How is it possible for binary stars to not show changes in aberration angles?

[exmarine]

I thought I understood how stellar aberration conformed to Special Relativity. The CHANGE in that angle comes from the CHANGE in our orbital velocity direction about the sun over six months. And it is the same for all stars. That is fine if there are no significant changes in a star’s state of motion relative to our sun over short periods of time. “Significant” is relative to our orbital velocity; and “short” is relative to six months.

Now I read that there are binary stars out there that DO have significant velocity component changes parallel to the plane of our orbit during short periods of time. Yet we observe no corresponding changes in the aberration angles from those stars.

How can that be consistent with SRT? Only SOME changes in relative velocities between source and observer cause changes in aberration angles?

 

[jbriggs444]

The source-relative direction of the light that is emitted from a source and detected at a receiver will vary with the motion of the source at the time of transmission. It will not vary with the motion of the receiver at the the time of reception.

[Change the frame of reference that the source measures angle against and you change the measured angle. Change the speed of the target all you like and it doesn't matter as long as it's in the right place at the right time when the light hits it].

The receiver-relative direction of the light that is emitted from a source and detected at a receiver will vary with the motion of the receiver at the time of reception. It will not vary with the motion of the source at the time of transmission.

[Change the frame of reference that the receiver measures angle against and you change the measured angle. Change the speed of the source all you like and it doesn't matter as long as it was in the right place at the right time when it emitted the light]

 

[Meir Achuz]

The difference between the aberration angle for SR is so close to that for a classical non-relativistic calculation,
that the difference would not be noticed for a moving star.

 

[exmarine]

quote…

And, after a month or two, when the binary’s contribution to the change in relative velocity with us is significant? But still the only effect we observe in the aberration angle is due to our contribution to that change in relative velocity. How do you explain that? And we are talking about first order effects, not some exotic higher orders.

The only treatment of aberration with binaries I’ve been able to find in the literature is in Kevin Brown’s book “Reflections on Relativity”. In an otherwise fine chapter, he finally gets to this issue, and then ignores the binary’s change in orbital velocity. I am quite surprised. It would be nice if someone else could verify my understanding of his analysis. You can find that chapter of his book on MathPages.

 

[Histspec]

And, after a month or two, when the binary’s contribution to the change in relative velocity with us is significant? But still the only effect we observe in the aberration angle is due to our contribution to that change in relative velocity. How do you explain that? And we are talking about first order effects, not some exotic higher orders.

The only treatment of aberration with binaries I’ve been able to find in the literature is in Kevin Brown’s book “Reflections on Relativity”. In an otherwise fine chapter, he finally gets to this issue, and then ignores the binary’s change in orbital velocity. I am quite surprised. It would be nice if someone else could verify my understanding of his analysis. You can find that chapter of his book on MathPages.

I think you are referring to
http://www.mathpages.com/rr/s2-05/2-05.htm
There is another chapter in this book where this question of aberration of binary stars is discussed in more detail
http://www.mathpages.com/home/kmath160/kmath160.htm

Here is another treatment:
Liebscher, D.-E.; Brosche, P. (1998): Aberration and relativity. In: Astronomische Nachrichten. 319,
http://adsabs.harvard.edu/full/1998AN...319..309L
See fig. 10 on p. 313 where the aberration of double stars is discussed, and where they showed that there is no "active" aberration due to the motion of the source alone. This refutes the claims of some "anti-relativists" of the 1920ies who thought that the lack of "active" aberration of double stars contradicts relativity.

So even though there seem to exist different descriptions of stellar aberration (depending on the interpretation of velocity "v" in the aberration formula) - all of them agree that the absence of "active" aberration in the appearance of double stars is in agreement with the predictions of special relativity.

PS: Liebscher et al. also remarked that the erroneous concept of "active" aberration of double stars was already discussed in the 19th century, until it was refuted in the following paper by Herschel in 1844:
http://articles.adsabs.harvard.edu/full/1844AN...22..249H

 

[jartsa]

How can that be consistent with SRT? Only SOME changes in relative velocities between source and observer cause changes in aberration angles?

