Why does the photon bounce vertically in the light-clock?

[Saw]

I have always had this difficulty with understanding the example of the light-clock: what keeps the light pulse bouncing to and fro between the mid-points of the top and bottom mirrors?

Assuming the Earth is inertial for most practical purposes, a coin dropped from a tower hits the ground right below my hand. If instead of a coin, it is a ball, it keeps for a while bouncing up and down on the very same point. But there is a physical cause for that: those effects, according to Galileo, happen because the coin and the ball, before being dropped, share the state of motion of the ground. If they were dropped from the tower on a racing train, that would not happen.

If I emit sound upwards on a moving train, sound will bounce up and down right on my head. But again there is a similar physical cause for that: the air has been accelerated by the walls of the train until it has acquired the state of motion of the latter.

Light is different. It does not acquire the state of motion of the source and it cannot be dragged along.

First consequence, its speed is the same for all observers. I have no problems with that. I very much thank help received in this forum, thanks to which I understand why it is so. If the speed of light is measured as it is, it must be so.

But, second, for the measurement instruments to render that result, they must work: the light pulse must keep bouncing with a purely vertical trajectory, without any deviation. But if the shell of the clock is accelerated, how does the light pulse learn so? How does it know that it must now take another direction?

One explanation I have seen somewhere is: because of the principle of relativity. But that is only an idea. A wonderful idea, in my opinion, which is the basis of modern science and rightly so, but things do not happen just in order to fit into theories. Things happen because of a reason. It may happen that the reason is yet undiscovered. That is not so dramatic and science makes progress because it can live without the ultimate explanations for many phenomena. But there must lurk somewhere a reason, an explanation for everything and no doubt knowing it is "enlightening" and boosts further progress. In this case, don’t we know the reason why the light pulse "conforms to the principle of relativity"?

My own humble understanding was that light remains in the mirror because it expands in all directions. So, if not one, another photon will hit the right place. But then the photons that did not hit the target would bounce around, thus rendering the instrument impractical. Given so, I thought: well, the light-clock thought experiment is just that, a pedagogical tool, it does not have to work itself. And I also thought: atomic clocks work analogously to light-clocks and they do not have such practical inconvenient. Is this explanation right?

Sorry for the long post, but I wanted to refine the question. Thanks in advance.

 

[JesseM]

I have always had this difficulty with understanding the example of the light-clock: what keeps the light pulse bouncing to and fro between the mid-points of the top and bottom mirrors?

Assuming the Earth is inertial for most practical purposes, a coin dropped from a tower hits the ground right below my hand. If instead of a coin, it is a ball, it keeps for a while bouncing up and down on the very same point. But there is a physical cause for that: those effects, according to Galileo, happen because the coin and the ball, before being dropped, share the state of motion of the ground. If they were dropped from the tower on a racing train, that would not happen.

If I emit sound upwards on a moving train, sound will bounce up and down right on my head. But again there is a similar physical cause for that: the air has been accelerated by the walls of the train until it has acquired the state of motion of the latter.

Light is different. It does not acquire the state of motion of the source and it cannot be dragged along.

"It does not acquire the state of motion of the source" is too broad. It's true that it doesn't acquire the speed of the source. But its direction is influenced by the source--if a directed source of light like a flashlight or a laser is moving inertially, then the direction of the beam will always be parallel to the direction of the source in the source's own rest frame (for example, if you point a laser straight up at the ceiling, it goes straight up in the frame where the laser is at rest). Presumably you can derive this from Maxwell's laws.

One explanation I have seen somewhere is: because of the principle of relativity. But that is only an idea. A wonderful idea, in my opinion, which is the basis of modern science and rightly so, but things do not happen just in order to fit into theories. Things happen because of a reason.

Well, you can find a mathematical reason--any theory whose equations are Lorentz-invariant is guaranteed to be unchanged when a Lorentz transformation is applied to those equations to find out how the phenomena being described by the theory would behave in a different inertial frame. And all the fundamental laws of physics, including those governing electromagnetic waves, are Lorentz-invariant. Physicists don't try to explain why nature obeys any given set of mathematical laws, they just try to find what the correct laws are (although it can happen that one set of laws is not really fundamental, and can be 'explained' in terms of some more fundamental laws).

