Unraveling Redshift and Blueshift Confusion in Relation to Relativity

[mysearch]

I am trying to clarify a number points regarding both redshift and blueshift in the context of relativity. Standard texts seem to list four possible causes, although it seems that some of these explanations overlap each other.

A. Doppler Redshift caused by relative velocity.
B. Gravitational Redshift caused by a change in frequency.
C. Time Dilation Redshift is caused by relative time.
D. Cosmological Redshift caused by the expansion of space.

I have numbered a list of assumptions, which I accept may be wrong, but it is hoped that some of the members of the physics forum might be able to clarify some of the points. Specific questions associated with these assumptions are highlighted:

1. In vacuum, light as an electromagnetic wave is generally assumed to travel at a constant speed [c]. This speed can be related to frequency [f] and wavelength $$\lambda$$ by the equation $$c=f\lambda$$.

2. The energy of a light wave is linked to the Planck equation E=hf.

3. As a wave, energy defines the frequency. If [c] is constant, then the wavelength is defined by $$\lambda=c/f$$. However, in a wider context, it might be said that the media defines the propagation speed, which for a vacuum might be interpreted as permittivity and permeability.

4. The introduction of quantum theory suggests that light travels in discrete quanta, i.e. photons. If the Planck and Einstein equations are linked, i.e. $$E=mc^2=hf$$, then photons have an analogous particle nature and a kinetic mass, although no rest mass.

5. However, there appears to be no generally accepted description of the structure of a photon, either as a wave or particle.

The first question is simply whether these general assumptions are OK?
The next set of assumptions are linked to the effects associated with gravity, specifically in connection to the Schwarzschild metric and black holes event horizons:

6. In any frame of reference time passes at a rate of 1 second per second.

7. However, the observed time from another frame of reference can differ due to the effects of gravity and velocity.

8. If two twins (A) & (B) are initially collocated, but twin (B) then starts to approach an event horizon of a black hole, (A) observes time in (B) running ever slower.

Note: In order to initially restrict the issues to gravity, assume that the velocity of (B) is always non-relativistic and therefore has no appreciable effect on spacetime.

9. The time dilation is `real` in the sense that if (B) returns to (A) then (B) will be physically younger than (A).

10. If time in (B) runs slower than (A), any photons emitted from (B) and received at (A) must have reduced energy based on the Planck equation E=hf, because frequency [f] is a function of time.

11. Photons from (B) received at (A) will be increasingly redshifted.

Again, are these assumptions OK?
Does this effect explain why the in-falling twin will disappears, from the perspective of (A), before reaching the event horizon?

If we assume that twin (B) stops along the way, there is no relative velocity between (A) and (B). Therefore, any redshift has to be explained by either gravitational redshift or time dilation. In the context described, time dilation appeared to be a factor, although we have not mention anything about the relative effects on space, as yet. The next set of assumption switch the frame of reference to (B), i.e. twin (B) looking back out at twin (A):

12. If time in (B) runs slower than (A), then time in (A) is running faster than (B).

13. Therefore, photons from (A) received at (B) should be increasingly blueshifted by the arguments of time dilation alone.

14. While the previous redshift scenario ultimately leads to photons having no effective energy, the reverse scenario seems more problematic in that it implies that photons would be received at (B) from (A) with ever increasing energy.

15. However, if the radial distance from (B) to (A) effectively expands due to the relativistic effects of gravity, the wavelength of a photon $$\lambda$$ would effectively increase during propagation from (A) to (B).

16. Based on the assumptions in [1] and [2], any change in wavelength during propagation would seem to suggest that frequency would also change on route, if [c] remains constant.

17. So while the photon is sourced at a higher frequency, due to the relative time rates at (A) and (B), space expansion along the way compensates by stretching the wavelength and lowering the frequency. If so, no blue shift would occur from (A) to (B) and the ever-increasing energy issue is avoided.

If gravitational redshift differs from time-dilation redshift is it because it affects both space and time?

It is realized that the space expansion argument in [17] would also have to be applicable to [10, 11], albeit in reverse, thereby negating the expected redshift. I realize these assumptions probably contradict theory and observation, but would like to better understand why. The final sets of bullets essentially try to summarise the outcome of the previous assumptions:

19. Photons emitted at (B) have a lower frequency due to time dilation.

20. At (A) the tick of the clock is faster than (B)
21. Therefore, photons emitted at (A) have a higher frequency.

22. Photon wavelength increases when propagating from (A) to (B).
23. Photon wavelength decreases when propagating from (B) to (A).

