# Was Einstein's postulate for the speed of light a consequence of Maxwell's equations?

1. Jun 24, 2012

### Boorglar

Einstein postulated that the speed of light in vacuum is constant and is the same for all observers. It this related to the fact that in Maxwell's equations for electromagnetic waves in a vacuum,

$c = \frac {1} {\sqrt{\mu_0 \epsilon_0}}$?

The electric and magnetic constants, which are properties of free space, should indeed remain constant no matter how you are observing.

In this case, why do we say that he "postulated", when in fact it must be true by Maxwell's equations? Shouldn't we say that he actually prove it?

EDIT:

Actually now that I think about it, its the other way around. I'm confused, now, because since no matter at what speed you move, you obviously will measure the same electric and magnetic constants, and so light ought to have the same speed. But as you move faster, your speed is added to that of the light and so you should see light moving faster. Since we know this is false, it would follow that the e/m constants are not, in fact, constants???
Can someone clarify that to me?

Last edited: Jun 24, 2012
2. Jun 24, 2012

### Integral

Staff Emeritus
Re: Was Einstein's postulate for the speed of light a consequence of Maxwell's equati

Yes, that is precisly where the postulate originates, and why AE was able to make that postulate and no one raised an eyebrow.

That result of Maxwells was the initiator of the Great Schism of physics which lasted from the publishing of Maxwells work till AE's 1905 paper on relativity. This used to be a topic taught in elementary school, guess not anymore.

3. Jun 24, 2012

### Bill_K

Re: Was Einstein's postulate for the speed of light a consequence of Maxwell's equati

Einstein postulated that Maxwell's Equations remain unmodified regardless of the velocity of the rest frame. Also that the group of linear transformations that leave Maxwell's Equations unchanged also leave the rest of physics unchanged, including mechanics.
Many eyebrows were raised.

4. Jun 24, 2012

### TSny

Re: Was Einstein's postulate for the speed of light a consequence of Maxwell's equati

It could be that the motivation for the light speed postulate was that Einstein felt that Maxwell's equations should be valid in all inertial frames. However, in the first 1905 paper, he took the light speed postulate as an independent postulate. The other postulate was of course the relativity postulate which implied that the true laws of electromagnetism would have to be the same in all inertial frames.

In the paper, he did not postulate that Maxwell's equations satisfy the relativity postulate. Rather, he first derived the Lorentz transformations from the light postulate. Then he spent a good deal of the paper proving (not postulating) that Maxwell's equations do indeed take on the same form in all inertial frames if the electric and magnetic fields transform in certain ways.

5. Jun 24, 2012

### TSny

Re: Was Einstein's postulate for the speed of light a consequence of Maxwell's equati

My previous remark was based on memory and is not correct. After digging out the paper I see that after deriving the Lorentz transformations from the light postulate, Einstein goes on to show that if you assume (postulate) that the Maxwell equations have the same form in all inertial frames, then the electric and magnetic fields must transform in certain ways. Overall, he's proving the consistency of Maxwell's equations with the postulates of relativity. And this only takes up 2 or 3 pages of the paper.

Nevertheless, I believe that in the paper Einstein was taking the light postulate as an independent postulate on which to base the theory of relativity.

6. Jun 24, 2012

### cosmik debris

Re: Was Einstein's postulate for the speed of light a consequence of Maxwell's equati

To be picky Einstein's postulate was that, the speed of light was independent of the speed of the source. They amount to the same thing in the end I guess.

7. Jun 25, 2012

### Histspec

Re: Was Einstein's postulate for the speed of light a consequence of Maxwell's equati

Note that when you talk about "Maxwell's equations" of that time, then you are actually talking about Maxwell's theory as formulated by Lorentz in 1895. Here, only in one "aether" frame is the speed of light constant in all directions and independent of the speed of the source. Einstein took this as a postulate, generalized it to all inertial frames, and abandoned the aether. Einstein wrote in 1912 ("Relativity and Gravitation. Reply to a remark of M. Abraham", in: The Collected Papers of Albert Einstein, Volume 4: The Swiss Years: Writings, 1912–1914:)
and in 1928 Einstein said about Lorentz: (in: A. Pais, Subtle is the Lord, p. 169):
Here is Lorentz's 1895 paper that Einstein referred to:
http://en.wikisource.org/wiki/Attem...trical_and_Optical_Phenomena_in_Moving_Bodies

8. Jun 26, 2012

### lugita15

Re: Was Einstein's postulate for the speed of light a consequence of Maxwell's equati

