# Second Postulate of Special Relativity Explained

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• Wolfgang Stracke
In summary, according to the article, the second postulate says that the speed of light in vacuum is the same for all observers, regardless of the motion of light source.

#### Wolfgang Stracke

Once my understanding of the 2nd postulate was something like that:

Let's say there are 2 points of reference frame ##K##, we can denote these points as ##A## and ##B##. Speed of light between these points is ##c##, that doesn’t depend on chosen direction, ##A## to ##B## or ##B## to ##A##.

Let's there is inertial frame ##K'## that moves with velocity ##v## relatively to ##K##. Let's there are 2 points of reference frame ##K##’, we can denote these points as ##A’## and ##B’##. Speed of light between these points must always be ##c## and does not depend on the direction of propagation, ##A’## to ##B’## or ##B’## to ##A’##.

However, the article in Wikipedia claims that according to the 2nd postulate „speed of light in vacuum is the same for all observers, regardless of the motion of light source

https://en.wikipedia.org/wiki/Special_relativity

Why does it say „regardless of motion of light source“? It doesn't say "regardless of relative speed of observer and the source“.

Moreover, there is the following sentence in the article:

The Principle of Invariant Light Speed – "... light is always propagated in empty space with a definite velocity [speed] c which is independent of the state of motion of the emitting body" (from the preface). That is, light in vacuum propagates with the speed c (a fixed constant, independent of direction) in at least one system of inertial coordinates (the "stationary system"), regardless of the state of motion of the light source.

What do they mean by “light in vacuum propagates with the speed ##c## in at least one system of inertial coordinates”? Are there some others moving frames and speed of light differs from ##c## in these frames? How can this be reconciled with the relativity of simultaneity?

It sounds like touching a surface of a pond by a paddle of a boat . Speed of waves does not depend on the speed of a boat, but in the frame of the boat it will be different in different directions.

I feel completely lost and confused. Does Special Relativity says us there is some kind of preferred frame or even Ether? Or maybe my interpretation was wrong? What is actually meant in the second postulate?

The second postulate means that the speed of light, measured in any inertial frame, is ##c##. Full stop. The motion of the source does not matter - if a moving lamp and a stationary lamp emit a flash of light as they pass each other, any observer will receive both flashes simultaneously (although they may be Doppler shifted when compared). Furthermore, there is no ether to provide a preferred frame as the water does in your pond example.

The thing you seemed to be missing in your other thread was that simultaneity is relative. Two pulses of light entering the arms of an interferometer simultaneously, stationary in one frame, will strike the mirrors simultaneously and return to the beam splitter simultaneously. Viewed in a frame where it is moving, however, the pulses leave and arrive simultaneously (they must, otherwise they can't interfere), but do not strike the mirrors simultaneously.

The easiest way to get your head around this is to learn to draw Minkowski diagrams. They're the tool that finally showed me how to understand this stuff in an intuitive way.

vanhees71
Wolfgang Stracke said:
The Principle of Invariant Light Speed – "... light is always propagated in empty space with a definite velocity [speed] c which is independent of the state of motion of the emitting body" (from the preface). That is, light in vacuum propagates with the speed c (a fixed constant, independent of direction) in at least one system of inertial coordinates (the "stationary system"), regardless of the state of motion of the light source.
Sounds silly to me. Light propagates at c in ALL inertial coordinates. That's the trouble with using wiki as a source. They get a lot of things right but not everything.
I feel completely lost and confused. Does Special Relativity says us there is some kind of preferred frame or even Ether?
Absolutely not

Wolfgang Stracke
Wolfgang Stracke said:
Why does it say „regardless of motion of light source“? It doesn't say "regardless of relative speed of observer and the source“.
We can always (as a consequence of the first postulate) consider the observer to be at rest, so the two statements are equivalent.
Moreover, there is the following sentence in the article:...
That's just unnecessarily confusing. Wikipedia is not a great learning tool. and I suggest that you not use it if you're trying to figure out special relativity.

phinds said:
Sounds silly to me. Light propagates at c in ALL inertial coordinates. That's the trouble with using wiki as a source. They get a lot of things right but not everything.
The quoted part is from the introduction to Einstein's 1905 paper. The rest seems to be a reference to the second time Einstein mentions the second postulate (section 2), which does talk about "the stationary system". He promptly goes on to use the fact that the speed of light is constant in the moving frame to derive the relativity of simultaneity, though.

