Question about Relativity and the apparent direction of light

[W.RonG]

I read elsewhere that when one travels in a spaceship "very close to the speed of light" that objects behind the ship (light emitters that the spaceship is accelerating away from) start to appear to the side and eventually toward the front. This is based on SR, contraction, etc. and is posited as a valid effect due to Relativity. There is even a movie on one website showing the effect. I find this scenario impossible to square with Relativity, if for no other reason than - no matter how fast one thinks one is traveling, one always measures the same c. What one would see is the light in front shifting in perceived frequency since the wavelength is seen as shorter (I believe this is blue shift), and light from behind shifting the opposite way (red shift) due to the perceived wavelength getting longer. but would the direction of light coming from an object astern ever appear to come from somewhere other than from behind?
help?
thanks,
rg

 

[1effect]

I read elsewhere that when one travels in a spaceship "very close to the speed of light" that objects behind the ship (light emitters that the spaceship is accelerating away from) start to appear to the side and eventually toward the front. This is based on SR, contraction, etc. and is posited as a valid effect due to Relativity. There is even a movie on one website showing the effect. I find this scenario impossible to square with Relativity, if for no other reason than - no matter how fast one thinks one is traveling, one always measures the same c. What one would see is the light in front shifting in perceived frequency since the wavelength is seen as shorter (I believe this is blue shift), and light from behind shifting the opposite way (red shift) due to the perceived wavelength getting longer. but would the direction of light coming from an object astern ever appear to come from somewhere other than from behind?
help?
thanks,
rg

You probably saw http://www.anu.edu.au/physics/Savage/TEE/site/tee/learning/aberration/aberration.html website on "relativistic aberration".

The mathematical explanation is given here.

 

[W.RonG]

If it's okay to post links to disinterested outside party websites, it was here:
http://www.fourmilab.ch/cship/aberration.html

 

[W.RonG]

Maybe that's the wrong question. How could anyone believe they are traveling "0.9999 times the speed of light"? I'm in a ship in space. I'm accelerating (expending thrust or whatever you want to call it). I measure c. I am always traveling at the-speed-of-light less than c. Perceived wavelengths change, sure, but why would the incoming direction change?
rg

 

[JesseM]

Maybe that's the wrong question. How could anyone believe they are traveling "0.9999 times the speed of light"? I'm in a ship in space. I'm accelerating (expending thrust or whatever you want to call it). I measure c. I am always traveling at the-speed-of-light less than c. Perceived wavelengths change, sure, but why would the incoming direction change?
rg

In the ship's own rest frame it is standing still while the galaxy is passing by it at 0.9999c, but the predictions about what it will see visually are the same in this frame as they would be in the galaxy's frame where the ship is moving at 0.9999c. Note that what an observer sees is different from what is measured in their frame--for example, in my frame a moving object will contract due to Lorentz contraction (if I measured the position of both ends simultaneously in my frame, I'd find the distance between them less than the distance in the object's rest frame), but visually I'll actually see the object as having its normal length, due to something called the Penrose-Terrell effect which is related to the fact that light from different parts of the object will take a different amount of time to reach me thanks to differences in the distance at which the light was emitted...this effect was discussed on this thread.

 

[W.RonG]

Thanks JesseM. There's quite a bit there to chew on.
We'll see if it helps.
rg

 

[W.RonG]

In the ship's own rest frame it is standing still while the galaxy is passing by it at 0.9999c...

Meanwhile I have this followup: the galaxy and I are moving toward, away from, or past each other at 0.9...c. However the light from the galaxy (which is the only way I know there's a galaxy there) is impingeing on my ship, my inertial frame, at c. Now the galaxy emitted light at some arbitrary wavelength(s). If I knew what those wavelengths were intended by the galaxy to be then I could calculate our closure/separation/passing relative speed based on the wavelengths I measured. But does the light wavefront impingement direction (my looking back at the ray) get altered; if so how?
If the answer is in the other thread then I guess that's a rhetorical question. But that's the disconnect I presently see.
rg
off for now

 

[JesseM]

Meanwhile I have this followup: the galaxy and I are moving toward, away from, or past each other at 0.9...c. However the light from the galaxy (which is the only way I know there's a galaxy there) is impingeing on my ship, my inertial frame, at c. Now the galaxy emitted light at some arbitrary wavelength(s). If I knew what those wavelengths were intended by the galaxy to be then I could calculate our closure/separation/passing relative speed based on the wavelengths I measured. But does the light wavefront impingement direction (my looking back at the ray) get altered; if so how?

