# The speed of light: Was Einstein's second postulate not so revolutionary?

• B
Summary:
If Maxwell and his contemporaries were asked the following question what would have been their answer? Does the speed of the emitter of a beam of light get added to the speed of light in a vacuum?
If the answer is yes then it seems that Einstein's second postulate was not so revolutionary.

etotheipi
I wonder if there is a redundancy in the second postulate. If the first postulate amounts to saying physical laws take the same form in all IRFs, then naturally Maxwell's equations take the same form in all IRFs. Then from Maxwell's equations you can derive the wave equation for ##\vec{E}## and ##\vec{B}##, and deduce that light propagates at ##1/\sqrt{\varepsilon_0 \mu_0}## in all IRFs. So perhaps the second postulate is more a case of asserting "Maxwell's equations are correct physical laws". I don't know, hopefully someone explains it better!

(P.S. when you take (Lorentz invariant) Maxwell's equations as true then you notice that the correct way to transform components between IRFs must be the Lorentz transform, and that Galilean velocity addition must only be approximation which holds in low speed regime.)

I wonder if there is a redundancy in the second postulate. If the first postulate amounts to saying physical laws take the same form in all IRFs, then naturally Maxwell's equations take the same form in all IRFs. Then from Maxwell's equations you can derive the wave equation for ##\vec{E}## and ##\vec{B}##, and deduce that light propagates at ##1/\sqrt{\varepsilon_0 \mu_0}## in all IRFs. So perhaps the second postulate is more a case of asserting "Maxwell's equations are correct physical laws". I don't know, hopefully someone explains it better!

Do note that for the time of the development of special relativity there were several problems of the electromagnetic nature that put serious doubts in the universality of the Maxwell's equations, the stability of the Atom to name the most important.

So, Einstein could not take Maxwell's electrodynamics for granted.

Abhishek11235, Physics4Funn and etotheipi
Dale
Mentor
2020 Award
Summary:: If Maxwell and his contemporaries were asked the following question what would have been their answer? Does the speed of the emitter of a beam of light get added to the speed of light in a vacuum?

If the answer is yes then it seems that Einstein's second postulate was not so revolutionary.
You are completely missing the revolutionary part. The revolutionary part is “in every inertial frame”. Nobody got that part until Einstein.

cianfa72, Abhishek11235, Omega0 and 2 others
Buzz Bloom
Gold Member
Summary:: If Maxwell and his contemporaries were asked the following question what would have been their answer? Does the speed of the emitter of a beam of light get added to the speed of light in a vacuum?

If the answer is yes then it seems that Einstein's second postulate was not so revolutionary.
Underlining of "yes" is mine".
Hi Uuser:

I think you meant to write "no".
As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body.​
Underlining is mine".

Regards,
Buzz

StandardsGuy and PeterDonis
Nugatory
Mentor
I wonder if there is a redundancy in the second postulate.
That is a fun discussion, and one that you'll find in a few old threads here. In the past I have sometimes wedged my tongue thoroughly into my cheek to assert that the second postulate can be paraphrased as "And we really mean the first postulate, even when it comes to Maxwell's equations".

As a matter of history there's no redundancy. These days we are comfortable with the idea that we can accept the covariance of Maxwell's equations at face value, but this was far less natural at the end of the 19th century. We might also understand the second postulate as saying "The first postulate plus Maxwell is incompatible with Galilean relativity..... and we don't care, we're going to run with that!". At the time it was absolutely necessary to be explicit about what was being assumed and what was not being assumed.

Abhishek11235, atyy, vanhees71 and 3 others
pervect
Staff Emeritus
Summary:: If Maxwell and his contemporaries were asked the following question what would have been their answer? Does the speed of the emitter of a beam of light get added to the speed of light in a vacuum?

If the answer is yes then it seems that Einstein's second postulate was not so revolutionary.

The answer is no - the speed of light is independent of the motion of the source. The De-Sitter double star observation in 1913, https://en.wikipedia.org/wiki/De_Sitter_double_star_experiment, was one of the earliest and most basic tests - other later tests have refined this result, for instance ruling out effects due to the interstellar media.

PeterDonis
PeterDonis
Mentor
2020 Award
If the first postulate amounts to saying physical laws take the same form in all IRFs, then naturally Maxwell's equations take the same form in all IRFs.

Only if you assume that Lorentz transformations are the correct transformations between IRFs. But at the time, nobody but Einstein was saying that. Everyone else thought that Galilean transformations, which are the ones that leave Newton's laws invariant, were the correct transformations between IRFs; the fact that Maxwell's equations were not Galilean invariant, but Lorentz invariant, was viewed as an open issue, which everyone but Einstein thought would be solved by finding some more comprehensive theory of electromagnetism that would be Galilean invariant, and to which Maxwell's Equations would be an approximation.

