Relativistic Doppler and Hubble's law

In summary, Anna V is correct. The mechanism for the cosmological redshift is not the same as the above relativistic shift. There is a transverse doppler shift even in this case, caused by time dilation of the source.
  • #1
giulio_hep
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I have a quick question about the Special Relativity. Non-relativistically, we expect no doppler shift in the wavelength of the emitted light if the source is moving at right angles to the line of sight to the observer. However there is a transverse doppler shift even in this case, caused by time dilation of the source. Now, correct me if I'm wrong, but the mechanism for the cosmological redshift is not the same as the above relativistic shift. I'm confused because I often find the two associated together, like in this answer of anna v. On the opposite edge, I would reply that relativistic doppler effect is a more simple subject of a PHY206 (special relativity) while cosmological redshifts are discussed in PHY314 (relativity and cosmology) and PHY306 (introduction to cosmology). I think that the analogy between the Hubble expansion and a simple recession would be justified only if the scale factor would be increasing linearly: is it correct?
 
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  • #2
giulio_hep said:
the mechanism for the cosmological redshift is not the same as the above relativistic shift
Correct.
I don't see the transverse Doppler effect mentioned in the linked page.

For small distances, it is possible to consider the objects as moving away in space instead of an expansion of space. For large distances this does not work any more, at least not with "realistic" speed values (there is always some specific speed that gives the correct redshift of course).
 
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  • #3
It is certainly true that red shifts of distant objects in a realistic model of the universe do not correspond to any model using special relativity (in flat spacetime). However, it is completely up to interpretation whether or nor cosmological redshifts are Doppler generalized to curved spacetime versus something else altogether (e.g. expanding space).

To quickly justify that cosmological redshift can be treated as Doppler in curved spacetime, note that the correct prediction, in all cases, arises by parallel transporting the emitter 4-velocity along the light path to the receiver, and then using pure SR Doppler in a local frame at the receiver. Curvature is involved both in determining what the light path is, and what the behavior of parallel transport is. However, while curvature is involved in this formulation, nothing about expansion of space or recession rate is involved.
 
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  • #4
mfb said:
Correct.
I don't see the transverse Doppler effect mentioned in the linked page.

For small distances, it is possible to consider the objects as moving away in space instead of an expansion of space. For large distances this does not work any more, at least not with "realistic" speed values (there is always some specific speed that gives the correct redshift of course).
Another link/example here
 
  • #5
giulio_hep said:
Now, correct me if I'm wrong, but the mechanism for the cosmological redshift is not the same as the above relativistic shift. I'm confused because I often find the two associated together, like in this answer of anna v.

Anna V's answer is incorrect. Note that the question is marked as a duplicate. The one that it duplicates has a correct answer by Ted Bunn, who is a professional relativist. PF also has a FAQ that answers the question about energy conservation posed in the physics.SE thread that you linked: https://www.physicsforums.com/threads/what-is-the-total-mass-energy-of-the-universe.506985/ .

It is neither true nor false that cosmological Doppler shifts are the same phenomenon as special-relativistic Doppler shifts. To test whether they were the same, we would need to be able to define, in an unambiguous way, the velocity vector of galaxy A relative to cosmologically distant galaxy B. If we could do that, we could then plug that velocity vector into the equation for the special-relativistic Doppler shift and see whether it agreed with observation. But GR doesn't provide any unambiguous way of defining the relative velocities of distant objects.
 
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  • #6
PAllen said:
It is certainly true that red shifts of distant objects in a realistic model of the universe do not correspond to any model using special relativity (in flat spacetime). However, it is completely up to interpretation whether or nor cosmological redshifts are Doppler generalized to curved spacetime versus something else altogether (e.g. expanding space).

To quickly justify that cosmological redshift can be treated as Doppler in curved spacetime, note that the correct prediction, in all cases, arises by parallel transporting the emitter 4-velocity along the light path to the receiver, and then using pure SR Doppler in a local frame at the receiver. Curvature is involved both in determining what the light path is, and what the behavior of parallel transport is. However, while curvature is involved in this formulation, nothing about expansion of space or recession rate is involved.
They claim that the resulting relation between the transported velocity and the redshift of arriving photons is not given by a relativistic Doppler formula
 
  • #7
  • #8
giulio_hep said:
They claim that the resulting relation between the transported velocity and the redshift of arriving photons is not given by a relativistic Doppler formula

Note the following from the abstract: "Last but not least, we show that the so-called proper recession velocities of galaxies, commonly used in cosmology, are in fact radial components of the galaxies’ four-velocity vectors. As such, they can indeed attain superluminal values, but should not be regarded as real velocities."

