Stellar aberation, a One way measurement of c?

[TrickyDicky]

zonde, I will assume that you are acknowledging that astronomers can measure "right ascension aberration" as well as "declination aberration". Can they also measure "aberration" (which I will call "intrinsic aberration" henceforth)? Also, can you please tell me what kind of aberration is predicted by the Doppler Aberration equation that is in Einstein's 1905 paper "On the Electrodynamics of Moving Bodies"?

Not sure what you guys are going on about here, right ascension and declination are simply the equatorial coordinate components of the aberration, the direction northward-southward or eastward-westward of the apparent shift of the star. It looks like you are asking what the true position of a point on the Earth's sphere is, its latitude or its longitude.:uhh:

EDIT: Pallen was faster to clarify it anyway.

 

[harrylin]

[..] Otherwise, even if you are right (not likely), this constitutes original research at odds with peer reviewed opinion. It is therefore not allowed to be discussed here at all - unless you provide a reference for there being a discrepancy. [..]

This is not Wikipedia and its rules don't apply - however you are completely right about the benefit of giving good references.
Regretfully I'm not familiar with such astronomical terms as "ecliptic pole", so I can't comment on the question...

 

[harrylin]

[..] I don't think any of this has to do with relativistic aberration per se. The size of the relativistic correction to classical aberration is, last I checked, undetectable for Earth's orbital speed. [..] My guesstimate for the correction due to the difference between classical and relativistic aberration for seasonal aberration from Earth's motion would be of the order .002 arcseconds. [..]

Yes that is also what I remember to have read in textbooks; last time I read about it, the difference between classical and relativistic prediction was claimed to be negligible. Thanks for confirming that.

 

[PAllen]

This is not Wikipedia and its rules don't apply - however you are completely right about the benefit of giving good references.
Regretfully I'm not familiar with such astronomical terms as "ecliptic pole", so I can't comment on the question...

There used to be an original research forum. It was discontinued. Under the guideline against 'overly speculative posts' note the following:

"It is against our Posting Guidelines to discuss, in the PF forums or in blogs, new or non-mainstream theories or ideas that have not been published in professional peer-reviewed journals or are not part of current professional mainstream scientific discussion."

and:

"Unfounded challenges of mainstream science and overt crackpottery will not be tolerated anywhere on the site."

Claiming a discrepancy between SR and observation based on own research definitely falls into those. Changing the tone (as occurred here) to 'how is the discrepancy between x and this calculation I do resolved' is perfectly ok.

 

[TrickyDicky]

I think I understood the replies to my doubts, but still I'd like to be sure, so for instance the motion of the solar system wrt the remote stars is not observed as aberration because unlike the motion of the Earth around the sun, it has a constant velocity, is that right?

 

[PAllen]

I think I understood the replies to my doubts, but still I'd like to be sure, so for instance the motion of the solar system wrt the remote stars is not observed as aberration because unlike the motion of the Earth around the sun, it has a constant velocity, is that right?

Yes. We can't detect 'absolute' aberration any more tha 'absolute rest' or 'absolute motion'. We can detect change in apparent position between two reference frames. We could detect (in principle) aberration of some distant quasar over a period of time in which the solar system's motion around the galactic center is significant.

 

[harrylin]

There used to be an original research forum. It was discontinued. Under the guideline against 'overly speculative posts' note the following:

"It is against our Posting Guidelines to discuss, in the PF forums or in blogs, new or non-mainstream theories or ideas that have not been published in professional peer-reviewed journals or are not part of current professional mainstream scientific discussion."

and:

"Unfounded challenges of mainstream science and overt crackpottery will not be tolerated anywhere on the site."

Claiming a discrepancy between SR and observation based on own research definitely falls into those. Changing the tone (as occurred here) to 'how is the discrepancy between x and this calculation I do resolved' is perfectly ok.

Yes indeed - please simply stick to the rules and avoid Wikipedia jargon. :tongue:

 

[Ken More]

---Einstein's paper deals with total aberration, which is the combination of declination and ascension aberration (as a total displacement angle). I assume astronomers can detect both aberrations now. Having reviewed astronomic coordinates, I notice that stars at certain positions on the ecliptic will never undergo seasonal declination aberration; they will only have right ascension aberration. Stars at 90% on the ecliptic to these will have both aberrations, but the declination aberration will be smaller than the ascension aberration. Of course, for stars on the ecliptic, there will be no aberration at all twice a year.

For a star perpendicular to the ecliptic, there will always be aberration (of constant magnitude relative to position in a solar system frame), but twice a year it will include no declination aberration (it will be pure ascension aberration).

