# How is it possible for an observer to measure the speed of light as it moves AWAY from him?

I often come across statements such as this one, by N. David Mermin, a well-known physicist:

"Let P be a valid procedure for carrying out the time and distance measurements that allow one to determine the speed of an object in a given inertial frame. Let Bob, carrying out the procedure P in the frame of reference of a space station, measure the speed of a pulse of light as it zooms off into space."

In this thought-experiment, how can we simply assume in advance that Bob has such a "valid procedure" ? Doesn't this have to be demonstrated, not merely asserted? More specifically, how could any observer measure the speed of light as it moves away from him or her? Wouldn't the light photons have to interact with a measuring apparatus that the observer has at his disposal? - not away from him, but with him?

• Good question. I know of no way to measure the one way speed of light. – Lambda Mar 10 '17 at 16:17
• Isn't it a simple assumption that speed of light is "constant" for all observers? And once we assume this, for "being-constant" to work, towards and away speeds must be (by assumption) the same. – mami Mar 10 '17 at 19:51
• This would mean that one does not measure the speed of light moving away from oneself; one assumes that it is the same as light moving towards the observer. – Sumwun Yumaynotno Mar 10 '17 at 20:04
• Actually, if you do not presume some "invariance" beforehand, you can't measure any thing about "towards" direction for sure as well. You can equally suspect, for instance,time and location measurement with a synchronized clock placed in a point that the light comes from. If there is any issue with away direction, so is there the same one for toward direction. What about imagining that you are at the center of a set of mirrors placed in a circle and you simply measure the speed of light from one mirror to the other where there is no such toward and away issue? – mami Mar 10 '17 at 20:14
• I still don't see how this clarifies anything. It seems to me that the speed of light can only be measured if photons physically interact with a measuring device which is in "the same place" as an observer who is able to activate the device, calibrate it, record its activity, read the results, and interpret them. – Sumwun Yumaynotno Mar 10 '17 at 20:49

Bob could set up detectors ahead of time that are in his frame of reference that measure the time when the light reaches them, and then later look at the results. We can assume that Bob has done any amount of preparation, since it's just a thought experiment after all.

• And how would Bob know in advance that the clocks in those detectors are correctly synchronized with the clock sitting right by his side? This is the very question that Einstein attempted to answer in his 1905 electrodynamics paper. It requires that the light be reflected back to the observer. The result still measures light coming towards back toward the observer and the measuring device. This may be "just a thought experiment", but is it a good one? I think it side-steps the issue rather than addressing it directly. – Sumwun Yumaynotno Mar 10 '17 at 17:32
• No, Einstein answered the question of clocks in different reference frames. It is easy to make sure that clocks in your same reference frame (even ones that spatially removed from you) are synchronized with your own; if they're both atomic clocks, they will both run at the same rate if they're in the same reference frame. – Travis Mar 10 '17 at 17:36
• The opening pages of "On the Electrodynamics of Moving Bodies" deal exclusively with clocks in one reference frame: "In order to render our presentation more precise and to distinguish this system of co-ordinates verbally from others which will be introduced hereafter, we call it the “stationary system.” – Sumwun Yumaynotno Mar 10 '17 at 19:50
• In a footnote, Einstein admitted that "We shall not here discuss the inexactitude which lurks in the concept of simultaneity of two events at approximately the same place, which can only be removed by an abstraction." Much later in his life, he was to refer to this as his "original sin". – Sumwun Yumaynotno Mar 10 '17 at 19:57

Wave frequencies change, depending whether the source of the wave moves away from or toward you. This does not affect the speed of the wave.

As the source of a light pulse generated in your own inertial frame is moving neither toward nor away from you, the frequency of that light pulse should appear the same at all points in its journey as when it left your generator, provided that objects which reflect the light back to you are stationary with regard to your inertial frame.

As the light pulse moves away from you, it may leave traces of its passage on very dilute dust particles (for example) that are stationary with regard to your inertial frame. Light reflecting back to you from relatively stationary dust should have the frequency of the original pulse. Comparing incoming frequency with outgoing frequency would be a way to make certain that you are not moving with or against the light pulse.

The time between generation, reflection, and return of the original pulse can provide a way to measure the speed of the pulse, provided that distance to the point of reflection is known, and provided that the reflector is either stationary, or moving at a known velocity in a known direction relative to your inertial frame.

