High School Light Propagation: Doubts Answered Here

[Dale]

A more straightforward thing to analyse might be a lamp that emits a light pulse in all directions and a pinhole that let's through light going in a particular direction. The lamp emits a pulse of light. Which direction is the light that makes it through the pinhole going in according to each frame?

You don't need anything except the Lorentz transforms to analyse this. The answer should be in accordance with the relativistic aberration formula which is googlable.

This would be my recommended approach also.

 

[Herman Trivilino]

But can one in ground frame tell why should that pulse have that forward velocity like the way we can tell in case of the ball? In case of the ball, it is obvious since every particle of that ball has that forward velocity because of motion along the ship, but the situation with light seems different than that which I'm not understanding.

You are attributing the behavior of the ball to some property of the ball, but instead think of the behavior as an artifact of the observation. The ball's path is vertical in one frame, and it therefore cannot be vertical in frames that are moving in a horizontal direction relative to that frame.

 

[Dale]

You are attributing the behavior of the ball to some property of the ball, but instead think of the behavior as an artifact of the observation. The ball's path is vertical in one frame, and it therefore cannot be vertical in frames that are moving in a horizontal direction relative to that frame.

This is a good comment. This explains why the same thing happens for both the ball and the light. It isn't some physical property that balls and light has in common, it is simply the fact that the frames define what it means to fall vertically differently. So anything that meets that definition in one frame cannot meet it in any other frame. The nature of the thing that is falling is irrelevant.

 

[Adel Makram]

A more straightforward thing to analyse might be a lamp that emits a light pulse in all directions and a pinhole that let's through light going in a particular direction. The lamp emits a pulse of light. Which direction is the light that makes it through the pinhole going in according to each frame?

Does it mean the density of the light on the wall of the lamp in the direction of the motion is apparently larger than the other side relative to the ground observer?

 

[Ibix]

Does it mean the density of the light on the wall of the lamp in the direction of the motion is apparently larger than the other side relative to the ground observer?

Oddly, no.

The front wall is brightened due to aberration, true, but it is also running away from the source so is dimmed due to the inverse square law. The rear wall is dimmed due to aberration, but is rushing towards the source so is brightened due to the inverse square law. The net effect is the same for front and back wall - as it must be since the total energy absorbed by both walls must be the same since it's trivially the same in the rest frame.

 

[Adel Makram]

Oddly, no.

The front wall is brightened due to aberration, true, but it is also running away from the source so is dimmed due to the inverse square law. The rear wall is dimmed due to aberration, but is rushing towards the source so is brightened due to the inverse square law. The net effect is the same for front and back wall - as it must be since the total energy absorbed by both walls must be the same since it's trivially the same in the rest frame.

Nice explanation but still there are 2 points;
1) Are those two opposing effects, aberration and the inverse square law, exactly compensated? I am not familiar with the first.
2) Coming to the source, if the ground watcher draws a line between the filament of the lamp and the point where the light gets out of the lamp at 6 o`clock. This line is vertical relative to the rest frame of the lamp but oblique in the direction of the motion for him. He must see half of the light rays exits to right side of that line (in the direction of motion in the x-axis). But this would also mean the light rays must appear to him, aberrated in this direction, if aberrated means condensed as emerged from the filament. This is because the vertical line for the rest frame is an oblique steep one for him. If so, what caused this strange behavior from the source?

 

[Ibix]

1) Are those two opposing effects, aberration and the inverse square law, exactly compensated? I am not familiar with the first.

For the case where whatever we are illuminating is perpendicular to the direction of motion, yes. If it's not perpendicular then length contraction comes into play too and brightness may vary.

2) Coming to the source, if the ground watcher draws a line between the filament of the lamp and the point where the light gets out of the lamp at 6 o`clock. This line is vertical relative to the rest frame of the lamp but oblique in the direction of the motion for him. He must see half of the light rays exits to right side of that line (in the direction of motion in the x-axis). But this would also mean the light rays must appear to him, aberrated in this direction, if aberrated means condensed as emerged from the filament. This is because the vertical line for the rest frame is an oblique steep one for him. If so, what caused this strange behavior from the source?

