I don't understand photon clocks

[bshul]

The depiction of time dilation that is typically used to describe the situation,
shows the stationary photon clock, with mirrors one above the other in the observer's frame and the photon "bounces" back and forth between them.

In the moving frame the mirror pair moves as a unit let's say to the right and the photon bounces at an angle to these mirrors...and from this geometry the longer length traveled by the photon (always traveling at c) is the "cause" of time dilation.

My problems are:
why does the photon bounce at an angle to the mirrors?
the motion (angled trajectory) of the photon should not be dependent on the mirror's motion to the right, only to the angle of the mirror's surface.
So I think that depiction is not correct and some change in the angle of the mirrors is required.
OR is the photon shown as a bouncing point not accurate and should be shown as a circular wave front propagation thus intercepting the displaced mirrors at greater distance?

Thank you for your help.

 

[ghwellsjr]

It's not the motion of the mirrors that makes the photon follow a zig-zag path, it would do the same thing if you just had two very long stationary mirrors and you started the photon going on an angled path, don't you agree?

 

[bshul]

Is the photon emitted on an angled path to the mirrors? By definition, I believe not. Then what causes the change to an angled path?

 

[Dale]

why does the photon bounce at an angle to the mirrors?

Maxwell's equations hold in all frames, so the angle of incidence is equal to the angle of reflection in all frames. It bounces out at an angle becomes it bounces in at the same angle.

the motion (angled trajectory) of the photon should not be dependent on the mirror's motion to the right, only to the angle of the mirror's surface.

Correct. The angle of incidence is equal to the angle of reflection regardless of the speed of the mirror.

So I think that depiction is not correct and some change in the angle of the mirrors is required.

Not in this case, although in general the angle of the mirrors is frame-variant.

OR is the photon shown as a bouncing point not accurate and should be shown as a circular wave front propagation thus intercepting the displaced mirrors at greater distance?

Either way works for the light clock.

 

[Dale]

Is the photon emitted on an angled path to the mirrors? By definition, I believe not.

Yes, it is emitted on an angled path. Path directions are frame-variant.

What definition are you referring to here?

 

[jtbell]

Suppose you are standing on a railway flatcar and throw a ball straight upward (from your point of view). If the flatcar is moving, someone standing on the ground sees the ball going up at an angle. The photon in the moving light-clock moves at an angle for the same reason.

 

[ghwellsjr]

Is the photon emitted on an angled path to the mirrors? By definition, I believe not. Then what causes the change to an angled path?

Let's pretend you have a photon gun with some sort of a barrel that guides the photon along the path you want it to take, in other words, it let's you aim the photon. This barrel will not be angled but pointing straight up. As the photon travels up the barrel, it has to travel at an angle as viewed from the stationary frame because the barrel is moving to the right during the time that the photon is moving up the barrel. If it doesn't move on an angle, it will hit the left side of the barrel and not make it out. Doesn't this make sense to you?

 

[Janus]

Is the photon emitted on an angled path to the mirrors? By definition, I believe not. Then what causes the change to an angled path?

Try looking at it from the other direction. The clock is "stationary" and you are moving past it. The photons for the clock go straight up and down, but from your perspective, relative to you, they follow a zig-zag pattern.

The thing is, according to the principle of Relativity, there is no difference between the clock moving past you and you moving past the clock. There is no absolute frame against which you can use to say which of you is "really" moving and it actually meaningless to talk about who is "really" moving. All you can know is that have have a relative motion with respect to each other. So when we talk about a "stationary" clock and a "moving" clock, we just mean stationary or moving relative to some convenient frame of reference (usually ourselves) and not in any absolute sense.

So if you also have a light clock, you would see it tick straight up and down and see the other clock's photons travel in a zig-zag, while someone with the other light clock would see your clock's photons follow a zig zag pattern and see his clock's tick straight up and down.

 

[bshul]

I thought laws of physics are preserved in every refernece frame and between reference frames...So angle of incidence does not equal angle of reflection?
when both reference frames were traveling at the same speed the photon bounces perpendicular to perpendicular mirrors and when one reference frame moves to the right at constant velocity with repsect to the other, the observed photon start to reflect at an angle to the perpendicular mirrors? What am I missing.

 

[Dale]

So angle of incidence does not equal angle of reflection?

Angle of incidence does equal angle of reflection in every frame. Otherwise Maxwell's equations would not hold in every frame and it would be possible to determine an absolute rest frame by measuring angles of incidence and reflection.

What am I missing.

I am not certain but I suspect that you are missing the fact that the angle of incidence is frame variant.

 

[ghwellsjr]

I thought laws of physics are preserved in every refernece frame and between reference frames...So angle of incidence does not equal angle of reflection?
when both reference frames were traveling at the same speed the photon bounces perpendicular to perpendicular mirrors and when one reference frame moves to the right at constant velocity with repsect to the other, the observed photon start to reflect at an angle to the perpendicular mirrors? What am I missing.

