# On light clocks and reference frames

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

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?

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?

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Mister T
Gold Member
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
Mentor
, 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
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2019 Award
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
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I know how the maths work, and I know that they give the same numbers as our observations
Then what's the problem?

PeterDonis
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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
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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
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2019 Award
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.

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?

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
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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
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