"Aberration" in this context just means that frames don't agree on angles in general. As to why the source behaves as it does, you'd have to go into quantum electrodynamics for a complete explanation of why moving atoms preferentially emit forwards. I'm not qualified to do that, I'm afraid. I did give a qualitative explanation of why a laser must behave like this in post #20.

 

[JulianM]

I think most of the respondents missed the meaning of the original question. The question was about a laser beam.

If we think of that beam coming straight down then it will also be perpendicular to the object passing below at the point that it strikes. It's speed is of course c.

This is very different from describing light as pulses and equating the pulses to oobjects or balls.

 

[Ibix]

It's speed is of course c.

Careful. What is the speed of the beam? You can talk about the speed of a wavefront, or the speed of some particular modulated pulse. In the frame where the rocket is moving, those are traveling at c on the diagonal. But if you are saying the beam is not traveling diagonally then it can't be doing c...

I think the point you are trying to make is that you can build a long straight tube out of the side of the rocket. It is perpendicular to the rocket's axis in both frames, and both frames would see the laser traveling straight along it. This is true.

But the two frames' explanations for why this should be so are very different. The rocket frame sees light emitted perpendicular to the rocket. The lab frame sees light emitted diagonally, "coincidentally" leaning exactly far enough forward that the forward component of its velocity "happens" to equal the rocket's velocity. It's not really just a coincidence, of course. It's the principle of relativity at work.

 

[Orodruin]

I think most of the respondents missed the meaning of the original question. The question was about a laser beam.

No, we willingly ignored that part (and clearly stated this) as using a continuous beam is an unnecessary complication and the typical question at B level is actually not about the beam as an object.

The beam will be orthogonal to the rocket in both frames but the speed of the beam itself will be v, not c. Individual wave packets in the beam are traveling at c, but those are equivalent to the light pulses. If the beam is not continuous, but started at some point, the front of the beam will travel diagonally downwards with speed c.

Edit: Ibix got to it first.

 

[Dale]

A thread derail has been deleted and the thread is reopened

 

[Adel Makram]

"Aberration" in this context just means that frames don't agree on angles in general. As to why the source behaves as it does, you'd have to go into quantum electrodynamics for a complete explanation of why moving atoms preferentially emit forwards. I'm not qualified to do that, I'm afraid. I did give a qualitative explanation of why a laser must behave like this in post #20.

I think I might have explanation of "why moving atoms preferentially emit forwards" without the help of quantum theory.
This is because if we suppose the filament is formed of multiple small elements, then firing the light by the rear element should be seen first before the near element by the ground watcher. This causes constructive interference with angle in the direction of the motion.
see a similar concept: https://en.wikipedia.org/wiki/Phased_array_ultrasonics

 

[PAllen]

Aberration can increase or decrease apparent brightness over and above any Doppler effect. Moving towards a light source which emits spherically symmetrically, aberration concentrates more of the solid angle of emission towards the line of relative motion. Blueshift adds to this effect, leading to extreme brightening, called relativistic beaming. The reverse happens moving away from spherically symmetric light source, so that any light source you are directly moving away from sufficiently fast becomes undetectable in practice. Since I am only discussing inertial motion. this has nothing to do with a Rindler horizon.

The impact of aberration on observed intensity is a very well known phenomenon in astronomy.

 

[Adel Makram]

Aberration can increase or decrease apparent brightness over and above any Doppler effect. Moving towards a light source which emits spherically symmetrically, aberration concentrates more of the solid angle of emission towards the line of relative motion.

So, if my explanation of the aberration concentrated beam, 3 posts back, is right, what makes it is still valid for a hypothetically single source element, say one atom radiating light?

 

[Adel Makram]

I hope my consideration is answered before the thread is closed for moderation.

 

[PAllen]

I hope my consideration is answered before the thread is closed for moderation.

Which post should I look at? You didn't give a link or a post number.

 

[Adel Makram]

Which post should I look at? You didn't give a link or a post number.

42 and 46

[Moderator's Note: Several posts were deleted after this post was made, so the post numbers above are no longer correct.]

 

[PAllen]

42 and 46

I don't see #42 as much related to aberration. Aberration does not involve interference; it is, if you will, a geometric optics phenomenon, or, more generally, just a question of how Lorentz transform affects angles.

 

[PeterDonis]

Thread closed for moderation.

Edit: The thread has run its course and will remain closed.