Maybe you're thinking that both reference frames and the mirrors at rest in them start out with zero velocity between them and then one of them starts to move to the right and you're wondering how a photon that was launched in the vertical direction at the stationary mirror would then hit the same mirror after it started moving while the photon was still in transit. Is that what you're thinking?

 

[bshul]

Maybe you're thinking that both reference frames and the mirrors at rest in them start out with zero velocity between them and then one of them starts to move to the right and you're wondering how a photon that was launched in the vertical direction at the stationary mirror would then hit the same mirror after it started moving while the photon was still in transit. Is that what you're thinking?

Yes, that's one thing I am thinking. What actually happens in that case. If initialy aimed at the mirror. it always hits the displaced mirror or does it miss the displaced mirror?

Also, what initially causes the photon to become angled to the mirror/emitter? i didn't think that moving the emitter/mirror to the right could effect the speed and/or direction of the emitted light.

The only response above, that I resonate with is "either way works for the light clock" i.e. that the photon could be thought of as a spherically propogating wavefront (circular in 2D) and that wavefront contacts the right displaced top mirror at a greater distance, than it would, a mirror directly above the bottom mirror. But I still would like to understand the emitted photon description of the clock.

 

[PatrickPowers]

Yes, that's one thing I am thinking. What actually happens in that case. If initialy aimed at the mirror. it always hits the displaced mirror or does it miss the displaced mirror?

Also, what initially causes the photon to become angled to the mirror/emitter? i didn't think that moving the emitter/mirror to the right could effect the speed and/or direction of the emitted light.

The only response above, that I resonate with is "either way works for the light clock" i.e. that the photon could be thought of as a spherically propogating wavefront (circular in 2D) and that wavefront contacts the right displaced top mirror at a greater distance, than it would, a mirror directly above the bottom mirror. But I still would like to understand the emitted photon description of the clock.

My advice is to go with the spherical waveform. I doubt that a pulsed photon clock could be constructed in real life.

 

[bshul]

My advice is to go with the spherical waveform. I doubt that a pulsed photon clock could be constructed in real life.

I'm getting the feeling that my original thought, that the zigzaging photon is not a good depiction and the spherical (2D circular) photon depiction is better, may be acceptable.
Thank you for your responses.
Burt

 

[bshul]

Originally Posted by PatricPowers "My advice is to go with the spherical waveform. I doubt that a pulsed photon clock could be constructed in real life".

Ok, so I'm getting some feeling that my original thought that the typical zigzag bouncing photon is not a good depiction and a circular wavefront depiction maybe more accurate.

Thank you all for your responses.
Burt

 

[Dale]

Ok, so I'm getting some feeling that my original thought that the typical zigzag bouncing photon is not a good depiction and a circular wavefront depiction maybe more accurate.

Both are fine. You should be able to understand both. If you do not understand the diagonal line, you should not try to "sweep it under the rug" but really confront the source of the confusion.

Let's, for a minute, consider a rubber-ball clock rather than a light clock (in the absence of gravity and with all v<<c). The clock is constructed with a spring-loaded rubber-ball launcher that launches the ball vertically at a fixed speed, it travels a fixed distance and hits a mark on the horizontal ceiling, bounces back, hits a mark on the horizontal floor right above the launcher, bounces up, ...

Now, for a minute, consider the same rubber clock moving inertially to the right at a speed equal to the lanuch speed. Immediately upon exiting the vertical launcher tube, which direction is the rubber ball travelling? Why is it traveling in that direction?

 

[jtbell]

To elaborate on Dale's setup, imagine the rubber-ball launcher to be a box with a spring inside it, on the bottom, and a hole at the top which ensures that the ball comes out moving vertically in the launcher's rest frame. Sometimes the spring pushes the ball off-center so it starts off at an angle and thereby misses the hole and fails to leave the launcher.

 

[ghwellsjr]

Maybe you're thinking that both reference frames and the mirrors at rest in them start out with zero velocity between them and then one of them starts to move to the right and you're wondering how a photon that was launched in the vertical direction at the stationary mirror would then hit the same mirror after it started moving while the photon was still in transit. Is that what you're thinking?

Yes, that's one thing I am thinking. What actually happens in that case. If initialy aimed at the mirror. it always hits the displaced mirror or does it miss the displaced mirror?

Also, what initially causes the photon to become angled to the mirror/emitter? i didn't think that moving the emitter/mirror to the right could effect the speed and/or direction of the emitted light.

In this case, where the mirrors are accelerated after the photon is emitted, the photon will not hit the mirror, but that's why we insist on inertial frames of reference when discussing a light clock. We have to assume that the mirrors have always been at a constant speed. So you need to assume that even though we might start out thinking about the mirrors as they first move away from each other, we really are considering the moving mirrors to have always been in motion and we're picking up the scene as they get close together.