I think this is a basic problem with working from original sources (edit: and Wikipedia's presentation thereof) like this. Nobody had the opportunity to file off the rough edges of Einstein's original presentation (and/or the translation from German). Much better to work from more modern sources - the maths is the same, the correspondence with experiment is the same, but the presentation has learned from a century of misunderstandings.

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phinds said:
Sounds silly to me. Light propagates at c in ALL inertial coordinates. That's the trouble with using wiki as a source. They get a lot of things right but not everything.
Absolutely not

Well, but Wikipedia is very reputable source and the second postulate sounds exactly as it is in the Einstein's paper. I don't believe, that the author of these words - "in at least one" added them due to misunderstanding.

Why this person - @Ibix says that

Ibix said:
Viewed in a frame where it is moving, however, the pulses leave and arrive simultaneously (they must, otherwise they can't interfere), but do not strike the mirrors simultaneously.

Why do not they strike the mirrors simultaneously?

Nugatory said:
We can always (as a consequence of the first postulate) consider the observer to be at rest, so the two statements are equivalent..

? Cannot we consider the observer to be moving?

Ibix said:
The quoted part is from the introduction to Einstein's 1905 paper. The rest seems to be a reference to the second time Einstein mentions the second postulate (section 2), which does talk about "the stationary sysyem". He promptly goes on to use the fact that the speed of light is constant in the moving frame to derive the relativity of simultaneity, though.

I think this is a basic problem with working from original sources (edit: and Wikipedia's presentation thereof) like this. Nobody had the opportunity to file off the rough edges of Einstein's original presentation (and/or the translation from German). Much better to work from more modern sources - the maths is the same, the correspondence with experiment is the same, but the presentation has learned from a century of misunderstandings.
Maybe, while writing the first chapter, Einstein still was convinced in existence of Ether, but changed his mind later, while writing the second chapter?

Oh, guys, Mein Gott, so much complex theory!

Wolfgang Stracke said:
Well, but Wikipedia is very reputable source
Um - no. It's a good start for a lot of things, but do not trust it without approval from an expert.
Wolfgang Stracke said:
Why this person - @Ibix says that
Why do not they strike the mirrors simultaneously?
Because frames do not necessarily agree on simultaneity. That's what I thought you were missing in your understanding, and I seem to be on target (it's the problem for 99% of students at least).

Wolfgang Stracke said:
Maybe, while writing the first chapter, Einstein still was convinced in existence of Ether, but changed his mind later, while writing the second chapter?

Oh, guys, Mein Gott, so much complex theory!
Seriously, Einstein's papers are one of the worst sources around for learning Special Relativity! Find a decent book or a course and learn properly, it really is much simpler than you are making it. And don't mention the ether ;)

Ibix
m4r35n357 said:
Seriously, Einstein's papers are one of the worst sources around for learning Special Relativity!
I'm not sure I'd go that far - there are a great many YouTube videoes that have him beaten by quite a margin. But it's certainly true that the intended audience of a paper (or at least, a paper like Einstein's) is experts in the field as it was at the time of writing. If you aren't one of those, papers can be difficult to follow. Textbooks, on the other hand, don't assume much familiarity with the field, and have access to a century of experience on how (and how not) to teach their subject. They typically do a much better job of explaining for people just starting in the field.

robphy and m4r35n357
OK, one of the worst correct sources then - I admire Einstein for coming up with special relativity despite the fog of physics. That is how good he was ;)

I would recommend to the OP to learn about Minkowski space and four vectors. Once the basic maths is assimilated, then application to things like the twin paradox become trivial.

m4r35n357 said:
OK, one of the worst correct sources then - I admire Einstein for coming up with special relativity despite the fog of physics. That is how good he was ;)

I would recommend to the OP to learn about Minkowski space and four vectors. Once the basic maths is assimilated, then application to things like the twin paradox become trivial.

I actually don't agree. I don't think it's hard to follow Einstein's argument (which is available online here: https://www.fourmilab.ch/etexts/einstein/specrel/specrel.pdf). He says at the beginning that he's just picking one inertial frame and calling it "the stationary system". It's just a name.

As for "regardless of the motion of the source", that doesn't have any logical force, but it's just letting you know that it isn't just some light signals (those from a stationary source) that travel at speed c. It's just to remind you that light is different from bullets from a gun. A bullet from a gun travels at a characteristic speed of maybe 770 meters per second. But that's relative to the gun, so it's only bullets fired from a stationary gun that will be measured to have that speed.

martinbn
Einstein states explicitly
light (as required by the principle of the constancy of the velocity of light, in combination with the principle of relativity) is also propagated with velocity c when measured in the moving system.
That is, light moves with this velocity not only in (as measured in) the stationary frame of reference, but also in the moving one, and this follows from the first postulate (principle of relativity).

