# Second postulate of SR quiz question

1. Sep 18, 2015

### loislane

I recently quizzed physicists in my workplace with the following question: The speed c in the second postulate refers to:
a) the one-way speed of light
b) the round-trip speed of light
c) Both
d) Neither

I was surprised at the variety of answers. What do you say?

2. Sep 18, 2015

### Staff: Mentor

I would say d). The "c" in the second postulate refers to an intrinsic property of spacetime: a conversion factor between units of time and units of distance.

3. Sep 18, 2015

### DrGreg

loislane, as the second postulate can be worded in a number of different ways, it would do no harm to quote which version you are referring to. Or is that ambiguity part of the quiz?

4. Sep 18, 2015

### stevendaryl

Staff Emeritus
Well, in Einstein's original paper seemed pretty definitely to be referring to the speed of light:

2. Any ray of light moves in the “stationary” system of co-ordinates with the determined velocity c, whether the ray be emitted by a stationary or by amoving body.​
http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_1905_relativity.pdf (top of page 4)

5. Sep 18, 2015

### Orodruin

Staff Emeritus
While this is true, I would agree with Peter regarding the modern view of relativity, where $c$ is just a conversion factor between units of space and units of time. It then follows that massless fields propagate at $c$, which means that light propagates at $c$. I would say that the nomenclature "speed of light" is a historical remnant due to light being the first thing discovered to propagate with the invariant speed. At the time of Einstein, it was natural and had light not had the property of travelling at the invariant speed, relativity would have taken significantly longer to develop.

6. Sep 18, 2015

### stevendaryl

Staff Emeritus
But the question was about Einstein's "second postulate", so it would seem to be more about Einstein's original presentation, rather than the modern understanding.

7. Sep 18, 2015

### Orodruin

Staff Emeritus
Einstein is not mentioned in the OP. That there is a speed which is independent of the observer can still be taken as a postulate of SR.

8. Sep 18, 2015

### PAllen

Going back to Einstein, c as two way speed was a measurement, one way speed was a postulate which produced the simplest models consistent with measurement. I believe Einstein was well aware that one way speed had to be a postulate of "immense convenience" but unknowable truth.

9. Sep 18, 2015

### Staff: Mentor

What do you say?

10. Sep 18, 2015

### MindWalk

Perhaps you could clarify what is meant by a two-way speed of light? If a beam of light strikes a mirror and gets bounced back, it travels at c (in vacuo) in each direction.

I do not see why we must choose between thinking of c as the speed of light in vacuo, on one hand, and thinking of c as a conversion factor between units of distance and units of time, on the other.

11. Sep 18, 2015

### Staff: Mentor

That is an assumption. It is a very good and very plausible assumption and most people are willing to accept it without argument, but it's still an assumption and not an experimentally proven fact. Many people have proposed experiments that appear to (at least in principle) measure the one-way speed of light, but if you dig deep into these proposals you'll find that there's a hidden assumption that the speed is the same in each direction. You'll find a number of threads about this if you search this forum.

That, I think, is a defensible position. The first is the historical path that brought us to special relativity. The second is the better (shorter, simpler, fewer hidden assumptions, fewer limitations, springboard for further progress) understanding that we found once we had arrived and realized what we had discovered.

Last edited: Sep 18, 2015
12. Sep 18, 2015

### Staff: Mentor

It's not that surprising when we consider that:
1) Neither Einstein's presentation of the "postulates" of SR nor his derivations based on them come anywhere near the level of precision that a mathematician would demand from a postulate and the proofs derived from it. That's an observation, not a criticism - but it does leave much room for difference of opinion about exactly what is being postulated.
2) The modern understanding of SR is quite different from the historical understanding, and that affects the interpretation of the second postulate.
3) The second postulate makes its point in a rather odd (in hindsight) way. If you accept the first postulate at face value, and accept Maxwell's electrodynamics, and apply Occam's razor, you'll find only two possibilities. Either the speed of light in vacuum is the same for all observers, or you have to make an additional assumption that there is a luminiferous aether or equivalent which allows us to distinguish the absolute state of motion of different observers. So why not state the second postulate as "And no additional assumptions needed" or "And I don't need no stinkin' aether!" or "And I really mean the first postulate, even when it comes to the electrodynamics of moving bodies"? The answer, of course, is that none of those formulations would have been convincing in 1905. Again, this creates much opportunity for the post-1905 crowd, blessed with hindsight, to disagree about exactly what truth lies behind the wording of the second postulate.

This might be a good time to quote F. Scott Fitzgerald: "The test of a first-rate intelligence is the ability to hold two opposed ideas in mind at the same time and still retain the ability to function". Considering the different ways that the second postulate can be interpreted is far more illuminating than arguing about which one is right.

13. Sep 19, 2015

### stevendaryl

Staff Emeritus
The difference between two-way speed and one-way speed is that two-way (or round-trip) speed doesn't require a convention for synchronizing distant clocks. You can measure (in principle) the round-trip speed of light using a standard meterstick and a single clock: Put a mirror at one end of the stick and measure the round-trip time for light to travel from the other end to the mirror, and back. That measurement gives you an average speed of light, but it doesn't give you the one-way speed unless you assume that light has the same speed in all directions.

