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- In Einstein's 2nd postulate, it is the motion of the light source that is important, not the motion of the observer. The observer is assumed to be "stationary".

Einstein's two postulates of special relativity reads, according to Wikipedia:

The postulates are most often formulated similarly to this. But in my opnion, the second postulate shouldn't be formulated as above, because then one misses the point. This is particular true for the second sentence: "the speed of light in free space has the same value

Indeed, Einstein himself writes, i his original 1905 paper:

In the next section in this paper, he states the postulates:

So, in Einstein's wording, the 2nd postulate does

That is the point. For observer at rest in the "stationary" frame, it doesn't matter if the light source is at rest, or moves towards or away from him/her, or sideways, (s)he will always measure the speed of this light to

This is different from how it is for slowly moving objects. For example, if a car is moving with velocity

It would be natural to think that the same holds for light rays: i.e. if the light source is at rest in the "stationary" frame, then the speed light is measured to

But the 2nd postulate says that it is not so: the stationary observer measures the light speed to

Again:

Of course, what Wikpedia says is also true: the light speed has the same value

When, as in the Wikipedia article and many other texts, this conclusion is lumped togther with the 2nd postulate itself, it is easy to miss the point and think that the 2nd postulate is about different observers all measuring the light speed to

This might be one reason why Einstein chose to single out one particular inertial frame and call it "stationary" and formulate the 2nd postulate about this frame only.

The weakness with talking about this "stationary" frame is, of course, that it is arbitrary. There is no way to single ot such a "stationary" frame in reality. All inertial frames are equivalent physically, by the 1st postulate. It is therefore understandable that one in pedagocical representations of SR does not want to invoke such a "stationary" frame: the reader might believe that it is something real, and also: why introdue this concept when it is immediately getting rid of, by concluding that the light speed is the same in all intertial systems (as we did above)?

Still, I think the pedagogicial gain is greater that its difficulties: if one just does not take the "stationary" frame too seriously, and thinks of it as the "ground" or the "laboratory frame" or something like that, it is useful, and it leads to a better understanding of what the 2nd postulate really is about.

1. First postulate (principle of relativity)

The laws of physics take the same form in all inertial frames of reference.

2. Second postulate (invariance ofc)

As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocitycthat is independent of the state of motion of the emitting body. Or: the speed of light in free space has the same valuecin all inertial frames of reference.

The postulates are most often formulated similarly to this. But in my opnion, the second postulate shouldn't be formulated as above, because then one misses the point. This is particular true for the second sentence: "the speed of light in free space has the same value

*c*in all inertial frames of reference". This is certainly true, but it is not what the postulate is about. The postulate is not about "all inertial frames of reference" it is about one*particular*intertial frame, which is considered*stationary.*Indeed, Einstein himself writes, i his original 1905 paper:

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

In the next section in this paper, he states the postulates:

- The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of co-ordinates in uniform translatory motion.
- 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. Hence

where time interval is to be taken in the sense of the definition in § 1.

So, in Einstein's wording, the 2nd postulate does

*not*talk about the value of the speed of light in*all*intertal frames, but only in one particular frame, which Einstein singled out and called "stationary". Einstein also writes what this really is about: "whether the ray be emitted by a stationary or a moving body".That is the point. For observer at rest in the "stationary" frame, it doesn't matter if the light source is at rest, or moves towards or away from him/her, or sideways, (s)he will always measure the speed of this light to

*c*.This is different from how it is for slowly moving objects. For example, if a car is moving with velocity

*V*and a ball is thrown from the car with velocity*v*relative to the car, then the ball will get the velocity*v+V*relative to an observer on the ground, if the car moves towards the observer, and*v-V*if the car moves away from the observer.It would be natural to think that the same holds for light rays: i.e. if the light source is at rest in the "stationary" frame, then the speed light is measured to

*c*by the "stationary" of observer, but if the light source moves towards the observer with velocity*v,*then the observer measures the light speed to*c+v*, and to*c-v*if the light source moves away from the observer with velocity*v.*But the 2nd postulate says that it is not so: the stationary observer measures the light speed to

*c*, independently of the motion of the light source.Again:

*This is the point of the second postulate.*Of course, what Wikpedia says is also true: the light speed has the same value

*c*in*all*inertial frames. But that is not what the 2nd postulate says, and it does not follow from that postulate alone, we also need the 1st postulate to infer this: The constancy of the light speed is considered as a law of physics, and those are the same in all intertial frames, by the 1st postulate. Therefore, the speed of light is measured to*c*in*all*intertial frames.When, as in the Wikipedia article and many other texts, this conclusion is lumped togther with the 2nd postulate itself, it is easy to miss the point and think that the 2nd postulate is about different observers all measuring the light speed to

*c,*when it in fact is about the light speed being independent of the motion of the*light source*.This might be one reason why Einstein chose to single out one particular inertial frame and call it "stationary" and formulate the 2nd postulate about this frame only.

The weakness with talking about this "stationary" frame is, of course, that it is arbitrary. There is no way to single ot such a "stationary" frame in reality. All inertial frames are equivalent physically, by the 1st postulate. It is therefore understandable that one in pedagocical representations of SR does not want to invoke such a "stationary" frame: the reader might believe that it is something real, and also: why introdue this concept when it is immediately getting rid of, by concluding that the light speed is the same in all intertial systems (as we did above)?

Still, I think the pedagogicial gain is greater that its difficulties: if one just does not take the "stationary" frame too seriously, and thinks of it as the "ground" or the "laboratory frame" or something like that, it is useful, and it leads to a better understanding of what the 2nd postulate really is about.