Okay, I have a question about the Doppler Effect, specifically in regards to relativistic velocities. Let me try and step through what I'm thinking with very simple examples.

The Doppler Effect is basically a result of the movement of the transmitter (or receiver). If, for example, the transmitter is moving away from me at a velocity equal to one-half the velocity of the signal, the signal would be red-shifted for me by a factor of 1.5, right? Basically, the number of waves the transmitter emits in one second would take 1.5 seconds to all reach me, because of how far the transmitter moved during that second.

However, if we're talking about an EM signal, and the transmitter is traveling at .5c, then we have the time dilation of SR to consider as well, correct? At that speed, the dilation would be at about 0.866, meaning I would see a clock on the transmitter as ticking off 1 second in 1.15 seconds of my own time.

So, that some number of wavefronts that is transmitted in one second for the transmitter would appear to take 1.15 seconds for me.

Including the Doppler effect, it seems to me that those wavefronts would take a total of 1.725 seconds to all reach me (1.15 x 1.5).

So, am I misunderstanding something? Would the measured red-shift on a transmitter moving at .5c be 1.725, or would it still be 1.5?

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SeanF

"Ask to understand, but don't challenge unless you have the knowledge."--NEOWatcher

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This page derives the relativistic Doppler effect, and it has figures which help considerably.

http://hyperphysics.phy-astr.gsu.edu...eldop2.html#c1

So I get 1.732 instead of 1.725?

Thanks for the link, Wiley . . . that does help. And GoW, you're right -- that 1.15 was a rounding, and I shouldn't be rounding that early in the computation. [img]/phpBB/images/smiles/icon_smile.gif[/img]

Now, the reason I was thinking about this was because of a discussion on the old board about recent discoveries that extremely distant galaxies were exhibiting a redshift indicating that they were moving away from us at superluminal velocities . . . anybody remember that? (I think JW was the one who originally brought it up)

The problem is that as the velocity approaches c, this calculation approaches infinity. With a velocity greater than c, the calculation becomes imaginary! (Square root of a negative number)

So I figured I must've been missing something, because I don't see how they could be measuring imaginary red-shifts for these supposedly superluminal galaxies; if the redshifts are measurable (i.e., not infinite or imaginary), then they should not calculate out to superluminal velocities, should they?

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SeanF

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You are correct. There can be no such thing as a "superluminal redshift. Redshift is an asymptotic function - as v => c, redshift => infinity. This is one of the areas where JW took any disagreement as a personal attack, so every body tended to let it slide rather than provoke an outburst. There are phenomena that "appear to be" superluminal, but these are the result of observational geometry.

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JW had a link to an online paper that discussed this seriously. If anyone can remember an author, or anything, I could find the link. There was a junior author, it's almost coming to me...

GoW, I've been trying to remember that paper or who wrote it, too.

As I recall, the authors of the paper were suggesting "expanding space" as a way of imparting sufficiently high red-shift to the light without the galaxies in question actually moving through space at superluminal velocities.

It wasn't until my thoughts of today that I realized I didn't see how there could even be a "sufficiently high red-shift," but at the time of the original discussion nobody questioned that or the idea of expanding space . . . that is, nobody doubted that scientists were legitimately measuring this absurdly high red-shift for distant galaxies.

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SeanF

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Yes, I got sucked into that discussion. The paper that JW misunderstood is (if I recall correctly) Davis & Lineweaver, "Superluminal recession velocities".

The main point of the paper is to show that for very distant objects you need to account for the expansion of the universe when calculating its velocity. For these objects you need general relativity not special relativity.

Very distant objects can appear to mover away from us faster than light because space itself is expanding faster than light. Special relativity is not violated since any observor would always measure the speed of light as "c" and nothing could overtake a photon.

Thanks Wile E., that's what I needed to find it in my archives. Here's the link to a pdf copy: Superluminal Recession Velocities.

OK, meet you back here for discussion in a month. [img]/phpBB/images/smiles/icon_smile.gif[/img]

Wiley,

That's it! That's the paper he was talking about . . .

But, how exactly do these galaxies "appear to move away from us faster than light"? Are the scientists looking at red-shift? If so, what kind of red-shift do they say gives the "appearance" of superluminal recession?

From the above formulae, it seems that no matter how high the red-shift is, it can not indicate anything more than c . . .