 

[Saw]

"It does not acquire the state of motion of the source" is too broad. It's true that it doesn't acquire the speed of the source. But its direction is influenced by the source--if a directed source of light like a flashlight or a laser is moving inertially, then the direction of the beam will always be parallel to the direction of the source in the source's own rest frame (for example, if you point a laser straight up at the ceiling, it goes straight up in the frame where the laser is at rest).

Thanks a lot, as usual, for the clear answer. That is, in fact, the question. So I can assume that my try for an explanation (the light-clock works because photons are spread in all directions and one or the other hits the target) is wrong, since, according to SR, the state of motion of the source does not influence the speed of the beam, but it does influence its direction.

Presumably you can derive this from Maxwell's laws.

Hum... Maybe the subject for another thread...

Physicists don't try to explain why nature obeys any given set of mathematical laws, they just try to find what the correct laws are (although it can happen that one set of laws is not really fundamental, and can be 'explained' in terms of some more fundamental laws).

Hum... I am not so sure of that. It is true that the mere description and prediction of phenomena, even when the root causes are unknown, is at the core of physics: it is the great methodological invention that has led to the unbelievable development of science in the last centuries. Newton formulated the law of gravitation and declared: "I frame no hypotheses" as to why gravity exists and how it operates at fundamental level. But probably he would have given one hand to know it and in fact he especulated a lot about the issue in private writings. Logical, since knowing the root causes, at one or another level, is like having a magical key that suddenly opens dozens of doors. Take the example of the kinetic theory of heat. In the past scientists could measure heat and artisans apply it. But knowing that heat was motion of molecules at microscopic level brought about dramatic progress of the discipline... Anyhow, in the end, I think we all agree, discussion on semantics not being worth it: as you say, the quest for "more fundamental laws" is always open. As to mathematical explanations, I would add, that is just a language with which you express what you know in a logical manner: as any other language, it can be shallow or deep, it depends on what you are expressing, on what you know. In this case, I understand, what we know is this, for example: a laser beam projected from a given source will keep heading forever towards the point in the source RF that the laser gun was pointing at when the beam was emitted... But it is weird, isn´t it?

 

[gonegahgah]

This is probably a silly question but how do you see a photon that is too busy bouncing between mirrors to ever bother moving to our eye to tell us where it is?
Is it just meant to be a rhetorical analogy or will we really see the photon?

 

[Saw]

This is probably a silly question but how do you see a photon that is too busy bouncing between mirrors to ever bother moving to our eye to tell us where it is?

You are right. You will not see the photon if it does not hit your eye. If you wish to detect that the photon has hit the mirror and thus "ticked", you need to lay on the mirror your eye or (better) a light detector. But then, if the photon is to be seen or detected, it is because it is absorbed by your retina or the detector and so it will stop bouncing.

Is it just meant to be a rhetorical analogy or will we really see the photon?

Probably a light-clock would not work with this configuration. I tested a reason for that, which seems wrong, according to the answer. But you point at another. Anyhow, what does work is an atomic clock. I would like to know in what sense its way of working is analogous to that of a light-clock. A farther-reaching question would be why "any" clock, even a mechanical one, would ultimately be (since it is also subject to time dilation) analogous to the light-clock. But that may be a question for another thread.

 

[gonegahgah]

"It does not acquire the state of motion of the source" is too broad. It's true that it doesn't acquire the speed of the source. But its direction is influenced by the source--if a directed source of light like a flashlight or a laser is moving inertially, then the direction of the beam will always be parallel to the direction of the source in the source's own rest frame (for example, if you point a laser straight up at the ceiling, it goes straight up in the frame where the laser is at rest). Presumably you can derive this from Maxwell's laws.

Which is what I would think too. So the following diagram would be along the correct lines wouldn't it Jesse?

http://img391.imageshack.us/img391/1684/directionallightpn3.th.jpg

It shows two light sources that blink when they meet in their paths. The top light is moving to the right and the bottom light is moving to the left. They meet to the right of the observer. The lights blink a rainbow pattern when they meet.

