# Thread: Stellar aberration and the principle of relativity

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## Stellar aberration and the principle of relativity

Why stellar aberration does not depend on the relative velocity:
Earth - star, but only on the speed of the Earth - an observer?

I know that we measure only the cyclic changes of aberrations
(on ​​an annual basis), but that does not change anything here.

But we can not use relative speed here, because then we have a very diverse aberrations of the stars, because of the fairly wide range of speeds that are at stake here.

For example, the star S2, seen in the center of the Milky Way:
http://en.wikipedia.org/wiki/S2_%28star%29

v = 5000 km/s, so the angle of aberration in this case, more than 3000'' - nearly 1 degree!
It is incredibly gigantic value - the whole orbit of the star is less than 0.1 '.

I suspect that the principle of relativity is not properly recognized.
Probably here the point is, that the description of the process
in question does not depend on the adopted reference system,
but not the process itself - a phenomenon.

2. Does the history of a photon somehow matter? The photon is on a path relative to us when we observe it. That's the end of the story.

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Originally Posted by antoniseb
Does the history of a photon somehow matter? The photon is on a path relative to us when we observe it. That's the end of the story.
It does not matter, because we observe the aberration of stars depending on the season, and the light from a star is flying here for thousands of years, not knowing our position in orbit at the time of arrival.

4. ...and depends only on the observer's instantaneous transverse velocity in certain frame of reference, at the moment of observation. The light beam from a distant object cannot itself have any transverse velocity component, or it could not (by definition) be seen by the observer, since it would miss the observer. Thus, any transverse velocity of the emitting source plays no part in aberration. Another way to state this is that the emitting object may have a transverse velocity with respect to the observer, but any light beam emitted from it which reaches the observer, cannot, for it must have been previously emitted in such a direction that its transverse component has been "corrected" for. Such a beam must come "straight" to the observer along a line which connects the observer with the position of the object when it emitted the light...
http://en.wikipedia.org/wiki/Stellar_aberration

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OK. But in the equation for the angle of aberration, which can be seen there (relativistic aberration) is the relative velocity between the source and observer.

where θ is the true angle SEE′, θ′ is the apparent angle S′EE′, and v is the relative speed between the presumed fixed frame of reference (such as heliocentric) and the observer's one.
This is incorrect.

Here is the same formula, in a different form:
http://en.wikipedia.org/wiki/Relativistic_aberration

These are not formulas for stellar aberration (for distant sources), but the usual adjustment due to the propagation time of light (we see a delayed images), and hence the angular offset - relative to the actual position (instantaneous).

This displacement is only possible to close sources, such as a planet.
It does not work for distant sources - stars; in this case, the angular offset is zero.

6. Originally Posted by Hetman
OK. But in the equation for the angle of aberration, which can be seen there (relativistic aberration) is the relative velocity between the source and observer.

This is incorrect.

Here is the same formula, in a different form:
http://en.wikipedia.org/wiki/Relativistic_aberration

These are not formulas for stellar aberration (for distant sources), but the usual adjustment due to the propagation time of light (we see a delayed images), and hence the angular offset - relative to the actual position (instantaneous).

This displacement is only possible to close sources, such as a planet.
It does not work for distant sources - stars; in this case, the angular offset is zero.
It is apparent to me that you have some major lack of understanding of the physics involved here, but from these words in a couple of posts I cannot tell in any detail just what the gaps in your knowledge are. If I could sit with you at a desk, make some sketches, and respond immediately to any comments or questions, I could zero in on the problem quickly and show you where you have gone astray. In a forum like this it is much more awkward.

I stand by the author's opinion that the distance to a star does not affect the aberration shift in apparent angular position in the presence of relative lateral motion. In addition, we get the same amount of displacement whether we treat it as a moving observer looking at a stationary star, or a stationary observer looking at a moving star.

