Light Propagation: Doubts Answered Here

[GAURAV DADWAL]

Hello There,
I have basic doubt about light propagation .So I'm hoping to get some help here.
The problem is ...Let us assume two frames, 'MOVING FRAME'[one moving with a certain velocity(constant)] and 'REST FRAME'[one wrt to which the first frame is moving]. If now moving frame emits a laser beam ...I want to know how the path of that laser will look like in both the frames mentioned above.
I'll ask further doubts depending on the answer I'll get.
Thanx for helping in advance.

 

[Orodruin]

It is better for understanding to talk about a light pulse rather than a continuous beam. A light pulse will move at speed c in a straight line in both frames.

Also note that your setup has nothing that actually identifies either frame as ”at rest”. The concept ”at rest” is relative and there is no way of identifying ”at rest” without a reference. Also, there is no such thing as a ”frame emitting a light pulse”. A frame is a way of assigning space and time coordinates to events, not a physical entity.

 

[Dale]

I want to know how the path of that laser will look like in both the frames mentioned above.

In both frames the speed will be c. The direction may differ.

 

[Ibix]

You can always rotate your axes so the light is traveling in the x-y plane. Write down the position at t=0 and t=T, then apply the Lorentz transforms to work out what happens as described in another frame.

 

[vanhees71]

Light is described by the electromagnetic field. Thus it's much easier and conceptually better to check how the plane-wave modes of the electromagnetic field transform under Lorentz boosts. You'll learn everything from this exercise relevant for the question, namely the Doppler effect for light and aberration.

 

[pervect]

Hello There,
I have basic doubt about light propagation .So I'm hoping to get some help here.
The problem is ...Let us assume two frames, 'MOVING FRAME'[one moving with a certain velocity(constant)] and 'REST FRAME'[one wrt to which the first frame is moving]. If now moving frame emits a laser beam ...I want to know how the path of that laser will look like in both the frames mentioned above.
I'll ask further doubts depending on the answer I'll get.
Thanx for helping in advance.

I'm not sure how to answer a "doubt", but it sounds more like you have a question.

Let's take a very simple case. We have an inertial frame S, and in that frame, for light moving in the x direction, we can say that x = ct.

Now we imaging another inertial frame S', which is moving relative to frame S with some velocity v along the x-axis. Then in frame S', we can write x' = c t'.

Things get more complicated if S' is moving in a direction other than along the x-axis, but it's easiest to talk about the simplest possible case first.

 

[GAURAV DADWAL]

I'm sorry for not explaining my doubt clearly... I was in a kind of a hurry when I posted this.Well now, I have attached the situation which was in my mind then. The problem is what my intuition says in the image seems to be opposite to the real scenario, but I don't know WHY.
I hope now I'm clear in what my 'doubt' or 'Question' Is.

PS. Sorry for bad handwriting

 

[jtbell]

I'm not sure how to answer a "doubt", but it sounds more like you have a question.

I suppose you've seen the bromide about the British and the Americans being divided by a common language? Indian English has its own characteristics which seem strange to the rest of us.

 

[Orodruin]

I suppose you've seen the bromide about the British and the Americans being divided by a common language? Indian English has its own characteristics which seem strange to the rest of us.

To be fair, this particular characteristic is actually not unique to Indian English. I have observed it quite often in southern Europeans as well.

 

[GAURAV DADWAL]

I'm happy that you got that I'm indian, but what about the answer to my 'doubt'.

 

[Orodruin]

Your situation is not very well defined because you have not stated in which frame the pulse is emitted straight down. If the pulse is emitted straight down in the ground frame, then indeed it will go somewhat in the "back" direction in the ship's frame. If it is emitted straight down in the ship's frame, it will go somewhat in the forward direction in the ground frame. This is called aberration of light.

 

[GAURAV DADWAL]

If it is emitted straight down in the ship's frame, it will go somewhat in the forward direction in the ground frame. This is called aberration of light.

This is actually what I'm not understanding .Why it should go in forward direction,it is not obvious to me as is to some of my peers.

 

[Orodruin]

Because, assuming that it is emitted straight down in the ship's frame, it will always be directly below the ship in the ship's frame. Since the relative velocity between the ship and the ground is orthogonal to this displacement, it always needs to be directly below the ship in the ground frame as well, which means that it needs to have a velocity component $v$ in the direction of the ship's motion in the ground frame.

This is not particular to light. The same would happen if you would drop a ball from the ship. The ball will then have a velocity in the ship's direction in the ground frame.

