Postulate of SR re speed of light

[grzz]

hello
One of the postulates in SR is that the speed of light in vacuum is constant for all observers. Is there a theory in which this is derived and is not a postulate?
Thank you.

 

[pervect]

Maxwell's equations would be such a theory, I think. I assume you've heard of them, if not, ask.

 

[bcrowell]

Pervect has given one possible answer, but to me it's not the best possible answer, since it doesn't really explain why Maxwell's equations have to be the way they are. There is another approach that I like better, which originated with Ignatowsky in 1911, in which the existence of a universal velocity is derived from symmetry of spacetime. The Pal paper is a modern exposition that you can access on the web. Here http://www.lightandmatter.com/html_books/0sn/ch07/ch07.html is my own presentation with minimal mathematics.

W.v.Ignatowsky, Phys. Zeits. 11 (1911) 972
Palash B. Pal, "Nothing but Relativity," Eur.J.Phys.24:315-319,2003, http://arxiv.org/abs/physics/0302045v1

 

[nitsuj]

...in which the existence of a universal velocity is derived from symmetry of spacetime.

brrowell - is that the same as saying "...which the existence of a universal velocity is derived from [the] symmetry [between space & time].

 

[xts]

Is there a theory in which this is derived and is not a postulate?

Historically, Einstein made it a fundamental postulate of Special Relativity, deriving space-time symmetry from it, rather than opposite.

"Zur Elektrodynamik bewegter Körper" ("On the Electrodynamics of Moving Bodies"):

...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, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body.
​

 

[bcrowell]

brrowell - is that the same as saying "...which the existence of a universal velocity is derived from [the] symmetry [between space & time].

No, the symmetry assumed is homogeneity and isotropy.

 

[grzz]

hello all
thanks for the replies ... so far!
Yes, I agree with PERVECT that the speed of light in vacuum is derived to be a constant from Maxwell's Equations. What I really meant was, "Can 'the speed of light in vacuum being constant' be derived from some SINGLE principle?
Now I notice that I should have put my question in a more exact way!

 

[harrylin]

hello
One of the postulates in SR is that the speed of light in vacuum is constant for all observers. Is there a theory in which this is derived and is not a postulate?
Thank you.

In SR it is in fact not a postulate, although many textbooks simplify its derivation to a postulate.

The first postulate is the principle of relativity, and the second postulate is that the speed of light as measured in one reference system is constant, independent of the motion of the source.

From the combination of the first and the second postulate follows that the speed of light in vacuum is constant for all reference systems in uniform motion. You can read it here (as sketched in the intro and defined at the start of section 2):

http://www.fourmilab.ch/etexts/einstein/specrel/www/

Harald

 

[ghwellsjr]

hello
One of the postulates in SR is that the speed of light in vacuum is constant for all observers. Is there a theory in which this is derived and is not a postulate?
Thank you.

In SR it is in fact not a postulate, although many textbooks simplify its derivation to a postulate.

The first postulate is the principle of relativity, and the second postulate is that the speed of light as measured in one reference system is constant, independent of the motion of the source.

From the combination of the first and the second postulate follows that the speed of light in vacuum is constant for all reference systems in uniform motion. You can read it here (as sketched in the intro and defined at the start of section 2):

http://www.fourmilab.ch/etexts/einstein/specrel/www/

Harald

If you look at Einstein's 1905 paper which you referenced, near the end of section 1, you will see this:

In agreement with experience we further assume the quantity

$$\frac{2AB}{t'A-tA} = c,$$​

to be a universal constant—the velocity of light in empty space.​

where t'A is the final time on a clock at A and tA is the start time on the same clock at A and AB is the distance to a mirror. He is affirming the experimental measurement of the round-trip speed of light to be c but this is not his second postulate.