7. One way to look at it: the "static" component of aberration, due to the relative motion of the Sun and emitting star, is not observable, since we don't know the "zero-motion" direction to the star - we see only the annual modulation due changes in the vector of the Earth's orbital motion. (If observing from a satellite, there s an additional component due to its relative motion; this is a big deal for Hubble observations in particular). We don't measure some absolute value of aberration, only its change as the observer accelerates.
Last edited by ngc3314; 2012-Jul-21 at 02:55 PM. Reason: precision

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Originally Posted by Hornblower
I stand by the author's opinion that the distance to a star does not affect the aberration shift in apparent angular position in the presence of relative lateral motion. In addition, we get the same amount of displacement whether we treat it as a moving observer looking at a stationary star, or a stationary observer looking at a moving star.
Of course. The formula for the relativistic aberration is symmetric, because it is not stellar aberration, but the usual angular offset, which is a consequence of the delay the observed image.

cosa' = (cosa - v/c)/(1 - v/c cosa)

and for angle a = 90:

O-----> v
|
| cT
|
| \ a = 90 => cosa = 0;
S------

cosa' = -v/c - what does this mean?

|-vT-|O-----> v
|...../ a'
|.../
|../ cT
|/
S

The observer sees the delayed image, the source is in the position of the past: cosa'= -vT/cT = -v/c

This has nothing to do with Bradley's stellar aberration.

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Originally Posted by ngc3314
One way to look at it: the "static" component of aberration, due to the relative motion of the Sun and emitting star, is not observable, since we don't know the "zero-motion" direction to the star - we see only the annual modulation due changes in the vector of the Earth's orbital motion. (If observing from a satellite, there s an additional component due to its relative motion; this is a big deal for Hubble observations in particular). We don't measure some absolute value of aberration, only its change as the observer accelerates.
Yes, but in the past people have suggested that the speed of the Sun can be determined by measuring the absolute angle of aberration.

Simply: a uniformly distributed system of sources, observed from a moving system would be a little different - anisotropic.
Knowing this anisotropy, we can determine the velocity of the observer.

10. If light behaved like macro particles then the motion of the observer would be indistinguishable from that of the emitter. It would be the matter of which frame of reference, the motion is observed from.

However, light does not behave rationally. It's speed is observed to be equal in all frames of reference.

Thus the observed speed of light by the observer is not encoded-with/a-factor-of the speed of the emitter.

Stellar aberration is a factor of the speed-of-light which has no information about the speed/motion of the emitter.

All hope is not lost however. The motion of the emitter (versus the observer or vice versa) is-encoded-in/affects the frequency of the observed light. This however, has no effect on the stellar aberration.

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Originally Posted by a1call
If light behaved like macro particles then the motion of the observer would be indistinguishable from that of the emitter. It would be the matter of which frame of reference, the motion is observed from.
I do not know if this is relevant in this case, but has long been known
that light is a wave, means: some systematic propagation of disturbances.

Originally Posted by a1call
All hope is not lost however. The motion of the emitter (versus the observer or vice versa) is-encoded-in/affects the frequency of the observed light. This however, has no effect on the stellar aberration.
if the source is running on the side - tangentially, then the receiver gets
the light emitted back slightly (angle ~ v/c), so there will be a redshift,
probably proportional to (v_t/c)^2, i.e. transverse Doppler, ignoring other components.

A few pictures:
http://www.fourmilab.ch/cship/aberration.html

12. This seems more like "mainstream bashing" than asking questions.
If you have a problem with the mainstream interpretation of abberation, you should take it to ATM.
I have moved the thread for you, please note the special rules of the ATM section.

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This may indeed be a more appropriate forum for this problem,
because even with the naked eye can see that the stellar aberration
is completely contrary to the principle of relativity (in the traditional form).

Within the framework of special relativity, such a phenomenon
could not exist at all, due to the full symmetry of the source and receiver in this approach.

I originally put on the question-answer section, because I was hoping
that someone will try to reasonably explain the discrepancy
of theory with observation, but it was virtually impossible.