Here are two true sentences:

1: Aberration depends on the velocity of the observer.
2: Observer does not know his velocity.And here is a false statement:

3: Aberration depends on the relative velocity of the observer and the light source.
I guess there may exist some aberration formula, where the relative velocity of observer and light source is one parameter. My comment regarding that formula is: Ok, but sentence number 3 is still false.

 

[Bill_K]

From the point of view of an observer riding on the binary star, the position of Earth in the sky varies back and forth. If he had to aim his photons, he would need to take this motion into account. But he does not - he sprays photons in all directions. The photon that winds up hitting Earth goes straight to Earth. His motion changes only which photon this is.

 

[jbriggs444]

1: Aberration depends on the velocity of the observer.

Aberration relative to a baseline measurement, real or imagined, depends on velocity relative to the baseline frame.

2: Observer does not know his velocity.

An earth-bound observer can know his velocity relative to many things that could be used as baseline frames.

 

[exmarine]

And here is a false statement:

3: Aberration depends on the relative velocity of the observer and the light source.

I thought aberration depended on the Lorentz transform. And does that transform not depend on the relative velocity?

I need to see if I can obtain those papers mentioned by the other fellow. And the other chapter by Brown doesn't seem to be in my printed book? Will look at it online.

 

[jartsa]

I thought aberration depended on the Lorentz transform. And does that transform not depend on the relative velocity?

It depends on observer's velocity relative to a baseline frame. (Thank you jbriggs444)

(baseline frame = whatever frame the observer decides to pick as a baseline frame)

 

[exmarine]

The most rigorous treatment I can find - by far - is in a book by Thomas Phipps, and he credits Aharoni. It appears to be a perfectly orthodox treatment. I suppose I could type the derivation here, but I assume many of you have access to that original source - I don’t. So I’ll just type the result from my rework of Phipps’ rendition.

$cos\left(\alpha\right)=1-\frac{1-\ell^{2}}{1-\beta\ell}\left(1-\sqrt{1-\beta^{2}} \right)$

The expansion of the inverse cosine of the aberration angle to second order: (tricky!)

$\alpha=\sqrt{1-\ell^{2}}\beta+\frac{\ell\sqrt{1-\ell^{2}}}{2}\beta^{2}+...$

el is the direction cosine of the light ray from the source to that inertial axis of the source parallel to the relative velocity with the sink. And beta is of course the relative velocity divided by c. I can’t find any questionable or buried assumptions in the derivation.

Thanks for all the responses, but many of you - or at least some of you - seem to be pointing at a straw man. Of course we don’t know alpha. We only observe changes in alpha. Note the number of times I tried to emphasize the word "CHANGES" in my original post. And I see nothing in the derivation that limits those changes in alpha to being caused only by changes in the observer’s state of motion.

I am going away now. I remain puzzled by this.

 

[jartsa]

Thanks for all the responses, but many of you - or at least some of you - seem to be pointing at a straw man. Of course we don’t know alpha. We only observe changes in alpha. Note the number of times I tried to emphasize the word "CHANGES" in my original post. And I see nothing in the derivation that limits those changes in alpha to being caused only by changes in the observer’s state of motion.

Change of velocity of a light source does not cause a change of position of the light source according to an inertial observer.

There's a good intuitive explanation what happens when the velocity of light source changes in post #7.

 

[Meir Achuz]

$$\tan\theta'=\frac{\sin\theta}{\gamma(\cos\theta+v/c)}$$,
where v is the velocity of the star wrt the observer, $\theta$ is the angle between v and the direction from the star to the observer, $\theta'$ is the angle that the telescope should be set at.
The aberration angle is $\theta'-\theta$.
This relativistic is close to the non-relativistic result
$$\tan(\theta'-\theta)=\frac{v}{c}\sin\theta$$,
which was originally derived, and measured, in 1729 by James Bradley.

