On the relativity of red shift

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wolram
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arXiv:1605.08634 (cross-list from physics.pop-ph) [pdf]
On The Relativity of Redshifts: Does Space Really "Expand"?
Geraint F. Lewis
Comments: 6 pages, 5 figures, appeared in Australian Physics
Journal-ref: Australian Physics (2016), 53(3), 95-100
Subjects: Popular Physics (physics.pop-ph); Cosmology and Nongalactic Astrophysics (astro-ph.CO)

In classes on cosmology, students are often told that photons stretch as space expands, but just how physical is this picture? Does space really expand? In this article, we explore the notion of the redshift of light with Einstein's general theory of relativity, showing that the core underpinning principles reveal that redshifts are both simpler and more complex than you might naively think. This has significant implications for the observed redshifting of photons as they travel across the universe, often refereed to as the cosmological redshift, and for the idea of expanding space


There has been a lot of posts about the expansion of or stretching of space
i thought this article may clear up some of the confusion.
 

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  • #2
Orodruin
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I largely agree with the author. Although I am not sure that there is enough time in the typical introductory cosmology course to introduce local normal coordinates instead of the FRW ones and seeing that locally the co-moving observers are in fact moving apart with a velocity ##Hd##. Without showing the maths, I would feel that I was hiding something from the students. It is a good point worth considering though.
 
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PeterDonis
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I am not sure that there is enough time in the typical introductory cosmology course to introduce local normal coordinates
I'm not sure that's actually necessary to get across the basic idea of the article. The basic idea is that a photon's energy/frequency is not a property of the photon alone; it's a property of the photon plus the measuring device. Different measuring devices in different states of motion will measure the same photon to have different energies/frequencies. In the cosmological case, the usual "redshift" of photons that is attributed to "space expanding" assumes that the emitter and receiver are both comoving; so it's not just a property of the photons, or of "space"; it's a property of photons being exchanged between particular observers.

The more detailed math behind this, of course, would require more time, since you would need to introduce the concepts of 4-vectors, spacetime geometry, and parallel transport. But the basic idea, it seems to me, could be given in more or less non-mathematical terms, as I just did above.
 
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Orodruin
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I'm not sure that's actually necessary to get across the basic idea of the article. The basic idea is that a photon's energy/frequency is not a property of the photon alone; it's a property of the photon plus the measuring device.
I thought this was clear already from the SR treatment. Just changing frame it is still the same photon with a frame dependent wavelength. The problem only arises when we start talking about expanding space and implicitly talk about cosmological redshift with an underlying assumption of comoving observers. If you do not have comoving observers, it should be clear from SR that you get a different wavelength. The same should go for stationary observers and gravitational redshift.
 
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PeterDonis
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I thought this was clear already from the SR treatment.
It is as long as we're within the confines of a single local inertial frame. But we can't just extend the SR treatment to cover, for example, a photon emitted from a galaxy a billion light years away and observed on Earth; a single local inertial frame doesn't cover that entire process. So just saying "it's a Doppler shift", which is what the SR treatment essentially says, isn't sufficient, IMO. We have to justify applying the "frame dependent wavelength" idea (or, as I put it, the "photon plus measuring device" idea) in a regime where the effects of spacetime curvature are not negligible. The SR treatment can't justify that on its own.
 
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Orodruin
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It is as long as we're within the confines of a single local inertial frame.
On the contrary, the photon is observed locally. And the SR treatment in terms of the product of the wave 4-vector with the 4-velocity of the observer generalises just as you would expect.

So just saying "it's a Doppler shift", which is what the SR treatment essentially says, isn't sufficient, IMO.
This might be where we differ. I do not teach SR redshift in this fashion. At least not in my course on introductory master level. I would expect students taking intro GR/cosmology to be aware of this.
 