The only response above, that I resonate with is "either way works for the light clock" i.e. that the photon could be thought of as a spherically propogating wavefront (circular in 2D) and that wavefront contacts the right displaced top mirror at a greater distance, than it would, a mirror directly above the bottom mirror. But I still would like to understand the emitted photon description of the clock.

You shouldn't give up on the single-photon idea. If a circular wavefront makes sense to you, why can't you think of it made up of individual photons, all traveling in a straight line at the same speed but at different angles so that the sum total of all of them looks like a circular wavefront? But then if you just remove all the photons except the one that hits the mirror, you will have the solution for the single-photon idea. And then go back and read post #7 and see if that now makes more sense to you.

 

[bshul]

So what I am hearing:
1). A moving emitter can effect the direction of the emitted photon.
2). The moving frame's velocity can add to the light's velocity.The light will then have a velocity in the emitted direction of c and a velocity in the right direction of the moving frame? but the reultant velocity is still c?
3). A moving flashlight has an angled beam in the observers frame?
4). In an accelerating frame, other effects take place (in addition?) to the velocity effect aka gravitational lensing?

 

[darkhorror]

An easy way to think about it is look at it as you are moving and the emitter is stationary. Then that you are stationary and the emitter is moving. This is one situation, just looking it from different positions.

 

[ghwellsjr]

So what I am hearing:
1). A moving emitter can effect the direction of the emitted photon.

Be aware that without the rigor of a Frame of Reference and the definitions it provides, we cannot talk meaningfully about the trajectory of a photon.

2). The moving frame's velocity can add to the light's velocity.The light will then have a velocity in the emitted direction of c and a velocity in the right direction of the moving frame? but the reultant velocity is still c?

That's the wrong way to get from one frame to another. What you need to do is describe the location and time of the event of the emission of the photon and the location and time of the event of the final destination of the photon in one frame and then use the Lorentz Transform to see what the coordinates of those two events are in the second frame.

3). A moving flashlight has an angled beam in the observers frame?

The individual photons will travel an angled path but the beam is not angled.

4). In an accelerating frame, other effects take place (in addition?) to the velocity effect aka gravitational lensing?

There's no standard way to deal with accelerated frames or gravity in Special Relativity.

 

[Passionflower]

There's no standard way to deal with accelerated frames or gravity in Special Relativity.

I agree with the gravity part but I disagree with accelerated frames.

Could you describe what you think is the problem with accelerated frames and SR?

 

[Iridescent]

Thing I don't get about photon clocks is why they are used to measure time intervals... because if they are affected by motion, why are they used to measure time?

Btw I'm kind of a noob here, so sorry if I broke some posting rules xD

 

[ghwellsjr]

Photon clocks are used in illustrating time dilation precisely because they are obviously affected by motion, but you can rest assured that any other clock will be similarly affected.

 

[Dale]

1). A moving emitter can effect the direction of the emitted photon.

Yes.

2). The moving frame's velocity can add to the light's velocity.The light will then have a velocity in the emitted direction of c and a velocity in the right direction of the moving frame? but the reultant velocity is still c?

No. The component of the velocity up must be less than c so that the speed is c. Speed is the magnitude of the velocity vector.

3). A moving flashlight has an angled beam in the observers frame?

Each photon travels at an angle, but the beam is not angled. Think about a rubber ball clock that launches a rapid series of balls.

4). In an accelerating frame, other effects take place (in addition?) to the velocity effect aka gravitational lensing?

Yes. I would recommend sticking with inertial clocks until you understand them.

 

[robphy]

The only response above, that I resonate with is "either way works for the light clock" i.e. that the photon could be thought of as a spherically propogating wavefront (circular in 2D) and that wavefront contacts the right displaced top mirror at a greater distance, than it would, a mirror directly above the bottom mirror. But I still would like to understand the emitted photon description of the clock.

You shouldn't give up on the single-photon idea. If a circular wavefront makes sense to you, why can't you think of it made up of individual photons, all traveling in a straight line at the same speed but at different angles so that the sum total of all of them looks like a circular wavefront? But then if you just remove all the photons except the one that hits the mirror, you will have the solution for the single-photon idea. And then go back and read post #7 and see if that now makes more sense to you.

This video of mine may be useful:
http://www.phy.syr.edu/courses/modules/LIGHTCONE/LightClock/VisualizingProperTime-y-pair-A-with-photons.avi

 

[ghwellsjr]

There's no standard way to deal with accelerated frames or gravity in Special Relativity.

I agree with the gravity part but I disagree with accelerated frames.

Could you describe what you think is the problem with accelerated frames and SR?

Let me just quote from one of the masters:

...An accelerating object doesn't have a unique accelerating frame, unlike with inertial frames there is no single "correct" way to construct a coordinate system where an accelerating object is at rest, in fact there are an infinite number of ways of doing this...