In section 2, he is restating his two postulates where he now calls them principles. The second one is stated as:

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

$$velocity = \frac{light path}{timeinterval}$$​

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

Note that he uses the word "ray" here meaning light traveling in one direction as opposed to a round trip. Notice that he is not saying this is measured. Rather he states that the time interval is according to the definition that he stated in article 1.

So looking back to article 1, you can see where he defines the time interval as being the same for each portion of the round-trip measurement of the speed of light.

So Einstein is postulating that the one way speed of light for both directions of a round-trip measurement are each equal to c.

 

[harrylin]

If you look at Einstein's 1905 paper which you referenced, near the end of section 1, you will see this:

In agreement with experience we further assume the quantity

$$\frac{2AB}{t'A-tA} = c,$$​

to be a universal constant—the velocity of light in empty space.​

where t'A is the final time on a clock at A and tA is the start time on the same clock at A and AB is the distance to a mirror. He is affirming the experimental measurement of the round-trip speed of light to be c but this is not his second postulate.

In section 2, he is restating his two postulates where he now calls them principles. The second one is stated as:

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

$$velocity = \frac{light path}{timeinterval}$$​

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

Note that he uses the word "ray" here meaning light traveling in one direction as opposed to a round trip. Notice that he is not saying this is measured. Rather he states that the time interval is according to the definition that he stated in article 1.

So looking back to article 1, you can see where he defines the time interval as being the same for each portion of the round-trip measurement of the speed of light.

So Einstein is postulating that the one way speed of light for both directions of a round-trip measurement are each equal to c.

Not exactly: he postulates that if we define the time intervals such that the one-way speed equals the round-trip speed (second emphasis his), then the one-way speed of light is equal to c.

That is a complicated way of postulating that the round-trip speed of light is equal to c, and that we won't be able to determine the "true" one-way speed of light wrt our chosen reference system as anything else than c.

In 1907 he reformulated the light postulate as follows (and that really clarified his 1905 paper for me):

"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.
[..this] "principle of the constancy of the velocity of light," is at
least for a coordinate system in a certain state of motion [..] made
plausible by the confirmation through experiment of the Lorentz theory
[1895], which is based on the assumption of an ether that is
absolutely at rest".

- http://www.soso.ch/wissen/hist/SRT/E-1907.pdf

Harald

 

[ghwellsjr]

Not exactly: he postulates that if we define the time intervals such that the one-way speed equals the round-trip speed (second emphasis his), then the one-way speed of light is equal to c.

That is a complicated way of postulating that the round-trip speed of light is equal to c, and that we won't be able to determine the "true" one-way speed of light wrt our chosen reference system as anything else than c.

In 1907 he reformulated the light postulate as follows (and that really clarified his 1905 paper for me):

"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.
[..this] "principle of the constancy of the velocity of light," is at
least for a coordinate system in a certain state of motion [..] made
plausible by the confirmation through experiment of the Lorentz theory
[1895], which is based on the assumption of an ether that is
absolutely at rest".

- http://www.soso.ch/wissen/hist/SRT/E-1907.pdf

Harald

First off, I'd like to thank you for bringing this paper to my attention--I had not previously known of its existence. However, your link is to the original in German but I found one that contains an English translation:

www.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_1907_Jahrbuch.pdf

Now, I don't see that his 1907 paper "reformulated the light postulate". Both papers are saying exactly the same thing which is that only if you take special precautions to synchronize all the clocks in a reference frame will the one-way speed of light be equal to the round-trip speed of light.

I have a lot of trouble with your statement:

That is a complicated way of postulating that the round-trip speed of light is equal to c, and that we won't be able to determine the "true" one-way speed of light wrt our chosen reference system as anything else than c.​

He is never "postulating that the round-trip speed of light is equal to c". Why would or should he do that? That's determined by measurement, not postulating. He, of course, agrees that it is "equal to a universal constant c", but that is not part of his postulate.