Ibix
Wolfgang Stracke said:
Well, but Wikipedia is very reputable source ...
As others have noted, if you actually want to learn science, you need to disabuse yourself of this seriously fallacious notion.

They ARE (as has also been noted) good for getting a general idea about things but they are not to be trusted with the details (and often with the big stuff as well).

It is often about frame - "stationary" or "moving". Is here any difference? What is "moving"?
https://en.wikipedia.org/wiki/Motion_(physics)

As far as I understand, if something "moves" relatively to me, it means it changes spatial coordinate in my frame. As I understand,, "my frame" is an imaginary lattice, attached to myself.

However, if I "move", that probably means that I change myself my spatial position in someone's frame.

I understand, that in Special Relativity contraction does not take place in my own frame, but it is some sort of perspective. I look at another guy who is moving and his length turns to be shorter, than my own.

Can I think about myself in terms "I move in another's frame"?

Wolfgang Stracke said:
As far as I understand, if something "moves" relatively to me, it means it changes spatial coordinate in my frame. As I understand,, "my frame" is an imaginary lattice, attached to myself.
Correct, but you don't have to associate yourself with just one frame. Decide on a fixed frame and then you can tell whether or not you are moving in that frame. "my chair" is a frame in which you are not moving when you are sitting in the chair but in which you ARE moving when you get up to go down the hall.

However, if I "move", that probably means that I change myself my spatial position in someone's frame.
Yes, but better to just say "a frame". It doesn't have to be associated with another person/observer.

I understand, that in Special Relativity contraction does not take place in my own frame, but it is some sort of perspective. I look at another guy who is moving and his length turns to be shorter, than my own.
correct. Same for time dilation.

Can I think about myself in terms "I move in another's frame"?
see above

phinds said:
Correct, but you don't have to associate yourself with just one frame. Decide on a fixed frame and then you can tell whether or not you are moving in that frame. "my chair" is a frame in which you are not moving when you are sitting in the chair but in which you ARE moving when you get up to go down the hall.

Yes, but better to just say "a frame". It doesn't have to be associated with another person/observer.

correct. Same for time dilation.

see above
As far as I understand from here
https://en.wikipedia.org/wiki/Michelson–Morley_experiment
and here
https://en.wikipedia.org/wiki/Lorentz_ether_theory

that, according to Lorentz, we cannot detect our motion due to contraction and dilation of ourselves, but simply cannot notice that, because our tools are also distorted by motion, and that makes measured speed of light equivalent c in all directions (or better to say propagation times).

According to Einstein, velocity of light along the legs of the interferometer is c by definition (I thought so!), and there is no distortion at all, and we can never say "I am contracted but cannot detect it due distortion of my ruler" about ourselves, though, moving observer (who changes spatial position in our frame) appears to be shorter and dilated.

I am greatly surprised by the negligence of the definitions that Einstein himself gives in the second postulate and in the Wikipedia article. As if they do not understand the difference. I believe, that definitions play a crucial role.

Now I do not understand Einstein's attitude towards Michelson Morley experiment.

Wolfgang Stracke said:
It is often about frame - "stationary" or "moving". Is here any difference? What is "moving"?
https://en.wikipedia.org/wiki/Motion_(physics)

It's an arbitrary choice. He could have called if "Frame A" and "Frame B". Analyzing things from the point of view of someone at rest in Frame A, it seems that his frame is stationary and the other frame is moving. There is no distinction, other than the fact that it is two different inertial frames.

Wolfgang Stracke said:
As I understand,, "my frame" is an imaginary lattice, attached to myself.

No, a frame in relativity is a criterion for determining two things: (1) What objects are "at rest" and (2) which clocks are synchronized. An "inertial frame" is one where the objects that are at rest are moving inertially (that is, they are not acted on by any force) and clocks at rest are synchronized.

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Wolfgang Stracke said:
according to Lorentz, we cannot detect our motion due to contraction and dilation of ourselves, but simply cannot notice that, because our tools are also distorted by motion, and that makes measured speed of light equivalent c in all directions (or better to say propagation times).

