Light Puzzle

[Towlie]

Light behaves almost exactly like any other wave (with speed c) unless the relative velocity of the emitter and receiver is close to c - in which case you must take time dilation etc. into account.

Not according to nathan, unless you regard half of c as being "close to c."

Who's right?

 

[sol invictus]

Not according to nathan, unless you regard half of c as being "close to c."

Who's right?

Both of us, because c/2 is indeed "close to c". The corrections are of order (v/c)^2. That means one expects corrections that will be (v/c)^2 times a number of order 1 (like 2, or 1/2). if v=c/2, (v/c)^2 is .25 (i.e. one can expect a correction around 25%, or 10%, or 50% - but not .001% or 99.9%).

Remember that c/2 is an extremely high speed: 150,000 km/second. For objects moving at human-scale speeds the corrections due to time dilation etc. are tiny, and the standard Doppler effect is the dominant contribution.

 

[ynot]

Ignore time dilation and length contraction for now.

Emitter is moving towards a stationary receiver at speed v. Emitter emits a light pulse once per second, which moves towards the receiver at speed c. Receiver receives pulses more often than once per second, because the emitter moves towards the receiver between each pulse emission. It receives them with frequency (1/second)(1+v/c).

Receiver is moving with speed v towards a stationary emitter. Emitter emits a light pulse once per second, which moves towards the receiver at speed c. Receiver receives pulses more often than once per second, because the receiver moves towards the emitter between each pulse reception. It receives them with frequency (1/second)(1+v/c).

That is the standard Doppler effect up to terms of size (v/c)^2. You'd get exactly the same result for sound, except with c replaced with s (the speed of sound), again up to terms of size (v/s)^2.

Light behaves almost exactly like any other wave (with speed c) unless the relative velocity of the emitter and receiver is close to c - in which case you must take time dilation etc. into account.

But we aren’t ignoring that light moves relative to everything at c regardless?

I can only see what you say as being true if the receiver receives the light bursts at a speed faster than c (speed of emitter toward receiver + c).
There are two separate events - The emitting of the light bursts and the receiving of the light bursts.

Regardless of the relative motion of the receiver the light bursts must always travel relative to the emitter at c even if the emitter changes degree and direction of motion while emitting the bursts. Otherwise previously emitted light bursts would be moving at less or more than c relative to the emitter. In other words the emitter moving closer to the receiver isn’t the emitter moving closer to previously emitted light bursts (or compressing them).

The receiver must also receive the light bursts at c regardless of the relative motion of the emitter or whether the receiver changes degree and direction of motion while receiving the bursts.

The bursts can’t change their lengths because in doing so their ends would be moving slower or faster than c relative to the emitter and receiver during the period of length change.

Had to write that very quickly so hope what I’m trying to say can be understood (don’t expect agreement)

 

[MattusMaximus]

I imagine a beam of laser light as being a solid steel bar that is mysteriously always emitted and received at a constant speed regardless of relative speeds of senders and receivers. If a stationary sender emits a bar then moves in the direction of the bar being emitted then the leading end of the bar would have to speed up accordingly. The bar couldn’t compress because that would mean the leading end would have slowed to less than c relative to the sender.

No. If your "bar" represents a light beam, then no matter what the frame of reference all parts of it are always moving at c, in accordance with lightspeed invariance.

 

[ynot]

No. If your "bar" represents a light beam, then no matter what the frame of reference all parts of it are always moving at c, in accordance with lightspeed invariance.

I thought that’s what I said. If the emitter changes it’s motion then an already emitted light burst would also have to also change it’s motion accordingly to remain travelling at c relative to the emitter. The point I’m trying to make is that not only the relative speed would have to remain c but so would the length of the beam because any uniform shortening or lengthening would require a speed of more or less than c of the ends of the beam during the period of the length change.

 

[MattusMaximus]

I thought that’s what I said. If the emitter changes it’s motion then an already emitted light burst would also have to also change it’s motion accordingly to remain travelling at c relative to the emitter. The point I’m trying to make is that not only the relative speed would have to remain c but so would the length of the beam because any uniform shortening or lengthening would require a speed of more or less than c of the ends of the beam during the period of the length change.

That is where you have it wrong. If it's light, it's moving at c - no change in its motion (i.e. velocity), period.

I think you might be talking about something else. You need to be more careful about your terminology.

 

[Reality Check]

I thought that’s what I said. If the emitter changes it’s motion then an already emitted light burst would also have to also change it’s motion accordingly to remain travelling at c relative to the emitter. The point I’m trying to make is that not only the relative speed would have to remain c but so would the length of the beam because any uniform shortening or lengthening would require a speed of more or less than c of the ends of the beam during the period of the length change.

That is incorrect. All of the photons in the light burst always travel at the speed of light. So the photons at the start of the burst travel at the same speed as the photons at the end. Thus the length of the burst remains constant. It does not matter what the emiter does.

When talking about light there is no "relative speed". Its speed is always c. The only relative speed is between the emitter and receiver.

 

[sol invictus]

But we aren’t ignoring that light moves relative to everything at c regardless?

Nope.

I can only see what you say as being true if the receiver receives the light bursts at a speed faster than c (speed of emitter toward receiver + c).
There are two separate events - The emitting of the light bursts and the receiving of the light bursts.