 

[jartsa]

$$\tan\theta'=\frac{\sin\theta}{\gamma(\cos\theta+v/c)}$$,
where v is the velocity of the star wrt the observer, $\theta$ is the angle between v and the direction from the star to the observer, $\theta'$ is the angle that the telescope should be set at.
The aberration angle is $\theta'-\theta$.
This relativistic is close to the non-relativistic result
$$\tan(\theta'-\theta)=\frac{v}{c}\sin\theta$$,
which was originally derived, and measured, in 1729 by James Bradley.

How does the observer measure the direction from the star to the observer? (By aiming his telescope so that the star is in the view, I guess)

$\theta'-\theta$ that might be the angle between the apparent direction of a star and the "real" direction of the star.

The apparent direction is the direction the telescope should be aimed at.

The "real" direction is the direction to use if the observer becomes static reletive to the star, but not if the star accelerates to the observer frame, observer must accelerate to the star frame.

 

[PhilDSP]

Liebscher and Brosche seem to have done an excellent job of compiling the historical publications and debates about the subject. Of all of their references, I'd have to give most credence to Pauli, who as they say disagrees with their assessment and solution.

But aren't Liebscher and Brosche missing the crucial observation that's it's the relative transverse velocity or motion between the source and observer, in principle, that determines the aberration?

 

[Meir Achuz]

How does the observer measure the direction from the star to the observer? (By aiming his telescope so that the star is in the view, I guess)

$\theta'-\theta$ that might be the angle between the apparent direction of a star and the "real" direction of the star.

The apparent direction is the direction the telescope should be aimed at.

The "real" direction is the direction to use if the observer becomes static reletive to the star, but not if the star accelerates to the observer frame, observer must accelerate to the star frame.

Theta is the angle for the direction of the star would be seen at with no aberration. Theta' is the actual angle of the telescope to best see the star. Theta' varies as the relative transverse velocity varies. Bradley measured the wobble in a stars apparent direction in half year intervals, with the transverse velocity being the speed of the Earth in its orbit. For a binary star, the transverse velocity causing the wobble is the velocity of one star in its orbit. Theta is unimportant, as it is the variation of theta' that is measure.

 

[PAllen]

But aren't Liebscher and Brosche missing the crucial observation that's it's the relative transverse velocity or motion between the source and observer, in principle, that determines the aberration?

I don't think so. If the observer is moving inertially, there is no aberration detectable, period. To detect aberration you need to compare observations from two states of motion (e.g. times of the year - different velocity). Thus, the key is observations in different states of motion, and the motion of the source is irrelevant except to the extent that it changes position of the distant source in relation to other distant sources.

 

[xox]

Theta is the angle for the direction of the star would be seen at with no aberration. Theta' is the actual angle of the telescope to best see the star. Theta' varies as the relative transverse velocity varies. Bradley measured the wobble in a stars apparent direction in half year intervals, with the transverse velocity being the speed of the Earth in its orbit. For a binary star, the transverse velocity causing the wobble is the velocity of one star in its orbit. Theta is unimportant, as it is the variation of theta' that is measure.

I would like to add to the excellent post above that $\theta$ cannot be known, whereas $\theta'$ is what we measure, therefore, we do not need to spend too much time dwelling on the relationship between $\theta'$ and $\theta$. More exactly, astronomers need to incline the telescope by the angle:

$$\theta'(t)=arctan\frac{v(t)}{c}$$

as seen in this picture.

The angle $\theta'(t)$ is not constant, it varies with time because the speed of the Earth (where the telescope is located) $v=v(t)$ varies during the astronomical year in a rather complicated way:

$$v=v_e sin(\Omega_e t) cos \Phi_e +v_d sin(\Omega_d t) cos \Phi_d$$

where:

$v_e=30km/s$ is the Earth orbital speed
$v_d=0.355km/s$ is the Earth rotational speed
$2\pi/\Omega_e=$1 year
$2 \pi/\Omega_d=$1 day
$\Phi_e=$Earth axle inclination with respect to the orbital plane
$\Phi_d=$angle between the location on the Earth and the equatorial plane

The above is valid for the case of a star fixed with respect to the Sun. The case of a star moving with respect to the Sun gets more complicated, we need to adjust $v(t)$ in order to incorporate the relative motion between the star and the Sun:

$$v(t)=v_s(t)+v_e sin(\Omega_e t) cos \Phi_e +v_d sin(\Omega_d t) cos \Phi_d$$

where $v_s(t)$ is the relative speed between the star and the Sun. I hope this answers the OP question to his satisfaction.

