Redshift FAQ article development

[Naty1]

PAllen:

...3000K on the collapsed surface corresponds to 2.7K far away; thus the photon was emitted at local temp of 3000K=2.7K far away perspective, and didn't change at all along the way to being received.

That's another nice example...so ok, I guess the dichotomy I am struggling with is my 'flat space' mind with the vagaries of 'curved space-time'...

Towards the end of the article linked above, Tamara Davis expands this perspective a bit..., so I guess these ideas are as 'good as it gets'...thank you once again!

...because in small enough regions
the universe makes a pretty good approximation
of flat spacetime. But in flat spacetime
there is no gravity and no stretching of waves,
and any redshift must just be a Doppler effect

So we can think of the light as making many
tiny little Doppler shifts along its trajectory.
And just as in the case of the police car—where
it would not even occur to us to think that photons
are gaining or losing energy—here, too, the
relative motion of the emitter and observer
means that they see photons from different perspectives
and not that the photons have lost energy
along the way.
In the end, therefore, there is no mystery to
the energy loss of photons: the energies are being
measured by galaxies that are receding from
each other, and the drop in energy is just a matter
of perspective and relative motion.

 

[Naty1]

PAllen...
I did not mention it in my prior post but I do understand [I think] about FLRW cosmologies not addressing energy conservation...On the other hand, I don't really understand this part of your prior post and I am remiss in skipping over it:

...There is a fundamental difference between 'sufficiently static geometry' in 'sufficiently flat very large region', where we can define quasi-local energy in a consistent way (and for which 3000k photon near the collapsed surface adds the same total energy as a 2.7 K photon far away), coming up with a conserved quantity.

I'm confused by this description because I don't see how you are disentangling motion and curvature...I assume near the 'collapsed surface' there is curvature [a change in gravitational potential??] and hence gravitational redshift as a photon is emitted ...If there is no curvature and a 'static' geometry, [do you mean 'no expansion'??] then should I not expect to see the photon at distance as emitted, unchanged, at 3,000 K??

 

[Ich]

Hi PAllen,

Meanwhile the static bodies do not fit the 'relatively motionless' criteria you give (no vanishing redshift).

I think you misread what I wrote. I was talking about vanishing two-way redshift, which clearly vanishes for static observers. Sending light down the potential, you get gravitational blueshift, which is exactly canceled by the redshift on the way back if there is no radial motion between the observers.

I agree that there is derived, practical, approach of 'gravitational redshift'. But attaching more significance to it implies that one must distinguish Doppler between non-inertial world lines in SR from that between inertial world lines.

Why is that? This is a coordinate based concept, we're not talking about right or wrong here, we're talking about "useful" or "useless". If it's useful, use it. If not, let it be.

Conceptually, this last is silly.

Well, using fictitious concepts like a "gravitational field" may in fact be "silly" at times. That's no reason to generally forbid its use, as they may be very helpful in other situations.
Remember what you're arguing against: There are those who insist that one must not see cosmological redshift as a doppler shift. Why would you insist that one must not see redshift (under the appropriate circumstances) as a "gravitational" redshift. Why would you forbid it, when it's clearly of use somtimes? (If that's your intention at all, I may have misunderstood you.)

Also, the parallel transport is the 'second order' phenomenon sensitive to curvature. The 'first order' difference between inertial Doppler and non-inertial Doppler (to coin a phrase) has nothing to do with parallel transport, because that is a no-op in SR.

Comparison via parallel transport is trivial in SR and yields standard relative velocity, at least for the frame where the compared events are simultaneous. If the events are null-separated, you might also want to interpret the result as a gravitational redshift, if it suits your purposes. No special significance to it, it may just be useful and even reflect something important in nature.
I think there may be a misunderstanding concerning my use of "first" and "second order" effects: in a homogeneous universe, if you make a series expansion of redshift as a function of normal distance (in the quasistatic frame), the Hubble flow will show up as a first order effect, while the gravitational potential is parabolic with distance. I did not intend to say that, generally, gravitational redshift is a second order effect. Sorry for the confusion.

BTW, this thread's going too fast for my limited (and phase-shifted) time online.
To sum up, my point is: there are times to call a redshift cosmological, doppler, or gravitational. Don't call it "doppler" under all circumstances, you're going to sow confusion. It's good to say that GR itself doesn't care about these concepts, it's ok to say that the redshift concept you propose is kind of "canonical" in GR, and it's ok to explain that it might be seen as related to a doppler shift. But there's no use henceforth calling every redshift "doppler".
Make of it what you will, I'll have a look at this thread from time to time and be happy to answer to your (and anybody's) comments, if it doesn't disturb the many strands in this discussion.