Stars in between, will have varying total aberration, and will also have no declination aberration twice a year.

Finally, I don't think any of this has to do with relativistic aberration per se. The size of the relativistic correction to classical aberration is, last I checked, undetectable for Earth's orbital speed. My guesstimate for the correction due to the difference between classical and relativistic aberration for seasonal aberration from Earth's motion would be of the order .002 arcseconds. Thus, none of this discussion has anything to do with special relativity. It only relates to the finite speed of light (Galilean versus Special relativity is not distinguished).

Stars in between declination θ₀ = 90° and θ₀ ≈ 0° will have varying declination aberration and varying right ascension aberration. However, stars in this range will have zero declination aberration when α₀ = 90° and 270° according to the Declination Aberration Model described in the 2010 Astronomical Almanac (AA). I agree there is no declination aberration for a star in the ecliptic plane; however, the attached "AA Declination Aberration Model for a star near the ecliptic plane" the declination aberration is zero two times a year (when α₀ = 90° and 270°). As for right ascension aberration, I can only say that the AA Right Ascension model seems to confirms that right ascension aberration is zero for a star in the ecliptic plane only when α₀ = 0.

According to Einstein’s 1905 paper: If we call the angle between the wave-normal (direction of the ray) in the moving system and the connecting line “source-observer” θ, the equation for θ assumes the form cos θ = - (cos θ₀ − v/c)/(1 − cos θ₀• (v/c)). This equation expresses the law of aberration in its most general form. If θ₀ = π/2 (i.e. if θ₀ = 90º) the equation becomes simply: cos θ = − v/c.

Therefore: When θ₀ = 90º, v = -29.783, c = 299792.458, then cos θ = -29.783/ 299792.458 = -0.005692072º = -20.491458542 arc seconds. This value agrees very closely to James Bradley’s Constant of Aberration (= -atan(v/c) = -20.491458475 arc seconds) which is the declination aberration for a star at the zenith (at θ₀ = 90º) according to Bradley’s Falling Rain Model. Bradley's model may be referred to as the "Classical" aberration model because it was the first since Bradley discovered stellar aberration in the late 1720's. Therefore, you can see that Bradley's "Classical" model and Einstein's 1905 "Relativistic" model closely agree to within 0.000001 arc seconds: That is, they both agree that the declination aberration of a zenith star (at θ₀ = 90°) has a declination aberration of -20.491458 arc seconds. I believe the Bradley model assumes a declination aberration close to 20.5 arc seconds every day of a year. Since many physicists claim that Bradley's "Classical" model and Einstein's "Relativistic" model closely agree, I must also assume that Einstein's "Relativistic" model predicts that declination aberration is about 20.5 arc seconds every day of a year.

The attached "AA Declination Aberration Model for a star at the ecliptic pole" disagrees with those who say that declination aberration is about 20.5 arc seconds every day of the year for a star at or very near an ecliptic pole. This attachment shows that declination aberration is zero when right ascension (α₀ = 90° and 270°). Also, the "AA Declination Aberration Model for declination = 75°" and "AA Declination Aberration Model for a star near the ecliptic plane" show that declination aberration is near zero when right ascension is 90° and 270°.

Finally, I believe that the AA Declination Aberration Model is the most accurate model because the Astronomical Almanac is a universally accepted authority on prediction of the precise apparent location for a star on a specific future date and time. Also, the AA Models predicted locations of important stars such as Polaris and gamma-Draconis at θ₀ = 75° (the star Bradley studied) (see attached AA Declination Aberration for Declination = 75 degrees) have been verified many times by telescopic observation.

 

[PAllen]

I don't have time to go into the details of you discussion, but I note you are repeating the same error Zonde first note, and I tried to explain in more detail:

The Bradley and Relativistic aberration formulas you quote determine total aberration not declination aberration. They say for a star at the ecliptic pole, the total aberration is constant. However, twice a year it is all right ascension aberration, twice a year it is all declination, with a mix in between.

Also note that the AA tables you quote are considered to be derived by their authors from the aberration model you dispute. They are an application of the one accepted aberration model, not an alternative model.

If you want to discuss the details of the AA conventions and calculations, you should take this over to the astronomy forum.
Further, this whole discussion of 'supposed discrepancy' has nothing to do with the topic of this thread (one way measurement of light speed using aberration).

PLEASE open a new thread in astronomy on the topic of derivation of Almanac tables from aberration formulas.

 

[Dale]

Also, as previously requested, please post a mainstream scientific reference to demonstrate that this conflict actually exists. I completely doubt it.

