If clocks themselves are based on light signals, wouldn't we expect the measured speed of light to always be the same constant?7t d Eh IXKk p Cc m89506eGgQqK Liv e4 Jf AaGA
I'm trying to work out if there is an alternative starting point for the second postulate of special relativity. My main observation is that all "clocks" are, internally, based on light signals. So all clocks can essentially be thought of as light-mirror-clocks (I won't expand on this idea much, but it is motivated by the fact that the time difference measured by light-mirror-clocks is independent of the orientation of the light mirror, i.e. independent of whether the light-mirror-clock is up-down or left-right).
Given this, what we think of as time is just the number of bounces of light inside clocks.
In a similar manner, an apparatus for measuring the speed of light is also essentially just a light-mirror-clock (with some known height h). In which case, we can think of the measuring apparatus as being essentially identical to the clock, except that clocks are generally regarded as smaller, say with height h/N where N is some integer for convenience.
Now imagine two moving laboratories moving to the right, lab A is moving faster than lab B (hence the angle theta is smaller than the angle phi in the diagram):
Each lab has its own clock, whose height is smaller than the apparatus by the factor N.
When A's apparatus has completed one bounce, A's clock has completed N bounces. Therefore lab A concludes the speed of light is distance moved/time = h/N.
When B's apparatus has completed one bounce, B's clock has completed N bounces. Therefore lab B also concludes the speed of light is distance moved/time = h/N.
So both laboratories measure the same speed for light, and so will all laboratories. This is because the clocks they use always mimick the apparatus.
Note that this result is independent of the "actual" speed of the rays in the sense that I did not need to use a velocity in the above calculations. If the rays "really" move faster in the apparatus they will also move faster in the clock, but the measured speed is the same.
So, can we say all observers should be expected to measure the same speed for light because all observer's clocks are based on the same light signals they are trying to measure?
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$\\begingroup$ You completely missed that an experiment selected to measure speed of light in a material is not just a scaled up clock (which contains vacuum) but actually contains the material. So it can easily measure a different ratio than the ratio of the distances. I think you failed to completely describe what you are trying to analyze. $\\endgroup$ – Ben Voigt 5 hours ago
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$\\begingroup$ Compare the measured speed light to the speed calculated by Maxwell's equations. The speed predicted by Maxwell's equations is constant. The measurements are confirming the prediction and fixing the value. $\\endgroup$ – Cinaed Simson 6 mins ago
3 Answers
This has absolutely nothing to do with relativity. Of course A says that his own clock ticks at one second per second, as does B. This is as true in Newton's world (or in Aristotle's) as in Einstein's. The key question for relativity is: How fast does A say that B's clock ticks? And your analysis does not address this at all.
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7$\\begingroup$ Technically it does relate to relativity in the sense that all inertial observers should experience the same laws of physics. But of course that's not what the OP is going for :) $\\endgroup$ – Aaron Stevens 14 hours ago
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2$\\begingroup$ In particular, if the speed of light was frame-dependent (which was very much a live possibility until the Michelson-Morley experiment, at least), then we would expect A's and B's clocks to run at different rates. $\\endgroup$ – Michael Seifert 4 hours ago
We have that currently our most accurate time measurement technology is Cesium clocks. As we know, the energy levels of electron distribution of atoms is governed by electromagnetism.
In that sense a 'light clock' and a Cesium clock have in common that in both cases the physics of the system is electromagnetism-based.
I infer that you would like to raise the question: is it perhaps the case that any form of time measurement boils down to electromagnetism?
Thought experiment: What if it is possible to construct a clock that uses the Mössbauer effect for accurate time keeping?
As we know, the main factor holding a nucleus together is the strong nuclear force. The strong nuclear force gives rise to nuclear energy levels. The Mössbauer effect involves transitions between nuclear energy levels.
So if it is possible to construct a clock that uses the Mössbauer effect for accurate time measurement then that is a counterexample to the case that perhaps any form of time measurement boils down to electromagnetism.
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1$\\begingroup$ What's wrong with a weak decay clock (i.e. muons) as an alternative to E&M? Or alpha decay which is controlled partly by E&M and partly by the effective nuclear force? $\\endgroup$ – dmckee♦ 3 hours ago
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$\\begingroup$ @dmckee Indeed muon decay is not E&M, and experiments show that muon decay is subject to time dilation as described by Lorentz transformation. I guess I didn't think of muon decay because you'd have a hard time constructing a muon decay clock accurate enough to measure the speed of light. $\\endgroup$ – Cleonis 3 hours ago
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$\\begingroup$ Ah. A precision measurement of $c$ based on muons would be tough. I'm not aware that anyone has tried it. On the other hand it is easy to find a muon system that demonstrates the gross behaviors of SR that are out of reach to more massive experimental kit. $\\endgroup$ – dmckee♦ 3 hours ago
This is a very good question, although of course, this is still open question. Indeed, it is absolutely impossible to send neither a light signal nor a particle that has mass from a material body to a distant mirror and back immediately (so that no changes occur within this material body), if we assume that massless particles (force carriers, messenger particles) move inside material bodies with the speed of light. As you have noted, measured by this clock value will be the same and finite, even if the God makes the light “infinitely fast”, because "observer's clock are based on the same light signals". Maybe this gives some insight to actual behavior of speed of light.
I have already seen several articles that develop this idea. First of all, this article and even this book simulates the whole kinematic effects of theory of relativity, reciprocal Lorentz transformations, finite speed of light on the simplest example of floating in a water ships. The ships, that simulate „clocks“ in the paper, are similar to yours and material bodies have been "built" from these ships.
Another paper suggests that as soon as interactions within material bodies are carried by particles that move at the speed of light, that ultimately leads to the fact that the measured value of the speed of light is always finite and unattainable for particles that have mass.
As long as I remember, this young person developed similar to your idea in his video and got lump sum of money for it.
https://curiosity.com/topics/a-teenager-won-dollar250000-for-his-video-explanation-of-einsteins-special-theory-of-relativity-curiosity/
So, apparently, this question begs itself.
On the simplest example of floating ships (that simulate your light- clocks) we can also simulate time dilation in its reciprocal form.
How can time dilation be symmetric?
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1$\\begingroup$ About that video that got a Junior challenge award. That video is supposed to be about special relativity, yet the Lorentz transformations are absent from it. They're not even hinted at in some visual form. I mean, come on! That's like making a video that is supposed to educate about sex and then it turns out the video doesn't even mention kissing. Joking aside: that junior challenge submission is a disservice to physics education. (Yeah, it was awarded a 250.000 dollar prize; still a disservice.) I recommend removing that link. $\\endgroup$ – Cleonis 8 hours ago