Regardless of the relative motion of the receiver the light bursts must always travel relative to the emitter at c even if the emitter changes degree and direction of motion while emitting the bursts. Otherwise previously emitted light bursts would be moving at less or more than c relative to the emitter. In other words the emitter moving closer to the receiver isn’t the emitter moving closer to previously emitted light bursts (or compressing them).

OK, i understand your confusion now. You think that the speed of light relative to anything is always c. That's wrong and not what relativity says.

What relativity says is that if you transform to a frame, for example the frame in which either the emitter or receiver is at rest, light will propagate at speed c in that frame. It does not say that light always moves at speed c relative to something that's in motion.

Here's an example. The emitter is at rest, and the receiver is moving towards it at speed c/2. The emitter sends out a pulse of light, which (as always) propagates at speed c, in this case towards the receiver.

Question #1: what's the relative speed of the receiver and the light pulse, in the rest frame of the emitter?

Answer: c - (-c/2) = 3c/2. (Yes, that's greater than c, and yes, it's correct and what relativity predicts.)

Question #2: what's the speed of the light pulse in the rest frame of the receiver?

Answer: c, as always. (No, that's not inconsistent with the above.)

Question #3: what's the relative speed of the emitter and the light pulse, in the rest frame of the receiver?

Answer: 3c/2.

 

[sol invictus]

Question #4: Two light pulses are emitted directly towards each other from two emitters. What's their relative speed?

Answer: 2c.

 

[ynot]

no matter what the frame of reference all parts of it are always moving at c, in accordance with lightspeed invariance.

That is where you have it wrong. If it's light, it's moving at c - no change in its motion (i.e. velocity), period.

That is incorrect. All of the photons in the light burst always travel at the speed of light.
When talking about light there is no "relative speed". Its speed is always c. The only relative speed is between the emitter and receiver.

Nope.
OK, i understand your confusion now. You think that the speed of light relative to anything is always c. That's wrong and not what relativity says.

Can you see why I might be confused? Thanks for your clear explanation sol. I understand what you say but still don’t understand the why or how.

 

[sol invictus]

Can you see why I might be confused? Thanks for your clear explanation sol. I understand what you say but still don’t understand the why or how.

Yes, I can.

Perhaps this will make it easier. Forget about light for a moment, and forget about changing frames. Think about sound in a huge room. We'll use the frame in which the walls of the room and the air inside it are at rest.

In that frame sound always propagates at the same speed - s - regardless of the velocity of the emitter or the receiver (just like light does). And yet, clearly there are Doppler shifts for emitters or receivers in motion with respect to each other (just as for light, and for the same reason).

The difference is that in any frame light has the property that sound has only in the rest frame of the air. But all that means is that you can pick any frame you like, and then think of it as if there were an "air" (or aether, to use the historical term) that's at rest, so that light propagates at speed c in that frame.

 

[orange31]

Keep in mind, ynot, that although a relative speed of 2c, etc can exist as above, it's not a "thing" (particle, photon, etc) actually moving at 2c.

No particle can move faster than light (c), and essentially therefore no form of communication (ie, electromagnetic waves - radio, light etc)- can exist faster than c. (I know there's some possible exceptions on the c thing experimentally, but I'm ignorant of how significant they are).

 

[ynot]

So “normal” things can have their relative motion proportionally attributed to either thing or wholly attributed to one thing by defining that the other thing is stationary but this can’t be done with light. If two “normal” things are each moving relative to each other at greater than half c can one still be defined as being stationary which would make the other to be moving faster than c? I know the answer is no and that time dilation will put it’s hand up.

 

[nathan]

So “normal” things can have their relative motion proportionally attributed to either thing or wholly attributed to one thing by defining that the other thing is stationary but this can’t be done with light.

I cannot understand that sentence.

If two “normal” things are each moving relative to each other at greater than half c can one still be defined as being stationary which would make the other to be moving faster than c?

In the rest frame of one of those objects, the other object's velocity will be less than c.

I know the answer is no and that time dilation will put it’s hand up.

Time dilation refers to the clocks in the moving frame of reference running slower than the clocks in the stationary frame of reference. It doesn't refer to subluminal observed velocities -- the underlying cause is the same (SR), but the terms are different.

You have three frames of reference in your example:
1) Frame A in which both objects are moving. The difference of their velocities in frame A is > c/2 (by stipulation)

2) The rest frame of Thing-1. The speed of Thing-2 in this frame is < c (by SR).

3) The rest frame of Thing-2. The velocity of Thing-1 in this frame is the negation of the velocity of Thing-2 in Thing-1's rest frame (by symmetry & presuming the frames are not rotated)

Can you clarify your original statement in terms of these three frames?

 

[sol invictus]

So “normal” things can have their relative motion proportionally attributed to either thing or wholly attributed to one thing by defining that the other thing is stationary but this can’t be done with light. If two “normal” things are each moving relative to each other at greater than half c can one still be defined as being stationary which would make the other to be moving faster than c? I know the answer is no and that time dilation will put it’s hand up.

That's right - although you need more than just time dilation, you also need Lorentz contraction of lengths. As a result of those two velocities don't add "normally" when you change frames, at least not when they are close to c either in the initial or final frame.

The correct velocity addition formula is such that if something has speed c in one frame, it has speed c in any frame (which in fact is the condition from which all these things - including time dilation and length contraction - can be derived).