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View Full Version : Doppler thought experiment

AFJ
2016-May-25, 06:52 PM
Don't worry i'm not spamming, after this one i'll restrain myself.

Just a thought experiment, the objects used on this are emitting light than can be used for spectroscopic measurements. The relation between relativistic velocity and astronomical redshift is non-lineair, as can be seen on the v/c vs redshift z graph on this page:

http://www.asterism.org/tutorials/tut29-1.htm

A central object (CO) is moving away at high relativistic velocity from a stationery observer. Close by on the left side of this central object is an object (LO) that is moving away from the observer at a slightly higher velocity than CO (CO+x). On the right side of the central object is an object (RO) that is moving away from the observer at a slightly lower velocity than CO, equal to the difference in velocity from the left and central object (CO-x).
At the moment the spectrum is taken from the three objects they are exactly aligned with respect to the observer.

After the measurement there are three spectral line shifts from three different objects. Now the difference in shift of absorption lines / emission lines between CO-LO and CO-RO can be measured.

It was a bit silly to call it an observer because he is not shown the spectral measurements eg absolute wavelenght lines.

He/she is only given:

- the measured differences in spectral line shift between CO-LO and CO-RO
- the graph / formulae of relativistic redshift from above link
- the fact that the difference in relativistic velocity between CO-LO and CO-RO is exactly the same

Is it correct that (since the relative velocity-spectral line shift relation is not lineair):

- the difference in line shift between CO-LO is always greater than that of CO-RO?
- And the magnitude of this difference depends ONLY on the absolute relativistic velocity? (Not x?)
- the 'observer' can deduce the relativistic velocity of CO because of this?

Reality Check
2016-May-25, 09:46 PM
A central object (CO) is moving away at high relativistic velocity from a stationery observer. Close by on the left side of this central object is an object (LO) that is moving away from the observer at a slightly higher velocity than CO (CO+x). On the right side of the central object is an object (RO) that is moving away from the observer at a slightly lower velocity than CO, equal to the difference in velocity from the left and central object (CO-x).
At the moment the spectrum is taken from the three objects they are exactly aligned with respect to the observer.
So basically a rotating galaxy and the first step in measuring galaxy rotation curves. There will be the redshift of CO. LO will have a slightly higher redshift. RO will have a slightly lower redshift. Taking differences will give LO a small redshift and RO a small blue shift.

What the observer does is take known measurements of the spectral lines here on Earth which have no redshift (relative velocity = 0). They identify the same spectral lines in the spectra of CO, LO and RO. They see that to match the spectra they have to shift those from CO, LO and RO toward the red end of the spectrum.

Is it correct that
- The non-linear relation as in your link (equation 4) (http://www.asterism.org/tutorials/tut29-1.htm) means that LO and RO will have slightly different shifts from each other relative to CO. For example: CO has v/c = 0.6 (z=1), LO has v/c = 0.8 (z = 2), RO = v/c = 0.4 (z = 0.5). That is a difference in z of 1 and -0.5. This is an extreme example. As the speed x becomes smaller, the relation becomes more linear until the relative redshift can be treated as the same in practice.
- I would guess that the observer cannot deduce the velocity of CO since there is no sign of this in a literature search.

AFJ
2016-May-25, 10:24 PM
So basically a rotating galaxy and the first step in measuring galaxy rotation curves. There will be the redshift of CO. LO will have a slightly higher redshift. RO will have a slightly lower redshift. Taking differences will give LO a small redshift and RO a small blue shift.

What the observer does is take known measurements of the spectral lines here on Earth which have no redshift (relative velocity = 0). They identify the same spectral lines in the spectra of CO, LO and RO. They see that to match the spectra they have to shift those from CO, LO and RO toward the red end of the spectrum.

- The non-linear relation as in your link (equation 4) (http://www.asterism.org/tutorials/tut29-1.htm) means that LO and RO will have slightly different shifts from each other relative to CO. For example: CO has v/c = 0.6 (z=1), LO has v/c = 0.8 (z = 2), RO = v/c = 0.4 (z = 0.5). That is a difference in z of 1 and -0.5. This is an extreme example. As the speed x becomes smaller, the relation becomes more linear until the relative redshift can be treated as the same in practice.
- I would guess that the observer cannot deduce the velocity of CO since there is no sign of this in a literature search.

Thank you for the calculation example and literature search. I have also not been able to find it. Yes a rotating galaxy ofcourse but without conversion to z. And that difference between CO-LO and CO-RO is what i am aiming at, even without converting to z or velocity.

To me it seems this relation is completely defined by the relativistic velocity, and not influenced by any different values of x, because they balance out.