 

[PhilDSP]

It will be necessary, won't it?, to take the integral of the relative change of position between the source and observer over the time that the photon is in flight. That is, once the photon has been emitted, any further motion of the source is immaterial.

That means that anyone instantaneous relative velocity contributes only infinitesimally. But the calculation can't be performed properly without determining the relative motion based on where the source was at the time of photon emission.

If r is the position of the observer relative to the point of photon emission then
$$\Delta r = \int_{t_e}^{t_a} v dt$$
where $t_e$ is the time that the photon was emitted, $t_a$ is the time that the photon was absorbed by the observer and v, i.e. v(t) is the relative velocity between the point of emission and the observer at time t

 

[PAllen]

It will be necessary, won't it?, to take the integral of the relative change of position between the source and observer over the time that the photon is in flight. That is, once the photon has been emitted, any further motion of the source is immaterial.

That means that anyone instantaneous relative velocity contributes only infinitesimally. But the calculation can't be performed properly without determining the relative motion based on where the source was at the time of photon emission.

Suppose all distant objects and observer are mutually stationary. Then, the observer moves and takes observations in its new state of motion. There is observable aberration. Contrast with observer remains inertial, distant sources move in various way. There is no observable aberration. Thus, the determining feature is clearly comparing observations at relative motion to each other.

 

[PhilDSP]

Yes, the "real" aberration is not observable except by comparing two or more optical observations at different times.

I think the "real" aberration would be the cross product of the vector $\Delta r$ above and the dot product of the unit vector in the direction of the star and the unit vector normal to the plane containing the Earth's orbit.

$\textrm{aberration} = \Delta r \times (\hat{r_e} \cdot \hat{o_n})$

The difference between relativistic and classical calculations would be how you relate $t_e$ and $t_a$ to v(t).

 

[exmarine]

...

$$v(t)=v_s(t)+v_e sin(\Omega_e t) cos \Phi_e +v_d sin(\Omega_d t) cos \Phi_d$$

where $v_s(t)$ is the relative speed between the star and the Sun. I hope this answers the OP question to his satisfaction.

And if $v_s(t)$ changes due to changes in the star's motion, yet we observe no corresponding changes in $\theta'(t)$? How can that be consistent with SRT? That was my original question. Thanks.

 

[xox]

And if $v_s(t)$ changes due to changes in the star's motion, yet we observe no corresponding changes in $\theta'(t)$?

Sure we do, this is why we observe the "aberrant" motion of binary stars , for example.

How can that be consistent with SRT? That was my original question. Thanks.

Is your question answered to your satisfaction now?

 

[jartsa]

How can that be consistent with SRT? That was my original question. Thanks.

Almost the same way that twin paradox is consistent wit SRT. Let's compare:Time dilation and differential aging, also known as twin paradox:

There are two identical observers A and B. A acccelerates. A sees B's clock slowing down, when he sees B accelerating, which is at the same time that A is feeling a g-force.

B sees A's clock slowing down, when he sees A accelerating, which is some time after A feels a g-force.

If A returns back to were he started, then we have a case of differential aging (A is younger than B, everybody agrees about this)

Differential radiation:

There are two identical observers A and B. A acccelerates. A sees the light emitted by B changing intensity and direction, when he sees B accelerating, which is at the same time that A feels a g-force.

B sees the light emitted by A changing intensity and direction, when he sees A accelerating, which is some time after A feels a g-force.

If A returns back to were he started, then we have a case of differential light emitting (A has emitted less light, and the light emitted by A was beamed, and A observed aberration while B did not observe aberration, everybody agrees about these things)

 

[xox]

Almost the same way that twin paradox is consistent wit SRT. Let's compare:


Time dilation and differential aging, also known as twin paradox:

There are two identical observers A and B. A acccelerates. A sees B's clock slowing down, when he sees B accelerating, which is at the same time that A is feeling a g-force.

