I was working on an assignment (rest assued, it's been passed in -- I'm not seeking homework help) this past weekend when one of the problems sort of pushed me into the Transverse Döppler Effect. The notion really caught my interest, but not as much as a second question that was tagged on to the end of the assignment:

Would the redshift due to the Transverse Döppler Effect be empirically distinguishable from the redshift due standard, radial Döppler Effect?

I couldn't think of a reason why it would be, but the question was phrased in such a way that made me feel like they were distinguishable. Honestly, I couldn't even figure out how someone would go about testing such a thing. So, are the two effect measureably different? Why or why not?

__________________
"The plan does not involve mayonaise."
"... I knew there was a catch."

You can't take the sky from me.

Redshifts may be due to a lot of causes, and they are all the same-- they simply multiply all wavelengths by a fixed factor. Thus if all you have is a spectrum, there is no way to distinguish various redshift mechanisms. Perhaps if you could detect the proper motion, you could infer the radial motion using the total redshift, but it seems to suggest that all you have is the spectrum. By the way, you can include cosmological redshift, and gravitational redshift, etc.-- none are empirically distinguishable without some additional information. What's not clear is if the question is really asking, what additional information would you need to distinguish these? Good luck if you don't know the distance to the object.

Um, it's "Doppler effect", not with umlauts, named after this fellow.

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Science is a way of trying not to fool yourself. The first principle is that you must not fool yourself, and you are the easiest person to fool.
-- Richard Feynman

I spells it as my professor spells it. And he be spellsing it as theys spells it (with appologies to Gillianren) on several non-wiki pages I just stumbled upon a minute ago (here, here, and a rather interesting historical transcription here, for a couple of non-authoritarian references).

Hmm, now I'm suddenly interested in this ATM spelling theory. Time to move in next door to the electric universe.


Oh, and thanks, Ken G. I couldn't think of a reason why the time dialation redshift should be visibly different from any other kind. I guess a redshift is a redshift is a redshift.

__________________
"The plan does not involve mayonaise."
"... I knew there was a catch."

You can't take the sky from me.

Quite so, though it seems a strange answer to the homework question I admit. I'd like to know what the teacher was driving at there, perhaps this was just the conclusion that was being sought.

Sounds like hypercorrectness... I've never seen "Doppler" used with umlauts (or as "Doeppler") when referring to the effect¹. However, "Döppler" is a German surname so the error may originate from that.

¹) Google finds one German page with "Döppler-Effekt" and 136,000 pages with "Doppler-Effekt".

__________________
Science is a way of trying not to fool yourself. The first principle is that you must not fool yourself, and you are the easiest person to fool.
-- Richard Feynman

Well, it was a question just sort of tagged on to the end of a problem set dealing with the relativistic Doppler effect. The question was specifically comparing the wavelength of absorption lines coming from the Sun and a nearby star moving with a given radial velocity. The second part of the question asked what the transverse velocity of another star would have to be in order to see its absorption line redshifted the same amount as the first star. It followed that up with "Would the light from Star B be distinguishable from that received from Star A?"

Could very well be. I've had one English, one Canadian, and now one Polish professor all use the Döppler spelling, but never a German or Austrian. I've also never seen it written as "Doeppler" either, though it is what I searched for to stumble across the above links.

__________________
"The plan does not involve mayonaise."
"... I knew there was a catch."

You can't take the sky from me.

OK, yeah, the answer is "not really", unless you have additional information (radial motion causes "relativistic beaming", for example, which changes how bright it would look, but we're probably talking about a tiny radial motion. Very fast transverse motion will cause length contraction of one of the star's dimensions, which should also affect its brightness, but in ways that aren't so easy to calculate, and anyway you'd need to know how bright the star was supposed to be to pretty high accuracy.) That's an interesting conclusion, so that must have been the point of the question.

Radial vs Transverse Doppler Effect

Would this be like the measure of variation at one end of the observation
platform?
Say a star you are looking at on the horizon is 100 million light years
away so it takes 100 million years to reach you.
Walk toward it and you perceive it to be arriving sooner say by a few days
walk backwards and it seems to take a few days longer to arrive.
The light arriving hasn't shifted time frame just your perception of it
has. The chance of noticing such a change is pretty remote though
as the variation is a factor of 1 in 10^10 very roughly.

Yes, that phenomenon is part of the radial Doppler effect. The other part of the radial Doppler effect is called the transverse Doppler effect, because it is the only thing that happens if the motion is tranverse. The point of this question is that both effects produce the same thing, frequency shift, and hence are hard to disentangle from each other in theory (in practice, it's pretty easy-- it's always radial unless there's a short period orbit involved).