• I can't say that this clarifies the matter to me. When physicists talk about the speed of light, they are almost always talking about the speed of light in a vacuum. If we hypothesize particles of dust and gas that act as intermediaries, then it is no longer a vacuum. And those particles would exhibit a kind of Brownian motion that would distort the results. Perhaps only a tiny percentage of the light that hits them would be reflected back to the observer and his measuring apparatus. And this would still be measuring the speed of photons that are moving towards the observer, not away. – Sumwun Yumaynotno Mar 10 '17 at 17:18
• It would also presume that the speed of light moving away from me is the same as its speed moving towards me. This is now a postulate of SR. But I'm trying to conceive of the situation before we know this to be true. Postulating dust and gas particles only throws smoke and mirrors - literally - on the subject matter. – Sumwun Yumaynotno Mar 10 '17 at 17:20
• @SumwunYumaynotno : You are correct that I made some assumptions, dust and gas "smoke and mirrors"(that's a good one!), of questionable value. I should have assumed dust to be very dilute, and gas to exist only in separate and isolated patches away from dust, so that Brownian motion would not be a significant issue. But even if only a small bit of light were reflected back, that would not alter the result. If we and the dust particles are stationary relative to the light pulse generator, what conceivable reason could make return speed differ from outbound speed? Let's forget the gas. – Ernie Mar 10 '17 at 20:59
• @SumwunYumaynotno : I edited the answer to address your comments, and explained how to use light wave frequency to test whether we and the reflectors remain stationary relative to the direction of the light pulse during the light pulse's journey. – Ernie Mar 10 '17 at 21:10
• @SumwunYumaynotno : You seem to be asking for a discussion rather than an explanation or clarification. If you have your own views about the problem, why don't you post your own answer? – sammy gerbil Mar 10 '17 at 22:41

It is impossible to detect light in a vacuum, that is moving away from the detector.

Setup-1

Place N stationary mirrors on the corners of a polygon with equal sides such that the pulse will loop indefinitely unless it is observed by some measurement device or any other obstacle. Take a space ship which will orbit around the center of the mirrors. As you orbit, you will pass by each mirror at equal time intervals depending on on the speed of the ship.

As you just by pass by a mirror, send a pulse to the next mirror and continue the trip as the pulse starts its looping. Depending on the speed of the ship and N and relative direction of pulse and the ship, you can arrange things such that the ship and pulse will encounter at the Mth mirror where you would like to measure the time (locally) and try to detect the pulse and confirm that the pulse is really there locally in that Mth mirror. Do the experiment for different M values in both counter-clock or clock wise directions. If you fail to meet the pulse for any calculated M value (by changing the speed of ship) in any orbit direction, you would start suspecting that speed of light might not be the same for away or towards direction.

Note that the ship is actually rotating. To avoid its complication, more mirrors can be put on the sides of the polygon and M values can be arranged to correspond mirrors on one experiment side of the polygon. So only the light makes direction change.

Actually whole idea is to switch places once the pulse starts its journey.

Setup-II

In this setup instead of measuring speed with delta-position and delta-time, use a property of pulse which indirectly depends on its speed (momentum with presumed directions, energy with full absorption etc.). So arrange interactions in three places: Here and now; a distant place where pulse moving away will reach and interact (then you will go there to read out interaction outcome), here but at a later time after the outgoing is reflected back to here; here but at a later time after pulse is reflected three times etc. If all measurements are the same, then you are convinced that the speed of light is what I measure here or there and independent of pulse being away or towards.

Note: It seems to me that it is almost impossible, in certain situations at least, to conduct a measurement of absolute significance that is INDEPENDENT of your theory or implicit assumptions. Roughly, I am telling that sometimes part of reality that we try to independently verify would actually be unreachable and we need a priory assumptions about it.

• These must be the most intricate, convoluted, and bloated thought-experiments that I have come across. I don't see how loading apparatus upon apparatus would resolve the issue. "you can arrange things such that the ship and pulse will encounter at the Mth mirror". Maybe, maybe not. Your calculations and calibrations might be off every time. It might be that light moves so fast that it "outwits" your spinning wheel spaceship every time. (And, parenthetically, is this a plausible thought-experiment, one that we could conceivably carry out? I would say not). – Sumwun Yumaynotno Mar 11 '17 at 17:03
• Appealing to "momentum with presumed directions" and "energy with full absorption" does not THROW ANY LIGHT on the subject; at least, not to me. Too much hand-waving, without specifics. I would have to see a fully-configured diagram or animation and a set of equations to make any sense out of all this. I'm not going to make the effort myself. – Sumwun Yumaynotno Mar 11 '17 at 17:11
• You are right that a diagram would work perfectly but i really could not find time to do that. But in a thought experiment you can lay down mirrors hundreds of light year apart. And your space ship can travel at a fraction of light speed: Send the pulse; follow it. It will come back and catch you at the next mirror (or adjust your speed and meet at next Mth mirror). What is wrong with that? For the second part, remember that photon has momentum and you can observe its particle-like interaction with, say, electrons. – mami Mar 11 '17 at 21:17
• To mami: "Lay down mirrors hundreds of light years apart" ? - traveling at a fraction of light speed? You propose this as a useful thought-experiment? If you don't have time to compose a diagram, then you probably wouldn't have have time to set up this utterly preposterous thought-experiment. You're operating in the realm of Alice in Wonderland, in outer space. I cannot take any of this seriously. It would probably take thousands of years to accomplish, to lay down even a single mirror. Bon voyage! Don't bother to R.S.V.P. – Sumwun Yumaynotno Mar 12 '17 at 1:01
• Lol... The idea really sounds funny, right? :) If you are asking something doable "at the large scale" you can use the moon or a couple of satellites (man-made or other planets) as reflectors. It is also possible to establish earthly setups like the one we use for detecting gravitational waves. But i think you should rather focus on the core idea of the experiments not the mechanics, especially for a thought-experiment one. – mami Mar 12 '17 at 7:19