You said that the travel of the light moves with the source (if not its speed). So the observer would see - ignoring red/blue shift and contractions - for the top light the green part of the rainbow centred in their vision, and for the bottom light the blue part of the rainbow centred in their vision; even though both lights were at the same relative point from the eye when they blinked.

That is correct isn't it?

 

[GOD__AM]

But, second, for the measurement instruments to render that result, they must work: the light pulse must keep bouncing with a purely vertical trajectory, without any deviation. But if the shell of the clock is accelerated, how does the light pulse learn so? How does it know that it must now take another direction?

I'm no expert certainly, but it's my understanding that an accelerating light clock will not count seconds properly in its own frame. The photons will travel at an angle away from the direction of acceleration causing the photon to either miss the reflector (if the reflector was small enough) or take a longer path resulting in more elapsed time.

As for the how does it know question, I think it relates to an object being able to considered itself at rest when it is not accelerating.

 

[Naty1]

This is probably a silly question but how do you see a photon that is too busy bouncing between mirrors to ever bother moving to our eye to tell us where it is?

You are right. You will not see the photon if it does not hit your eye.

The light clock is of course a theoretical and impractical construct... but I'm not at all sure it's as simple as the above suggests. For one thing there is wave particle duality and an associated infinite extent schrodinger probability. For another, would you argue " You can't see a proton" until it bonks you in the eye"?? likely no, because reflected photons from that object apparently impinge on your eye. Other threads here HAVE indicated the human eye can perceive individual incident photons. I do not know the precise theoretical answer, but when you say "see" instead of "measure" or "detect" you move into the subjective interpretation of human senses. Is it possible to "see" effects of a photon bouncing/reflecting from a mirror..exactly what is a bounce/reflection??

 

[JesseM]

Which is what I would think too. So the following diagram would be along the correct lines wouldn't it Jesse?

http://img391.imageshack.us/img391/1684/directionallightpn3.th.jpg

It shows two light sources that blink when they meet in their paths. The top light is moving to the right and the bottom light is moving to the left. They meet to the right of the observer. The lights blink a rainbow pattern when they meet.

You said that the travel of the light moves with the source (if not its speed). So the observer would see - ignoring red/blue shift and contractions - for the top light the green part of the rainbow centred in their vision, and for the bottom light the blue part of the rainbow centred in their vision; even though both lights were at the same relative point from the eye when they blinked.

That is correct isn't it?

Yes, your diagram looks conceptually right to me...obviously the exact points on each source where the light is sent would depend on how far the observer is to the left of the position where the two sources meet, and how fast the sources are moving in the observer's frame.

 

[gonegahgah]

Yes, your diagram looks conceptually right to me...obviously the exact points on each source where the light is sent would depend on how far the observer is to the left of the position where the two sources meet, and how fast the sources are moving in the observer's frame.

I agree.

The following diagram shows how the observer starts and ends up in relation to the two sources that blink when they meet. The observer started to the left of both sources and ends up about perpendicular to the left moving source when it receives its blink and ends up further left of the right moving source when it receives that one's blink.

The diagram shows why the the observer sees the middle of the rainbow as green for the right moving source and blue for the left moving source as it collides with their light beams which emit out in a direction perpendicular to the movement of the sources.

http://img338.imageshack.us/img338/3968/directionallight2sh1.th.jpg

The part that has always puzzled me is that despite colliding with the light in the direction it emits perpendicular to the source's movement the speed is determined not by this but by the immediate distance between the source and the observer at the time of emmision.

This means effectively that it would not matter if you traveled toward the sun or away from the sun the light would take 8 minutes to reach you no matter how fast you moved; away or towards. Even if you raced really fast towards the light it would reach you in 8 minutes the same as if you raced away from the light. All that matters is your initial distance from the source.

It amazes me but I guess it just is. Is all of this okay?

 

[JesseM]

The diagram shows why the the observer sees the middle of the rainbow as green for the right moving source and blue for the left moving source as it collides with their light beams which emit out in a direction perpendicular to the movement of the sources.