  • #7
PeterDonis
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the photon is observed locally.
Yes, but in order to know what its observed frequency will be given a local observer's 4-velocity, you need to know what the photon's 4-momentum is. And in order to know that, you need to parallel transport the photon's 4-momentum along its worldline from the event of emission. You can't model that process in a curved spacetime using SR in a single local inertial frame.

I do not teach SR redshift in this fashion.
I agree that redshift can be taught using the dot product of the observer's 4-velocity and the photon's 4-momentum, in the context of SR, rather than just saying "it's a Doppler shift". But that still doesn't tell you what the photon's 4-momentum is to begin with, as above. So a better way of phrasing my objection would be that just saying "it's the dot product of the observer's 4-velocity and the photon's 4-momentum, evaluated locally", which is what the SR treatment essentially says, is not sufficient, IMO.
 
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Orodruin
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And in order to know that, you need to parallel transport the photon's 4-momentum along its worldline from the event of emission. You can't model that process in a curved spacetime using SR in a single local inertial frame.
I agree, but that can equally well be inferred with the comoving observers. The article's idea, as you said, was to underline that the frequency is observer dependent and this is already a thing in SR and should therefore be a thing for a local observation in GR too.

which is what the SR treatment essentially says, is not sufficient, IMO.
I am not trying to argue that it is. You also need the results of light rays being null geodesics with the wave vector as its tangent. One such solution is a plane wave in Minkowski space, for which the wave vector is constant and therefore independent of the event at which it is onserved. If you find yourself in a curved space-time you have to take that into account properly.
 
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The article's idea, as you said, was to underline that the frequency is observer dependent and this is already a thing in SR and should therefore be a thing for a local observation in GR too.
...
You also need the results of light rays being null geodesics with the wave vector as its tangent. One such solution is a plane wave in Minkowski space, for which the wave vector is constant and therefore independent of the event at which it is observed. If you find yourself in a curved space-time you have to take that into account properly.
Interesting comments Orodruin, on a very interesting article.

If the doppler shift is due to the movement of the source (at the photons emission point) with respect to the observer and the gravitational shift is due to the emitted photon traveling up or down a gravity well during transit then does the cosmological shift just stretch the combined result of the previous 2 shift components?

I agree that any combined SR and GR components would have to be closely aligned (frame wise) for any combination to be accounted for properly but does this mean that the cosmological shift is just the result of a close alignment between SR and GR or is it something else on top of the result of this alignment (i.e. expansion of doppler and gravitational shifts or just doppler and gravitational shifts alone)?

Also, how are the 3 components of doppler shift, gravitational shift and cosmological shift broken down in different situations (intergalactic and intragalactic) considering that we only observe the frequency shift in our local frame?
 
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Orodruin
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I think you have misinterpreted the entire discussion. The point is that there are not three different mechanisms of redshift. They are all manifestations of the same physics, which necessarily includes information not only of the photon but also of the observer.
 
  • #11
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I think you have misinterpreted the entire discussion. The point is that there are not three different mechanisms of redshift. They are all manifestations of the same physics, which necessarily includes information not only of the photon but also of the observer.
I was just wondering if there was any way to account for all 3 different manifestations to reduce any incompleteness to a minimum.

Some circumstances would be expected to be different from others and you seemed to be referring to gravitational and doppler shift (intragalactic) while intergalactic observations would involve doppler and cosmological shift with minimal gravitational shift (in a flat universe). In both these cases the observer is us.

http://arxiv.org/abs/astro-ph/9905116v4
Redshift is almost always determined with respect to us (or the frame centered on us but stationary with respect to the microwave background), but it is possible to define the redshift z12 between objects 1 and 2, both of which are cosmologically redshifted relative to us:
 
  • #12
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So I understand how relativity determines what we see but I'm confused about the question, is space expanding? Surely the question is, does the expansion explain redshifting? or is the reason that Brooklyn isn't expanding, not that it is gravitationally bound, but because expansion is just a pedagogical picture. If it's the latter, then I'd appreciate an explanation or useful link.
Thanks
 

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