On light clocks and reference frames

[Dale]

Once light is emitted from a body, it is expected to conserve its speed, its frequency and its direction forever, not only wr to this body, but wr to any other body at a time.

Yes, with the important caveat that neither the frequency nor the direction are frame invariant. Another way of expressing this is that the energy and momentum of the light are conserved but not invariant.

To me, this reasoning suggests that its not the distance traveled by light between the mirrors that produces the slowing of the light clock since it would not suffer any doppler effect or aberration even if it was traveling this way,

Why? I agree with all of the facts you mention previously to this, but I don't see the connection. Why would the conservation of energy and momentum lead to invariance of path length?

there would be no way for an observer sited on one of the mirrors of the light clock to record that slowing since its own clock would also be slowed. For one slow back and forth motion of the beam, one slow second would be recorded by that clock, but one second would also be recorded for each bouncing whether the clock would be in motion or not.

Yes. This is a direct consequence of the principle of relativity.

 

[SlowThinker]

Anyway, you say that, in fig. 2, A has to send light at an angle, but it shows A at a vertical to B. What do you mean exactly?

As the line A'-a' shows, the beam of light is staying behind the source A as it is moving. That is only possible if A sends the light at an angle, same as Fig.1 shows.

In fig. 3, you say that A has to send light vertically, but you show a diagonal line between source and observer, so what do you mean again?

The light is sent from A vertically, but A is moving. The position of light in point a' has to be vertically below A', because that's what "sent vertically" means.
It is easier to understand if you imagine A being a car, and it's throwing a ball at B. The ball moves vertically as seen from A, but also keeps the car's horizontal speed. The same mechanism applies with light.

Truth is, your scenario does not deal with Einstein's relativity at all, it can be explained with just Galilean relativity. Relativistic aberration and time dilation are subtle effects, that are not clearly seen in your (or my) pictures.

 

[Raymond Potvin]

Here is the argument you had MT. Sorry, I should have answered this more directly earlier.

If those directions are the same, then yes. But if they're perpendicular, then no. If they were in perpendicular directions in every frame you could use that notion to identify a special frame, distinguishing it from all others. Imagine the interior of a passenger train where a Point F on the floor is directly below a point C on the ceiling. We check that it's directly below by connecting C and F with a straight line, and making sure that line is perpendicular to the level floor. We then shoot a laser beam from F towards C and it hits C. Now we move the train in the usual way that trains move, which is in a direction parallel to the floor of the train. With the train in motion we repeat the shooting of the laser beam, from F towards C. But by the time it gets there it will miss C if its path remains perpendicular to the floor. It would have to move along a diagonal path to hit C. Thus we could use this experiment to determine whether the train was moving or not.

You are right, and we could use it to detect the rotation of the Earth too, so it seems that it would contradict the result of the Michelson/Morley experiments, but not for the same reason. M/M wanted to test the aether dragging possibility, whereas this one would test the possibility that doppler effect and aberration would be unobservable for two bodies in the same reference frame even if they really existed. An interferometer is a very precise instrument, precise enough to detect that kind of speed, but unfortunately, I think that it cannot be used to detect the direction of light, and it cannot be used to detect doppler effect and aberration either since the source and the detector are in the same reference frame. A laser beam could, but wouldn't it spread out too much with distance? MM results also lead to the conclusion that the speed of light would be the same in all directions, and it seems to me that this experiment would not show the contrary, because on the paper, it seems obvious that it would take less time for the vertical beam to hit the floor than for the angled one. I must make a mistake somewhere since it seems to contradict SR, but I still can't see where!

 

[Mister T]

A laser beam could, but wouldn't it spread out too much with distance?

There are technical difficulties associated constructing a real light clock, and this is a valid one. In the light clock like the one I described in the train car, the spreading of the beam is an issue. But in principle making the train move fast enough would overcome that. Of course, we can't move real trains fast enough to do that. However, we are confident that the reasoning used in the thought experiment is valid because there are no apparent flaws in it and it yields quantitative predictions that match the way real clocks behave.

I must make a mistake somewhere since it seems to contradict SR, but I still can't see where!

This passage explains where ...