There's one thing that should be noted. It is indeed true that special relativity, in particular the second postulate, follows from the assumption that Maxwell's equations are true in all inertial reference frame. However, this assumption would have seemed absurd to the physicists of the nineteenth century, including Maxwell himself. When Maxwell completed his four equations, he realized that they lead to the implication that electromagnetic waves (light) propagate at a speed c. Now Maxwell was a firm believer in Newtonian mechanics, so he reasoned that since his equations were clearly not invariant under Galilean transformations, by the Principle of Relativity they could not be "real" laws of physics, i.e. they could only be true in one reference frame. And he assumed that this was the rest frame of the aether. In any other frame, he assumed that the correct equations describing the electromagnetic field would not be his original equations, but rather equations that were slightly different because they would include terms dependent on the velocity of the aether with respect to that frame. These are the so-called modified Maxwell equations (formulated by Hertz), and they include aether velocity terms added to the Ampere-Maxwell Law and Faraday's Law. According to these modified equations, the speed of light in a frame moving with respect to the aether is either c+v or c-v depending in which way the light is headed, where v is the speed of the aether with respect to your frame. This is exactly analogus to sound waves: the sound wave equation is only exactly true in the rest frame of the air, and in moving frames it must be replaced by another equation that includes a term dependent on the speed of the air.

This was the context in which the Michelson-Morley experiment was done: they believed that the speed of light would not be c as predicted by the original Maxwell equations, but rather would be c+v or c-v as predicted by the modified equations, and they hoped to find that value v. But instead, of course, they found that the speed of light seemed to be the same in all inertial reference frames, and thus Maxwell's equations true in all frames. (In stark contrast to the wave equation for sound.) But as mentioned above, Maxwell's equations are not Galilean-invariant, so this posed a perceived threat to the Principle of Relativity. Lorentz's solution to this problem was to say that objects moving with respect to the aether experienced length contraction and time dilation (due to electromagnetic effects), which made the speed of light appear to be constant even though it "really" wasn't. He assumed that if we had "accurate" rulers and clocks, which did not experience these effects, then they would show that the speed of light IS c+v or c-v in frames moving with respect to the aether, and thus the modified Maxwell equations are what are "really" true in all frames, even Maxwell's original equations appear to be true.

Now although Lorentz believed that the "errors" caused by length contraction and time dilation prevented accurate measurement of the speed of light and thus the speed of the aether, he still held out hope that the speed of the aether could in principle be determined. Perhaps if A and B were moving at different speeds with respect to the aether, A could measure how much B's ruler contracted, and B could measure how much A's ruler contracted, and by comparing results they could somehow deduce their speeds relative to the aether. But then Poincare demonstrated that the Lorentz transformations relate not only the aether frame to a moving frame, but also related moving frames to each other. (Specifically, he showed that the composition of LT's is an LT, and the inverse of an LT is an LT.) However, Poincare just viewed this as a curious phenomenon. It took Einstein to realize the real significance of all this: that the invariance of Maxwell's equations was fully compatible with the Principle of Relativity, and that it was our traditional notions of space and time that needed rethinking.

9. Jun 26, 2012

### Staff: Mentor

Re: Was Einstein's postulate for the speed of light a consequence of Maxwell's equati

Lugita's comments about the historical perspective are spot-on, and it's easy to lose sight of just how strange and perplexing the electrodynamics of moving bodies once seemed.

To the modern ear, the second postulate sounds redundant ("Postulate 2: We really mean what we're saying in postulate 1" would be a fair paraphrase). It didn't sound that way at the turn of the last century.

10. Jul 17, 2012

### PhilDSP

Re: Was Einstein's postulate for the speed of light a consequence of Maxwell's equati

If the answer is "yes" then it can only apply in a vacuum. I believe Maxwell was fully cognizant that the speed of light is highly variable when charges are interspersed in the space that light travels but it will take a bit of sorting through his material to find an appropriate quote.

His contemporary, Helmholtz, had already worked out the specifics of EM dispersion and how the speed of EM propagation is effected in a most sophisticated manner. All of that really is quite apart from whether there is or isn't an aether and whether a theoretical aether does or doesn't move with respect to a particle. Both Hertz and Lorentz benefited from Helmholtz' work.

The presence of charges and current density causes the constants $\epsilon_0$ and $\mu_0$ to become the variables $\epsilon$ and $\mu$.

Last edited: Jul 17, 2012
11. Jul 17, 2012

### harrylin

Re: Was Einstein's postulate for the speed of light a consequence of Maxwell's equati

Not exactly: you refer here to two different postulates. However, getting back to your title: Yes, Einstein's postulate for the speed of light (see posts #6 and #7) was a consequence of Maxwell's theory, which had been firmly established by then. The issue was how to combine it with the relativity postulate, which seemed to be incompatible with it. Einstein explained that succinctly as follows:

"We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body. These two postulates suffice for the attainment of a simple and consistent theory of the electrodynamics of moving bodies based on Maxwell's theory for stationary bodies." (emphasis mine).
- http://www.fourmilab.ch/etexts/einstein/specrel/
That's exactly why Einstein wrote "apparently irreconcilable" - that was the main riddle that the new theory was meant to solve (and it did)! Lorentz in 1904 (with one or two glitches) and next Einstein in 1905 (very smoothly) showed how it is possible that one can observe the same natural phenomena even if the speed of light in vacuum is, as Maxwell's theory has it, independent of the motion of the source. The essential change was that Newton's theory had to be modified, so that the measurement of more physical quantities than before had to be made "relative" - in particular measures of distance and time.

