# If clocks themselves are based on light signals, wouldn't we expect the measured speed of light to always be the same constant?

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?

• 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. – Ben Voigt Aug 12 at 13:23
• 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. – Cinaed Simson Aug 12 at 18:18
• Whenever you consider this kind of question about speed and relativity, you should never consider a "Speed" without a point of reference. Things only have speed relative to other things. For your question, consider if both of those "Clocks" you discuss are stationary relative to a fixed point (earth?) but you are measuring them from a space ship traveling from a to the b--so from that point one would be moving in one direction, the other in the opposite direction. Now your question makes no sense at all. – Bill K Aug 13 at 16:29
• @BenVoigt A Caesium atom is not in a material, and all other clocks are adjusted so that they agree with Caesium clocks. – kotozna Aug 17 at 2:55
• @CinaedSimson Other wave equations do though depend on the speed of the source and the medium, so Maxwell's equations alone weren't enough to prove the second postulate. – kotozna Aug 17 at 3:01

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.

• 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 :) – Aaron Stevens Aug 12 at 3:37
• 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. – Michael Seifert Aug 12 at 13:27
• @MichaelSeifert They do run at different rates, AFAIK, no matter where you are when you measure the rates. – immibis Aug 13 at 0:26
• The issue in frame-dependent-light world isn't that different observers get different clock speed. It is that the same observer would get a different clock speed just by turning the clock 90 degrees (which is in fact exactly what the Michelson-Morley experiment did) – John Dvorak Aug 13 at 9:11
• The question that the OP wonders about is the invariance of the speed of light. It does relate to (special) relativity because the OP is thinking about a mechanism by which the invariance would already be obtained in classical mechanics. Or at least a mechanism by which the observation would not be able to differ the light speed because any time difference of a light signal whose speed we wish to measure would be influencing our (light)clocks as well. ----- Of course, the idea is false (as John Dvorak points out) but it does relate to relativity. – Martijn Weterings Aug 13 at 20:29

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.

Note that the Lorentz transformations arose prior to 1905 Relativity. Lorentz invariance arose in the context of Maxwell's equations, decades earlier. Given this property of Maxwell's equations it follows logically that any form of time measurement that is electromagnetism based will be Lorentz invariant. So: examining lightclock details can't reveal something new; Lorentz invariance is guaranteed anyway. The fundamental step of 1905 Relativity is the sweeping hypothesis: all physics, including forms of interaction not yet discovered, will be seen to be Lorentz invariant.

• 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? – dmckee Aug 12 at 14:51
• @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. – Cleonis Aug 12 at 15:03
• 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. – dmckee Aug 12 at 15:05
• Gamma rays are still electromagnetic... – immibis Aug 13 at 0:27
• This makes me think if it is possible to construct a clock that - completely new concept! - is gravity-driven, say by hanging a weight to a rope and let it swing ... – Hagen von Eitzen Aug 13 at 14:14

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?

• 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. – Cleonis Aug 12 at 9:57

This seems like an interresting idea. If we measure light speed by a clock that itselve depends on light (or some other dependency of electromagnetism), then could the observer independent light speed, maybe, just be an effect of the clocks having the same delay as the light whose speed is being measured?

The OP is right in one way: when we measure the time it takes for light to travel a certain path and our clock to measure this time uses the very same principle and layout (a light signal traveling a specific path) then we will (seemingly) observe the same light speed (by measuring the time of travel) independent from our speed relative to the aether (even with classical mechanics and Galilean coordinate transformations).

However the idea is false in many other ways.

• A quick response can be made by noting that the Michelson and Morley experiment, which is the typical experiment that got everything started, doesn't use a clock.

The experiment used light moving in different directions (and it in the first place more like being intended to measure the presence of aether and not a measurement of the speed of light).

This can be made analogous to the hypothetical light clock case; When one would compare clocks with different orientations (e.g. one turned 90 degrees) then the argument will break down. With classical theory one would expect the light clocks to tick with the same speed (and consequently measure same duration for light to travel some path back and forth) only when they have the same orientation. But in general the clocks will be expected (assuming classical mechanics) to have different ticking rates depending on the difference in the orientation (and depending on the observer speed relative to the aether).

A classical way to think of the Michelson Morley experiment would be a diving clock moving under water. If some experimenter (inside that clock) would measure speed of waves in the water by bouncing back and forth, then he would observe different time duration when bouncing in different directions (perpendicular/parallel) relative to the velocity of the diving clock relative to the water (so the thing that was expected/tested is a different time of travel in different directions, and not so much an equal light speed). With the measurement of the light waves, in different directions, this unequal travel time did not occur (hence the analogy the earth moving in aether, that behaves like a classical medium for waves like the diving clock moving in water, is falsified).