 

[Ken More]

I don't have time to go into the details of you discussion, but I note you are repeating the same error Zonde first note, and I tried to explain in more detail:

The Bradley and Relativistic aberration formulas you quote determine total aberration not declination aberration. They say for a star at the ecliptic pole, the total aberration is constant. However, twice a year it is all right ascension aberration, twice a year it is all declination, with a mix in between.

Also note that the AA tables you quote are considered to be derived by their authors from the aberration model you dispute. They are an application of the one accepted aberration model, not an alternative model.

If you want to discuss the details of the AA conventions and calculations, you should take this over to the astronomy forum.
Further, this whole discussion of 'supposed discrepancy' has nothing to do with the topic of this thread (one way measurement of light speed using aberration).

PLEASE open a new thread in astronomy on the topic of derivation of Almanac tables from aberration formulas.

Some do say that for a star at the ecliptic pole total aberration is constant but twice a year it is all right ascension aberration and twice a year it is all declination aberration with a mix in between. However, for an ecliptic pole star right ascension aberration is only an "apparent" spin of the pole star. This apparent spin does not change its apparent location. Therefore, we are left with a total aberration that is declination aberration only and this applies at all times during a year for an ecliptic pole star.

I have noted that the AA tables I quote are considered to be derived by their authors from the SRT relativistic aberration model. Also, they do say that their AA model equations are an application of Einstein's SRT relativistic aberration model. However, when I do the AA model math and the SRT model math Einstein's relativistic model gives very different predictions from the AA model (I am not saying that their is a discrepancy, you can do the math to see for yourself whether there is a discrepancy).

Finally, I will take your advice and open a new thread in astronomy on the topic of the aberration of ecliptic pole stars and stars near the north ecliptic pole and the south ecliptic pole. Therefore, I will hereby terminate this discussion and will not respond to any future replies to my posts on this thread.

 

[PAllen]

Some do say that for a star at the ecliptic pole total aberration is constant but twice a year it is all right ascension aberration and twice a year it is all declination aberration with a mix in between. However, for an ecliptic pole star right ascension aberration is only an "apparent" spin of the pole star. This apparent spin does not change its apparent location. Therefore, we are left with a total aberration that is declination aberration only and this applies at all times during a year for an ecliptic pole star.

This is incorrect. The ecliptic pole is not the celestial pole. It is only the north polar star for which right ascension is undefined. The ecliptic pole will differ in declination from the polar star by the tilt of Earth's axis.

I have noted that the AA tables I quote are considered to be derived by their authors from the SRT relativistic aberration model. Also, they do say that their AA model equations are an application of Einstein's SRT relativistic aberration model. However, when I do the AA model math and the SRT model math Einstein's relativistic model gives very different predictions from the AA model (I am not saying that their is a discrepancy, you can do the math to see for yourself whether there is a discrepancy).

All this shows is that they know what they are doing and you don't. Since this is purely a question of the details of applying aberration in a particular astronomic coordinate system, the appropriate forum to clarify the calculations and find your error is the astronomy forum.

Finally, I will take your advice and open a new thread in astronomy on the topic of the aberration of ecliptic pole stars and stars near the north ecliptic pole and the south ecliptic pole. Therefore, I will hereby terminate this discussion and will not respond to any future replies to my posts on this thread.

Fine.

 

[ghwellsjr]

Now that the hijacking is over, can any of you experts on aberration please answer the OP's question?

 

[harrylin]

Now that the hijacking is over, can any of you experts on aberration please answer the OP's question?

Oops you're right. OK then, let's make a start. I think that it has already been clarified that aberration is caused by the velocity difference due to the Earth's orbit. The Earth's orbital speed is simply its speed relative to the Sun; and the Sun does not designate an absolute reference frame. Instead we could for example choose the combined speed of Earth + Sun through the Milky way. That would yield a very different one-way speed of light if we use the same t.

It always boils down to the same thing: if we choose a certain reference system as "rest" frame, then we will measure the speed of light relative to it as c, but else we won't. And then it depends on what one means with "one way measurement of c".

 

[PAllen]

Oops you're right. OK then, let's make a start. I think that it has already been clarified that aberration is caused by the velocity difference due to the Earth's orbit. The Earth's orbital speed is simply its speed relative to the Sun; and the Sun does not designate an absolute reference frame. Instead we could for example choose the combined speed of Earth + Sun through the Milky way. That would yield a very different one-way speed of light if we use the same t.

I don't think this is true. I think a very careful analysis (which I have not done) would show that this case is equivalent to slow clock transport - the one way speed would always be measured as c, but this measurement would be an artifact in the theories that have underlying anisotropy of one way c in most frames.

