The Single Postulate for SR

[geordief]

"The Lorentz transformations, up to a nonnegative free parameter, can be derived without first postulating the universal lightspeed. "

https://en.m.wikipedia.org/wiki/Special_relativity_(alternative_formulations)

 

When I read through this link it is not clear to me how this is shown.

Clearly c is the central feature of the Lorentz Transformations ; so  is the above quote saying that the invariance of c   is not postulated (but that a light speed is) ?

If those  Lorentz Transformations  are derived w/o "first postulating a universal light speed" what does c actually stand for?

[studiot]

 

6 hours ago, geordief said:

so  is the above quote saying that the invariance of c   is not postulated

No it is saying that if you take the results of an experimental measurement as one of your axoims you can reduce the number of theoretical axioms.

The idea of theoretical Physics is that it tries to answer the question, "Whys did we obtain that particular measurement and not a different one ?"
Theoretical Physics may have some of its inquiries promted by the results of experiment, but it also like to use experiment to confirm predictions.
You can't use an experiment both as an axiom and as a confirmation.

This is much the same comment I am making in the current trhead on SR.

[geordief]

7 minutes ago, studiot said:

 

No it is saying that if you take the results of an experimental measurement as one of your axoims you can reduce the number of theoretical axioms.

The idea of theoretical Physics is that it tries to answer the question, "Whys did we obtain that particular measurement and not a different one ?"
Theoretical Physics may have some of its inquiries promted by the results of experiment, but it also like to use experiment to confirm predictions.
You can't use an experiment both as an axiom and as a confirmation.

This is much the same comment I am making in the current trhead on SR.

Well, that Wikipedia page just previously  says "The real question here is whether universal lightspeed can be deduced rather than assumed"

 

I have already made enquiries elsewhere as to whether this (well the Universal Speed Limit,which might cover it)  might be possible  

https://www.physicsforums.com/threads/is-the-case-for-a-universal-speed-limit-experimental-or-theoretical.973679/page-2#post-6197363

 

and came away with the impression that the attempt I was looking at *only seemed to work (if it did) for Galilean Relativity.

 

So would I be right to be sceptical as to  the validity of the Single Postulate for now? 

 

*https://arxiv.org/pdf/physics/0302045.pdf

 

 

[studiot]

4 hours ago, geordief said:

So would I be right to be sceptical as to  the validity of the Single Postulate for now? 

 

Quote

The Lorentz transformations, up to a nonnegative free parameter, can be derived without first postulating the universal lightspeed.

Hmm a bit of a copout for someone deducing basic theory from fundamental axioms dont' you think ?

Quote

Experimental results rule out the validity of the Galiliean transformations.

Another copout. Why does it rule these out?

Quote

Given a maximal speed V

'Given' is another word for axiom or postulate.

[Eise]

geordief,

Maybe Brian Cox, Why does E=mc²? is an interesting book for you. With a minimum of mathematics is makes plausible that:

• there is a cosmic speed limit
• that it turns out that this speed limit is the speed of light

Of course it is not mathematically rigorous, but I think it is good enough.

[Eise]

What I personally do not understand is why it even needs the second postulate. Doesn't it follow logically from the first?

The first postulate says, simplified (hopefully not too much simplified...) that in a 'closed laboratory', i.e. where it is not possible to 'look outside' , there is no experiment that tells you that you are moving. That means all laws of nature are exactly the same, including electromagnetism. Doesn't it follow that in a laboratory in an inertial frame one should always measure c for the velocity of light? If this were not the case, one could do a Michelson-Morley kind of experiment to determine one is moving.

[swansont]

53 minutes ago, Eise said:

What I personally do not understand is why it even needs the second postulate. Doesn't it follow logically from the first?

The first postulate says, simplified (hopefully not too much simplified...) that in a 'closed laboratory', i.e. where it is not possible to 'look outside' , there is no experiment that tells you that you are moving. That means all laws of nature are exactly the same, including electromagnetism. Doesn't it follow that in a laboratory in an inertial frame one should always measure c for the velocity of light? If this were not the case, one could do a Michelson-Morley kind of experiment to determine one is moving.

c could be be a constant but not invariant and that would fit within "the laws of physics work the same in any inertial frame." It would just have to be different laws. Those laws may have to have a dependence on your absolute speed.

 

[studiot]

The relativity chapters in this (free) E- book might help

https://static1.squarespace.com/static/544a8c3de4b03e16957ae263/t/54b6d789e4b0a3e130d1e7cc/1421268873531/Nolan_Modern_Physics.pdf

This 2019 book comes from Peter Nolan's lectures at NewYork state college a couple of years ago and has lots of useful background and diagrams not usually offered.

[Eise]

4 hours ago, swansont said:

c could be be a constant but not invariant and that would fit within "the laws of physics work the same in any inertial frame." It would just have to be different laws. Those laws may have to have a dependence on your absolute speed.

Sorry, I still have some problems with the terms 'invariant' and 'constant'. What is the difference, and how is this relevant for my example? If the speed of light would just be a constant, how would that effect my MM-experiment in my 'closed laboratory'? Could I then conclude from some experiment that my laboratory is moving?