14. Originally Posted by Hetman
Of course. The formula for the relativistic aberration is symmetric, because it is not stellar aberration, but the usual angular offset, which is a consequence of the delay the observed image.

cosa' = (cosa - v/c)/(1 - v/c cosa)

and for angle a = 90:

O-----> v
|
| cT
|
| \ a = 90 => cosa = 0;
S------

cosa' = -v/c - what does this mean?

|-vT-|O-----> v
|...../ a'
|.../
|../ cT
|/
S

The observer sees the delayed image, the source is in the position of the past: cosa'= -vT/cT = -v/c

This has nothing to do with Bradley's stellar aberration.
The angles according to each are taken from the direction opposite the line of motion of the other, so you can see from your image that cosa' = -v/c, yes, for greater than 90 degrees according to S from the direction O travelled from, while cosa = 0 for 90 degrees according to O. The angles are just an angular offset due to the delay, yes, but it includes relativistic factors between the frames, such as the length contraction of an emitting laser tube or observing telescope, which affects the angle each would say the other measures, although you cannot see that clearly with your example because the photon travels in a direction tangent to the line of travel and no length contraction takes place in that direction. The biggest relativistic factor, however, is that the light travels at c according to both observers. In Galilean relativity, the speed of an emitted photon would add or subtract to the speed of the source, which would change the delay times and the angles measured, but the main contribution of Bradley's measurements of stellar aberration was that they showed the speed of light to be the same regardless of the motion of the source or receiver.

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Bradley did not show anything like that.

And contraction, or rather the Lorentz transformation
is merely a mathematical procedure, which normalizes the wave equation.

16. Originally Posted by Hetman
Bradley did not show anything like that.

And contraction, or rather the Lorentz transformation
is merely a mathematical procedure, which normalizes the wave equation.
I don't know what you mean by that, but read the couple of paragraphs here under "annual abberation". Bradley was able to determine the speed of light from the aberration. Later telescopes were filled with water to see if that changed the angle of observation, but it didn't, which followed the Fresnel drag equations, later explained through Relativity.

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Originally Posted by grav
I don't know what you mean by that, but read the couple of paragraphs here under "annual abberation". Bradley was able to determine the speed of light from the aberration. Later telescopes were filled with water to see if that changed the angle of observation, but it didn't, which followed the Fresnel drag equations, later explained through Relativity.
There simply is no formula for stellar aberration in the theory of relativity.

There is just this transformation of angles - correction of angular position,
due to the movement of the source (relative to the observer) and the finite speed of light.

This does not apply in the case of aberration of light from the stars,
because stars are too far away - do not move at all (no need to adjust anything here,
distant stars are always at the same point in the sky).

18. Originally Posted by Hetman
There simply is no formula for stellar aberration in the theory of relativity.

It is just this transformation of angles - correction of angular position,
due to the movement of the source (relative to observer).

This does not apply in the case of aberration of light from the stars,
because stars are too far away - do not move at all (no need to adjust anything here,
distant stars are always at the same point in the sky).
The burden of proof is on you to walk us step by step through the mainstream theory and to show us, in appropriate mathematical detail what you think Einstein, et. al. did wrong and why you think so. Then show us your way, also in appropriate mathematical detail, and reconcile with the 20 arcseconds of aberration that all stars show as a result of Earth's motion. If you are unable to do so, we have no cause to take your presentation seriously. If you simply do not yet have the mathematical knowhow to do so, I would suggest emulating Einstein. If it takes ten years, so be it. That is how much time he spent boning up on the math after getting a Bright Idea for a general theory of relativity after announcing the special theory. He already had a Ph.D. in physics, and had the basic knowledge to recognize his limitations in 1905, along with the good sense to consult the world's top mathematicians for assistance.