 

[harrylin]

I don't think this is true. I think a very careful analysis (which I have not done) would show that this case is equivalent to slow clock transport - the one way speed would always be measured as c, but this measurement would be an artifact in the theories that have underlying anisotropy of one way c in most frames.

I basically agree with that (except for a subtle difference which has been discussed); thus I don't know what you think is not true...

 

[PAllen]

I basically agree with that (except for a subtle difference which has been discussed); thus I don't know what you think is not true...

I thought you were saying you could measure something different from half the two way speed. If that's not what you meant, then I misunderstood.

 

[harrylin]

I thought you were saying you could measure something different from half the two way speed. If that's not what you meant, then I misunderstood.

Oh sure that is what I meant, but likely not in the way that you understood it, since we seem to agree on all essential points.

I tried to make the OP realize (in a continuation in part of my post #15) that if we assign a different velocity to the Earth by accounting for the motion of the Sun (as we may) while keeping the same time t (which he/she seems to take for granted), then necessarily v/t differs from what the OP calculated. I thus stressed a mathematical fact to the OP in the hope to bring home that although one might call his/her method a "one way measurement of c", it remains a very "relative" measurement.

Thus -again- it depends on what Tracer exactly means with "one way measurement of c". I think that it undeniably a method to determine the constant c with a certain precision. Next it may deteriorate in another argument about words, in which I won't participate.

 

[PAllen]

Oh sure that is what I meant, but likely not in the way that you understood it, since we seem to agree on all essential points.

I tried to make the OP realize (in a continuation in part of my post #15) that if we assign a different velocity to the Earth by accounting for the motion of the Sun (as we may) while keeping the same time t (which he/she seems to take for granted), then necessarily v/t differs from what the OP calculated. I thus stressed a mathematical fact to the OP in the hope to bring home that although one might call his/her method a "one way measurement of c", it remains a very "relative" measurement.

Thus -again- it depends on what Tracer exactly means with "one way measurement of c". I think that it undeniably a method to determine the constant c with a certain precision. Next it may deteriorate in another argument about words, in which I won't participate.

Ah, but what one actually measures is difference in angle between frame E1 (earth in January, for example), and frame E2 (earth in June). This difference in angle will be dependent only on the relative velocity of E1 and E2, irrespective of whether one treats E2 relative to E1, both relative to a Solar frame, or both relative to a galactic frame.

Note that if, in addition to measuring change, you choose to express the result as deviation from an average position, the length of averaging selects which inertial frame you are implicitly choosing for your coordinates: a day (earth centered frame; rotation aberration, which exists but not discussed much in this thread), a year (solar frame), the solar orbital period in milkyway (galactic frame).

As for time, you only (directly) need one clock (which you must assume measures time uniformly). You also need to know the relative velocity between E1 and E2, which does raise tricky issues if you don't want to be circular (as discussed earlier in this thread).

 

[PAllen]

I found reference to the statement that pages 94-5 of the following:

Special Relativity and Its Experimental Foundations (Advanced Series in Theoretical Physical Science) [Hardcover]
Yuan-Chung Chang (Author), Yuan-Zhong Zhang (Author)

discuss the details of how stellar aberration gives no more information about one way light speed than other attempts of this type (e.g. slow clock transport).

Unfortunately, I can find no 'search in book' type feature to find this online, and this book is apparently not easy to find.

 

[harrylin]

Ah, but what one actually measures is difference in angle between frame E1 (earth in January, for example), and frame E2 (earth in June). This difference in angle will be dependent only on the relative velocity of E1 and E2, irrespective of whether one treats E2 relative to E1, both relative to a Solar frame, or both relative to a galactic frame.

Note that if, in addition to measuring change, you choose to express the result as deviation from an average position, the length of averaging selects which inertial frame you are implicitly choosing for your coordinates: a day (earth centered frame; rotation aberration, which exists but not discussed much in this thread), a year (solar frame), the solar orbital period in milkyway (galactic frame).

As for time, you only (directly) need one clock (which you must assume measures time uniformly). You also need to know the relative velocity between E1 and E2, which does raise tricky issues if you don't want to be circular (as discussed earlier in this thread).

Yes, thanks for the elaboration.

Note that we don't necessarily assume that a clock measures time uniformly; however that assumption is quite OK for clocks in orbit around the Sun if we use the solar frame; and I don't think that such calculations and measurements are based on atomic clocks anyway.

