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Constancy of c - second postulate

by mangaroosh
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ghwellsjr
#73
Feb16-12, 07:39 AM
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Quote Quote by mangaroosh View Post
Quote Quote by ghwellsjr View Post
Can you tell me what the meaning of "event" is in the context of Special Relativity?
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.
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
#74
Feb16-12, 07:49 AM
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Quote Quote by ghwellsjr View Post
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?
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
#75
Feb16-12, 07:55 AM
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Quote Quote by DaleSpam View Post
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
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
#76
Feb16-12, 08:51 AM
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Quote Quote by mangaroosh View Post
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.
Tell me what you know about this mathematical transform, please.
DaleSpam
#77
Feb16-12, 08:54 AM
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Quote Quote by mangaroosh View Post
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.
That is precisely the value of homework problems, and one reason why I recommend it as the best way to learn.
mangaroosh
#78
Feb19-12, 07:28 PM
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Quote Quote by ghwellsjr View Post
Tell me what you know about this mathematical transform, please.
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
#79
Mar10-12, 12:20 PM
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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
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Mar10-12, 05:22 PM
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Hi rjaindia, welcome to PF!
Quote Quote by rjaindia View Post
from this obviously it follows that the velocity of light has to be constant for all observers...otherwise relativity will not hold
How so? It is not so obvious to me.
ghwellsjr
#81
Mar10-12, 06:18 PM
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Quote Quote by mangaroosh View Post
Quote Quote by ghwellsjr View Post
Tell me what you know about this mathematical transform, please.
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).
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
#82
Mar10-12, 06:24 PM
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Quote Quote by rjaindia View Post
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....
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
#83
Mar11-12, 04:23 AM
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Quote Quote by rjaindia View Post
[..] Hence really there is only ONE postulate...that of relativity...the other (constancy of the velocity of light) is a corollary of it....
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
#84
Mar11-12, 05:58 AM
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Quote Quote by ghwellsjr View Post
The constancy of the measured two-way velocity of light is covered under the first postulate
How so?
DrGreg
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Mar11-12, 12:14 PM
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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)
ghwellsjr
#86
Mar12-12, 02:26 AM
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Quote Quote by DaleSpam View Post
Quote Quote by ghwellsjr View Post
The constancy of the measured two-way velocity of light is covered under the first postulate
How so?
In his 1905 paper, near the end of section 1, Einstein makes the following statement:
In agreement with experience we further assume the quantity
to be a universal constant—the velocity of light in empty space.
He's talking about the measured round-trip speed of light. "A" is the location of the clock, "B" is the location of the mirror, so "2AB" is the round-trip distance the light has to travel, "tA" is the time the light starts from the clock at "A" and "t'A" is the time the reflection arrives back at the clock at "A", and the calculation, by experience always yields c no matter what was the inertial state of motion under which the measurement was made.

This was the measurement that lead to the Lorentz Transformation as the basis for the new Principle of Relativity because the old one based on the Galilean Transformation didn't work any more. In the Lorentz Ether Theory, the presumed second postulate was that light propagated at c only in one absolute ether rest state but due to length contraction and time dilation, the measured round-trip speed of light always came out the same even when the experiment was done in motion through the ether.

When Einstein proposed his second postulate, it was a follow-on to the first one and he noted that it was apparently irreconcilable with the first one because it seemed impossible that light could make both parts of the trip in the same amount of time under differing states of inertial motion in any measurement of the round-trip speed of light.

Quote Quote by DrGreg View Post
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)
Here's Einstein's first formulation of the second postulate from the introduction of his paper:
light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body
And here is his second formulation of the second postulate from the beginning of section 2:
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.
Note that in both of these formulations, Einstein specifically states that the speed is c, the same as the measured round-trip speed of light.

However, Einstein calls this second postulate "the principle of the constancy of the velocity of light", which I presume is the same as "the invariance of the speed of light", as you called it. I would repeat that the second postulate is a follow-on to the first one in which the value of the speed of light has already been "determined" (as Einstein says) to be c and so I agree with your two-part summary but I would say that (a) is part of the first postulate and (b) is the second postulate.

It is obvious from Einstein's elaboration of the second postulate in section 2 that he is excluding the two-way speed of light from it since he calls it a "ray" of light and defines its velocity as:
where the time interval is one-half of the measured round-trip interval.
harrylin
#87
Mar12-12, 03:21 AM
P: 3,184
Quote Quote by DrGreg View Post
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)
Yes, that is exact.
Recycling in part my post #29, that directly follows from Einstein's 1907 formulation of the second postulate:

"We [...] assume that the clocks can be adjusted in such a way that
the propagation velocity of every light ray in vacuum - measured by
means of these clocks - becomes everywhere equal to a universal
constant c, provided that the coordinate system is not accelerated."

As we discussed in the past, for this to be possible the two-way speed must be the same in all directions.
harrylin
#88
Mar12-12, 03:34 AM
P: 3,184
Quote Quote by ghwellsjr View Post
[..] Einstein calls this second postulate "the principle of the constancy of the velocity of light", which I presume is the same as "the invariance of the speed of light" [..]
George, please take note that with "invariant" people do not mean the same as "constant".

See my post #132 here:
http://physicsforums.com/showthread....ight=invariant

Best regards,
Harald
DaleSpam
#89
Mar12-12, 07:51 AM
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Quote Quote by ghwellsjr View Post
In his 1905 paper, near the end of section 1, Einstein makes the following statement:

He's talking about the measured round-trip speed of light. "A" is the location of the clock, "B" is the location of the mirror, so "2AB" is the round-trip distance the light has to travel, "tA" is the time the light starts from the clock at "A" and "t'A" is the time the reflection arrives back at the clock at "A", and the calculation, by experience always yields c no matter what was the inertial state of motion under which the measurement was made.

This was the measurement that lead to the Lorentz Transformation as the basis for the new Principle of Relativity because the old one based on the Galilean Transformation didn't work any more. In the Lorentz Ether Theory, the presumed second postulate was that light propagated at c only in one absolute ether rest state but due to length contraction and time dilation, the measured round-trip speed of light always came out the same even when the experiment was done in motion through the ether.

When Einstein proposed his second postulate, it was a follow-on to the first one and he noted that it was apparently irreconcilable with the first one because it seemed impossible that light could make both parts of the trip in the same amount of time under differing states of inertial motion in any measurement of the round-trip speed of light.
Yes, I understand all of that, but that was not what I was asking. I was asking how the constancy of the measured two-way velocity follows from the first postulate as you claimed. Einstein did the definition of simultaneity using the two-way speed of light in the section before introducing his postulates, so it is not clear to me how the claim follows merely from the first postulate. I certainly don't see anything to that effect in his writing.
harrylin
#90
Mar12-12, 11:31 AM
P: 3,184
Quote Quote by DaleSpam View Post
[..] it is not clear to me how the claim follows merely from the first postulate. I certainly don't see anything to that effect in his writing.
It's quite the contrary. The PoR is perfectly consistent with Galilean relativity and the issue was how to combine Maxwell's laws with the PoR.

Harald


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