I don't understand the phrase "light wavefront impingement direction"...do you just mean the angle the light reaches you, or are you talking about the wavelength, or something else?

 

[W.RonG]

yes, the angle I perceive the light came from (I'm looking back at the ray). This direction tells me where that specific light emitter was a specific period of time ago. I realize that since the emitter is moving while it continues to emit light, I receive each wave from that previous direction. for instance go outside and note the position of the sun. we see where it was about 5 minutes ago. but the light that hits us still appears to come from the direction where the sun actually was 5 minutes ago. whew.

Back to Mr. Walker's description of relativistic aberration, here's the killer:
the aberration of light depends on the ratio of the speed I am going, to the speed of light. But that ratio is always c! No matter how much I accelerate in space I always get c when I measure the speed of light, so I am always going the-speed-of-light slower than c.
rg

 

[JesseM]

yes, the angle I perceive the light came from (I'm looking back at the ray). This direction tells me where that specific light emitter was a specific period of time ago.

Right. In this case the angle will depend on the speed the emitter is moving relative to you, and its distance from you both along the axis that it is moving in your frame and also along the axis perpendicular to this one.

Back to Mr. Walker's description of relativistic aberration, here's the killer:
the aberration of light depends on the ratio of the speed I am going, to the speed of light. But that ratio is always c! No matter how much I accelerate in space I always get c when I measure the speed of light, so I am always going the-speed-of-light slower than c.
rg

"c" is not a ratio, it's a speed--I guess you mean the ratio is 0? But I'm pretty sure Walker is talking about the ratio of your speed to the speed of light in the rest frame of the stars that are emitting the light.

 

[W.RonG]

Yes that was clumsy on my part. the ratio of my speed to c never changes.
that's what I meant.
hence aberration does not occur.
rg

 

[JesseM]

Yes that was clumsy on my part. the ratio of my speed to c never changes.
that's what I meant.
hence aberration does not occur.
rg

There is no frame-independent truth about this ratio, it depends on one's choice of frame. Again, I think Walker is talking about the frame in which the stars emitting the light are at rest, and if you're moving at 0.5c in that frame, the ratio is 0.5. In your own frame the formula would be a little different, I'd imagine it would depend on the ratio between the speed of the light-emitter and c.

 

[yuiop]

Yes that was clumsy on my part. the ratio of my speed to c never changes.
that's what I meant.
hence aberration does not occur.
rg

Say I am looking at a distant galaxy to the East through a long narrow telescope with a very narrow field of view. (Imagine we have a intergalactic compass system with N,E,S,W, Up and Down). Now say you pass me at some relativistic speed, traveling from South to North. If you look exactly to the East with a telescope like mine you do not see the galaxy because a photon from the galaxy entering the front lens of your telescope impinges on the side of your teleoscope before it reaches the rear lens. To view photons coming from the galaxy you have to point the telescope in the North East direction so that photons that enter the front lens also pass through the rear lens. From your point of view the galaxy is to the North East and not directly to the East as it appears to me.

From my point of view you are not stationary and have a velocity that is a fraction of the speed of light(v/c). From my point of view your opinion of the direction of the galaxy is distorted by your relative velocity to me. The greater your relative velocity to me the greater the difference between the angle you perceive and the angle I perceive. That is what Mr Walker means when he says "the aberration of light depends on the ratio of the speed I am going, to the speed of light." He is talking about your speed as measured by another observer. You can consider yourself as stationary and from your point of view that galaxy has always been to te North East. From your point of view it is me that is moving (form North to South) with velocity v/c relative to you and it is me that is seeing a distorted direction due to aberration and that is why I think the galaxy is to the East.

Interestingly, if I accelerate violently in a given direction to some extreme velocity aproaching the speed of light (relative to the rest frame I started in) then almost the entire universe will appear as a distant blob in front of me. Visually it would like I am accelerating backwards while the seat of my pants is telling me I am accelerating forward. This is the exact opposite of the star movement seen in Startrek when they go to warp speed.

[EDIT] As JesseM points out you can consider your speed relative to the galaxy (or vice versa). In the description I gave above I was assuming that I was at rest with respect to the distant galaxy.