And then the rest of your statement, "we won't be able to determine the 'true' one-way speed of light wrt our chosen reference system as anything else than c" is in direct contradiction to what Einstein says elsewhere. We can arbitrarily set the times of the two parts of the round-trip path of light to be something other than equal, but if we do, the principle of "the constancy of the velocity of light" (in all directions) will not be true.

That is what the problem with LET (Lorentz Ether Theory) was. It defined the constancy of the velocity of light to be true only with repect to the absolutely stationary ether. For all other states of motion, the (one-way) velocity of light was not equal to c, although the round-trip speed of light was equal to c. This is because there was only one absolute time for all states of motion and the radical idea of redefining time for each state of motion had not been considered, until Einstein, that is.

Now maybe your point is that there is only one way to have a consistent Theory of Special Relativity which forces us to define the one-way speed of light to be c, and to that I would agree, but my point is that until we recognize Einstein's brilliant insight into making the bold step of having relative time in a theory, there is no a priori reason to define the one-way speed of light to be equal to the universal constant c.

 

[harrylin]

[..] He is never "postulating that the round-trip speed of light is equal to c". Why would or should he do that? That's determined by measurement, not postulating. He, of course, agrees that it is "equal to a universal constant c", but that is not part of his postulate.

Of course "independent of the speed of the source" must be included for the full postulate, sorry if that wasn't clear. And he stressed that the postulate is based on observation. As a matter of fact, both postulates are based on observation - that was important for him to point out. As he formulated it:

"In agreement with experience we further assume the [round trip speed] to be a universal constant—the velocity of light in empty space."

The one-way speed automatically follows from the conventional definition of distant time.

And then the rest of your statement, "we won't be able to determine the 'true' one-way speed of light wrt our chosen reference system as anything else than c" is in direct contradiction to what Einstein says elsewhere. We can arbitrarily set the times of the two parts of the round-trip path of light to be something other than equal, but if we do, the principle of "the constancy of the velocity of light" (in all directions) will not be true.
[..]

If we change the postulate, than the postulate will of course be different.
Einstein's 1907 explanation is crystal clear, adding more words can only make it less clear.

And I merely summarised a recent discussion (one that is ever repeated and should become a FAQ), here, from post #36:

https://www.physicsforums.com/showthread.php?t=512189&page=3

Anyway, all of this is a bit off-topic, but here's an overview of the development at that time:

http://en.wikipedia.org/wiki/Histor...onstancy_and_the_Principle_of_relative_motion

Cheers,
Harald

 

[harrylin]

In this context, the following paper may also be instructive:

http://www.uio.no/studier/emner/matnat/fys/FYS-MEK1110/v06/MythsSpecRelativAJP193.pdf

Cheers,
Harald

 

[ghwellsjr]

Of course "independent of the speed of the source" must be included for the full postulate, sorry if that wasn't clear. And he stressed that the postulate is based on observation. As a matter of fact, both postulates are based on observation - that was important for him to point out. As he formulated it:

"In agreement with experience we further assume the [round trip speed] to be a universal constant—the velocity of light in empty space."

The one-way speed automatically follows from the conventional definition of distant time.

If we change the postulate, than the postulate will of course be different.
Einstein's 1907 explanation is crystal clear, adding more words can only make it less clear.

Let me see if I understand: you are saying that Einstein's second postulate is only about the measured two-way speed of light and excludes the defined one-way speed of light, correct?

I'm saying that the second postulate is about the defined one-way speed of light and not about the measured two-way speed of light.

Is that your understanding of our disagreement?

And I merely summarised a recent discussion (one that is ever repeated and should become a FAQ), here, from post #36:

https://www.physicsforums.com/showthread.php?t=512189&page=3

Here is what you linked to:

No, technology cannot measure the one-way speed of light. It can only measure the round-trip speed of light by the technique I described earlier: one timing device and a mirror a fixed, measured distance away from it, or something equivalent.

If you had all the technology at your disposal, what would you do to measure the one-way speed of light?