What's really going on here was explained by Galileo in the 1600's. Stand still and toss a ball directly upward. It's path is a straight line. Now do the same while standing on a moving train. Again the ball goes up and down along a straight and vertical line. But to an observer on the ground watching you through a window in the train car, the ball's path is a parabola. So, which is the ball's "true path"? The straight line or the parabola? The answer is that there is no "true path". The path depends on your frame of reference.

As you move horizontally and launch something vertically it stays above its source regardless of the state of (uniform horizontal) motion of the source, but the only way that can happen is if its path has different shapes in different frames of reference.

 

[Raymond Potvin]

I think that this example works for a ball because it carries mass, and because we can detect its path while observing the light rays that it reflects, but a light ray is not supposed to carry mass and it doesn't reflect other light rays so we cannot really detect its path. The only way to detect a light ray is to put the detector on its path and orient it against its direction. Its what we would have to do to detect the laser beam on the train or between two spaceships. This way, we would know the position of the source and that of the observer, but we wouldn't know for sure the path followed by the beam, not because it depends of the reference frame, but simply because a light path cannot be observed. This is precisely why I had the idea to add doppler effect and aberration to the light clock, because if we could see a light ray as it is shown on the drawings, we would probably know how it really travels between the two mirrors, and we might not have though to make this mind experiment. But then, without it, how to predict that the light clock would be slow? Worse, how to even suspect that it could be? Again, it seems to contradict SR, but I think that it doesn't contradict the properties of light, and I think that it doesn't contradict SR postulates either.

I just had another idea for a mind experiment. I am probably not the first one to present it, but It supports my reasoning on the light clock, so here it is:

Let two spaceships pass by the Earth on inertial motion and one beside the other wr to earth, and let the farthest from Earth send a laser beam towards an observer on Earth exactly when the two ships align with this observer. If light is considered traveling as in the train, it will hit the other ship thus it will never reach the earth, but if it is considered traveling as in my drawing, it will miss the other ship and it will hit the observer on earth. Both solutions might be true, but certainly not both at a time, and it seems to me that the beam would probably hit the Earth since the other ship will have moved by the time it takes for light to travel between the two ships. Again, it seems to me that my drawings do not contradict SR, but they do not explain how the light clock would slow down either.

 

[SlowThinker]

I just had another idea for a mind experiment. I am probably not the first one to present it, but It supports my reasoning on the light clock, so here it is:

You keep repeating the same mistake.
When I shine a laser across the width of a standing train, it will land at some spot on the opposite wall.
When I repeat this experiment in a moving train, it will land on the same spot.
It seems you think it will land a bit behind that spot, which is wrong.

If I then remove the wall, the light will keep going in that same direction,
- that is, perpendicular to the movement of the train as seen from the train,
- that is, at an angle as seen from above by an observer that is not moving with the train.

 

[Mister T]

I think that this example works for a ball because it carries mass,

A very common misconception. For example, if you shoot a bullet out of a gun barrel, what keeps the bullet moving after it leaves the barrel? The common answer is it has inertia. Objects in motion tend to stay in motion, that's inertia. The bullet has inertia because it has mass.

But this language fosters the misconception that the effect is a property of the bullet. It's not. The effect is due to the fact that you're viewing the bullet from a particular frame of reference. View it instead from a different frame and it's at rest.

In my opinion the term inertia has no purpose in the lexicon of physics. Most people use it as a constant of proportionality between force and acceleration, but in fact there is no constant of proportionality between force and acceleration. The two are not in general even in the same direction!

[...], and it seems to me that the beam would probably hit the Earth since the other ship will have moved by the time it takes for light to travel between the two ships.

There are three points to be made here.

1. If light beams travel the way you think they do the 1st Postulate is not valid.

2. If light beams behave the way you think they do the light clock would keep time in a way that's different from the way real clocks keep time.

3. If light beams travel the way you think they do, countless experimental outcomes would be different, including but not limited to, interferometer measurements like those performed in the MM experiments.

 

[Raymond Potvin]

As the line A'-a' shows, the beam of light is staying behind the source A as it is moving. That is only possible if A sends the light at an angle, same as Fig.1 shows.

