly they must be receding. 

Why not phrase this as the equally true statement, "The more distant they are the more rapidly we must be receding.", which is then consistent with your first paragraph?

Anyway, I'm glad you resolved it to your own satisfaction.

Brent

Thanks for your kind thought, but unfortunately I am still confused. I think the geometric model is conclusive; the more distant a galaxy is, the more rapid is its recessional velocity, which is Hubble's Law. Moreover, considering the red shifts of two galaxies of different distances, from the pov of time moving forward, there is slowing of recessional velocity due to gravity (ignoring the speed up discovered in 1998). But my problem arises when I consider time flowing backward, where in remote times the recessional velocity inferred from the red shift is huge. Clark seems to be of two minds on this; he has stated that in very early times, after the manifestation of the CMB of course, the galaxies were very close and receding from each other slowly; and once recently he stated the opposite. What, IYO, is going on the very early universe wrt recessional velocities, and why? TY, AG 

Which galaxies? 

Let's consider two galaxies, one measured with a standard candle to 10 billion light years distant, the other 1 billion light years distant. The former has a very large red shift, the latter considerably less. AG

 

Galaxies that were close to each other were receding slowly. 

That's what has to be proven! And if so, why is the red shift of the more distant one so large if its recessional velocity is small? The likely explanation is that the red shift we observe today was acquired during the time the light emitted from that galaxy traveled toward us, and was red shifted due to the expansion of the universe. It can likely be shown that the amount of red shifting due to expansion is sufficient to explain what we measure. IOW, there was likely precious little red shifting of the light leaving that galaxy when it was emitted. Even though that galaxy is far from us now, and rapidly moving away from us NOW as described by Hubble's Law, this wasn't the situation 10 billion years ago. AG

 

Now that they're far from each other they are receding more rapidly.  This is a little different from Hubble's idea that obtained up until the '90s.  The early model was that the Big Bang provided an impetus and the galaxies flew apart while gradually slowing due to gravity. 

Still sounds applicable, but the initial flying apart was not rapid since the red shift we observe now, did not exist soon after the BB (explained below). AG

 

So the furthest galaxies were furthest because they had been furthest and the universe had just uniformly expanded, rapidly at first but gradually slowing due to gravity. 

Not "rapidly at first". That would imply a high red shift initially, but the expansion of the universe likely accounts for the entire red shift we observe today for the most distant galaxies. AG 

 

But now it seems that the expansion has not been uniform and following an initial rapid expansion there was period of things just coasting apart followed by the current period of increasing expansion rate of space.  It's a matter of fitting models to the observations and observations have been reaching back further and further.  Keep in mind that "expansion rate of the universe" doesn't usually mean the recession rate of galaxies; it means a fitted Hubble parameter...like this:

Offhand, I don't see how this explains or is related to my problem with this issue.  AG

r

https://science.psu.edu/news/great-space-coaster-expansion-universe-now-measured-era-dark-energy-takes-over

Brent

[Alan Grayson]

In your model of photons reddening as traveling in an expanding universe, are they modeled as waves extending in infinite directions, forward and back, or some other way, perhaps as pulses composed of different frequencies? AG  

[Alan Grayson]

On Friday, August 8, 2025 at 10:24:01 PM UTC-6 Brent Meeker wrote:

On 8/8/2025 8:38 PM, Alan Grayson wrote:

On Friday, August 8, 2025 at 2:10:19 PM UTC-6 Brent Meeker wrote:

On 8/7/2025 10:17 PM, Alan Grayson wrote:

I finally was able to identify and resolve my confusion about Hubble's Law. First, let's use a geometric model to establish that the recessional velocity of distant galaxies increases as the universe expands. For convenience, assume the universe is spherically shaped and uniformly expanding, and consider two galaxies at distances of one and ten billion light years removed from our own. As r, the radius of the universe increases linearly, so will the separation distances of these remote galaxies, since the arc distances to these galaxies, if they placed e.g, on the equator, will also increase linearly. So in some unit of time, if say the rate of increase is 10%, the closer galaxy will recede by 10% of 1 billion light years, or 100 milllion light years, whereas the most distant galaxy will recede 1 billion light years in the same time duration. So clearly, in an expanding universe, more distant galaxies will recede faster than nearer galaxies.

Let's now consider the light emitted from these galaxies. The light reaching us left those galaxies 1 and 10 billion years ago respectively. If their red shifts represent their recessional velocities when the light was emitted, it would imply that in the early universe those galalaxies were receding very rapidly, the farther away in time they are, that is the more distant they are, the more rapidly they must be receding. 

Why not phrase this as the equally true statement, "The more distant they are the more rapidly we must be receding.", which is then consistent with your first paragraph?

Anyway, I'm glad you resolved it to your own satisfaction.

Brent

Thanks for your kind thought, but unfortunately I am still confused. I think the geometric model is conclusive; the more distant a galaxy is, the more rapid is its recessional velocity, which is Hubble's Law. Moreover, considering the red shifts of two galaxies of different distances, from the pov of time moving forward, there is slowing of recessional velocity due to gravity (ignoring the speed up discovered in 1998). But my problem arises when I consider time flowing backward, where in remote times the recessional velocity inferred from the red shift is huge. Clark seems to be of two minds on this; he has stated that in very early times, after the manifestation of the CMB of course, the galaxies were very close and receding from each other slowly; and once recently he stated the opposite. What, IYO, is going on the very early universe wrt recessional velocities, and why? TY, AG 

Which galaxies?  Galaxies that were close to each other were receding slowly.  Now that they're far from each other they are receding more rapidly. 