24. (A) to (B)
25. Starts with higher frequency due to faster clocks at (A)
26. Wavelength increases due to space expansion from (A) to (B)
27. These effects cancel, hence no blueshift.

28. (B) to (A)
29. Starts with lower frequency due to slower clocks at (B)
30. Wavelength decreases due to space contracting from (B) to (A)
31. These effects would cancel, hence no redshift.

Would appreciate any clarification offered on any of these assumptions.
Thanks

 

[MeJennifer]

The doppler effect and the effects of special and general relativity are not due to any change in the property of the photon but it is entirely due to the condition of the absorber. In other words what many call a redshifted photon is really a blueshifted measuring apparatus.

It's like drinking a lukewarm glass of water when it is freezing cold outside, it feels warmer than it actually is.

 

[mysearch]

Request for further clarification

Thanks for the response but, on the basis that everything is relative, I would have thought the properties of the photon are subjective to the frame of reference in question. As such, my assumption was that a photon is initially emitted, i.e. electron transition to a lower state, near the event horizon of as black hole. In this frame of reference, the frequency is measured by an in-falling observer, i.e. (B), as a function of local time $$d\tau$$. The photon then heads off in the direction of the distant observer (A). When it arrives at (A), its frequency is measured against the local time [dt] at (A). The assumptions I was trying to clarify were:

1) Does the time dilation between (A) and (B) affect the measured energy of the photon at both points, i.e. energy is a fiunction of frequency which is a function of time?

2) Does the effect of space contraction, traveling from (B) to (A), then counteract the effect of time dilation, i.e. wavelength expands in transit from (B) to (A) and therefore frequency changes as a function of wavelength if the speed of light remains constant?

Would really appreciate any clarification of any/all the assumptions/questions raised in the original post. Thanks

 

[Dale]

Hi mysearch,

You might want to start a new post where you identify one single key question clearly and concisely. I don't know about most other people, but I am not even inclined to read a 31-point list of questions, let alone respond to it.

 

[yuiop]

Hi Mysearch,

I tend to agree with DaleSpam. Too much to digest in one sitting :P

I'll just add a few notes for discussion.

Cosmological Redshift:
The commonly quoted equation for relatavistic redshift includes a classical doppler shift component and a time dilation shift. On a cosmological scale, say when observing a galaxy or supernova billions of light years away, it is concievable that the object in question has no proper motion relative to the local "space" and all the observed redshift is simply "stretching" of the wavelength due to expansion of space during the propagation of the light. I think they came to this conclusion because the classical doppler component+time dilation component interpretation seemed to suggest that galaxies were receding at superluminal velocities which is not good. The stretched space interpretation is supported by the observed remant wavelength of the cosmic background radiation. The doppler plus time dilation effect is still a valid concept for proper motion relative to the local space and is clearly seen in galaxies where part of the galaxy is rotating away from us and the other part is rotating towards us. All these effects add components to the total observed redshift and gravitational redshift adds yet another.

Gravitational Redshift:
When a photon is emitted by a given process, for example a transition of an electron from one specific energy level to another speific level in a specific element the photon is emitted at an intrinsic frequency irrespective of where the element is located in the gravity well. Say the photon is moving upwards, then measurements made further up, by clocks with faster coordinate time make it appear as if the frequency of the photon is getting slower but the coordinate frequency (and energy) remains constant and it is the wavelength (and coordinate speed of light) that is increasing. You could view the increasing wavelength as a gravitational length contraction effect. Local observers progressively further up the gravity well, see the frequency as slowing down and so to them the photon appears to be losing energy and the wavelength increasing which is consistent with the local speed of light being constant for any observer. Depends on your point of view :P

 

[mysearch]

Discussion transferred to `Gravitational Redshift`

Based on the advice from DaleSpam, I shall open a new thread entitled `Gravitational Redshift` and then try to focus my questions on the issue raised in the previous post by Kev. So apologises for raising an excessive number of issues, although post #3 did reduce the list to just 2 questions. Of course, should anybody be inclined to address any of the earlier points raised it would still be appreciated.