Constancy of c - second postulate

[mangaroosh]

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.

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

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.

 

[Dale]

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

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]

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]

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]

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]

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.

 

[Dale]

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]

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]

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...

 

[Dale]

Hi rjaindia, welcome to PF!

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]

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]

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]

[..] 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:
https://www.physicsforums.com/showthread.php?p=3742805 #29
https://www.physicsforums.com/showthread.php?p=3187482 #2

 

[Dale]

The constancy of the measured two-way velocity of light is covered under the first postulate

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,

• the two-way speed of light is constant (something we can confirm or falsify by experiment)
• 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]

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, "t_A" 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.

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,

• the two-way speed of light is constant (something we can confirm or falsify by experiment)
• 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]

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,

• the two-way speed of light is constant (something we can confirm or falsify by experiment)
• 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]

[..] 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:
https://www.physicsforums.com/showthread.php?t=575332&page=9&highlight=invariantHarald

 

[Dale]

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, "t_A" 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]

[..] 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

 

[John232]

https://www.youtube.com/watch?v=DRDN7ceu6UU

Wow, this video is amazing, they actually solve for the Lorentz and assigned the time vairables correctly in the light clock experiment like I mentioned in another thread. Every other source I have seen on this doesn't. Guess you can't win them all.

I would have to say that Newton rigged physics to allow the equation of velocity to work for light, he did this by dividing the amount of length something traveled by the amount of time it traveled. It's funny people say Einstein overturned Newtonian Physics, but to start out he had to use this same equation to do it.

Say you drew the line of velocity on a coordinate plane, the line is true from -∞ to ∞. If you draw out the function for the lorentz transform on a coordinate plane, it has a hole at c. At the hole the two sides of the triangle become the same line, this line then gives the same values for spacetime dialation, so then you get your original equation for velocity. The concept of v=d/t may be more true for light than it is for anything else in the known universe.

You could show this by drawing where these two functions intersect at v=c. The Lorentz Transformation isn't true, but the velocity equation is true at this point.

 

[Dale]

The Lorentz Transformation isn't true, but the velocity equation is true at this point.

Then kindly explain the outcome of each of these experiments without using the Lorentz transform or formulas derived from it:
http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

 

[ghwellsjr]

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, "t_A" 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.

Before developing the definition of simultaneity, Einstein said in the introduction of his 1905 paper:

...unsuccessful attempts to discover any motion of the Earth relatively to the “light medium,” suggest that the phenomena of electrodynamics as well as of mechanics possesses no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate...

I assumed that he was talking about such experiments as MMX which compared the two-way speed of light along two paths at right angles to each other and established them to be the same.

 

[Dale]

Before developing the definition of simultaneity, Einstein said in the introduction of his 1905 paper:

I assumed that he was talking about such experiments as MMX which compared the two-way speed of light along two paths at right angles to each other and established them to be the same.

Sure, that gives some historical background that the measured invariance of the two way speed of light was already experimentally established. It does not support your claim that said invariance follows from the first postulate.

 

[ghwellsjr]

Sure, that gives some historical background that the measured invariance of the two way speed of light was already experimentally established. It does not support your claim that said invariance follows from the first postulate.

It's not my claim, I got it from Einstein.

If experiments indicated that the measured speed of light was not the same under different inertial states, wouldn't that disprove the Principle of Relativity? Isn't that what Maxwell thought his equations would lead to?

 

[Dale]

It's not my claim, I got it from Einstein.

For brevity let's use the abbreviation 2C for the statement that the measured two way speed of light is invariant. I see in the introduction Einstein's statements that 2C was an established experimental fact in his mind. After he introduced the two postulates 2C clearly follows from the second postulate. I don't see anywhere where he shows that the first postulate alone is sufficient to show 2C.

 

[ghwellsjr]

For brevity let's use the abbreviation 2C for the statement that the measured two way speed of light is invariant. I see in the introduction Einstein's statements that 2C was an established experimental fact in his mind. After he introduced the two postulates 2C clearly follows from the second postulate. I don't see anywhere where he shows that the first postulate alone is sufficient to show 2C.

