Do We Need ESC in Earth's Atmosphere?

[Bob Enyart]

TL;DR Summary

ESC is always defined for the one-way speed of light in a vacuum. So is Einstein's Synchrony Convention needed also for light travelling only within Earth's atmosphere (where it travels more slowly, apparently at about 99.9% c)?

Einstein's synchrony convention (ESC) defines the one-way speed of light as equal to the roundtrip speed IN A VACUUM, at least, the discussions and papers I read on it (even Einstein's 1905 paper) always seem to set the context as in space (a near vacuum) or in a (theoretical) vacuum. I'm wondering then if the ESC is needed for a light transmission starting and ending and traveling only within Earth's atmosphere? If the stat I looked up is accurate, it appears that light travels in a vacuum only three hundreths of 1% faster than it travels through air. So, do you think ESC is needed also in Earth's atmosphere, or might there theoretically be a way to measure its one-way speed because it's not traveling as fast as in a (near) vacuum. (Sorry if this question isn't worded as well as it should be.)

 

[Ibix]

You can't, strictly speaking, measure the one way speed of anything. You always, more or less by definition, have clocks at the start and end of the "racecourse" over which you do your speed test, and those clocks need to be synchronised. So you need a synchronisation convention.

For anything that's drastically slower than $c$ this is a non-issue because it's lost in measurement error anyway. But for anything moving at a large fraction of $c$, yes, your synchronisation convention is important. Note that there is no invariant speed for "light in air", since it isn't traveling at $c$. The speed relative to the rest frame of the air is the obvious thing to measure, but it isn't obligatory to do that.

 

[Bob Enyart]

Thanks Ibix, that all makes sense and you've made me realize that a reword of my question could get closer to what I'm wondering. So I'll try this...

As light propagates through mediums that make it travel slower than in a vacuum (such as air, water, diamond, cold sodium atoms, etc.), might there be a slower speed at which it could be theoretically possible to demonstrate that the one-way speeds of a roundtrip are approximately equal?

 

[Ibix]

I'm not sure I understand your question. If you use Einstein synchronisation and we assume that the medium doesn't have any funny directional behaviour, then the one-way times for anything that will pass through the medium will be equal. If you don't use the Einstein synchronisation convention then they won't be equal.

You can't escape the relativity of simultaneity, if that's what you are asking.

 

[Bob Enyart]

Perhaps your first statement answered my question, when you said, "You can't, strictly speaking, measure the one way speed of anything." I'm wondering, does Einstein's Synchrony Convention only apply to light in a vacuum, or does it apply to all motion in all media? If it doesn't apply to all motion in all media, might there be a threshold, or a way of describing a condition, whereby actual physical measurement could determine that the one-way speeds of a roundtrip are approximately equal? (As an example, at Cambridge and Harvard researchers, through cold sodium atoms, slowed down light to 38 mph, so might it be theoretically possible to show that the one-way speed of light in such conditions approximately equaled its roundtrip speed?)

 

[Ibix]

Clock synchronisation isn't about things moving. It's about how you synchronise clocks.

The problem with a one-way speed measurement (of anything at any speed) is that you cannot use one clock to do it - you have to have two clocks at different places and those clocks must be synchronised. This affects measurements of 100m sprint times as well as the speed of light - it's just that no clock synchronisation choice will add more than ~330ns to the time for 100m, so no-one cares. But, in principle, if the runners turn round and come back, their measured speed could be slightly higher or slightly lower than their first speed, depending on clock synchronisation. Obviously, such effects will be swamped by more mundane sources of variation, but in principle they are there.

 

[Bob Enyart]

Thanks so much for bearing with me Ibix. The intro to Wikipedia's article on the one-way speed of light has a standalone sentence that states, "The 'speed of light' in this article refers to the speed of all electromagnetic radiation in vacuum." I'm wondering if that clarification is needed. Would discussions of Einstein's Synchrony Convention be just as accurate if they dropped the "vacuum" context which, it seems, they virtually all include?

 

[PeterDonis]

The intro to Wikipedia's article on the one-way speed of light has a standalone sentence that states, "The 'speed of light' in this article refers to the speed of all electromagnetic radiation in vacuum."

Wikipedia's phrasing might be misleading you. There are two distinct concepts involved here:

(1) The invariant speed--the speed which is the same in all reference frames.

(2) The speed of electromagnetic radiation in vacuum.

It just so happens that #1 and #2 are the same in our universe. But they are still different conceptually. Einstein clock synchronization, conceptually, involves #1, not #2; we are simply fortunate that #2 happens to be the same as #1 in our universe, so we have an easy way of physically realizing #1, by using EM radiation in vacuum.