Are the different positions of the observer in the second diagram showing his position relative to the source in both the rest frame of the top source and the rest frame of the bottom source?

The part that has always puzzled me is that despite colliding with the light in the direction it emits perpendicular to the source's movement the speed is determined not by this but by the immediate distance between the source and the observer at the time of emmision.

This means effectively that it would not matter if you traveled toward the sun or away from the sun the light would take 8 minutes to reach you no matter how fast you moved; away or towards. Even if you raced really fast towards the light it would reach you in 8 minutes the same as if you raced away from the light. All that matters is your initial distance from the source.

Not sure I follow you here. It's true that if you're moving inertially and the sun is 8 light-minutes away in your rest frame, that means the light will take 8 minutes to reach you in this frame regardless of how you're moving relative to the Earth. But if we're looking at things in the rest frame of the Earth (ignoring GR and treating this as an inertial frame), then if the Earth sees an observer on a ship pass by at the same moment a particular photon is being emitted from the sun, then the time for that photon to catch up with the ship would certainly be different depending on whether the ship was headed towards the sun or away from it.

 

[gonegahgah]

Are the different positions of the observer in the second diagram showing his position relative to the source in both the rest frame of the top source and the rest frame of the bottom source?

The two light sources aren't actually meant to be in rest frames - except to show how the direction of the light corresponds approximately to their rest frames; if not the speed of the light. The eye is still the rest frame for the light travel but the diagram is just meant to show where the eye ends up approximately relative to the two sources at both blink time and when the eye receives the light of both. I've just superimposed the two light sources from the two time moments - rather than having three places (meeting & two apart) - just to illustrate the relative distance between the eye and the sources when the light is received. So the light sources are still the movers - just illustratively superimposed - and the eye is still the stationary object but just being shown relative to the illustratively superimposed sources.

Not sure I follow you here. It's true that if you're moving inertially and the Sun is 8 light-minutes away in your rest frame, that means the light will take 8 minutes to reach you in this frame regardless of how you're moving relative to the Earth. But if we're looking at things in the rest frame of the Earth (ignoring GR and treating this as an inertial frame), then if the Earth sees an observer on a ship pass by at the same moment a particular photon is being emitted from the Sun, then the time for that photon to catch up with the ship would certainly be different depending on whether the ship was headed towards the sun or away from it.

I'm not looking at it in the Earth's rest frame. What I mean is that if you are 8 light minutes from the Sun (by Earth's measure) when the Sun blinks and the Sun is traveling towards you really quickly at the time the light will take 8 minutes to reach you and if you are 8 light minutes from the Sun (by the Earth's measure) and the Sun blinks and the Sun is traveling really quickly away from you the light will still take 8 minutes to reach you. This is because the light moves relative to you the observer. So the time the light takes to reach you is based upon you initial separation; not upon how close you end up in relation to the emitter when the light reaches you.

So in my examples you the observer are stationary; as is always the situation (except under acceleration I guess). The Sun moves towards or away from you. When the Sun moves towards you the Earth retreats behind you. When the Sun moves away from you the Earth moves with the Sun in the same direction away from you.

Because the Sun is moving towards or away from you then the time taken for the light is not based upon the Sun's rest frame but upon your rest frame. So no matter where the Sun ends up relative to you the light traveling from its same initial distance from you will reach you in the same amount of time.

So you can't say "I get the light sooner when I end up closer to the Sun traveling towards it" and vice versa because the observer is always stationary. The Sun is the object that is not in a rest frame so the time is always measured from where the Sun is relative to our observer at the time of the blink.

Let's say you had a marker in space that stayed in position relative to the Sun; maybe it is in orbit. If the marker passed you opposite to the Sun's direction - ie the sun is traveling towards you - the light emitted from the Sun at that time would take the same time to travel to you as the opposite situation where the marker passed you in the Sun's direction - ie the Sun is traveling away from you.

The time taken for light to travel is always based upon the observer and is proportional directly to how far the source is away from the observer at the time of emmission; unlike the direction of the light which is based approximately on the direction of the light from the source being stationary.

That is my interpretation. Or have I got something wrong?