Whenever Einstein discusses the second postulate, he always specifically refers to 1C and not 2C. He always uses terms like "propagation of light" or "a ray of light" or "how light travels" or "the progress of light" or "tracking light" or other similar terms. The point about 2C is that it establishes the universal constant value of c, the speed of light, a value that needs to be determined before the second postulate can be introduced. The second postulate does not say anything about the value of c or how to determine it or even what its value is. Instead, it establishes that the two portions of the round-trip measurement of the speed of light (whatever that is) takes the same amount of time in either direction.

 

[Dale]

Yes, I understand the relationship between 2C and 1C and I understand that the second postulate refers to 1C. That is not a point of disagreement.

I can see how you can easily arrive at 2C from only the second postulate. I cannot see how you can arrive at 2C from only the first postulate. That is the point of disagreement, and so far nothing you have shown even remotely resembles proof of that point.

I am not looking for more quotes from Einstein's OEMB, I am looking for a clear derivation that starts only with the first postulate and arrives at 2C. It is not in OEMB.

 

[ghwellsjr]

Yes, I understand that you can easily arrive at 2C from only the second postulate. That is not a point of disagreement.

I won't give you more quotes from Einstein's OEMB, but I will repeat some that I quoted earlier and provide your responses and then you can explain to me why you don't think Einstein was claiming that 2C comes out of the first postulate and does not require the second postulate. And I would like answers to my previous questions that you ignored.

Ok, here's the quote from the introduction:

...unsuccessful attempts to discover any motion of the Earth relatively to the “light medium,” suggest that the phenomena of electrodynamics as well as of mechanics possesses no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate...

to which you replied:

Sure, that gives some historical background that the measured invariance of the two way speed of light was already experimentally established.

and:

I see in the introduction Einstein's statements that 2C was an established experimental fact in his mind.

So if he wasn't talking about 2C when he said (previously quoted in post #86):

In agreement with experience we further assume the quantity c to be a universal constant—the velocity of light in empty space.

then what "laws of electrodynamics and optics" was he referring to when he conjectured they "will be valid for all frames of reference for which the equations of mechanics hold good"?

And finally, I would appreciate answers to my previous questions:

If experiments indicated that the measured speed of light was not the same under different inertial states, wouldn't that disprove the Principle of Relativity? Isn't that what Maxwell thought his equations would lead to?

 

[Dale]

I will repeat some that I quoted earlier and provide your responses and then you can explain to me why you don't think Einstein was claiming that 2C comes out of the first postulate and does not require the second postulate.

I don't think that he was claiming that 2C comes out of the first postulate alone because none of those quotes are even a vague outline of a proof that 2C comes out of the first postulate.

If experiments indicated that the measured speed of light was not the same under different inertial states, wouldn't that disprove the Principle of Relativity?

Not necessarily. The alternative is that Maxwells equations as written are not a law of nature, and that the real laws of electrodynamics were Galilean invariant.

Isn't that what Maxwell thought his equations would lead to?

I have no idea what Maxwell thought.

I have revisited the quotes and answered your questions, now answer mine: Can you or can you not provide a proof that 2C follows from the first postulate alone? I am not interested in history nor expert opinion (even Einstein's), either there is such a proof or there is not such a proof. To me the reasoning doesn't seem sound. I see no way to start only with the first postulate alone and follow a logical chain to get 2C

 

[harrylin]

[..] The alternative is that Maxwells equations as written are not a law of nature, and that the real laws of electrodynamics were Galilean invariant. [...]

Exactly, as I also mentioned - that is what Newton's theory of light had, and probably also Ritz's theory was Galilean invariant. The issue was how to match Maxwell's theory with the PoR.

Cheers,
Harald

PS: Maxwell thought that the speed of light was Galilean invariant in the same way as sound (to good approximation): that is also a law of nature, but it is expressed as the velocity relative to the medium.