# Special Relativity, 2nd Postulate — Why? [duplicate]

As a lowly physics undergrad who has been chewing on this 2nd postulate of special relativity for a year or more, I simply can't wrap my head around reasons why it is true or how Einstein might have been convinced enough to propose this postulate.

Consider Alfred who is riding in a car travelling at 88 m/s with his headlights on and Bernard who is on the side of the road hitch hiking. Why does the light propagating from Alfred's car move at $c$ relative to both Alfred and Bernard, and not at $c$ + 88 m/s relative to Bernard?

The nifty results of special relativity all kind of hinge on this idea, and asking my professors in class hasnt really yielded an answer much more than "because we have never observed a case otherwise".

## marked as duplicate by John Rennie, Brandon Enright, Danu, Jim, Kyle KanosSep 7 '14 at 16:10

• possible duplicate of Special Relativity Second Postulate – John Rennie Sep 7 '14 at 5:54
• The question I've linked shows how the second postulate can be regarded as a consequence of the invariance of the line element. Of course you may consider this to be replacing one unintuitive assumption with a different unintuitive assumption - welcome to relativity :-) – John Rennie Sep 7 '14 at 6:09
• Related: physics.stackexchange.com/q/79331/2451 , physics.stackexchange.com/q/133366/2451 , and links therein. – Qmechanic Sep 7 '14 at 6:30
• I don't think either of the two links is a duplicate. Neither answers the question raised in the title and then expanded upon in the first paragraph of the question. – David Hammen Sep 7 '14 at 6:36
• The speed of waves doesn't depend on the speed of the source even for sound. Why should it be for light? Sound however can move faster towards the observer if the medium mooves with it. In 19th century they thought the medium for light was aether but they couldn't explain some things. See Michelson-Morley experiment: en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment – Puzzled student Dec 4 '17 at 17:02

Actually given that the first postulate says that all physical laws are the same in all inertial frames, you could replace the second postulate by the postulate: "Maxwell's equations are the physical laws for electromagnetism".

From Maxwell's laws you can derive that the speed of light in vacuum has a specific, constant value, in SI units $c=1/\sqrt{\epsilon_0\mu_0}$. Now there are three possibilities:

1. Maxwell's laws are valid only in a specific inertial frame (or rather, in a specific set of inertial frames at rest relative to each other).

That's the essence of the aether hypothesis. It would violate the first postulate. Also, experiments failed to measure that preferred frame.

2. Maxwell's laws are not the correct description of electromagnetism (that is, they are valid in no inertial frame).

That option would, of course, have been compatible with the first postulate, but not very likely, given the huge experimental support for Maxwell's equations.

3. Maxwell's laws are valid in all inertial frames.

If that is the case, then all of the consequences of Maxwell's equations have to be valid in all inertial frames. One of the consequences of Maxwell's equations is the value of the speed of light in vacuum.

However, it turns out that the only thing from Maxwell's equations you actually need in order to derive special relativity is the constant speed of light. Therefore it makes sense to postulate that directly; that way even if it turned out that Maxwell's theory had to be revised, you don't need to revise relativity as long as the revised theory still predicts a constant speed of light.

• +1. Nice answer. Note: You have a few spelling errors in the last paragraph. – David Hammen Sep 7 '14 at 12:12
• Thank you; I've corrected the spelling errors (and improved some formulations). – celtschk Sep 7 '14 at 12:17

The answer is simple: Maxwell's equations.

Maxwell published his electromagnetic theory in the 1860s. This generated a huge schism in physics. Maxwell's electromagnetism was in direct conflict with Newtonian mechanics. There is no allowance in Maxwell's electrodynamics for the speed of the emitter or the speed of the receiver. The speed of light is constant per Maxwell's equations. This conflict became even more apparent in 1887 with the Michelson–Morley experiment, which shot down the idea of a luminiferous aether as a carrier of Maxwell's electromagnetic waves.

Many other physicists besides Einstein were trying to attack this conflict at that time. All but Einstein tried to rectify the two theories. The leading contender to Einstein's relativity was the Lorentz ether theory. This solved the problem by handwaving it away. The Lorentz length contraction and time dilation together conspired to hide the ether frame from us. There's no difference mathematically between Lorentz ether theory and Einstein's relativity. Both predict the same outcome for any special relativistic experiment. Yet no one teaches Lorentz ether theory.

Einstein's path was based on the fact Maxwell's equations strongly imply that the speed of light is the same to all observers. Einstein simply took Maxwell's equations at their word. It was such a simple solution to the conflict, and yet it was extremely game changing.

• A mathematical representation of a phenomena is not an explanation of a phenomena, hence the word "Theory" tends to often pop up. – Sean Sep 21 '14 at 6:15

The way I think of it, as a non physicist who quite likely has a few things wrong, is as follows: time actually passes slower for Alfred, and thus there is no difference in the speed of light.