Examples;

- CO is moving at 'low' relative velocity (rv), spinrate (x) is low; difference CO-CL and CO-CR is small ( thus rv is low)
- CO moving at low rv, x is high, difference is small (rv is low)
- CO moving at high rv, x is low, difference is big (rv is high)
- CO moving at high rv, x is high, difference is big (rv is high)

Seems spinrate x has no influence

But also this it seems;

Suppose CO (+LO and RO as a system of 3) has an actual rv of, let's say 0.6c, but for some unknown reason the light of all 3 objects is redshifted (equally) more to a value of 0.7c. Just making up numbers here. So we measure this spectral line shift and calculate it to an rv of 0.7c.

But since the redshift increase holds equally for all three objects, the difference between CO-CL and CO-CR has not changed, and that was defined by 0.6c. So knowing the relationship of difference between CO-CL / CO-CR and relative velocity would no matter what give an exact correct rv of 0.6c.

It looks like knowing this relation you can deduce a correct rv independent of spinrate x or any incorrect redshifted light (equal up or down line shift for all three objects).

Sort of check or optimize the standard redshift - recessional velocity calculation, independant of the value of z.

Am i thinking straight here?

Reality Check
2016-May-25, 11:16 PM
To me it seems this relation is completely defined by the relativistic velocity, and not influenced by any different values of x, because they balance out.
Of course different values of x give different velocities and so different redshifts. The point is that the equation for redshift at relativistic velocities gives different redshifts for the same x which was your question.
Let CO have v/c = 0.6. Let x = 0.2 so that LO has v/c = 0.8 and RO = v/c = 0.4. CO has z=1. LO has z =2. RO has z=0.5. LO-CO = 1. RO-CO = -0.5. This are different redshifts.

But say you were given the results: LO-CO = 1, RO-CO = -0.5. I can see no way to get CO. If you can do it then please show your calculations.

ETA: There is the question of why bother? If we have measured the redshift of CO then we have the redshift of CO.

AFJ
2016-May-26, 04:44 AM
Of course different values of x give different velocities and so different redshifts. The point is that the equation for redshift at relativistic velocities gives different redshifts for the same x which was your question.
Let CO have v/c = 0.6. Let x = 0.2 so that LO has v/c = 0.8 and RO = v/c = 0.4. CO has z=1. LO has z =2. RO has z=0.5. LO-CO = 1. RO-CO = -0.5. This are different redshifts.

But say you were given the results: LO-CO = 1, RO-CO = -0.5. I can see no way to get CO. If you can do it then please show your calculations.

ETA: There is the question of why bother? If we have measured the redshift of CO then we have the redshift of CO.

I'm thinking the ratio between LO-CO and RO-CO is a direct consequence of relativistic velocity, regardless of the magnitude of measured redshift. That's what i'm asking really, this looks to me like a 'direct' measurement of relativistic velocity without even the need to measure how big LO-CO or RO-CO is in absolute sense. The ratio alone would be sufficient to tell rv (given you have plotted the difference-rv graph). Then the outcome would not necessarily be the rv value following out of its direct measured redshift.

Yes would need calculations to check i agree, right now i have limited time. So before this gets ATM stamped, i only ask to the CQ members;

Am i correct that the LO-CO / RO-CO ratio is rv dependend only? So that this ratio in itself follows a lineair rv function?
In other words it generates an rv value independent of absolute redshift value? Which would give it measurable predictions that can be verified by observations?

If this is correct; if nothing else it could be used to check or refine the usual redshift-rv conversion.

AFJ
2016-May-26, 07:39 AM
Lets call it recap ratio for short & handy (recessional-center-approaching)

If the recap ratio is relative velocity dependent-only ( not accounting for asymmetric bulges); you can measure the recap ratio, which gives a relative velocity. The relative velocity then gives a value for what the redshift should be. This can be matched with the actual redshift measurement?

Reality Check
2016-May-26, 09:16 PM
I'm thinking the ratio between LO-CO and RO-CO is a direct consequence of relativistic velocity, ....
Actually it is a direct consequence of any velocity and basic arithmetic, AFJ .
The Doppler effect does not vanish for v << c.
The redshift of CO is a direct consequence of velocity. The redshift of LO is a direct consequence of velocity. The redshift of RO is a direct consequence of velocity. Subtracting 2 numbers is basic arithmetic (LO-CO and RO-CO). Dividing two numbers to get a ratio is basic arithmetic.

You are not correct. The LO-CO / RO-CO ratio is dependent on the velocity of CO, LO and RO. So the rest of the post is moot.

Reality Check
2016-May-26, 09:19 PM
Lets call it recap ratio for short & handy (recessional-center-approaching?
It is also wrong with a nonsense "short & handy" phrase, AGJ :D! There is no recessional center that is being approached.

AFJ
2016-May-28, 02:57 PM
Hmm turns out ratio is not independent of spin rate at relativistic velocities. And error margin gets worse very fast with increasing v/c. Ah well