The light is sent from A vertically, but A is moving. The position of light in point a' has to be vertically below A', because that's what "sent vertically" means.
It is easier to understand if you imagine A being a car, and it's throwing a ball at B. The ball moves vertically as seen from A, but also keeps the car's horizontal speed. The same mechanism applies with light.

Truth is, your scenario does not deal with Einstein's relativity at all, it can be explained with just Galilean relativity. Relativistic aberration and time dilation are subtle effects, that are not clearly seen in your (or my) pictures.

From wiki on aberration of light, here is an animation that shows how aberration is calculated using the Lorentz transforms:
https://upload.wikimedia.org/wikipedia/en/6/6d/Aberrationlighttimebeaming.gif
It is presented as in my fig. 2, namely, at the right, it shows the distance traveled by the source while the light ray reaches the observer, the only difference being that the source appears to be at an angle to the observer because it was at an angle when it emitted its light. On my fig. 2, the source appears to be right above the observer because it was there when its light was emitted. You say that my scenario does not need relativity, but I made my drawings so that they would match this animation. To me, saying that light would not travel vertically in fig. 2 is like saying it would not travel as it does on the right part of the animation. I'm sorry but I think I still don't understand your drawings, could you use that animation instead.

 

[SlowThinker]

To me, saying that light would not travel vertically in fig. 2 is like saying it would not travel as it does on the right part of the animation. I'm sorry but I think I still don't understand your drawings, could you use that animation instead.

The Wikipedia animation clearly demonstrates that the light is sent vertically, but arrives at an angle.
To arrive vertically, as it does in your Fig.2, it has to be sent at an angle "behind" the source. That angle is A'-a' in my Fig.2, or A'-B in your Fig.2.

 

[Mister T]

Note that the wiki sim starts after that wave train has fully formed. I wish you could watch, in slow motion, a simulation that showed the formation of that wave train. It would show every crest and trough of that wave being formed directly below the source at each instant. There is no diagonal aiming of the wave train to make it hit its target.

Imaging a ball with a piece of ribbon trailing behind it. Focus your attention on the left panel of the wiki sim. The ribbon trails directly behind the ball forming a line segment that's perpendicular to the target's direction of motion. If you view that same scenario from the observer's rest frame you'll see just what's shown in the right panel of the wiki sim.

So, does the ribbon take a straight path as shown in the left panel, or a longer diagonal path as shown in the right panel?

The answer depends on your frame of reference.

 

[Raymond Potvin]

In my opinion the term inertia has no purpose in the lexicon of physics.

I agree with you that our concept of inertia is confusing: on one hand, it is a resistance to a force, and on the other, it is motion without a force. But isn't that the same for our concept of mass? If we reject the term inertia, we would have to reject the term mass too, no? But we can't do that, because we would have to replace it by a better term, thus by a better theory, and as far as I know, we don't have any on hand.

1. If light beams travel the way you think they do, the 1st Postulate is not valid.

I think that it could be valid if we would consider that a laser beam is made of light rays that travel in many different directions, as for any light source, because then, even if those directions are limited for a laser, they would suffer enough spreading to account for the motion involved. In other words, the beam on the train would spread enough for part of it to precede the motion, thus to travel at an angle, and aberration would straighten it for an observer on the wall, exactly as my fig. 3 shows.

2. If light beams behave the way you think they do the light clock would keep time in a way that's different from the way real clocks keep time.

I agree with you this time, because it seems to me that there would be no way for an observer on the light clock to register the longer path, which means that a traveling clock would not slow down for real, but it doesn't mean that it would not appear to slow down from a distance, as for the experiments with the muon for instance.

3. If light beams travel the way you think they do, countless experimental outcomes would be different, including but not limited to, interferometer measurements like those performed in the MM experiments.

As I said earlier, I think that an interferometer could not account for the direction of light, because it is made to account for its difference in frequencies. But as I just said above, if a laser beam would spread enough, part of it would still hit the mirror when it travels sideways to the motion, and aberration would also straighten it, so I think that it would not change the null result. I may be wrong though, do you still think it would? And if so, how?

 

[Raymond Potvin]

The Wikipedia animation clearly demonstrates that the light is sent vertically, but arrives at an angle.
To arrive vertically, as it does in your Fig.2, it has to be sent at an angle "behind" the source. That angle is A'-a' in my Fig.2, or A'-B in your Fig.2.