B sees A's clock slowing down, when he sees A accelerating, which is some time after A feels a g-force.

If A returns back to were he started, then we have a case of differential aging (A is younger than B, everybody agrees about this)




Differential radiation:

There are two identical observers A and B. A acccelerates. A sees the light emitted by B changing intensity and direction, when he sees B accelerating, which is at the same time that A feels a g-force.

B sees the light emitted by A changing intensity and direction, when he sees A accelerating, which is some time after A feels a g-force.

If A returns back to were he started, then we have a case of differential light emitting (A has emitted less light, and the light emitted by A was beamed, and A observed aberration while B did not observe aberration, everybody agrees about these things)

The aberration has nothing to do with differential acceleration, nor does it have to do with differential radiation . As an aside, your "explanation" of the twins paradox is incorrect as well.

 

[jartsa]

The aberration has nothing to do with differential acceleration, nor does it have to do with differential radiation . As an aside, your "explanation" of the twins paradox is incorrect as well.

I didn't say what causes the differential aging. It's so difficult to explain.

Let's consider two identical spaceships side by side. They start to accelerate identically. Both see the other one to move ahead, this is the aberration.

When acceleration ends, they must see each other side by side again. Something must counter the aberration. It's the time dilation of the information transfer between the spaceships. They see the old positions of each other.

I have a question:
There's no time dilation in the spaceships' frame. Is it possibe for the spaceship passangers to explain what happened?

 

[xox]

I didn't say what causes the differential aging. It's so difficult to explain.

Let's consider two identical spaceships side by side. They start to accelerate identically. Both see the other one to move ahead, this is the aberration.

You are comingling the aberration with the Bell paradox. Let me ask you a question, in which frame do the rockets accelerate identically? What is the role of relativity of simultaneity in the above exercise?

When acceleration ends, they must see each other side by side again. Something must counter the aberration.

There was no aberration to begin with since there was no relative motion.

It's the time dilation of the information transfer between the spaceships.

What is "time dilation of the information"? Where did you get this term?

I have a question:
There's no time dilation in the spaceships' frame. Is it possibe for the spaceship passangers to explain what happened?

I have no idea what you are asking.

 

[PhilDSP]

Exmarine, I quite agree that there is a serious lack of clarity on this issue and that you should not feel patronized for honestly desiring a clear resolution.

I'm wondering now if the reason for the lack of clarity or the disconnect in conception is that very many regard a single absolute value of the relative velocity as the operative characteristic in a solution of this problem when it really isn't and cannot be unless your observational equipment has a resolution that is an order of magnitude finer than today's.

If you consider that the orbit of the Earth is rectilinear, then you know that its relative transverse velocity with respect to a star changes significantly over several weeks or several months. Even the very nearest stars require that several Earth orbits will have been completed during the time that any single photon is in flight. That means that $\Delta r$ calculated as I have shown will be several or many times smaller than a value one will arrive at with a single v(t) value approach.

I believe that may be why the raw Pauli, Einstein, et al, formulas don't work for stars compared with planets. In principle, the physics of aberration is the same for planets or satellites in our solar system as it is for stars. With stars, the Earth's motion wraps around itself several or many times during the photon's flight so no simple single-valued relative velocity will work properly.

 

[jartsa]

You are comingling the aberration with the Bell paradox. Let me ask you a question, in which frame do the rockets accelerate identically? What is the role of relativity of simultaneity in the above exercise?

I forgot to draw a picture. Picture of two rockets side by side:

The left rocket goes up /|\  then there's some distance .. and the right rocket goes up /|\

And the rockets are identical, and preprogrammed to do the maneuvers.

There was no aberration to begin with since there was no relative motion.

Yes there was. Aberration is an optical phenomenom where an instrument measuring the light direction butts the light ray.
Aberration approaches zero when butt direction approaches ray direction. So we can say there's aberration when the observer moves, and the direction of the motion is not exactly the same as the direction of the light ray.

