# I Hubble's Law and Star Velocity

#### Mordred

The radius of the observable universe being roughly 46 billion light years isn't small. Think about how far into the past you are looking at when you see the surface of last scattering at z=1100. Does that sound like something SR handles ?

Edit: I should specify in this scenario as certainly the FRWL metric applies GR and SR. Example being it's light cone and worldline applications.

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#### Gege01

The radius of the observable universe being roughly 46 billion light years isn't small. Think about how far into the past you are looking at when you see the surface of last scattering at z=1100. Does that sound like something SR handles ?

Edit: I should specify in this scenario as certainly the FRWL metric applies GR and SR. Example being it's light cone and worldline applications.
If the universe is finite but unbounded, it means that the universe is smaller than the observable universe. In this case, galaxies that look far away may be illusions of neighboring galaxies, which are illusions created by light circling the universe. This hypothesis is very difficult to detect because galaxies are different at different ages, or even completely different.

#### Mordred

No it doesn't the observable portion is certainly finite as the cosmological event horizon sets an observational limit. The full universe could very well be finite or even infinite.
We simply do not know as we cannot observe or measure the entire universe. We however do know it is far larger than our observable portion.

The mirror effect you described was once studied but observational evidence of objects at extreme distances have different metalicity percentages than objects nearby. Then there is also different temperatures involved. As you approach the CMB the temperature rises.

Observational data doesn't rely solely on distance estimates but also includes thermodynamic changes due to expansion.

#### Gege01

No it doesn't the observable portion is certainly finite as the cosmological event horizon sets an observational limit. The full universe could very well be finite or even infinite.
We simply do not know as we cannot observe or measure the entire universe. We however do know it is far larger than our observable portion.
If we use the formula in this post, some data may be changed.

#### Gege01

This conclusion is based on the following assumptions:
1. Hubble's law is valid at small distances and velocities.
2. Special relativity can be satisfied in a very small space-time range.
3. There is a functional relationship between star velocity and distance:
V=V (r)

#### Mordred

We cross posted see my edits on above post in terms of other data such as metalicity and temperature changes

#### Mordred

Your conclusion is in error as your not aware of the extent of the observational data

#### Gege01

This conclusion is based on the following assumptions:
1. Hubble's law is valid at small distances and velocities.
2. Special relativity can be satisfied in a very small space-time range.
3. There is a functional relationship between star velocity and distance:
V=V (r)
Although there are other factors affecting the observed data, the above three assumptions are still valid.

#### pervect

Staff Emeritus
I would suggest that the OP read something like Ned Wright's Cosmology tutorial. A cosmology textbook would be better, but Ned Wright's tutorial would be a good attempt at start.

Specific quotes from part 2 follows, though I'd recommend starting at part 1.

Ned Wright said:
Many Distances
With the correct interpretation of the variables, the Hubble law (v = HD) is true for all values of D, even very large ones which give v > c. But one must be careful in interpreting the distance and velocity. The distance in the Hubble law must be defined so that if A and B are two distant galaxies seen by us in the same direction, and A and B are not too far from each other, then the difference in distances from us, D(A)-D(B), is the distance A would measure to B. But this measurement must be made "now" -- so A must measure the distance to B at the same proper time since the Big Bang as we see now. Thus to determine Dnow for a distant galaxy Z we would find a chain of galaxies ABC...XYZ along the path to Z, with each element of the chain close to its neighbors, and then have each galaxy in the chain measure the distance to the next galaxy at time to since the Big Bang. The distance to Z, D(us to Z), is the sum of all these subintervals:

Dnow = D(us to Z) = D(us to A) + D(A to B) + ... D(X to Y) + D(Y to Z)

And the velocity in the Hubble law is just the change of Dnow per unit time. It is close to cz for small redshifts but deviates for large ones. The space-time diagram below repeats the example from Part 1 showing how a change in point-of-view from observer A to observer B leaves the linear velocity vs. distance Hubble law unchanged:
And another brief quote:

Ned Wright said:
Note that the redshift-velocity law is not the special relativistic Doppler shift law
I won't give the details of the redshift formula at this point, but will refer the original poster (OP) to the article I quoted.