The animation shows that aberration not shown on the left part is calculated from the angle shown on the right part. The way I see things, except for the initial position between the source and the observer, my fig. 2 is the same as the right part, and my fig. 1 is the same as the left part. Do you agree with that?

 

[PeterDonis]

isn't that the same for our concept of mass?

No. Mass is the invariant length of an object's 4-momentum vector. It is perfectly well-defined and doesn't have any of the problems you mention.

I think that it could be valid if we would consider that a laser beam is made of light rays that travel in many different directions

For any real laser, this will in fact be true; but the discussion in this thread is assuming an idealized laser that only emits light in one single direction, i.e., a pulse of light from this laser is just one ray.

What you are failing to do in this entire thread is actually do the math. Write down the equation of the light ray emitted by the laser in one inertial frame; then transform into another inertial frame and look at the properties of the light ray in that frame, as given by the transformed equation. You will see aberration, Doppler, etc. all pop out of this analysis with no problem at all. But you have to actually do the math; you can't just guess, which is what you've been trying to do.

 

[Mister T]

I agree with you that our concept of inertia is confusing: on one hand, it is a resistance to a force,

That's mass, but only in the Newtonian approximation. In a more general theory, which is the theory discussed here, mass doesn't play that role, for the reasons I stated.

and on the other, it is motion without a force.

Apparently you missed my point entirely. Motion without a force is not a property of the object that's moving. It's a consequence of the observer's relative motion or lack thereof.

But isn't that the same for our concept of mass?

No, it's the pre-Einsteinian concept of mass.

If we reject the term inertia, we would have to reject the term mass too, no?

No, mass has a precise meaning. We can keep it and do just fine without inertia.

But we can't do that, because we would have to replace it by a better term, thus by a better theory, and as far as I know, we don't have any on hand.

Einstein showed that the concept of mass has a meaning that's different from the prior meaning it had. There's no way to resurrect that old meaning with a new theory. The concept of inertia is a historical artifact that, in my opinion, should no longer be part of the lexicon of physics. I see no pedagogical value in it, even when teaching Newtonian physics.

As I said earlier, I think that an interferometer could not account for the direction of light, because it is made to account for its difference in frequencies.

But to measure that frequency you need a detector of some kind, and you have to aim the beam so that it hits the detector. No adjustment needs to be made when the interferometer is rotated. Even MM knew this, as it's part of Galilean relativity.

 

[Raymond Potvin]

Hi Peter,

Yes, I know how the maths work, and I know that they give the same numbers as our observations, but I never saw aberration applied to two bodies in the same reference frame with light traveling between them the way it travels between the mirrors of the light clock, so I did, and I came to the conclusion that this possibility might change the way we think that light travels between bodies in motion. Of course, its one thing to imagine how light would travel, and its another one to see it traveling for real, but then, we might be wrong to use the idea that the rays contained in a laser beam could all travel in the same direction as you suggest. Is it logically permitted to use an impossibility to demonstrate a possibility? Even if there was only two light rays in a laser beam, they couldn't have been sent absolutely parallel, could they? On the other hand, how could a muon appear to live longer as our observations show an not live longer for real??

 

[Mister T]

On the other hand, how could a muon appear to live longer as our observations show an not live longer for real??

Raymond, please read Post #45.

Do the GPS clocks only "appear" to run slower and not run slower for real? Are the adjustments made by the engineers to account for time dilation done only to satisfy appearances?

 

[Raymond Potvin]

That's the question I was asking myself while talking to Peter about the muon, but I think its not quite the same question for GPS clocks, because gravitation is affecting them. I'm not sure, but I think that the GPS experiment cannot be considered as an experiment about SR. The clocks from two spaceships traveling at constant speed would not be affected by their gravitational well, whereas while traveling at constant speed too, the GPS clocks change directions all the time.

Imaging a ball with a piece of ribbon trailing behind it. Focus your attention on the left panel of the wiki sim. The ribbon trails directly behind the ball forming a line segment that's perpendicular to the target's direction of motion. If you view that same scenario from the observer's rest frame you'll see just what's shown in the right panel of the wiki sim.

So, does the ribbon take a straight path as shown in the left panel, or a longer diagonal path as shown in the right panel?