14. Sep 19, 2015

### stevendaryl

Staff Emeritus
Yes, but when someone says "THE second postulate of SR" without adding "according to the presentation in such-and-such book or paper" I would think that it would mean the original presentation by Einstein. No other presentation is famous enough to use the definite article.

15. Sep 19, 2015

### stevendaryl

Staff Emeritus
But loislane has seemingly dropped out of the discussion; otherwise, she could confirm what she meant by "the second postulate".

16. Sep 19, 2015

### harrylin

The way Einstein phrased it in 1905 was ambiguous.
He was clearer in 1907, as he phrased it in terms of a), but such that it effectively refers to b):

"We [...] assume that the clocks can be adjusted in such a way that
the propagation velocity of every light ray in vacuum - measured by
means of these clocks - becomes everywhere equal to a universal
constant c, provided that the coordinate system is not accelerated."

The essential point is that distant simultaneity is not postulated.

17. Sep 19, 2015

### stevendaryl

Staff Emeritus
Yes. In a certain sense, one-way speed of light is purely a matter of convention, because it depends on how distant clocks are synchronized.

18. Sep 19, 2015

### vanhees71

This thing with the mirror in the "two-way speed of light" definition brings me to another question. The question is, which "speed" is meant here. Is it (the magnitude of) phase velocity, group velocity, front velocity or whatever else you can think of?

Without thinking much about it, seen from the perspective of Einstein 1905 it's the constant occuring in Maxwell's equations in vacuo (nowadays it's hidden in the mess of the SI, but it's of course there in form of $c^2=1/(\epsilon_0 \mu_0)$, and that's the phase velocity, as seen when looking for the plane-wave modes. That's also what's measured in the Michelson-Morley experiment, where one looks on interference fringes of a stationary wave in the interferometer.

Now, what about the literal "two-way speed of light", where you send a signal (i.e., a wave packet) to a mirror and observe the reflected wave packet. Couldn't there be some delay since the signal has to reflect at the mirror? I'd have to do the calculation to check this. It's perhaps also not so easy to really do this as an experiment, I guess. So are there experiments measuring the "two-way speed of light" really in this way, i.e., sending a wave packet and measuring the arrival time of this back reflected wave packet and how accurate can this be made? Note that wave packets have a finite width and each photodetector has a threshold. Of course you can use the same detector for the outgoing and the reflected wave packet. You also need a large enough distance in order to measure well separated wave packets. If you are to close to the mirror you may measure some wave field which is a superposition of the incoming and the reflected partial waves. As I said, I have to do the calculation.

The same is of course also true for the one-way speed, but there's no possible delay due to a reflection at the mirror. There you'd of course need to photodetectors to measure the time the wave packet needs to travel the distance and consequently a convention to synchronize the clocks to measure the arrival time between the two detectors. A la Einstein that's done by assuming that the one-way speed is the same as the two-way speed (assuming that there's no time delay due to the reflection.

19. Sep 19, 2015

### loislane

Actually that way out of the question was not considered valid by me because as commented by other posters considering c a conversion factor is independent of its being a speed and certainly in all the variants of the second postulate that is its meaning, even when defined as conversion factor either for the meter or the second it is referred to as distance travelled by light in a certain time or time it takes light to traverse a certain distance in vacuum.
Not intentionally, but then I realized that ambiguity is inevitable due to the ambiguous way the postulates are worded in different sources, and even within Einstein's first formulation in 1905. This has also been acknowledged by some posters.
I think he was quite aware of the ambiguity he was allowing into the theory. He was mainly after a way to rationalize the Lorentz transformations in a way completely different from Lorentz and Poincare and their absolute rest. A certain calculated ambiguity was essential for that basically interpretational goal.

I find this an essential point too. But then the relativity of simultaneity was his very clever way to depart from the Lorentz ether. After all distant simultaneity is more philosophical than physical(in the sense of empirically showing whose clocks are really the correctly synchronized ones from their point of view, being a symmetrical situation there is no "correct" observer) . The real physics and math of the theory lies on the Lorentz transformations themselves.

I have to first say that even though the 4 options showed up most people answered b, maybe because the context of Einstein first paper was more implicitly assumed, and in that paper it is the case that c is defined in a formula as the average speed over twice the distance AB, but indeed there is room and arguments to choose any of the four options due to the commented ambiguity and lack of mathematical rigor of the postulates.
I went for d) basically because with any of the other three one can find ways to convince oneself that the postulates lead to contradictions that anyway cannot be proved precisely due to the ambivalence of the semantics of the postulates and the concept of distant simultaneity.

Last edited: Sep 19, 2015
20. Sep 19, 2015

### bcrowell

Staff Emeritus
My answer would be that I don't know, because the question refers to a particular formulation of an obsolete axiomatization, and I don't think anyone in the year 2015 should be memorizing that kind of historical trivia (what's postulate #1, what's postulate #2, etc.). I think it's unfortunate if people are still teaching their students SR using Einstein's postulates, because they reinforce various misconceptions, such as the belief that c has something to do with the speed of light, or that light plays some fundamental role in relativity. Since Einstein himself had a view of SR that, looking back from 2015, seems to have been in many ways hazy and incorrect, why would it be of interest to anyone other than historians of science to try to figure out exactly what he had in mind?