 

[Tracer]

Originally Posted by PAllen
Ah, but what one actually measures is difference in angle between frame E1 (earth in January, for example), and frame E2 (earth in June). This difference in angle will be dependent only on the relative velocity of E1 and E2, irrespective of whether one treats E2 relative to E1, both relative to a Solar frame, or both relative to a galactic frame.

Yes, thanks for the elaboration.

Note that we don't necessarily assume that a clock measures time uniformly; however that assumption is quite OK for clocks in orbit around the Sun if we use the solar frame; and I don't think that such calculations and measurements are based on atomic clocks anyway.

I tracer am a he. Thanks to all who have responded to my question. Your posts and references have been very enlightening on the subject of stellar aberration. Yes, my question is does stellar aberration offer a means to measure the speed of light in just one direction? I gather from your responses that the answer is yes but that the Earth's orbital velocity and the length of an AU would be difficult to measure noncircularly, accurately and realistically.

Therefore, somewhere in this thread I proposed that the speed of light in opposing directions could be determined without involving the length of an AU or the Earth's orbital velocity or a wait of six months between measurements. If a device much more simple than a massive telescope is used which can be quickly reversed 180° easily and accurately to view a reflected image of a star, then if the angle of aberration is the same for reversed positions of the viewing device, then wouldn't the speed of light be the same for passage through the device in opposite directions? If this is true then it should be correct to assume that all measurements that show the two way measurements of the average speed of light to be c are actually the average of two one way passes of light at c in both directions.

 

[PAllen]

Originally Posted by PAllen
Ah, but what one actually measures is difference in angle between frame E1 (earth in January, for example), and frame E2 (earth in June). This difference in angle will be dependent only on the relative velocity of E1 and E2, irrespective of whether one treats E2 relative to E1, both relative to a Solar frame, or both relative to a galactic frame.



I tracer am a he. Thanks to all who have responded to my question. Your posts and references have been very enlightening on the subject of stellar aberration. Yes, my question is does stellar aberration offer a means to measure the speed of light in just one direction? I gather from your responses that the answer is yes but that the Earth's orbital velocity and the length of an AU would be difficult to measure noncircularly, accurately and realistically.

Therefore, somewhere in this thread I proposed that the speed of light in opposing directions could be determined without involving the length of an AU or the Earth's orbital velocity or a wait of six months between measurements. If a device much more simple than a massive telescope is used which can be quickly reversed 180° easily and accurately to view a reflected image of a star, then if the angle of aberration is the same for reversed positions of the viewing device, then wouldn't the speed of light be the same for passage through the device in opposite directions? If this is true then it should be correct to assume that all measurements that show the two way measurements of the average speed of light to be c are actually the average of two one way passes of light at c in both directions.

You can't measure aberration in one frame, at all, period. Aberration relative to what? You have to involve two frames with known relative velocity, which has been determined in some non-circular way. I think this can be done, and the result is similar in character to slow clock transport measurements: the result is not known a priori (unlike with light based synchronization; so it is a real experiment), but as long as two way light speed isotropy holds, and the prinicple of relativity holds, the measurement will yield c even if there is underlying anisotropy of one way lightspeed (in such a way as to preserve two way isotropy and the principle of relativity). One sense in which it is a real measurement is that if you detected anisotropy of c, this would mean that SR (and all equivalent theories) are false; and then it could be giving unambiguous information about one way light speed.

 

[Tracer]

You can't measure aberration in one frame, at all, period. Aberration relative to what? You have to involve two frames with known relative velocity, which has been determined in some non-circular way. I think this can be done, and the result is similar in character to slow clock transport measurements: the result is not known a priori (unlike with light based synchronization; so it is a real experiment), but as long as two way light speed isotropy holds, and the prinicple of relativity holds, the measurement will yield c even if there is underlying anisotropy of one way lightspeed (in such a way as to preserve two way isotropy and the principle of relativity). One sense in which it is a real measurement is that if you detected anisotropy of c, this would mean that SR (and all equivalent theories) are false; and then it could be giving unambiguous information about one way light speed.

I respectfully disagree with you. I would like to provide additional details of the experiment which was proposed. However, If doing so will cause me to be locked out or banned I will just shut up and go away. What I have proposed is not speculation, a new theory, or an attempt to disprove anything. I am only proposing a test of which I think you misunderstood my description.

 

[harrylin]

I respectfully disagree with you. I would like to provide additional details of the experiment which was proposed. However, If doing so will cause me to be locked out or banned I will just shut up and go away. What I have proposed is not speculation, a new theory, or an attempt to disprove anything. I am only proposing a test of which I think you misunderstood my description.