The waving arrows that represent the light wave train can be considered such a ribbon, and the simulation shows that the apparent direction of that ribbon would be the same in both situations, which is also what my drawings show. What if the way a light ray travels between moving bodies was absolutely not observable, in such a way that, even in the same reference frame as the source, it would be absolutely impossible to determine its original direction? Would that make an acceptable postulate for studying relative motion?

 

[Mister T]

That's the question I was asking myself while talking to Peter about the muon, but I think its not quite the same question for GPS clocks, because gravitation is affecting them.

Right. It's more complicated because of the difference in the gravitational field gradient. But there is still some adjustment due to motion. It's real, not apparent. That was my point and still is.

The waving arrows that represent the light wave train can be considered such a ribbon, and the simulation shows that the apparent direction of that ribbon would be the same in both situations, which is also what my drawings show.

I thought your drawings showed that the light beam had to be aimed in a diagonal direction when launched from a moving platform, but not so when launched from a stationary platform. The ball I described, with its trailing ribbon, is not aimed in such a way. It is aimed in a direction perpendicular to the direction of motion.

 

[Dale]

, but I never saw aberration applied to two bodies in the same reference frame with light traveling between them the way it travels between the mirrors of the light clock, so I did, and I came to the conclusion that this possibility might change the way we think that light travels between bodies in motion. Of course, its one thing to imagine how light would travel, and its another one to see it traveling for real, but then, we might be wrong to use the idea that the rays contained in a laser beam could all travel in the same direction as you suggest.

First, aberration is well understood by the scientific community. This analysis is not presented because it is not informative, not because it is mysterious.

Second, it is quite easy to see how light travels between bodies as long as we are in the classical regime rather than the quantum regime. The phenomena that we are discussing are not unknowns. They are well established experimentally, not just theoretically. With a little dust in the atmosphere, we can easily see the path of the lasers.

Is it logically permitted to use an impossibility to demonstrate a possibility?

Yes, it is (https://en.wikipedia.org/wiki/Proof_by_contradiction) , but that is not what is happening here.

 

[PeterDonis]

I never saw aberration applied to two bodies in the same reference frame with light traveling between them the way it travels between the mirrors of the light clock

That's because, in the frame in which the two bodies are at rest, there is no aberration--which means that, as far as the two mirrors of the light clock are concerned, there is no aberration. The light just bounces back and forth between the mirrors. "Aberration" only comes into play if you insist on viewing things in a frame in which the light clock is moving; then the motion of the clock gives rise to aberration relative to you (meaning, relative to an observer at rest in the frame you're using, in which the light clock is moving). In other words, "aberration" is frame-dependent--at least, it is the way you are viewing it.

 

[PeterDonis]

I know how the maths work, and I know that they give the same numbers as our observations

Then what's the problem?

 

[PeterDonis]

Even if there was only two light rays in a laser beam, they couldn't have been sent absolutely parallel, could they?

Go back and re-read what I said about idealized models vs. real lasers.

 

[PeterDonis]

how could a muon appear to live longer as our observations show an not live longer for real??

Live "longer" relative to what? There is no such thing as "longer" in an absolute sense in the case of the muons coming from cosmic rays in the atmosphere vs. muons sitting at rest on Earth, because the two sets of muons start out spatially separated, so which set lives "longer" depends on what simultaneity convention you adopt; there is no physical fact of the matter.

 

[PeterDonis]

I think its not quite the same question for GPS clocks, because gravitation is affecting them.

It's true that there is a gravitational component to the observed behavior of GPS clocks relative to ground clocks, but there is also a component due to relative motion.

The first key point is that, since the GPS clocks are in closed orbits, there is an inherent periodicity to their behavior, relative to ground clocks, that is invariant--both ground observers and GPS clock observers can agree on when a GPS clock has completed exactly one orbit. That means that both sets of clocks can count the number of ticks per orbit, and those numbers can be compared to provide an invariant answer to the question of which set of clocks is running "slower" or "faster".