So, there are some important things to notice.

There are many notions of distance in cosmology, and they are not equivalent. Precision is needed to avoid confusion the different notions of distance. I do not belive "photometric distance" is a standard term, though it was the one the Original Poster (OP) asked about. It's not clear to me which of the several possibilities of distance in cosmology might be the same as (or close to) the OP's notion of "photometric distance", as I'm not quite sure what he means. Possibly he could mean luminosity distance.

I am not sure if Ned Wright has any discussion of "luminosity distance". Wiki has some discussion of distance measures in cosmolgoy in <<link>>., though Wiki is not necessarily a reliable source on this topic. Finding a cosmology book would be a much more reliable approach.

The doppler shift law for the "velocity" as used in the Hubble law formula is NOT the formula from special relativity, because neither the distance in Hubble's law nor the velocity in Hubble's law is the same as used in special relativity.

The origin of the difference is that special relativity is a special case of general relativity that applies when space-time is flat. Because the universe is not flat, on the large scales used in cosmololgy, one cannot use special relativity but must use general relativity instead. This is rather similar to the way that if one wants to sail across a pond, one can approximate the pond as being flat, but if one wants to sail across an ocean, one's calculations will have significant errors if one does not account for the curvature of the Earth.

I will also admit that I do not know the correct relationship between Hubble distance and luminosity distance offhand, but if that is the question that the OP would like answered, someone here or on the cosmology forums might be able to give a better answer. But it's not quite clear to me if that is really the question the OP wants to ask.

I think it'd be safest to use the observed redshift factor, z, as the "common denominator" of distances, as that's what's usually measured when one measured the "distance" to a far galaxy.

With this approach, one can find the relationship between redshift factor z and Hubble distance, and also the relationship between redshift factor z and luminosity distance, and come up with a formula that relates Lumionisty distance to Hubble distance.

#### Mordred

If you have evidence that counters a theory then that theory becomes invalidated by other evidence.

Cosmology didn't reply solely upon distance estimates. It also encompasses thermodynamic laws and utilizes those laws to validate LCDM.

#### Dale

Mentor
When we study specific problems, for example, the distance between A and B is R and r+dr, then, in the range of R to r+dr, it is a small area. Special relativity is satisfied
What is R now? Is it different from r or just inconsistent notation?

It would really help if you had a valid reference. I know you have the Chinese article that you have tried to post several times, but the language of this forum and the professional scientific community is English. If this is the only source where this concept is published then its credibility is minimal.

Without a valid reference this discussion cannot continue. @Gege01 please post a valid reference in your next post or this will be closed.

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#### Mordred

Ned Wright's tutorial is a good start point, its one I often point laymen to.

If you can afford a textbook though I recommend " Introductory to Cosmology by Matt Roose. It's an easy to learn format that doesn't require a large priori in higher mathematics.

#### Mordred

As you mentioned luminosity to distance the formula I am familiar with is $D_L=a_Or_1 (1+z^2)$ for k=0 where $r_1=f_k (z)$ if k=1 then $sin f (z)$ if k=-1 $sinh f(z)$

If I recall that was from one of Liddles textbooks

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#### Gege01

What is R now? Is it different from r or just inconsistent notation?

It would really help if you had a valid reference. I know you have the Chinese article that you have tried to post several times, but the language of this forum and the professional scientific community is English. If this is the only source where this concept is published then its credibility is minimal.

Without a valid reference this discussion cannot continue. @Gege01 please post a valid reference in your next post or this will be closed.
I'm sorry! R is r. I made a mistake

#### Gege01

As you mentioned luminosity to distance the formula I am familiar with is $D_L=a_Or_1 (1+z^2)$ for k=0 where $r_1=f_k (z)$ if k=1 then $sin f (z)$ if k=-1 $sinh f(z)$

If I recall that was from one of Liddles textbooks

#### Dale

Mentor
Since there is still no reference, this thread is closed.

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