PAllen is certainly right but it's unlikely that you will be banned for describing in detail the rather standard test which we probably already discussed here and understood.
However, you now clarified that you were not looking to establish the constant "c" with a certain precision by means of a one-way light signal; instead you propose that method, as some already suspected, as a means to determine the physical speed of light in one direction - correct? If so, in your more detailed explanation of what you have in mind, please include an reply to my assertion in post #49.

 

[PAllen]

I respectfully disagree with you. I would like to provide additional details of the experiment which was proposed. However, If doing so will cause me to be locked out or banned I will just shut up and go away. What I have proposed is not speculation, a new theory, or an attempt to disprove anything. I am only proposing a test of which I think you misunderstood my description.

If you clarify your proposed experiment, you may get useful responses. It is fine to propose experiments for analysis.

This is the key phrase I was responding to is:

"then if the angle of aberration is the same for reversed positions of the viewing device"

What is angle of aberration? It is a difference from what is expected. But what is expected is simply either the result of a measurement in a different frame, or (in the actually used convention) the derived position imputed to the solar system frame based on collection angles observed over a year (or by applying a formula based on known speeds - but then you have not a measurement of aberration but a computation of aberration which is computed from the assumption of c). Thus, in one frame, all you can measure is 'where it is'. The minimum needed to measure aberration is two frames at different relative speed (you then have two angular positions to compare).

So, if you have something else in mind, you should clearly specify it.

 

[Tracer]

If you clarify your proposed experiment, you may get useful responses. It is fine to propose experiments for analysis.

This is the key phrase I was responding to is:

"then if the angle of aberration is the same for reversed positions of the viewing device"

What is angle of aberration? It is a difference from what is expected. But what is expected is simply either the result of a measurement in a different frame, or (in the actually used convention) the derived position imputed to the solar system frame based on collection angles observed over a year (or by applying a formula based on known speeds - but then you have not a measurement of aberration but a computation of aberration which is computed from the assumption of c). Thus, in one frame, all you can measure is 'where it is'. The minimum needed to measure aberration is two frames at different relative speed (you then have two angular positions to compare).

o, if you have something else in mind, you should clearly specify it.

Mount a device like a super sniper scope onto a large refracting telescope which is on an equatorial mount and is compensating for the Earth’s rotation. Adjust the sniper scope and its mount so that it is aimed at the same object as the main refracting telescope. Build the sniper scope’s mount such that it can be turned to accurately reverse its viewing direction by exactly 180 degrees. Mount a system of mirrors on the main telescope to reflect the image being observed by the sniper scope by exactly 180 degrees so that when the sniper scope is turned from a looking forward to a looking backward position the direction of the light from the viewed object will also be reversed by 180 degrees.
Select a star for which the amount of aberration is well known. The angle of aberration is not important but the larger it is the better. Aim the main telescope at the targeted star and finely adjust the telescope so that the star image is in the center of its viewing field. Similarly, finely adjust the sniper scope so that the targeted star’s image is centered in the scope’s crosshairs. Note that this only amounts to a calibration of the measurement device and the actual angle of aberration being experience by that star is totally unimportant.
Now reverse the viewing direction of the sniper scope by 180 degrees so that it is now viewing the reflected image of the targeted star. This is in effect is similar to a measurement taken six months later than the first. If the speed of light is the same for the direct and reflected views then the image of the targeted star will be remain centered in the sniper scope’s cross hairs in both viewing directions. Any change in the speed of light between the two measured directions will cause the targeted star’s position to be in different positions in the viewing field of the sniper scope.
If this test proves that the speed of light is the same for both the direct (forward) and reflected (backward) direction through the sniper scope, then all of the many two way measurements of the average speed of light, can be known to be the average of two one way passes in which each pass is exactly c.
Admittedly, this method does not produce a direct measurement of c. However it should remove all doubt that the forward and backward speed of light in a two way measurement is at exactly c.

 

[PAllen]

...

Now reverse the viewing direction of the sniper scope by 180 degrees so that it is now viewing the reflected image of the targeted star. This is in effect is similar to a measurement taken six months later than the first.

This part is wrong. It is not at all the same as 6 months later. What characterizes 6 months later is that the Earth's direction of motion has reversed (relative to 6 months earlier). Your measurement will produce a null result, always, giving no information at all on the speed of light in any direction. In fact, your measurement now has nothing to do with the aberration or the speed of light. It asks: given an image, if I reflect it 180°, will it be reflected 180°?