The second key point is that, since the time dilation effect of gravitation depends only on altitude, and both observers (GPS clock observers and ground clock observers) agree on which altitude each one is at, there is an invariant way to factor out the effect of gravitation. When you factor this out, the effect due to motion is what's left. That effect, by itself, makes the GPS clocks run slower than clocks on the ground; heuristically, this is because the GPS clocks are moving faster relative to an inertial frame (i.e., a frame not rotating with the Earth) in which the Earth's center of mass is at rest. The effect of altitude is large enough in the case of GPS clocks, because of the altitude of their orbits (orbital radius about 4.2 Earth radii), that the overall clock rate of GPS clocks is faster than that of ground clocks. For a clock in low Earth orbit, however, (e.g., a clock on the International Space Station), the altitude effect is not large enough to overcome the velocity effect, so those clocks run slower than clocks on the ground.

 

[SlowThinker]

OK so I reread your first post but I still don't understand your question.

To me, fig. 3 means that if the source was a laser beam aimed perpendicularly to its motion, this beam would never hit the observer, which seems to contradict the reference frame principle. Does it?

This is not true, the light in Fig.3 needs to be aimed perpendicular to the motion to hit B. Situation in Fig.3 is different from Fig.1 and Fig.2.

Please try to avoid the style "I said this but I don't think it's true any more" and "I said this and he said that and I say this now" because it makes it really hard to understand what you're trying to say. Can you try to ask your question in a different wording?

 

[Raymond Potvin]

Yes, it is (https://en.wikipedia.org/wiki/Proof_by_contradiction) , but that is not what is happening here.

If a laser beam that would not spread is an impossibility, then it seems to me that we cannot use it to show how light would travel. To test my questioning with maths, I think that we would have to let the beam spread at a known rate and calculate if it spreads enough with distance to travel the way I suggest it could between the mirrors. If the calculations show that it could, then we could ask ourselves by what means that clock would slow down for real when it moves wr to the observer at rest. On the other hand, it seems to me that if a light clock would really slow down, while at the same time, light would not really travel this way between the mirrors, is also an impossibility. I can understand that the original direction of light might not be observable, because I think that it could be a real possibility, but I have a problem to accept that, for the same clock, an imaginary direction considered locally as a physical impossibility, can be transformed mathematically into a real possibility, again locally, but when observed at a distance. Why is it that a reasoning about an impossibility gives the same numbers as the data? Are we missing something? Do we really have to accept that as a given?

First, aberration is well understood by the scientific community. This analysis is not presented because it is not informative, not because it is mysterious.

To me, the information gets not informative only if the light path is not considered real, but as my fig. 3 shows, if light would really travel diagonally, it would still appear to travel directly, and there would be no doppler effect either, which is exactly what is expected to happen when observer and source are considered to be in the same reference frame.

With a little dust in the atmosphere, we can easily see the path of the lasers.

We see what we think is the original light path, but again, if light would really travel diagonally between the dust and us, it would be impossible to see its diagonal direction, because it would suffer aberration and it would always appear to travel directly from the source or directly to us.

Other's ideas are as difficult to follow as light paths, so maybe it would be wiser to end our discussion here. If I continue, I know I will only repeat the same questioning, and I think that I would always get the same answering, so I'm afraid it would get boring. If I had a proposition that doesn't seem to contradict the data, we could discuss its details, but I have none. Even if I am still not convinced that SR is already answering my questions, the discussion helps me to add precision to my ideas a bit, and everybody does it with kindness, which is all I need to be happy. You are very nice guys, nicer that on many forums I know, and you do a very good job too, but I know that you cannot suddenly accept the possibility that SR is not what it appears to be, and its what my OP is about. I hope that our discussion at least helps other readers to better understand SR!

 

[PeterDonis]

If a laser beam that would not spread is an impossibility, then it seems to me that we cannot use it to show how light would travel. To test my questioning with maths, I think that we would have to let the beam spread at a known rate and calculate if it spreads enough with distance to travel the way I suggest it could between the mirrors. I

Do you understand what an idealized model is? A laser beam that does not spread is an idealized model. Mathematically, it is perfectly consistent and allows us to "test with maths" claims like yours (and see that they are false).

 

[PeterDonis]

Thread closed for moderation.

Edit: the thread will remain closed, we are just going in circles now. Also, whenever you think something like "SR is not what it appears to be" then either you have misunderstood SR or you have been contradicted by experiment.