This confirms what we told you in #3 and #5, that there is no yes/no answer to your question.
 
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  • #9
bcrowell said:
Note the following from the abstract: "Last but not least, we show that the so-called proper recession velocities of galaxies, commonly used in cosmology, are in fact radial components of the galaxies’ four-velocity vectors. As such, they can indeed attain superluminal values, but should not be regarded as real velocities."

This confirms what we told you in #3 and #5, that there is no yes/no answer to your question.
Ok, fair enough.
 
  • #10
giulio_hep said:
They claim that the resulting relation between the transported velocity and the redshift of arriving photons is not given by a relativistic Doppler formula
They choose not to transport it on light path, but instead on a spatial hypersurface of their choosing. That is why I used the word 'could be interpreted'. I don't need to add anything to Bcrowell's #5. This paper together with Bunn's shows the fundamental ambiguity of both velocity and distance of 'far away' objects in GR.
 
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  • #11
bcrowell said:
Note the following from the abstract: "Last but not least, we show that the so-called proper recession velocities of galaxies, commonly used in cosmology, are in fact radial components of the galaxies’ four-velocity vectors. As such, they can indeed attain superluminal values, but should not be regarded as real velocities."

This confirms what we told you in #3 and #5, that there is no yes/no answer to your question.

Interesting and relates to a point I"ve made recently. Spatial component of a 4-velocity is (in some local frame) gamma(v)*v , where v is the speed of the 4-velocity in that local frame. That is exactly a celerity. If you divide by the time component in any such local basis, you get the relative velocity. Of course, more simply, parallel transport always preserved the timelike character of 4-velocity, so you always end up with with (totally ambiguous) relative velocity (<c).
 
  • #12
Parallel transport, shape space, holonomy... The energy–momentum method is applied to dynamic problems in many fields, including chemistry, quantum and classical physics, and engineering. If we want to find the shortest path with respect to a metric induced by the function we wish to minimize, it turns out that the solution is closely related to Wong’s equations that describe the motion of a colored particle in a Yang–Mills field... (an old problematic discussion with a reference to parallel transport in relativistic string theory here )

Since special relativity and quantum mechanics were combined, we know that, because of the equivalence of mass and energy (E2 = p2 + m2) and the uncertainty principle (∆E∆t ∼ ∆p∆x ∼ h), the number of particles is not fixed but subject to quantum fluctuations.
Also from http://math.ucr.edu/home/baez/physics/Relativity/GR/hubble.html
The Doppler explanation fails for very large redshifts, for then we must consider how Hubble's "constant" changes over the course of the journey.
And from http://alemanow.narod.ru/hubbles.htm
After putting Hubble's law into its quantum form vn = nH0 it becomes apparent that the cosmological redshift of the photon's frequency has a quantum nature ... If the frequency decreases by the Hubble constant with each new period, then such process presents wave energy dissipation and not the Doppler effect.
 
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Related to Relativistic Doppler and Hubble's law

1. What is the Relativistic Doppler Effect?

The Relativistic Doppler Effect is a phenomenon in which the observed frequency of electromagnetic radiation (such as light) is shifted due to the relative motion between the source of the radiation and the observer. This effect is based on the principles of special relativity and is different from the classical Doppler Effect.

2. How does the Relativistic Doppler Effect affect the color of light?

The Relativistic Doppler Effect can cause a shift in the wavelength of light, which in turn affects its perceived color. If the source of light is moving away from the observer, the wavelength is stretched and the light appears more red (known as redshift). If the source is moving towards the observer, the wavelength is compressed and the light appears more blue (known as blueshift).

3. What is Hubble's law?

Hubble's law states that the farther a galaxy is from Earth, the faster it appears to be moving away from us. This is due to the expansion of the universe, which causes space between galaxies to increase over time. The rate of this expansion is known as the Hubble constant.

4. How is Hubble's law related to the Relativistic Doppler Effect?

Hubble's law is related to the Relativistic Doppler Effect because it explains the redshift of light from distant galaxies. As these galaxies move away from Earth, their light is stretched by the expansion of space, causing a redshift. This redshift is directly proportional to the distance of the galaxy from Earth, as described by Hubble's law.

5. What evidence supports the validity of Relativistic Doppler and Hubble's law?

There is a wealth of evidence that supports the validity of Relativistic Doppler and Hubble's law. This includes observations of the redshift of light from distant galaxies, measurements of the Hubble constant, and the confirmation of predictions made by these theories in various experiments and observations. Additionally, the principles of special relativity on which Relativistic Doppler is based have been extensively tested and validated through experiments.

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