If you say, "Why does time pass slower for Alfred and not Bernard, after all, motion is relative, right!?" Well, this stumped me for a long time as a non-physicist, but ultimately I understand it as: Alfred must have accelerated from an inertial frame that he once shared with Bernard, and thus he is the one who experiences the slowing of time.

If I'm not mistaken, this accounts for the 'ether' parallel drawn in the other reply?

Anyway, as far as how anybody would have been 'convinced' of this, I believe it was due to direct experimental evidence.

• I'm not sure about this --- you could just as well argue that Bernard must have once accelerated from an inertial frame shared with Alfred, and is thus the one who experiences the slowing of time. In fact, time passes slower for both Alfred and Bernard, from the perspective of the other. This might sound somewhat paradoxical, but this is the way it is. – gj255 Sep 7 '14 at 10:54
• As I said, I've always been somewhat unclear on that part... but, if that were true, and time passes slower for both of them for the perspective of the other, then would it not be so that time diverges into two distinct timelines, such that in timeline A after a given amount of time, Alfred ages 5 minutes more than Bernard, but in timeline B, Bernard ages 5 minutes more than Alfred? This paradox is why I assumed there HAD to be some common inertial frame. Alternately, I presume that in order for their ages to be meaningfully compared one or the other must again accelerate, merging timelines? – Darren Sep 7 '14 at 17:34
• I'm not sure I can really do this justice in the comments, but I can at least assert to you that a) time does not diverge into distinct timelines and b) that the ages of A and B cannot be meaningfully compared in general, which is why this 'paradox' isn't one. Whether A is older than B or vice versa is a frame-dependent question, and it is not meaningful to talk about an absolute notion of 'who is older'. If one or both of them accelerated such that they were both traveling the same speed, their ages could be compared, and the details of the acceleration would determine who ends up older. – gj255 Sep 7 '14 at 21:57
• Excellent, thank you for your concise explanation of something I have struggled to discuss with people over the years. I know time does not diverge, thus my haziness on how exactly these things occur. In this example, however, I think it's reasonable to assume that both Alfred and Bernard not only come from a shared surface velocity, but will eventually again share a surface velocity. Lets say Alfred drives all around town and then back to Bernard. For him the passage of time relative to Bernard was variable, and slower. From our reference, he, not Bernard, experiences time dilation(?) – Darren Sep 9 '14 at 4:30
• I don't think it is reasonable to assume that Alfred or Bernard once did or ever will share the same velocity --- or more precisely, be stationary with respect to one another. I mean, if someone on another planet from the other side of the galaxy got on a ship and went shooting past Earth, and then continued onward indefinitely, she and I would never have the same speed. – gj255 Sep 9 '14 at 9:16

Einstein did not prove this postulate ; he simply asked "what if it is true?". He had very good reasons for asking that question.

His efforts to answer the question challenged a whole raft of "beliefs" about time and space, none of which were based on proof either ; they were (up until then) assumed true by so-called "common sense" alone.

He made predictions about how relative speed would dilate time and contract space, and about how acceleration could explain what we call "gravity" and so affect mass and also "bend" light.

His predictions are supported by experimental results. This is the reason we take his ideas seriously. He always said that his theories would stand or fall on experimental results alone. So far they have stood.

• This is the Einstein as a hero-scientist POV. It's not a good portrayal of Einstein or of scientists. What's worse, this is exactly backwards. Einstein didn't pull his second postulate as a magical rabbit out of the hat. It was well motivated by Maxwell's equations and by prior experiments. The first half of Einstein's 1905 paper on special relativity uses (and derives) the Lorentz (not the Einstein) time dilation and length contraction. The second half of the paper is dedicated to casting Maxwell's equations in a relativistic light. – David Hammen Sep 7 '14 at 11:14
• Finally, this question is not asking about gravity. This question is about special relativity, which predates general relativity by a decade. Altogether, -1. – David Hammen Sep 7 '14 at 11:16

Maxwell's theory had predicted that the speed of light varies with the speed of the observer. Initially (prior to Fitzgerald and Lorentz advancing the ad hoc length contraction hypothesis) the Michelson-Morley experiment was compatible with the assumption that the speed of light varies with the speed of the light source (as predicted by Newton's emission theory of light) and incompatible with the assumption that it is independent of the speed of the source (as predicted by the ether theory).

So in 1905 Einstein's constant-speed-of-light postulate had no justification. It was just a consequence of the Lorentz transforms. The principle of relativity was also a consequence of the Lorentz transforms. Einstein extracted the two consequences, called them "postulates", and deduced the Lorentz transforms from them. He also procrusteanized space and time to fit the new "theory".

• No, Maxwell's eqns predict waves with a speed determined by measured pure electric constant and pure magnetic constant, and has nothing in there concerning the speed of anything else. It shows that the speed is constant for all observers which was puzzling at the time. The profoundness of the result is important in history; yet you are saying something contrary to that. But, the statement about pure math is easily shown to be inaccurate, so you don't have to worry about human events. – JDługosz Dec 19 '14 at 19:16