 

[Tracer]

Oops you're right. OK then, let's make a start. I think that it has already been clarified that aberration is caused by the velocity difference due to the Earth's orbit. The Earth's orbital speed is simply its speed relative to the Sun; and the Sun does not designate an absolute reference frame. Instead we could for example choose the combined speed of Earth + Sun through the Milky way. That would yield a very different one-way speed of light if we use the same t.

Tracer asks: "Yes but why would anyone bother to do that. Many years would be required before differences in aberration due to galactic motion could be observed. In the meantime many cycles of stellar aberration of galactic objects could be observed using just the Earth's relative velocity with the sun. Even if the correct value is used for t for the Earth's relative velocity with the milky way wouldn't c still be the same?"

It always boils down to the same thing: if we choose a certain reference system as "rest" frame, then we will measure the speed of light relative to it as c, but else we won't. And then it depends on what one means with "one way measurement of c".

In a two mirror measurement of c, I would define a two way measurement of c as the distance (d) between the two mirrors divided by one half of the time (t) taken for light to travel from one mirror to the other and be reflected and arrive back at the first mirror.
c= d/0.5t.

A one way measurement would be for either half of light's travel in just one direction between the two mirrors. At least that is my understanding of the term.

 

[harrylin]

Yes but why would anyone bother to do that. Many years would be required before differences in aberration due to galactic motion could be observed. In the meantime many cycles of stellar aberration of galactic objects could be observed using just the Earth's relative velocity with the sun. Even if the correct value is used for t for the Earth's relative velocity with the milky way wouldn't c still be the same?

Evidently you agree that it is not the Earth's velocity that matters for the phenomenon, but the difference of its velocities between two measurements - else no time would be required to observe the effect, just the instantaneous velocity would do.

However, that is not the right information if you try to determine the velocity of light propagation; your method would only be correct if you could assume that the average velocity of the Earth is truly or absolutely zero: only then the differences correspond to twice the (absolute!) velocities of Earth and light. And as you know, there is no reason to think such a thing. Thus, again: please redo your analysis without assuming that the Sun is in rest, so that you take into account that the corresponding velocities of the Earth are for not +v and -v but for example V+v and V-v.

In a two mirror measurement of c, I would define a two way measurement of c as the distance (d) between the two mirrors divided by one half of the time (t) taken for light to travel from one mirror to the other and be reflected and arrive back at the first mirror.
c= d/0.5t.

A two way measurement is simply defined as the return distance divided by the return time.

A one way measurement would be for either half of light's travel in just one direction between the two mirrors. At least that is my understanding of the term.

Yes. I'm afraid that you misunderstood a remark of mine. c is a constant of nature, and you may be able to determine it with great accuracy, for example with the help of one-way light rays. However, you now indicate that you are not interested in trying to determine that constant of nature called c, but in trying to measure the one-way velocities of light rays that arrive from outer space on Earth, relative to the Earth.

 

[Tracer]

Evidently you agree that it is not the Earth's velocity that matters for the phenomenon, but the difference of its velocities between two measurements - else no time would be required to observe the effect, just the instantaneous velocity would do.

However, that is not the right information if you try to determine the velocity of light propagation; your method would only be correct if you could assume that the average velocity of the Earth is truly or absolutely zero: only then the differences correspond to twice the (absolute!) velocities of Earth and light. And as you know, there is no reason to think such a thing. Thus, again: please redo your analysis without assuming that the Sun is in rest, so that you take into account that the corresponding velocities of the Earth are for not +v and -v but for example V+v and V-v.QUOTE]

Why wouldn't the change in velocities over a six month period regardless of the value of V simply be:

delta v = (V + v) - (V-v) = 2v

 

[harrylin]

Why wouldn't the change in velocities over a six month period regardless of the value of V simply be:

delta v = (V + v) - (V-v) = 2v

Your equation relates to velocities, not differences of velocities - or at least, that is how you apparently apply it. In order to be able to truly measure ("confirm") the one-way speed of light relative tot the earth, you need to know the total speed of the Earth (V+v). However, as you remarked yourself, the effect that you measure corresponds to 2v.

According to relativity you can pick any V you like (but <c) and the experiment will not show you wrong (here relativistic corrections come at play that I did not mention as they are of less importance).

 

[PAllen]

Thinking more about aberration measurement, I notice something important:

1) If you use the relativistic derivation, you are Lorentz transforming light propagation angle from e.g. E1 (earth January) to E2 (earth June). The relation ship between angle, relative velocity of E1 and E2, and c is a consequence of the Lorentz transform (the only involvement of the light from the source is that it is light, thus follows a lightlike path). Thus, the only thing you are validating is the Lorentz transform. It seems to me, you are not even really measuring the velocity of light at all! You are just using light from one source to validate the form of the transform, and the constant c within it. Also, note, that in a correct relativistic treatment, motion of the source (star) is irrelevant.