Last edited: Jul 17, 2012
12. Jul 17, 2012

### harrylin

Re: Was Einstein's postulate for the speed of light a consequence of Maxwell's equati

Actually, such effects were his explanation in 1904 of why experiments like MMX could bring nothing at all - up to any precision. Perhaps we should explain how light from a spherical light source is measured as propagating at c in all directions according to relatively moving inertial reference systems. Boorglar, is that the issue that you have?

13. Jul 17, 2012

### grav-universe

Re: Was Einstein's postulate for the speed of light a consequence of Maxwell's equati

In addition to the excellent post by lugita15, the aberration of stars was the first important observation. It showed that the speed of light was the same regardless of the motion of the source, the stars in this case.

Last edited: Jul 17, 2012
14. Jul 17, 2012

### grav-universe

Re: Was Einstein's postulate for the speed of light a consequence of Maxwell's equati

Quote of nonsense post that refutes relativity deleted.

Yes, but the M-M experiment showed that light pulses will travel identical perpendicular distances and back in the same time, even when the apparatus is turned in any direction, so the two way time of propagation of the light in any direction away and back to a single clock is always the same, and from this it is then possible to synchronize clocks within the observing frame such that they measure the same one way speed of light in any direction using the Einstein simultaneity convention. But if that is the result of an experiment performed within our own frame, then since there is nothing special about our own (inertial) frame, for instance we cannot consider that only our frame just happens to be always at rest with the field, then it must be true for all inertial frames, so all inertial frames must measure a constant speed of light in any direction when stationary clocks within those frames are synchronized according to the Einstein simultaneity convention.

Last edited by a moderator: Jul 18, 2012
15. Jul 17, 2012

### lugita15

Re: Was Einstein's postulate for the speed of light a consequence of Maxwell's equati

I would word things slightly differently. The invariance of Maxwell's equations implies the invariance of the speed of light, but in the nineteenth century no one believed in the invariance of Maxwell's equations, precisely because it DID imply the invariance of the speed of light, and they believed that contradicted the principle of Relativity, and so they concluded that Maxwell's equations only held in one reference frame. That is why the null result of the Michelson-Morley experiment was so surpising (except for the believers in the aether drag hypothesis and the contraction hypothesis, who of course would have their own problems later on).

Last edited: Jul 17, 2012
16. Jul 17, 2012

### lugita15

Re: Was Einstein's postulate for the speed of light a consequence of Maxwell's equati

My understanding is that Lorentz didn't realize the symmetry of the Lorentz transformations until Poincare pointed it out, and that Poincare didn't realize the significance of that symmetry until Einstein explained it. So I'm guessing that by 1904 Poincare had already done his work, and Lorentz was building off of it. But I think in Lorentz's original aether theory, he still believed there was possibility that some combination of experiments could somehow find the aether frame. Do I have that right?

17. Jul 17, 2012

### DrGreg

Re: Was Einstein's postulate for the speed of light a consequence of Maxwell's equati

I can't claim to be an expert in the history of relativity, but everything lugita15 has said so far agrees with my understanding.

I would add (I don't think anyone's explicitly said this yet) that Lorentz came up with the Lorentz transform (between the aether frame and any other inertial frame) as exactly what was needed to make Maxwell's equations valid in all inertial frames.

18. Jul 17, 2012

### ardenmann0

Re: Was Einstein's postulate for the speed of light a consequence of Maxwell's equati

I would add that Lorentz came up with the right equations, Lorentz transform. But his interpretation of the contraction is very different from that of Einstein's.

19. Jul 17, 2012

### pervect

Staff Emeritus
Re: Was Einstein's postulate for the speed of light a consequence of Maxwell's equati

My impression of the times is that Michelson was motivated by wanting to replace the physical meter standard with an interferometric one, based on the wavelength of some particular light source.

(my source for this impresion isn't based on much reading, just the wiki article on the history of the meter: http://en.wikipedia.org/w/index.php?title=Metre&oldid=502620767)

This goal - replacing the physical meter with one based on the wavelength of light - wasn't actually accomplished until the 1960's, however.

To make progress towards this goal, Michelson needed to pin down experimental sources of error. One source of expected error was "ether wind". He , and everyone else, was rather surprised to find out that the expected effect didn't exist.

20. Jul 18, 2012

### harrylin

Re: Was Einstein's postulate for the speed of light a consequence of Maxwell's equati

Maxwell's equations did not imply the invariance of the speed of light - but yes, I should have written that Maxwell's theory for stationary systems was firmly established (which is of course what Einstein meant with "stationary bodies"; at the time he evidently did not distinguish bodies from systems).
I think that the part that I retained here is correct. However, such a discussion is a bit besides the topic.

PS. Strange: the OP did not react on our clarifications... I won't comment anymore if he/she isn't really interested in his/her topic!

Last edited: Jul 18, 2012