Constancy of c - second postulate

harrylin

There are quite different things called "Einsteinian relativity": his philosophy and his theories of physics, and those are often mixed up - although his philosophy is perhaps not well understood and it certainly changed over time.

For example, Ives was a physicist who claimed to reject SR - until he apparently realised that what he rejected was not really the theory itself but a popular interpretation of the theory which he deemed inconsistent. In one of his later papers he even re-derived SR, using other postulates (Maxwell + conservation laws). That could be instructive.

ghwellsjr

There are plenty of experiments that confirm PoR, Einstein's first postulate. There are plenty of experiments that confirm the round-trip speed of light is equal to c.
There are no experiments that violate Einstein's second postulate because they cannot measure the one-way speed of light.
The purpose of this forum is to learn relativity, not to try to find ways to disprove it.
Can you tell me what the meaning of "event" is in the context of Special Relativity?

mangaroosh

Surely a good way to learn it is to subject it to critical questioning without any bias as to the outcome?

I probably can't give the exact definition, and my terminology may not be exact, but roughly I think it refers to anything that to which 3 spatial and a temporal co-ordinate can be assigned in a given frame of reference; for example, the striking of a pole by lightning can be assigned 4 co-ordinates (the point of impact that is - another location on the pole would have a different spatial co-ordinate - and possibly temporal depending on the size of the pole).

These co-ordinates can then be mathmatically transformed to give the co-ordinates of the same event from the perspective of a different reference frame.

DaleSpam

There is no such thing as "without any bias". SR goes against both our hard-wired nervous system and against our Newtonian training. Every student is biased against SR (including myself).

The best way to learn it is:
1) do homework problems so that you understand how it actually works (i.e. so that you don't mistakenly think that SR claims something it does not)
2) read the experimental evidence for and against it

ghwellsjr

Good, but why did you say that another location on the pole might have a different temporal coordinate depending on the size of the pole?

mangaroosh

In the context of the lightning pole it mightn't make sense, but if the pole was enormous say, such that one end was higher up in the gravitational potential, then time would run at different rates at either end of the pole - I've heard it, somewhat lightheartedly said, that the time at our head and our feet is slightly different .

mangaroosh

The thing I have trouble with is trying to relate the maths to the physical, real world phenomena, which is why I find it helpful to discuss the physical phenomena and see what is being claimed.

ghwellsjr

Tell me what you know about this mathematical transform, please.

DaleSpam

That is precisely the value of homework problems, and one reason why I recommend it as the best way to learn.

mangaroosh

I'm a bit sketchy on this, I think I've got a general understanding of it but not a technically detailed one.

My understanding is that it is a means of translating the co-ordinates of an event in one reference frame into the co-ordinates of another. The scaling factor gamma, or Lorentz factor is involved.

I don't know the technical details of the formula, but what I've encountered suggests that it can be derived using the Pythgorean theorem - as per the video explanation I posted (in this thread I think it was).

rjaindia

I think there is only one postulate...that of relativity....that all observers in an inertial frame will find all phenomena to be described by the same equations....from this obviously it follows that the velocity of light has to be constant for all observers...otherwise relativity will not hold...
Hence really there is only ONE postulate...that of relativity...the other (constancy of the velocity of light) is a corollary of it....

DaleSpam

Hi rjaindia, welcome to PF!How so? It is not so obvious to me.

ghwellsjr

We're talking about the Lorentz Transform and there are actually two formulas (really four but the other two are trivial), one for the new time coordinate and one for the new x-coordinate, and both are functions of the old time coordinate, the x-coordinate, and the speed difference between the old frame and the new frame. They are really very simple, especially if you use compatible units where c=1. I'm assuming, like everyone else, that you only doing the standard convention.

But the reason I asked is because there is no provision for gravity in the Lorentz Transform or in Special Relativity. We pretend like the effects gravity don't exist when we're doing transforms in SR so you don't need to worry about how time is effected by height.

ghwellsjr

The constancy of the measured two-way velocity of light is covered under the first postulate, which is the principle of relativity--not Special Relativity. The second postulate concerns the one-way speed of light or the propagation of light which cannot be measured but is defined to be the same as the two-way velocity of light. It takes both of these postulates, the principle of relativity and the constancy of the propagation of light, in order to get Special Relativity, according to Einstein.

harrylin

No, the second postulate is not that the speed of light is the same for all observers; and it's not a corollary of the first postulate, but it is in apparent contradiction with it.

See my earlier posts in this thread:
http://physicsforums.com/showthread.php?p=3742805 #29
http://physicsforums.com/showthread.php?p=3187482 #2

DaleSpam

How so?

DrGreg

The second postulate asserts that, within any single inertial frame, the one-way speed of light is a constant value. (So it doesn't depend on the motion of the source or the direction of propagation.) It doesn't assert that the constant value is the same in every frame, but that is something that follows from the first postulate (otherwise you would have a method for distinguishing one frame from another). So to obtain the invariance of the speed of light in all frames you need both postulates.

The second postulate (without the first postulate) implies that, within any single inertial frame,

1. the two-way speed of light is constant (something we can confirm or falsify by experiment)
2. we will, by convention, use a clock-synchronisation method to make the one-way speed of light equal the two-way speed (a definition, once (a) is assumed)