So the real content of the first postulate was to dethrone Newton's laws--to assert that Lorentz transformations, not Galilean transformations, were the correct transformations between IRFs. And the real content of the second postulate, in that context, was to assert that the speed of light, considered not just as a speed of wave propagation as derived from Maxwell's Equations, but as a mechanically measured quantity--something measured with rulers and clocks, something that, prior to Einstein asserting the first postulate, everyone assumed that Newton's laws would govern--was the same in all IRFs.

cianfa72, Grasshopper, Omega0 and 1 other person
vanhees71
Gold Member
I wonder if there is a redundancy in the second postulate. If the first postulate amounts to saying physical laws take the same form in all IRFs, then naturally Maxwell's equations take the same form in all IRFs. Then from Maxwell's equations you can derive the wave equation for ##\vec{E}## and ##\vec{B}##, and deduce that light propagates at ##1/\sqrt{\varepsilon_0 \mu_0}## in all IRFs. So perhaps the second postulate is more a case of asserting "Maxwell's equations are correct physical laws". I don't know, hopefully someone explains it better!

(P.S. when you take (Lorentz invariant) Maxwell's equations as true then you notice that the correct way to transform components between IRFs must be the Lorentz transform, and that Galilean velocity addition must only be approximation which holds in low speed regime.)
Yes, and that's how Maxwell got to the conclusion that light might be electrocmagnetic waves. In our modern SI units the ##\mu_0## and ##\epsilon_0## can be measured by electrostatic and magnetostatic experiments and then from Maxwell's equations you get that there must be waves of the em. field in free space with the speed ##c=1/\sqrt{\epsilon_0 \mu_0}##, and that speed turned out to be equal (within the accuracy of the measurements by Kohlrausch and Weber) to the speed of light in vacuum (or air for that matter). Of course at that time the physicists used more natural (though less convenient) units, namely either the electrostatic or the magnetostatic units, and there this characteristic speed came from the relation between the electrostatic and magnetostatic charge units.

The difference in thinking at Maxwell's time, i.e., around 1865 when he discovered his equations, was however that the fact that these equations are not Galilei invariant was not to come to the conclusion that the spacetime model had to be adapted but to the contrary that this finally established an absolute inertial frame of reference a la Newton in an operational way. The idea was that em. waves are waves of a very strange medium, called the aether, and that this aether's restframe provided the absolute inertial restframe of Newtonian mechanics.

At the first glance this model worked very well, and today we know why: If you make experiments concerning the em. phenomena in moving media the now known relativistic laws lead to the same result as the aether-theoretical ones at the order ##v/c##, where ##v## is the velocity of the moving medium and ##c## the vacuum speed of light. To see deviations from aether theory you need experiments which can resolve deviations in the next order, ##(v/c)^2##. The classical experiments that achieved this were the well-known Michelson-Morley "aether-wind experiment" (with the famous null result in contradiction to aether theory) and the Trouton-Noble experiment (again a null result in contradiction to the expecations from aether theory).

It took quite some time to come to the quite radical conclusion that the space-time model and the mechanical laws had to be adapted such as to be consistent with the invariance of the Maxwell equations when changing from one inertial frame to another. The corresponding Lorentz transformations were known for quite a while. They were found (in preliminary form though) already by Woldemar Voigt, but taken as a mathematical curiosity rather than of physical value. Also Lorentz, FitzGerald, Poincare, et al did not give up aether theory too easily (I'm not sure whether they finally really gave it up) after Einstein's breakthrough in 1905.

nsaspook and etotheipi
vanhees71
Gold Member
That is a fun discussion, and one that you'll find in a few old threads here. In the past I have sometimes wedged my tongue thoroughly into my cheek to assert that the second postulate can be paraphrased as "And we really mean the first postulate, even when it comes to Maxwell's equations".

As a matter of history there's no redundancy. These days we are comfortable with the idea that we can accept the covariance of Maxwell's equations at face value, but this was far less natural at the end of the 19th century. We might also understand the second postulate as saying "The first postulate plus Maxwell is incompatible with Galilean relativity..... and we don't care, we're going to run with that!". At the time it was absolutely necessary to be explicit about what was being assumed and what was not being assumed.
Well, you can also go ahead without the light-speed postulate and ask for the most general spacetime structure which obeys (a) the special law of relativity (preferred class of inertial frames) and (b) assumes that space for any inertial observer is Euclidean with the implied symmetries of homogeneity and isotropy and (c) homogeneity of time. From these assumptions there are only two space-time structures left, the Galilei-Newton and the Einstein-Minkowskian spacetime model. The latter has a universal "limiting speed", the former doesn't. Now it's an empirical question, which spacetime model describes nature more accurately, and the answer of course is Einstein-Minkowski spacetime.

That the limiting speed of special relativity is the same as the speed of light is also an empirical question. In modern terms it's the measurement of the mass of the photon. According to the particle data booklet the upper limit is ##m_{\gamma} < 10^{-18} \text{eV}/c^2##.

atyy
Underlining of "yes" is mine".
Hi Uuser:

I think you meant to write "no".
As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body.​
Underlining is mine".