I'm wondering if that clarification is needed.

As the above should make clear, yes, it is. If you try to use EM radiation not in a vacuum to define your clock synchronization, the problem is not that the speed of the radiation is slower than its speed in a vacuum; the problem is that the speed of the radiation is no longer invariant--it's no longer the same as #1 above, so the logic that allows you to use #2 as a physical realization of #1 breaks down.

Would discussions of Einstein's Synchrony Convention be just as accurate if they dropped the "vacuum" context

It depends on what you mean by "just as accurate". As above, the point of the Einstein synchronization convention is that speed #1 above is invariant--it's the same in all reference frames--and speed #2, in our universe, is the same as speed #1, so we can use speed #2 as a physical realization of an invariant speed. But obviously you can only use EM radiation in a vacuum to do this, since, as above, the speed of EM radiation not in a vacuum is not the same as speed #2 above and is therefore not the same as speed #1 above.

However, if you have a set of clocks that have been synchronized using the Einstein convention correctly (i.e., using EM radiation in a vacuum to perform the synchronization), then you can use those clocks to measure the one-way speed of anything you like, including EM radiation not in a vacuum.

But in any case, as @Ibix has pointed out, your measured one-way speed will still be dependent on the clock synchronization you used; if you synchronized your clocks using some different method than the Einstein convention, you might measure a different one-way speed even for EM radiation in a vacuum. So there is no way of avoiding the fact that any one-way speed measurement requires a clock synchronization convention.

 

[Bob Enyart]

PeterDonis, thanks! I think you guys are helping me to understand where my confusion lies. What I've been wondering is whether some new technology (like CIT's 10-trillion frames per second cameras; slowing light down to 38 mph; etc.) might enable the direct measurement of the one-way speed of light at least sufficiently to indicate that it is approximately equal to the roundtrip speed. For example, if light is slowed down to 38 mph and the same clock is moved at 40 mph so that it marked both the start and end points of a laser pulse, theoretically, would that give a one-way speed of light measurement? And the Calif Inst of Technology's 10-trillion FPS camera has videotaped the progress of a femtosecond laser pulse through a millimeter of water vapor. So might such new technologies provide new ways of re-assessing whether, theoretically, the one-way speed of light could be measured?

 

[PeterDonis]

For example, if light is slowed down to 38 mph and the same clock is moved at 40 mph so that it marked both the start and end points of a laser pulse, theoretically, would that give a one-way speed of light measurement?

If the light is moving at 38 mph relative to the lab, and the clock is moving at 40 mph relative to the lab, the clock is moving faster than the light, so it is impossible for the clock to be at both the starting and ending points of the light pulse.

You could have the clock moving at 38 mph, right along side the laser pulse, sure. Then the clock would be present at the starting and ending points of the pulse (and that's the only way for a single clock to do that). And then the clock would tell you how much time elapsed on itself from, say, one side of the lab to the other. But this clock is not at rest relative to the lab, so its tick rate is not the same as the tick rate of lab clocks. Also, the lab is length contracted relative to this clock, so the distance involved is different from the lab distance, and this clock, by itself, cannot measure that distance anyway, so there is no way to convert its reading, taken alone, to a speed. So this clock by itself cannot measure the one-way speed of light relative to the lab.

 

[PeterDonis]

might such new technologies provide new ways of re-assessing whether, theoretically, the one-way speed of light could be measured?

The short answer is no. The theoretical conclusions about a clock synchronization convention being required to measure the one-way speed of anything are not dependent on any particular properties of any particular measurement technologies, so there is no way to invalidate them by discovering new measurement technologies.

 

[Ibix]

Whenever you try to measure a one-way speed, you will find that either you had to use two clocks or you have a disguised round-trip measure. The camera experiment is an example of the latter - the camera records light. So there is the light traveling through the vapour, but there is also light traveling to the camera. If you imagine a plan view of the light that is emitted at the beginning and end of the light pulse's passage through the gas then you should imagine a triangle. The path of the light passing through the gas forms the base, and the camera is at the apex. So you have a closed loop of light rays - and this is a disguised two-way measurement.

Remember that in relativity we talk about time as a dimension, similar (but not identical) to the three spatial ones. Using clocks and rulers is a way of making a regular grid in spacetime - the marks on the rulers mark off regular distances in space and the ticks of the clocks mark off regular distances in time. The freedom to choose a synchronisation convention stems from the same place as your freedom not to have orthogonal gridlines on a piece of graph paper. Technology cannot change that.

 

[Bob Enyart]

Thanks so much for all of that! Now I've got to continue pondering what you've each written.