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Originally Posted by Hornblower
The burden of proof is on you to walk us step by step through the mainstream theory and to show us, in appropriate mathematical detail what you think Einstein, et. al. did wrong and why you think so. Then show us your way, also in appropriate mathematical detail, and reconcile with the 20 arcseconds of aberration that all stars show as a result of Earth's motion. If you are unable to do so, we have no cause to take your presentation seriously. If you simply do not yet have the mathematical knowhow to do so, I would suggest emulating Einstein. If it takes ten years, so be it. That is how much time he spent boning up on the math after getting a Bright Idea for a general theory of relativity after announcing the special theory. He already had a Ph.D. in physics, and had the basic knowledge to recognize his limitations in 1905, along with the good sense to consult the world's top mathematicians for assistance.
Yes. I agree completely.

However, the relativistic aberration formula itself is very interesting, and worthy of attention.

we have: cosf = x/r; r = ct;

x = ct cosf; y = ct sinf

therefore similarly: cos f' = x'/r',
and simply substitute the Lorentz transformation:
x' = (x - vt)g, t' = (t - xv/c^2)g

It is probably quite a classic transformation, because here the dilation and contraction each other compensate.

The angles here are consistent with an ellipsoidal wavefront of the moving source.

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And this is probably the real meaning of the Lorentz transformation, ie a description of the wavefront of a moving source.

This is not a transformation of coordinates, but the reality - the real shape of the wavefront.
Something like that does not depend on the coordinate system,
such as the shape of the building, or the geometry of the gravitational field in general relativity.

The procedure for calculating the angles of aberrations allows us to reconstruct this ellipsoid,
only because it is in the Lorentz transformation - this transformation is precisely the equation of an ellipsoid.

r = ct

equation of the light signal in the direction of the vector r, from a source at rest at the point O=0,0.
After the Lorentz transformation: r'= ct'
and this is already a vector from the focus of the ellipsoid, not the center of the sphere.

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Originally Posted by Hetman
And this is probably the real meaning of the Lorentz transformation, ie a description of the wavefront of a moving source.
That is not right - the Lorentz transformation has nothing to do with the wavefront of a moving source.
The real meaning of the Lorentz transformation is
In physics, the Lorentz transformation or Lorentz-Fitzgerald transformation describes how, according to the theory of special relativity, different measurements of space and time by two observers can be converted into the measurements observed in either frame of reference.

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It was just a working hypothesis, then never sufficiently confirmed;
the subject is about stellar aberration, which ignores this symmetry condition.

Anyway, I'm talking about the physical sense.
Mathematically it can be interpreted in different ways, usually as some part of Minkowski space.

The transformation of physical space - together with the bodies, planets, galaxies, and the time, simply did not exist.
Sufficient is the correct geometry of the wavefront - of single source.
Last edited by Hetman; 2012-Jul-24 at 01:27 AM.

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Originally Posted by Hetman
There simply is no formula for stellar aberration in the theory of relativity.
Getting back to stellar aberration then: Your staetment is incorrect, see relativistic aberration. This is a formula for stellar aberration in the theory of special relativity.

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Originally Posted by Reality Check
Getting back to stellar aberration then: Your staetment is incorrect, see relativistic aberration. This is a formula for stellar aberration in the theory of special relativity.
I already explained that this formula does not apply to distant sources, but only those close once (ie planetary aberration).

At the same time it is the formula for the angles of a moving source, and only the outgoing rays.
The incoming rays are rather different here, just because the effect of aberration of light!

For example, the moving source gives a signal at the moment
when is over the receiver - an angle 90 degrees:

S --> v
|.\
|..\
|...\ vertical beam bypasses the receiver at a distance vt.
O

Source must emit a beam in the other direction:

cos 90 = 0 => cos a' = -v/c, that is, slightly to the rear:

....S --> v
.../|
../.|
./..|
O' O

receiver does not move, so there is no aberration.