So if we go back in time the recession is slowing. Doesn't this contradict Hubble's Law which IIUC says the opposite, that for each additional megaparsec in the distance past, the velocity of expansion increases by about 70 km/sec? AG

[Alan Grayson]

On Monday, August 11, 2025 at 3:13:08 AM UTC-6 Alan Grayson wrote:

On Friday, August 8, 2025 at 10:24:01 PM UTC-6 Brent Meeker wrote:

On 8/8/2025 8:38 PM, Alan Grayson wrote:

On Friday, August 8, 2025 at 2:10:19 PM UTC-6 Brent Meeker wrote:

On 8/7/2025 10:17 PM, Alan Grayson wrote:

I finally was able to identify and resolve my confusion about Hubble's Law. First, let's use a geometric model to establish that the recessional velocity of distant galaxies increases as the universe expands. For convenience, assume the universe is spherically shaped and uniformly expanding, and consider two galaxies at distances of one and ten billion light years removed from our own. As r, the radius of the universe increases linearly, so will the separation distances of these remote galaxies, since the arc distances to these galaxies, if they placed e.g, on the equator, will also increase linearly. So in some unit of time, if say the rate of increase is 10%, the closer galaxy will recede by 10% of 1 billion light years, or 100 milllion light years, whereas the most distant galaxy will recede 1 billion light years in the same time duration. So clearly, in an expanding universe, more distant galaxies will recede faster than nearer galaxies.

Let's now consider the light emitted from these galaxies. The light reaching us left those galaxies 1 and 10 billion years ago respectively. If their red shifts represent their recessional velocities when the light was emitted, it would imply that in the early universe those galalaxies were receding very rapidly, the farther away in time they are, that is the more distant they are, the more rapidly they must be receding. 

Why not phrase this as the equally true statement, "The more distant they are the more rapidly we must be receding.", which is then consistent with your first paragraph?

Anyway, I'm glad you resolved it to your own satisfaction.

Brent

Thanks for your kind thought, but unfortunately I am still confused. I think the geometric model is conclusive; the more distant a galaxy is, the more rapid is its recessional velocity, which is Hubble's Law. Moreover, considering the red shifts of two galaxies of different distances, from the pov of time moving forward, there is slowing of recessional velocity due to gravity (ignoring the speed up discovered in 1998). But my problem arises when I consider time flowing backward, where in remote times the recessional velocity inferred from the red shift is huge. Clark seems to be of two minds on this; he has stated that in very early times, after the manifestation of the CMB of course, the galaxies were very close and receding from each other slowly; and once recently he stated the opposite. What, IYO, is going on the very early universe wrt recessional velocities, and why? TY, AG 

Which galaxies?  Galaxies that were close to each other were receding slowly.  Now that they're far from each other they are receding more rapidly. 

So if we go back in time the recession is slowing. Doesn't this contradict Hubble's Law which IIUC says the opposite, that for each additional megaparsec in the distance past, the velocity of expansion increases by about 70 km/sec? AG

 

This is a little different from Hubble's idea that obtained up until the '90s.  The early model was that the Big Bang provided an impetus and the galaxies flew apart while gradually slowing due to gravity. 

What part of Hubble's Law remains intact? If the red shift increases as we go back in time, doesn't that still mean the universe was expanding more rapidly in the past than now? AG

 

So the furthest galaxies were furthest because they had been furthest and the universe had just uniformly expanded, rapidly at first but gradually slowing due to gravity. But now it seems that the expansion has not been uniform and following an initial rapid expansion there was period of things just coasting apart followed by the current period of increasing expansion rate of space. 

I remain confused. Clark was emphatic; in very early times the galaxies separated slowly, not rapidly, and he's using the same data as you. As far as red shift being caused by the expansion of the universe, what model of photons are you using? It seems to me that photons are point like particles, so the idea of their waves being expanded by an expanding universe is not a viable model of physical reality. AG 

[Alan Grayson]

Using the spherical geometric model for illustrative purposes, it's now clear that my habitual interpretation of Hubble's Law has been MISTAKEN; namely, that the increasing red shift of progressively more distant galaxies implies that the rate of expansion increases as we go backward in time or space. Imagine a set of galaxies at increasing distances from some fixed reference point. If the rate of expansion remains constant, it's easy to see that their red shifts increase with distance from some reference point due to increasing recessional velocity from that reference point, with a fixed rate of expansion. AG

Concerning the rate of separation of two closely located galaxies in the very early universe, whether they separate rapidly or slowly might be an undecidable question given the data available. It can possibly be done by calculating the total red shift of these galaxies due to the expansion of the universe, and compare the calculated value to the measured value of either galaxy. If they are close in value, it would establish that virtually all of the measured red shift was caused by the expansion, and therefore the initial expansion rate must have been small. Brent and Clark both claim it is small, but neither offers an argument for that conclusion. AG  

[Brent Meeker]

You need to distinguish between the expansion rate, Hubble's "constant", and the recession velocity of particular galaxies.  Stare at these two plots until you understand what they represent:





Brent

[Alan Grayson]

The first diagram shows we don't have enough data to determine the future of the universe. And the second diagram shows the belief that the universe initially expanding rapidly, then decreased, and subsequently expands, based presumably on 1998 data. Have I missed any pearls of wisdom? What exactly do you think I am missing? AG 

[Alan Grayson]

It seems to me that the Hubble parameter can be calculated by using the red shifts of progressively more distant galaxies. But if 1998 data indicates the rate of expansion of the universe is increasing, how is the Hubble parameter modified, given this information? AG