 

[GAURAV DADWAL]

This is not particular to light. The same would happen if you would drop a ball from the ship. The ball will then have a velocity in the ship's direction in the ground frame.

With ball, I'm clear with this view.But why should light behave like a ball?

 

[Orodruin]

Did you at all read what I wrote before the ball?

 

[GAURAV DADWAL]

Yes...I understood your argument. You are saying that since light needs to be below ship in ship's frame so should it be in the ground frame by which you are giving rise to that velocity in the positive direction.Am I right.
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.

 

[Orodruin]

It is no different at all. You could also emit the light so that it goes straight down in the ground frame, but then it will not go straight down in the ship's frame. It is a question of how you emit the light. You cannot have it going straight down in both frames.

 

[vanhees71]

Again my advice: Write down your problem in proper mathematical language, which is a wave description. You can simplify the task by thinking about scalar waves first. For a massless field (as the electromagnetic field) a particular solution of the wave equation are plane-wave packets,
$$\phi(t,\vec{x})=\phi_0 (k^0 c t-\vec{k} \cdot \vec{x}-c t)=\phi_0(x_{\mu} k^{\mu}),$$
where
$$k^0=|\vec{k}|.$$
Now take a Lorentz boost (e.g., in $x$ direction) and see what results for that plane-wave packet! Then all your puzzles should be resolved, and you get the relativistic Dopplereffect and aberration formula for light.

 

[Ibix]

If you analyse the emitter in the moving frame you'll also see that it should emit at an angle.

For example, a laser is basically a light clock with a lasing medium between the mirrors. In the rest frame it's light pulses bouncing "straight up and down" that go back and forth between the mirrors, repeatedly passing through the lasing medium and building up stimulated radiation. In the moving frame, the lasing medium and mirrors would move through "straight up and down" light and the amplification effect wouldn't happen. It's the "diagonal" bouncing light that repeatedly passes through the medium and produces the laser. So the beam comes out diagonally.

 

[GAURAV DADWAL]

@vanhees71 I'm not familiar with the mathematics of electromagnetic waves, and I also don't know what Lorentz boost is. @Orodruin In case of the ball there is a reason for that forward velocity (every particle had that velocity) but the light is not like a ball (i mean it's not a bunch of particles) so why? I think there is some other reason for that 'forward velocity' different from that of a ball.
It can also be like light can go in backward direction in ship's frame so that it appears to be going straight downward in ground frame instead of ships' one

 

[Orodruin]

Again my advice: Write down your problem in proper mathematical language, which is a wave description.

While I agree that this is the more proper way of handling things. Unfortunately, I suspect it is way beyond the OP's capabilities and expertise.

 

[GAURAV DADWAL]

If you analyse the emitter in the moving frame you'll also see that it should emit at an angle.

For example, a laser is basically a light clock with a lasing medium between the mirrors. In the rest frame it's light pulses bouncing "straight up and down" that go back and forth between the mirrors, repeatedly passing through the lasing medium and building up stimulated radiation. In the moving frame, the lasing medium and mirrors would move through "straight up and down" light and the amplification effect wouldn't happen. It's the "diagonal" bouncing light that repeatedly passes through the medium and produces the laser. So the beam comes out diagonally.

I think this is what I was looking for. Can you tell where I can study this thing in some detail?
Then I'll again come back if I didn't catch something there

 

[GAURAV DADWAL]

I know it's offtopic but what's OP.

 

[Orodruin]

I know it's offtopic but what's OP.

You are. (Original Poster or Original Post) Note the "OP" in the right left corner of your avatar in this thread.

 

[GAURAV DADWAL]

Ok...Thanx.

 

[Ibix]

Note the "OP" in the right left corner of your avatar in this thread.

...if you are on a device that displays avatars.

I think this is what I was looking for. Can you tell where I can study this thing in some detail?

Not a clue, to be honest. 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.

 

[OCR]

Unfortunately, I suspect it is way beyond the OP's capabilities and expertise.

Interestingly, though, his capabilities and expertise seemed sufficient to figure out where...

...the right left corner...

Of his avatar is... .

 

[Orodruin]

Interestingly, though, his capabilities and expertise seemed sufficient to figure out where...

Of his avatar is... .

If looking at yoir screen through a mirror

Upper left of course ...

 

[OCR]

..

Upper left of course ...

 

[Orodruin]

It is called fat fingers and an iPhone in conjunction with gym fatigue.

 

[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.

 

[Mister T]

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.