Requiem for Relativity

I've been thinking about my attempt to add some 3D effect to my artwork. I did this to make it more informative. To make it easier for you to see in your mind's eye what I see in my mind's eye.

But life has taught me that accurate communication with another mind is not as easy as it ought to be. I say po-TAY-to, you say po-TAH-to. Do we really mean the same thing? The same word can mean different things to different people.

And packing more information into a single drawing is not always the best way to convey more information.

Anyway, I've decided to reproduce my Fig 1 from above with a little more detail, in the hope that I will not further muddy the water. Any comments you might have are welcome.



Fig 1.1 is the original Fig 1.
Fig 1.2 shows only the coordinate axes used in 1.1

Fig 1.3 is Fig 1.1 with the attempt at 3D removed. Observer C is closest to you, so you cannot see A behind him and you cannot see B behind A. The y axis now comes straight up out of the page (or screen).
Fig 1.4 shows only the coordinate axes used in Fig 1.3 (Of course it is the same coordinate system, seen from a different angle.)

The dashed lines in Fig 1.1 and 1.3 still represent the light beam from S to each one of the observers, as seen by each particular observer.

If there is anything about the individual figures, or about them as a group, that is not clear, please ask. If I have failed to communicate, I cannot know that without feedback.

Our three observers (A, B and C) will indeed observe star S with different aberration angles. The magnitude and orientation of the aberration can exactly be calculated as described and the observers will indeed need to re-point their respective telescopes accordingly.

If we now look at the representation of occultation event: rocket O blocks the light beam for A and as a consequence, A can no longer see star S.

This is exactly where the paradox comes in: let's compare rocket 0 with the light passing the moon.

While rocket O has just come in between star S and observer A, A can still observe star S ... Tom Van Flandern pointed out that with the orbital velocity of the moon, a star S can be observed for an additional 40 seconds (for a star showing an aberration of 20 arcsec) from the moment when star S has gotten behind the border of the moon).

Imagine a balloon passing by at night: would our star S whose apparent position is right next to the balloon be invisible because its true direction is behind the balloon?


So how does this all fit together?

The pictures are missing one essential component: the light carrying medium.

For on observer who is completely 'static' relative to the light carrying medium, the aberration is occuring while the light is travelling through the solar system. The observed aberration equals the velocity/direction of the light carying medium (near the observer) relative to the 'static' star S. The aberration takes place where the tangential velocity of the light carrying medium is changing. (the formula to be used is exactly the same formula used to calculate the stellar aberration but the value changes only gradually with tiny increments ...)

For on observer who is in motion relative to the light carrying medium, there are two forms of aberration that add up to each other:
- the aberration that would be observed by the 'static observer' who is static relative to the light carying medium
- the aberration caused by the difference in speed of the observer relative to the the light carrying medium.

The observed magnitude and direction of the aberration (for a star S) can be determined in exactly the same way for a 'static' observer and for an observer in motion. So in order to calculate the aberration for any of the observers (in rocket A, B and C), the most simple approach is to assume that the aberration takes place near each of these observers and is only dependent on the tangential speed relative to the direction of the incoming light (and the observers will need to re-orient their telescopes accordingly).

We only need to consider the aberration occuring in the light carrying medium when we observe objects (Moon, Planets) for which we know that the observed aberration is different from the value calculated for stellar aberration (whereby we only need to consider the speed of the observer relative to the incoming light).

If we observe the stellar aberration for a star S right next to the moon or right next to a planet, we know that the stellar aberration for that star S is different from the aberration observed for the moon/planet (in addition to the effect of light-time correction).

I calculated the aberration for Jupiter as observed during the occulation by the moon on 7-Dec-2004 and published on:
www.gsjournal.net/Science-Journals/Research%20Papers/View/3802

What is interesting is that the observed (and calculated) planetary aberration for Jupiter was larger than the value of the stellar aberration observed for star S right next to Jupiter ...

And I say po-TOO-to (please forgive my outrageous accent).
Here's an attempt to do Larry's figure 1 with less detail.

In this diagram, O moves along with A. What O observes is also shown:

And in this diagram, O is stationary with respect to S:

If I understand correctly, S_A should be occluded by O_A in the second diagram.

___

So far, the star S was considered to be stationary, and A was moving.
In special relativity it's allowed to switch to the frame where A is stationary (for linear paths, at least).

This looks like a simple light-time correction.
___

If we observe a binary star, where the speed relative to the observer will differ a lot between both stars, we still see a simple light-time correction. Aberration is (almost) the same for both stars.
Of course, in this case the paths are not linear ...

[Sorry Larry, how do you make the board not eat the spaces in your diagrams? (Added code tags, apologies for the edit-spam)]

I see someone gave you the secret. Good job.

(It's not spam. It's a switchable function in the editor.)

The speed of light is the same for all observers. (All wave phenomena have this property.) So even if the source of the light is changing speed, the light that we see is not. Aberration is a function of the speed of the incoming particle or wave, not a function of the speed of the source of that particle or wave.

The Moon (O) and observer (A) move with largely the same velocity and orientation (up to 30km/s) relative to the star (S).
As a consequence, stellar aberration as observed on the mooon and the Earth are largely the same (up to 20.5 arcsec).

The moon rotates in 27.3 days around the Earth which equals a displacement of 0.55 arcsec/second.
Light takes 1.3 seconds to travel from the Moon to the Earth.
So light-time correction accounts for (up to) 0.7 arcsec which is way below the value for stellar (or planeteray) aberration.

So Light-time correction and stellar/planetary aberration are different effects ...

Yes Larry, but if the speed of light is the same for all observers (and in all directions), how can aberration be a function of the speed of the incoming particle or wave? In absence of some kind of local or absolute reference frame, there seems to be a catch 22.

Bart quoted from the wiki:

"[aberration] depends solely upon the transverse component of the velocity of the observer, with respect to the vector of the incoming beam of light (i.e., the line actually taken by the light on its path to the observer)."

Doesn't the word "actually" imply a pre-defined reference frame?
Maybe my confusion comes from the fact that we wouldn't able to recognize absolute aberration, we can only observe changes in aberration.