2) If you use Galilean relativity and a corpuscular light theory (the Bradley derivation), you are measuring one way c in one or the other frame. Theoretically, you will get deviations compared to (1), and your derivation is based on light speed being different in the two frames (rather than just angle being different). You would also expect to get a (slightly) different c if you used the moon over two weeks rather than the Earth over 6 months. You would also expect to see an effect of source motion. While many of these differences are too small to detect, source motion dependence has been rigorously ruled out by measurement of aberration from rapidly orbiting binary stars.

With (2) completely ruled out, we have the conclusion of (1) - within a relativistic framework, this doesn't measure actual light speed at all. It measures that light propagation direction transforms according to the Lorentz transform (which includes the constant c defined from the two way speed of light).

[EDIT: and thus we close the loop on how this is functionally the same measuring one way c with slow clock transport. If if measures something different from c, disproving SR equivalent theories, it can measure one way light speed between some source and target frame (light speed no longer being a universal constant). As long SR is confirmed, it doesn't provide any additional information about one way lightspeed.]

 

[harrylin]

Your equation relates to velocities, not differences of velocities - or at least, that is how you apparently apply it. In order to be able to truly measure ("confirm") the one-way speed of light relative tot the earth, you need to know the total speed of the Earth (V+v). However, as you remarked yourself, the effect that you measure corresponds to 2v.

According to relativity you can pick any V you like (but <c) and the experiment will not show you wrong (here relativistic corrections come at play that I did not mention as they are of less importance).

Theoretically [..] your derivation is based on light speed being different in the two frames (rather than just angle being different).

It may be useful to give a silly illustration with a better understood phenomenon.

You are on a huge cruise ship on which they even installed installed a giant wheel with a 50m diameter. As you have nothing else to do while the ship is cruising on the ocean, you decide to try it. Bad luck, it starts to rain. While stuck in that thing in the poring rain, you notice (thanks to your extremely developed senses) that when you are up high, the rain falls under a slightly different angle than when you are down below.

After pondering over this phenomenon, you think that you can determine the speed of the rain drops relative to you, simply by measuring the angles and the rotation frequency of the wheel. From that you first calculate your speed v and next you extract (or so you think!) the speed V of the raindrops from V= v/tan(Theta).

 

[Tracer]

It may be useful to give a silly illustration with a better understood phenomenon.

You are on a huge cruise ship on which they even installed installed a giant wheel with a 50m diameter. As you have nothing else to do while the ship is cruising on the ocean, you decide to try it. Bad luck, it starts to rain. While stuck in that thing in the poring rain, you notice (thanks to your extremely developed senses) that when you are up high, the rain falls under a slightly different angle than when you are down below.

After pondering over this phenomenon, you think that you can determine the speed of the rain drops relative to you, simply by measuring the angles and the rotation frequency of the wheel. From that you first calculate your speed v and next you extract (or so you think!) the speed V of the raindrops from V= v/tan(Theta).

I am not sure of what your point is here. But let me put some values on a sample problem so you can see if I am doing something illogical or my math is wrong.

A. Let the ships speed through the wind equal to 15 meters/sec directly fore to aft.


B. Let the rim velocity of the wheel be 10 meters/sec and its direction of rotation is such that the rim velocity adds to the ship’s wind velocity at the top of the wheel and subtracts from the ship’s wind velocity at the bottom of the wheel.


C. Let the rain drops fall vertically at 30 meters/sec when the wind velocity is zero. This will be treated as an unknown until it has been calculated based on its viewed angle of approach to the observer.

At the top of the wheel the wind velocity will be 25 meters/sec. If the angle of incidence (theta)to the observer at the top of the wheel is 50.194429 degrees, then the true vertical velocity of the rain drops is:

V = 25tan(theta)=25tan(50.194429) =25(1.2) = 30 meters/sec

The rain drops will strike the observer at the top of the wheel at:

V = 30/sin(theta) = 30/0.7682213 = 39.051248 meters/sec

At the bottom of the wheel the wind velocity will be -5 meters/sec. if theta at the bottom of the wheel is measured to be -80.537678 degrees, then the true vertical velocity of the rain drops is:

-5tan(theta) =-5tan(-80.537678) = -5(-6) = 30 meters/sec

The rain drops will strike the observer at the bottom of the wheel at:

V = 30/sin(theta) =30/0.9863939 = 30.413813 meters/sec

Is this correct? What can be determined from composite measurements from the top and the bottom of the wheel?