That is one of my posts, not yours. But you had plenty of posts on that thread, all of which agreed with me that you cannot measure the one-way speed of light, so I have to conclude that your objection to what I said on this thread was merely over what Einstein meant by his second postulate, correct?

Anyway, all of this is a bit off-topic, but here's an overview of the development at that time:

http://en.wikipedia.org/wiki/Histor...onstancy_and_the_Principle_of_relative_motion

Cheers,
Harald

Now here you provide a link to an article that I recently linked to on another thread that you also posted on:

You might find something of interest here:

http://en.wikipedia.org/wiki/History_of_special_relativity

So again, we agree on lots of things.

 

[harrylin]

Let me see if I understand: you are saying that Einstein's second postulate is only about the measured two-way speed of light and excludes the defined one-way speed of light, correct?

I'm saying that the second postulate is about the defined one-way speed of light and not about the measured two-way speed of light.

Is that your understanding of our disagreement? [..]

Not exactly. This appears to be just a misunderstanding about words.

I think that you agree with Poincare and Einstein that a measurement of the one-way speed of light can be made equal to the two-way speed of light by means of a convenient definition of distant time. And we explained in the other thread why such a free choice can hardly be called a measurement.

- A postulate of physics is a physical claim.
- A definition in physics is a free human choice.

A definition can be used to describe a postulate; however a definition cannot itself be a postulate.

The *physical* content of the second postulate is that the round-trip speed is the same everywhere in all directions and independent of the motion of the source (see section 1: physically there is no difference between that assumption and the definition in section 2).

However, in order to use this physical assumption for equations of motion, a definition for distant "time" is required, and this immediately affects the (apparent) one-way speed of light - sections 1 and 2.

As Poincare explained, the simplest laws are obtained by choosing the one-way speed of light equal to the two-way speed of light.

Einstein summarized that all in 1907 with the simple statement, that we assume that the clocks can be adjusted in such a way that the propagation velocity of every light ray in vacuum becomes everywhere equal to a universal constant c.

As most of this is not on-topic and about everything has been said already, I won't elaborate more.

Cheers,
Harald

 

[ghwellsjr]

Let me see if I understand: you are saying that Einstein's second postulate is only about the measured two-way speed of light and excludes the defined one-way speed of light, correct?

I'm saying that the second postulate is about the defined one-way speed of light and not about the measured two-way speed of light.

Is that your understanding of our disagreement?

Not exactly. This appears to be just a misunderstanding about words.

When there is a misunderstanding about words, an authoritative dictionary is the only way to resolve the problem. You are not entitled to make up your own definition of words that already have accepted meanings and demand that everybody else adhere to them.

I think that you agree with Poincare and Einstein that a measurement of the one-way speed of light can be made equal to the two-way speed of light by means of a convenient definition of distant time. And we explained in the other thread why such a free choice can hardly be called a measurement.

No, I don't agree that Einstein ever said that it is possible to measure the one-way speed of light. I would say it the other way around: Einstein postulated that the speed of light is always c and that fixes the definition of the meaning of distant time in his Theory of Special Relativity. You still can never measure the one-way speed of light, all you're doing is confirming your definition of distant time whenever you perform a so-called measurement of the one-way speed of light.

- A postulate of physics is a physical claim.
- A definition in physics is a free human choice.

A definition can be used to describe a postulate; however a definition cannot itself be a postulate.

What dictionary did you get these ideas from?

All I know is that every reference I can find all agree that a postulate is something that is not proven.

The *physical* content of the second postulate is that the round-trip speed is the same everywhere in all directions and independent of the motion of the source (see section 1: physically there is no difference between that assumption and the definition in section 2).