I'm confused!

[The following added in editing]:
Okay, I did this post before GoW posted the link to the paper. I'll stop whining now and read the paper. Afterwards, I'll come back and whine some more . . .

[img]/phpBB/images/smiles/icon_smile.gif[/img]

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SeanF

<font size=-1>[ This Message was edited by: SeanF on 2001-11-12 14:47 ]</font>

That's the problem, not the solution.
The normal Newtonian formulas (i.e., Doppler shift with Galilean invariance) don't work.


Galilean invariance suggests that there is a stationary frame that is somehow different from all the other inertial frames. However, there are two "pure" types of Galilean(nonrelativistic) formulas: source velocity adds and source velocity doesn't add.
Suppose the velocity of the source really does add to the velocity of the light. Then, one shouldn't even see an object moving faster than light in a stationary frame because the photon (with velocity of source added) is moving away from the earth. However, the Michaelson Morley experiment at least has a null result. Of course, so does the Sagnac experiment.

Now suppose the source velocity DOESN'T add to the velocity of light. Then one sees from a source moving away faster than the speed of light in the stationary frame, light with a huge red shift. Also, the Michaelson Morley experiment doesn't have a null result. Also the Sagnac experiment has have a null result.

Make believe that you believe in Galilean invariance (i.e., nonrelativistic Doppler shift). Since according to Lineweaver the galaxies are moving faster than the speed of light, you must have version two. However, the MM experiment does have a null result but the Sagnac effect doesn't have a null result.

To be fair, JW had an entrainment (aether drag) model that he picked up from somewhere which was nonrelativistic but was at the same time a mixture of the two Galilean models just described. It had an MM experiment with a null result, Sagnac effect with a nonnull result, and you could even see an object moving away from you faster than the speed of light in a stationary frame. Of course, it had extra parameters. For example, the distance from the earth where the aether drag dissappeared, and the coupling between aether drag and gravitational mass.




<font size=-1>[ This Message was edited by: Rosen1 on 2001-11-14 19:45 ]</font>

Yeah, Rosen, ol' JW had some interesting theories, didn't he?

After reading this paper, it almost seems like these folks are taking Hubble as a given and accepting that a galaxy past a certain distance must have superluminal recession, and the paper is intended to show how this superluminal recession could exist without violating SR or causing an infinite redshift. Is that how you read it?

So now I have a more general question . . . how do we determine the distance to these galaxies?

We're obviously not using Hubble the other way (using redshift to determine the velocity and determining the distance from that), and these galaxies are certainly too far away to use parallax, so how do we know they're so far away they should be superluminal?

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SeanF

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They claim that all objects with a red-shift greater than three are receding faster than the speed of light, by their calculations.

I may be able to answer your first question. I just beginning to learn GR, so one of the other more learned board members may correct me. They assume the simplest GR expanding universe model which is the FRW metric. This metric assumes that matter in the universe is homogeneous and the universe is expanding equally in all spatial directions. From what I understand these assumptions are very good.

According to this model, past the distance d = c/H, the recession velocities are superluminal. H is the Hubble constant which is derivable from this metric. However SR still holds locally, i.e. the observer measure light at "c".

As to how they measure distance. I thought redshift was the primary distance indicator. From redshift get recession velocity and from recession velocity get distance.

Here's a link to a couple of articles that discuss this:
Scaling The Universe ...
Supernovae, ...

Hope this helps,


<font size=-1>[ This Message was edited by: Wiley on 2001-11-15 12:45 ]</font>

Rosen1,

I'm not sure of the relevance of this. My apologies if I missing the point.

The Davis and Lineweaver work is based on GR which incorporates the two fundamental postulates of SR: "c" is constant for all observers and there is no preferred inertial frame. Implicit in the SR derivation is that space is flat, and of course this is not true in GR. In the FRW metric, locally space is approximately flat and SR holds.

The main point of the paper is that we can't use the (special) relativistic Doppler shift to measure recession velocity for high redshift objects. If we can't use the relativistic Doppler shift, why would we think that the Gallilean Doppler shift should hold?

No one is arguing against SR. We're trying to establish when we need to move from SR to GR.


<font size=-1>[ This Message was edited by: Wiley on 2001-11-15 13:13 ]</font>