Sidenote: A longer response can be made when we think Einstein's first work on special relativity. In this work the invariance of the light speed was more of an after thought. Or at least Einstein's first article on the topic did not use as the starting point experiments that (directly) measured lightspeed. The idea of relativity was based on more than just a measurement of light speed being equal for all observers (which is just the popular way to speak about the need for relativity and to explain what "problems" with classical theory special relativity was fixing). Einstein's motivation seemed to be much more in Maxwell's equations, which had a (subjective) dependence on the observer's speed (e.g. think of Lorentz Force which includes a velocity term $$\mathbf{F} = q\mathbf{E} + q \mathbf{v} \times \mathbf{B}$$), as well as the seemingly absence of aether relative to which these velocities could be defined objectively.

• You correctly understood my question:) The Michelson-Morley experiment was designed to check for the speed relative to the ether, not measure the speed per se. I'm struggling to see how your 2nd point disproves the concept? All relativity textbooks seem to say the 2nd postulate is essential. – kotozna Aug 17 at 3:22
• @kotozna Einstein does eventually compute the Lorentz transformation to have the speed of light equal in all reference frames. But I would say that the motivation was more to make Maxwell's electromagnetic equations invariant (for instance the equations of motion for an electron moving in an electricmagnetic field are not invariant under Galilean transformations) The entire 2nd half of the article is about this. Also he does not mention that the light speed needed to be equal because of direct experimental evidence; instead it was more because of thought experiments about simultaneity. – Martijn Weterings Aug 17 at 8:12
• Sure, but how does that answer the question one way or the other? – kotozna Aug 17 at 21:52
• @kotozna It's a sidenote. Your idea that lightspeed should be measured to be the same also with classical mechanics (but that is not true because it only depends on the specific setting of a light clock that is aligned with the experiment) would mean that there is no need for relativity theory. However, special relativity does not depend only on measurements of lightspeed. Other electromagnetic effects play a role as well. So the trivial way to improve your experiment is to turn your clock, but using a different experiment works too. – Martijn Weterings Aug 18 at 7:20
• What do you mean by "turn your clock"? Do you mean rotate the orientation of the mirrors in the plane? As I mentioned in the question this gives the same result (this surprising result was one of the motivating factors for the question). – kotozna Aug 18 at 17:58

Clocks aren't based on light signals generally. The fundamental postulate of Special Relativity is that two reference frames moving at constant speed in relation to each other are physically indistinguishable. All temporal processes are not able to establish different qualities of different reference frames. The light clock is just one of the simplest time-keeping devices one can design as a thought experiment which has the advantage of being directly tied into the speed of light. That makes it suitable for deriving a number of properties of reference frames in relative movement to each other. But other clocks using different mechanisms for tracking the flow of time will not deliver different results.

I want to try to state the problem clearly.

We want to be able to switch from one frame to another and get essentially the same results. What happens should not depend on the frame we choose to measure by.

If the results don't depend on the frame, then there should be a way to describe the physical truth without frames at all. We could do it all with relative linear velocities, without needing to choose a frame. (I don't know how to do that. Does someone?) (I think there would need to be absolute angular velocities of some sort.)

When we use simple-minded frames, we get bad results as follows:

Imagine that light travels at one space unit per time unit.
Call that speed "c".
Imagine A and B that have relative velocity -c.
They are D units apart and getting closer together.

If A is moving and B is stationary, then light from A must travel D space units in D time units.
If B is moving and A is stationary, then light from A must travel 2D/3 space units.

If it takes D time units then lightspeed is different in the different frames.

If it takes 2D/3 time units, then the clocks don't match up in the different frames.

Special relativity resolved the issue by having time and space be precisely the right amount different in different frames to get things to match up.

The obvious alternative was Ritz "ballistic theory" which goes as follows: If you want the results to come out the same in different frames, then when you switch frames add the velocity difference between the frames to everything. Then you will get the same results. Then lightspeed is constant relative to the source, but not the target.

Ballistic theory is generally considered to have failed.
Some people say that it fails the MM experiment, but others who have looked at it carefully say that if the math is done right it fits MM.

Some people say that it does not produce the Sagnac effect, but others say that if the math is done right then it does.

But there is physical evidence against it as follows: if a distant nova produces intense light from particles that are moving at high speeds in all directions, we should get light both from those moving toward us and from those moving sideways. By ballistic theory they should have different velocities, and over very long distances they would arrive at very different times. So the nova would appear to us to last a long time. It did not. Either novas don't behave as predicted, or ballistic theory is wrong.

So the simplest, most obvious approach is disproven. SR works, and it works to extremely high precision. (In circumstances where GR doesn't have much effect.) Any alternative which gets different results must be wrong.

And there is no alternative way to look at it which gets the same results. SR is the only possible way to imagine the reality. It is the only possible way to conceptualize time and space that can fit the observed data.

Wait, the only possible way to think about it? Are we sure there's no way to do it without those pesky hard-to-deal-with frames? I dunno. Maybe that claim is going beyond the data. If there are other ways to think about it, some of them may be easier for humans to follow. Some of them may give us intuitive insights which are not so intuitive with SR. But maybe SR is the only way that works.

Are there known alternatives that work?