According to Einstein, velocity of light along the legs of the interferometer is c by definition (I thought so!), and there is no distortion at all, and we can never say "I am contracted but cannot detect it due distortion of my ruler" about ourselves, though, moving observer (who changes spatial position in our frame) appears to be shorter and dilated.
In both of these interpretations all observers measure the speed of light to be c. All observers watching experiments moving with respect to them will see that clocks attached to that experiment are incorrectly synchronised and don't tick at the right rate, and rulers attached to it are shortened. So they are unsurprised that the moving experiment also yields c as the speed of light. Both interpretations agree that all observers can make this argument: their own clocks and rulers measure naturally and all clocks and rulers in motion do not.

The only difference between the interpretations is as follows. Einstein says no one is uniquely correct - everyone is just defining simultaneity slightly differently and the consequence is that they are all measuring slightly different aspects of a 4d reality. The maths is more complex, but fundamentally it's no different to viewing a square as a square or turning yourself 45° and calling it a diamond. If you take horizontal slices through the objects the slices look very different, but that's because you changed your mind about what horizontal means, not because anything changed about the object.

Lorentz, on the other hand, says that one choice of frame is Right. In all other frames, rulers at rest are really contracted and clocks really do tick slow. So measurements made using this frame's conventions are genuinely incorrect, but the errors just happen to cancel out so you can't tell if you are in the "real" rest frame. That means that which frame is the right one is undetectable. This interpretation also requires a physical mechanism by which this real contraction and clock dilation happen - to my knowledge no one has ever proposed such a mechanism and it's difficult to see how one could work.

So basically, both interpretations say that everyone regards themselves as measuring correctly. Lorentz adds that all except one frame are actually wrong, but he can't know which one is the right one.
Wolfgang Stracke said:
I am greatly surprised by the negligence of the definitions that Einstein himself gives in the second postulate and in the Wikipedia article.
We aren't neglecting it. We're pointing out that Einstein words it inconsistently even in one paper. But as @Nugatory points out, the principle of relativity requires that if "the speed of light is constant in frame S" is a postulate of the theory then the speed must be the same in S', so Einstein's different wordings are equivalent. And every time Einstein applies the second postulate he uses it in the sense that I gave in post #2 - the speed of light is the same in all inertial reference frames, full stop.

Wolfgang Stracke said:
Maybe, while writing the first chapter, Einstein still was convinced in existence of Ether, but changed his mind later, while writing the second chapter?

Oh, guys, Mein Gott, so much complex theory!
It's indeed true that usually papers and textbooks written some time after a new theory has been found are more clear than the original papers. There are a very few exceptions however, and one for sure is Einstein, who is among the clearest writers ever. Other examples are Dirac (whose original papers on QM are much better than many even new textbooks) and Pauli. Clear counterexamples are Bohr and Heisenberg, who wrote in a style which is as incomprehensible as possible (and Heisenberg's papers are mostly in German, so it's not a language problem I have ;-)).

That said, let's see what Einstein really writes in his famous paper of 1905 (of course, Minkowski's paper of 1907 is much simpler mathematically, because it uses or rather establishes the adequate mathematics for special relativity ;-)):

Already in the introduction (which in fact is the very theme of entire 20th-century physics, i.e., thinking about physics in terms symmetry principles) he clearly states that his two postulates are:

(1) Validity of the special principle of relativity for all phenomena, i.e., not only mechanical but also electrodynamical ones. The special principle of relativity states that (a) there exists an inertial reference frame, which implies that in fact there are arbitrarily many inertial reference frames each moving with constant velocity against any other such system and (b) the physical laws are independent of the particular inertial frame.

(2) (and here I quote Einstein's paper, translation mine): We make this assumption [the special principle of relativity for all physical phenomena, including electromagnetic ones] to a principle and also introduce the demand, which only apparently is incompatible with this principle, that light in empty space always propagates with the same speed, independent of the state of motion of the [light] emitting body.

and further: "The assumption of a "lumineferous ether" will turn out to be superfluous in the sense that there is neither an "absolute space at rest" nor any point in empty space, where electromagnetic processes occur, has a velocity vector assigned."

For sure, Wikipedia is much less accurate in explaining SR than Einstein in his seminal paper. Although the math occurs a bit complicated compared to the elegant formulation we use today thanks to Minkowski, but I think it's well worth to be studied today in detail, because it makes the physical idea very clear, particularly in emphasizing the importance of the "relativity of simultaneity".

There's only one serious sin in this paper, and that's the introduction of "moving masses" (even two different ones, i.e., longtudinal and transverse ones). Very soon Einstein corrected this error in strong statements in favor of using only the notion of invariant masses in SR (and by definition that's indeed the same as the mass used in the non-relativistic Newtonian limit).