In the case with the moving receiver, situation is more complicated,
especially when it moves parallel to this source, we get a situation
compatible with the first scheme, but this time the beam reaches the receiver.
Last edited by Hetman; 2012-Jul-24 at 12:28 PM.

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Originally Posted by Hetman
I already explained that this formula does not apply to distant sources, but only those close once (ie planetary aberration).

At the same time it is the formula for the angles of a moving source, and only the outgoing rays.
The incoming rays are rather different here, just because the effect of aberration of light!

For example, the moving source gives a signal at the moment
when is over the receiver - an angle 90 degrees:

S --> v
|.\
|..\
|...\ vertical beam bypasses the receiver at a distance vt.
O

Source must emit a beam in the other direction:

cos 90 = 0 => cos a' = -v/c, that is, slightly to the rear:

....S --> v
.../|
../.|
./..|
O' O

receiver does not move, so there is no aberration.
Motion is relative so, your claim that "receiver does not move" shows a bias towards "absolute motion" (that does not exist). This explains your absurd claim that "I already explained that this formula does not apply to distant sources, but only those close once (ie planetary aberration)."
Last edited by Grassman; 2012-Jul-24 at 02:35 PM.

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Unfortunately, the previous diagrams are consistent only with a simple kinematics of balls thrown from the train.
There are mixed values ​​measured in different systems.

With light is different.

For example, we measure the velocity v in the moving system,
thus in a stationary system must be: v / gamma = v * sqrt (1-v ^ 2 / c ^ 2)...
but this is recursion - velocity v occurs in gamma again.

Relativity theory avoids such complications, and why it's so simple.

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Originally Posted by Grassman
Motion is relative so, your claim that "receiver does not move" shows a bias towards "absolute motion" (that does not exist). This explains your absurd claim that "I already explained that this formula does not apply to distant sources, but only those close once (ie planetary aberration)."
That's right.
The assumption is inevitable, due to the lack of dependence
aberration angle on the relative speed: Star-Earth;
as I showed earlier on the example of the star S2: v = 5000 km/s.

We do not measure one-way speed of light, but only two-way, and this is constant - independent of direction.

equation of an ellipse, which represents a procedure for measuring two-way speed of light (or any wave in the undisturbed medium).

A hyperbola is also possible: for a superluminal source ellipse transforms into a hyperbola,
and then double images can be recorded the same source at the same time.
Last edited by Hetman; 2012-Jul-25 at 01:29 PM.

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Originally Posted by Hetman
That's right.
The assumption is inevitable, due to the lack of dependence
aberration angle on the relative speed: Star-Earth;
as I showed earlier on the example of the star S2: v = 5000 km/s.

We do not measure one-way speed of light, but only two-way, and this is constant - independent of direction.

equation of an ellipse, which represents a procedure for measuring two-way speed of light (or any wave in the undisturbed medium).

Hyperbole is also possible: for a superluminal source ellipse transforms into a hyperbola,
and then double images can be recorded the same source at the same time.
What does all the above have to do with the fact that you don't understand the fact that motion is relative and not absolute?
What does all have to do with the fact that you misunderstand the basics of relativistic aberration?

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Originally Posted by Grassman
What does all the above have to do with the fact that you don't understand the fact that motion is relative and not absolute?
What does all have to do with the fact that you misunderstand the basics of relativistic aberration?
Show how you compute the aberration of the star S2, starting from the relativistic aberration formula,
which explicitly includes the relative velocity source to the receiver, and then we'll see what you understand.

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Originally Posted by Hetman
Show how you compute the aberration of the star S2, starting from the relativistic aberration formula,
which explicitly includes the relative velocity source to the receiver, and then we'll see what you understand.
First off, it behooves on the ATM proponent to defend his/her theory. So, please do so.
Second off, you are not to ask the mainstream to prove their point.
Third off, it is very easy, just apply the formula of relativistic aberration. If you think that experimental observation disagrees with the theory, then you have just acquired another thing to prove.

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