Regards,
Buzz
You are correct, my original question should have asked about NO, not YES.
If the answer is NO then it seems that Einstein's second postulate was not so revolutionary.

I do have a related question.
How would Maxwell and other physicists at the time answer this question.
If an IFR were moving toward a light beam would the measured speed of the light be affected by the speed of the IFR?

PeroK
Homework Helper
Gold Member
2020 Award
You are correct, my original question should have asked about NO, not YES.
If the answer is NO then it seems that Einstein's second postulate was not so revolutionary.

I do have a related question.
How would Maxwell and other physicists at the time answer this question.
If an IFR were moving toward a light beam would the measured speed of the light be affected by the speed of the IFR?
As far as I know, Maxwell assumed there was an ether. Light would travel at ##c## through the ether. Anything moving wrt the ether would get a different measurement. To find this difference was the purpose of the Michelson-Morley experiment.

In other words, motion of the observer relative to the ether was relevant.

vanhees71 and etotheipi
Dale
Mentor
2020 Award
If the answer is NO then it seems that Einstein's second postulate was not so revolutionary.
Again, you are completely missing the revolutionary part. The revolutionary part is not that c was independent of the speed of the emitter (even sound waves do that) but that it was the same in all inertial frames.

It makes no sense whatsoever to claim that something is not revolutionary by ignoring the revolutionary part! Do you also measure the brightness of the sun by putting your sensor in the shade?

A.T.
... it seems that Einstein's second postulate was not so revolutionary.
The combination of both postulates is key, not either of them by itself.

vanhees71
Gold Member
Again, you are completely missing the revolutionary part. The revolutionary part is not that c was independent of the speed of the emitter (even sound waves do that) but that it was the same in all inertial frames.

It makes no sense whatsoever to claim that something is not revolutionary by ignoring the revolutionary part! Do you also measure the brightness of the sun by putting your sensor in the shade?
But sound waves are different, because there you have indeed a medium defining a preferred reference frame. Here the Doppler effect depends on both, the motion of the source as well as the motion of the observer relative to the medium. That holds for both, non-relativistic and relativistic (fluid-)dynamics.

https://doi.org/10.1119/1.14205

Staff Emeritus
Counting postulates seems to me to be a not-particularly-useful activity.

Sometime in the 1860's it was recognized that Maxwell's Equations were incompatible with Newtonian Mechanics. The working assumption was that Newton was correct and Maxwell was a very good approximation of an underlying Newtonian theory. Einstein's contribution was adopting the opposite position: Maxwell is correct, and Newton is a low-velocity approximation.

A.T., PeroK and Ibix
Dale
Mentor
2020 Award
But sound waves are different, because there you have indeed a medium defining a preferred reference frame
Obviously they are different. But the question that the OP is using as their "revolutionary" test does not capture the important difference.

vanhees71
vanhees71
Gold Member
That there is a difference in fact IS the "revolution" ;-)).

Nugatory
Mentor
Well, you can also go ahead without the light-speed postulate and ask for the most general spacetime structure....
Indeed we can. This is one of the (not uncommon) cases in which after we've reached our destination we see that there is another way of getting there.

vanhees71 and Ibix
Summary:: If Maxwell and his contemporaries were asked the following question what would have been their answer? Does the speed of the emitter of a beam of light get added to the speed of light in a vacuum?
Answer of Maxwell: "no". Answer of Einstein: "no". (proof against the emission theory - via double stars)

How would Maxwell and other physicists at the time answer this question.
If an IFR were moving toward a light beam would the measured speed of the light be affected by the speed of the IFR?

(proof against the theory of classical "stationary" ether - via Michelson Morley experiment)
(proof against the theory of classical ether, dragged by the earth - via stellar aberration)

Meir Achuz
Homework Helper
Gold Member
I haven't read all the posts but, if "Again, you are completely missing the revolutionary part. The revolutionary part is not that c was independent of the speed of the emitter (even sound waves do that) but that it was the same in all inertial frames.", then why didn't Einstein say that in 1905?

PeroK
Homework Helper
Gold Member
2020 Award
I haven't read all the posts but, if "Again, you are completely missing the revolutionary part. The revolutionary part is not that c was independent of the speed of the emitter (even sound waves do that) but that it was the same in all inertial frames.", then why didn't Einstein say that in 1905?
He does say that, albeit in a slightly roundabout way.

vanhees71
Dale
Mentor
2020 Award
why didn't Einstein say that in 1905?
He did, in both words and (more importantly) in math.

Last edited:
Omega0, nsaspook and vanhees71
Meir Achuz
Homework Helper
Gold Member
"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."

Dale
Mentor
2020 Award
Did you miss:

"the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good"

and

"Let us take a system of co-ordinates in which the equations of Newtonian mechanics hold good.2 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.” "

and

"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 a moving body."

You have to read the whole thing, not just one and a half sentences.

Grasshopper, Omega0, vanhees71 and 1 other person