What is "time dilation of the information"? Where did you get this term?

Time dilation of information transfer = dilation of the time between the sending of information and the receiving of information = dilation of lag

 

[exmarine]

Computer problems here. Thanks for all the responses! I will study them. I have a short follow-up for XOX. I wonder if I understand your post #23. Are you saying that there ARE observable differences in the annual changes in the aberration angles from binaries versus non-binary stars? Can you give me some references for that - hopefully that I can get from the internet as it is difficult for me to get to a technical library?

Sure we do, this is why we observe the "aberrant" motion of binary stars , for example.

 

[xox]

Computer problems here. Thanks for all the responses! I will study them. I have a short follow-up for XOX. I wonder if I understand your post #23. Are you saying that there ARE observable differences in the annual changes in the aberration angles from binaries versus non-binary stars? Can you give me some references for that - hopefully that I can get from the internet as it is difficult for me to get to a technical library?

No, this is not what I said. What I said is that the aberration is calculated (see http://en.wikipedia.org/wiki/Stellar_aberration_%28derivation_from_Lorentz_transformation%29) by using the velocity of the Earth and of the stars wrt. a frame anchored in the Sun. So, we need to know the motion of the star wrt. the Sun. (we know pretty well the motion of the Earth wrt. the Sun). Binary stars may have a different (more complicated) motion wrt. the Sun than single stars, that's all.
BTW: are you an ex-marine (I am ex-special forces).

 

[exmarine]

BTW: are you an ex-marine (I am ex-special forces).

Is it appropriate to post that kind of stuff here? If we keep it brief I guess. Yes, I was a Marine chopper pilot; VMO-2 believe it or not; Khe Sanh, 68 Tet, the whole 9 yards; 800 combat missions, 38 air medals, 2 distinguished flying crosses, etc. But now I am retired engineer, finally get to study physics, and pester all you kids with my dumb questions! Like this one I guess.

I understand what you are trying to explain. Not to belabor the point, but my problem is with significant changes in a binary source’s contribution over a short period of time to the changes in our relative transverse velocity NOT having any apparent influence on the observable changes in the aberration angle. See my original post for definitions of "significant" and "short".

Still trying to recover my computer and can’t keep up with all the responses. But I see none that confirm the equation I gave in post (11?) for the first and second order aberration angle being correct. I assume it is a standard result. Anyone? So how can one define "relative velocity" to exclude the source’s contribution to changes therein, and only include those of the observer’s contributions? Do we have to use General Relativity to address this problem? After all, both a binary source and our observation platform are accelerating. It is really about a photon going between the binary's geodesic and the Earth's - or actually 2 photons, one now, and another a month or two from now when BOTH velocities have changed.

Thanks again for all the responses. Semper Fi

 

[jartsa]

How about this aberration formula:Velocity of light according to a moving observer = Velocity of that light according to a static observer "+" velocity of the moving observer "+" means relativistic velocity addition

Velocity of light means the speed and the direction of light, velocity vector.

 

[Meir Achuz]

Velocity of light according to a moving observer = Velocity of that light according to a static observer

 

[xox]

Is it appropriate to post that kind of stuff here? If we keep it brief I guess. Yes, I was a Marine chopper pilot; VMO-2 believe it or not; Khe Sanh, 68 Tet, the whole 9 yards; 800 combat missions, 38 air medals, 2 distinguished flying crosses, etc.

Impressive.

I understand what you are trying to explain. Not to belabor the point, but my problem is with significant changes in a binary source’s contribution over a short period of time to the changes in our relative transverse velocity NOT having any apparent influence on the observable changes in the aberration angle.

The link I sent you says exactly the opposite, the formula is valid if and only if the change in position of the observed star is much smaller than the distance star-observer (Earth).

See my original post for definitions of "significant" and "short".

I'll look at your example. In the meanwhile, check http://en.wikipedia.org/wiki/Stellar_aberration_%28derivation_from_Lorentz_transformation%29#Application:_Aberration_in_astronomy example of calculation.