Hubble law in co-moving frame

In summary: However, in measuring velocities between two points, you can never really know the relative velocity between them.
  • #1
johne1618
371
0
We normally assume that the recession of distant galaxies is due to the expansion of the space between the galaxies and us.

In a co-moving frame the expansion of space is factored out so that all objects remain at a fixed distance away from us in cosmological time. Thus the co-moving frame is equivalent to our local inertial frame extrapolated out to large distances.

In this co-moving frame, at the present cosmological time, the Hubble law defines a velocity field that increases linearly with distance away from us according to the expression:

v(t) = H_0 r(t).

where H_0 is the present value of the Hubble parameter and t is our local time.

Can these velocities be taken to be "true" velocities relative to us such that the proper time for a galaxy, at distance r moving with velocity v, is relativistically dilated compared to our local time?

John
 
Last edited:
Space news on Phys.org
  • #2
It is fundamentally impossible to speak of a true velocity of a far-away object.
 
  • #3
Chalnoth said:
It is fundamentally impossible to speak of a true velocity of a far-away object.

The following article linked from the Wikipedia entry on the Hubble Law seems to argue that the Hubble linear velocity law:

V = H(t) L

where V is recession velocity and L is proper distance is generally true for all distances.

http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1993ApJ...403...28H&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf [Broken]

Thus this author implies that one can speak of the velocity of a far-away object.

However the author says that recession velocities can be greater than the speed of light according to this linear formula. I question that statement. I think relativistic time dilation would occur between the distant galaxy's local time and our own. This would imply that the distant galaxy cannot receed faster from us than the speed of light (or else the Lorentz factor would cease to be real valued).
 
Last edited by a moderator:
  • #4
johne1618 said:
The following article linked from the Wikipedia entry on the Hubble Law seems to argue that the Hubble linear velocity law:

V = H(t) L

where V is recession velocity and L is proper distance is generally true for all distances.

http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1993ApJ...403...28H&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf [Broken]

Thus this author implies that one can speak of the velocity of a far-away object.

However the author says that recession velocities can be greater than the speed of light according to this linear formula. I question that statement. I think relativistic time dilation would occur between the distant galaxy's local time and our own. This would imply that the distant galaxy cannot receed faster from us than the speed of light (or else the Lorentz factor would cease to be real valued).

Your problem seems to stem from adopting a special relativistic view. In cosmology, you have to apply general relativity to explain the situation. It is my understanding that in general relativity, there is no unique way of defining the velocities and distances of far away objects. This FAQ posting addresses the question and may clear things up for you:

https://www.physicsforums.com/showthread.php?t=508610 [Broken]
 
Last edited by a moderator:
  • #5
johne1618 said:
The following article linked from the Wikipedia entry on the Hubble Law seems to argue that the Hubble linear velocity law:

V = H(t) L

where V is recession velocity and L is proper distance is generally true for all distances.

http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1993ApJ...403...28H&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf [Broken]

Thus this author implies that one can speak of the velocity of a far-away object.
I chose my wording very carefully. You can certainly speak of a velocity of a far-away object. But you can't speak of the true velocity of a far-away object. The relative velocity between you and a far-away object depends entirely upon your definitions. There is no single definition of far-away velocity.

This is contrasted with measuring velocities at a single point: there you absolutely can compare velocities, and there is a unique way of doing it consistently.
 
Last edited by a moderator:

1. What is the Hubble law in co-moving frame?

The Hubble law in co-moving frame is a fundamental concept in cosmology that describes the relationship between the distance and the recession velocity of galaxies in the expanding universe. It states that the farther a galaxy is from us, the faster it appears to be moving away from us.

2. How is the Hubble law in co-moving frame related to the expansion of the universe?

The Hubble law in co-moving frame is directly related to the expansion of the universe, as it demonstrates the phenomenon of galaxies moving away from each other due to the expansion of space. This law is a key piece of evidence for the Big Bang theory.

3. What is the significance of the Hubble constant in the Hubble law in co-moving frame?

The Hubble constant, represented by the symbol H₀, is a value that represents the rate of expansion of the universe. It is a critical component of the Hubble law in co-moving frame, as it allows us to calculate the distance to a galaxy based on its observed recession velocity.

4. How does the Hubble law in co-moving frame support the idea of an expanding universe?

The Hubble law in co-moving frame provides strong support for the idea of an expanding universe, as it demonstrates that galaxies are moving away from each other at a rate that is directly proportional to their distance. This suggests that the universe is expanding uniformly in all directions.

5. Can the Hubble law in co-moving frame be used to determine the age of the universe?

Yes, the Hubble law in co-moving frame can be used, in combination with other measurements and calculations, to estimate the age of the universe. By measuring the Hubble constant and using it to calculate the expansion rate of the universe, scientists can estimate the age of the universe to be approximately 13.8 billion years old.

Similar threads

Replies
6
Views
335
Replies
50
Views
2K
Replies
6
Views
2K
Replies
9
Views
1K
  • Cosmology
3
Replies
85
Views
7K
Replies
18
Views
1K
Replies
3
Views
947
  • Cosmology
Replies
13
Views
2K
Replies
5
Views
1K
Replies
12
Views
3K
Back
Top