Section 1 of Einstein's 1905 paper discusses both the definition of distant time based on the one-way speed of light and later the round-trip speed of light towards the end of section 1 which does not depend on that definition. He is stating that the value of c, "a universal constant--the velocity of light in empty space" is measured by means of experience and has the value of twice the distance between the light source/detector and the mirror some fixed distance away, divided by the time interval for the light to traverse the round trip. No definition here. No postulate here. It's a pure measurement. But he's adding that this measured value of c is also the unmeasureable speed of every ray of light in his Theory of Special Relativity. That's the postulate. And the definition of distant time comes out of that postulate. And so it's legitimate to say that the one-way speed of light is defined to be c or stipulated to be c or assumed to be c or postulated to be c, merely to emphasize that it is not measured, not observed, not seen and not proved, nor can it ever be measured, observed, seen or proved.

However, in order to use this physical assumption for equations of motion, a definition for distant "time" is required, and this immediately affects the (apparent) one-way speed of light - sections 1 and 2.

Here again, I must go to the dictionary to understand what you mean here by "apparent". It always implies something that is seen and so I would have to disagree. We cannot observe the one-way speed of light. So here is how I would rather say what Einstein is saying in sections 1 and 2: the postulate of all light rays (one-way) propagating at c leads us to a definition of distant time that forms the basis of the Theory of Special Relativity in which we can consistently use that definition of distant time in conjunction with the first postulate of SR.

As I said before, at the beginning of section 2 he specifically repeats his two postulates saying "we define as follows:" and proceeds for his second postulate to refer to a ray of light giving the definition of its velocity in terms of his previous definition of distant time. I just don't know how you can continue to say that the second postulate is only about the measured round-trip speed of light and not about the defined one-way speed of light.

As Poincare explained, the simplest laws are obtained by choosing the one-way speed of light equal to the two-way speed of light.

Einstein summarized that all in 1907 with the simple statement, that we assume that the clocks can be adjusted in such a way that the propagation velocity of every light ray in vacuum becomes everywhere equal to a universal constant c.

Fine, like I said before, his 1907 paper is in complete agreement with his 1905 paper and adds nothing new.

As most of this is not on-topic and about everything has been said already, I won't elaborate more.

Cheers,
Harald

I think it is on-topic and I think you really ought to reconsider your position after you study my posts and study Einstein's 1905 paper or his 1907 paper or his 1920 book. They all say the same thing.

 

[harrylin]

[..] I think you really ought to reconsider your position after you study my posts and study Einstein's 1905 paper or his 1907 paper or his 1920 book. They all say the same thing.

After studying those (partly in the original* German) as well as many other of his papers and commentaries, I paraphrased and cited from them here in this thread.

Both postulates of SR are can be put to the test; it was only long after after 1905 that the independence of the speed of light of the motion of the source could be directly verified (and still not to high accuracy in all directions).

Anyway: happily we both agree with Einstein that we can adjust our clocks in such a way that the one-way speed of light becomes equal to the roundtrip speed of light, which is assumed to be a universal constant, independent of the motion of the source.

Note that with GRT the here intended meaning of "universal constant" turned out to be partly incorrect; consequently the field of application of SR was reduced, just as the field of application of Newtonian mechanics had been reduced with SR. He also explained that in his popular 1920 book:
- http://www.bartleby.com/173/22.htmlHarald

*translations sometimes contain inaccuracies and errors; in particular those of the 1907 paper

PS. "apparent" has in physics meaning no.3:
http://dictionary.reference.com/browse/apparent
See also:
http://dictionary.reference.com/browse/appearance

 

[harrylin]

I also noticed a misunderstanding in an earlier post. After I linked to:

http://en.wikipedia.org/wiki/Histor...onstancy_and_the_Principle_of_relative_motion ,

[..] Now here you provide a link to an article that I recently linked to on another thread that you also posted on: [..]
So again, we agree on lots of things.

You may have linked to it yourself; nevertheless your claim:

"my point is that until we recognize Einstein's brilliant insight into making the bold step of having relative time in a theory, there is no a priori reason to define the one-way speed of light to be equal to the universal constant c."

is contradicted by the facts that are discussed in the section to which I gave the link; which is why I suggested that you read it.Harald