E.g. would I find the same Maxwell laws as an observer in rest, with a different value of c, or would I find different laws (with maybe the same value of c)?

Could you elaborate a little?

[studiot]

26 minutes ago, Eise said:

Sorry, I still have some problems with the terms 'invariant' and 'constant'.

A circle is the locus of the path swept out by the end of a rotating arm of constant radius.

But that radius, though constant is not invariant; I can trace out different circles, spirals etc by altering the arm length (radius).
 

 

 

[swansont]

49 minutes ago, Eise said:

Sorry, I still have some problems with the terms 'invariant' and 'constant'. What is the difference, and how is this relevant for my example? If the speed of light would just be a constant, how would that effect my MM-experiment in my 'closed laboratory'? Could I then conclude from some experiment that my laboratory is moving?

E.g. would I find the same Maxwell laws as an observer in rest, with a different value of c, or would I find different laws (with maybe the same value of c)?

Could you elaborate a little?

Constant means the same in one reference frame. Invariant means the same in all reference frames.

Energy, for example, is conserved — pick a frame and the value will not change. But it is not invariant — it can have a different value in another frame. (KE being an obvious example of this)

The rule that energy is conserved is the same, even though the value doesn't have to be. Constancy/conservation does not imply invariance.

[Eise]

Thanks, Swansont, clear and concise. 

But I am afraid I still need a little help to see the consequences for experiments in the 'closed laboratory'. Rephrased: doesn't the invariance of the speed of light follow from the requirement that the laws of physics are exactly the same in every inertial frame?

Say, I do experiments like the ones Faraday did, and I experimentally determine the strength of magnetic and electrical fields: based on the first postulate alone, I would say I cannot conclude that I am moving in relation to some absolute frame of reference. That means I would find the same values for u₀ and e₀ as in an absolute frame of reference. And then with Maxwell I can calculate the speed of light. And then, to think my point to the end, if I actually measure the speed of light, and find a different value than the calculated one I can only conclude that one of my presuppositions is false:

• u₀ and e₀ are dependent on my speed relative to an absolute frame of reference
• In my 'Maxwell theory' I have not accounted for my speed relative to an absolute frame of reference

But both are in contradiction with the first postulate. So why I need the second postulate? Doesn't it follow from the first?

[studiot]

3 hours ago, Eise said:

But I am afraid I still need a little help to see the consequences for experiments in the 'closed laboratory'. Rephrased: doesn't the invariance of the speed of light follow from the requirement that the laws of physics are exactly the same in every inertial frame?

 

That's a fair question to consider so let's try.

Suppose we do without the second postulate.
What are the logical consequences?
 

Why should light behave in any way differently from sound or rockets or other physical entities in motion?
If that were the case then would that contravene the principle of relativity or are the two principles independent?

The short answer is no it would not because they are independent.

Einstein himself realised this and noted

Quote

1905 paper top of page 6

We now have to prove that any ray of light, measured in the moving system, is propagated with the velocity c, if, as we have assumed, this is the case in the stationary system; for we have not yet furnished any proof that the principle of constancy of the velocity of light is compatible with the principle of relativity.

It is this meticulous checking through the logic, here and elsewhere in the paper, that makes Einstein's derivation longer than most modern ones.

Naturally he then goes on to prove the compatibility of the two axioms.

 

Remember that the principle of relativity was not revolutionary and had long been known.

It was the second (light) principle that was the breakthrough.
 

Does this help?

[swansont]

5 hours ago, Eise said:

Thanks, Swansont, clear and concise. 

But I am afraid I still need a little help to see the consequences for experiments in the 'closed laboratory'. Rephrased: doesn't the invariance of the speed of light follow from the requirement that the laws of physics are exactly the same in every inertial frame?

It follows from knowing what those laws are, i.e. there is experimental data which requires it. But it does not follow from just that basic requirement. We had theories with an aether and potentially a variable speed of light, but the physics equations didn't necessarily have to be different in different frames. 

 

Quote

Say, I do experiments like the ones Faraday did, and I experimentally determine the strength of magnetic and electrical fields: based on the first postulate alone, I would say I cannot conclude that I am moving in relation to some absolute frame of reference. That means I would find the same values for u₀ and e₀ as in an absolute frame of reference. And then with Maxwell I can calculate the speed of light. And then, to think my point to the end, if I actually measure the speed of light, and find a different value than the calculated one I can only conclude that one of my presuppositions is false:

• u₀ and e₀ are dependent on my speed relative to an absolute frame of reference
• In my 'Maxwell theory' I have not accounted for my speed relative to an absolute frame of reference

But both are in contradiction with the first postulate. So why I need the second postulate? Doesn't it follow from the first?

These are experimental results that tell us the rules in our universe. The postulate for relativity has to be applied before you know the form of any of the laws, or values of any constants. 

 

edit: We don't, for example, have any requirement that the speed of sound be an invariant. One might wonder why that is, if the laws of physics having to be the same in all frames has some implications on wave propagation speed.

[geordief]

 

2 hours ago, studiot said:

Why should light behave in any way differently from sound or rockets or other physical entities in motion?
If that were the case then would that contravene the principle of relativity or are the two principles independent?

The short answer is no it would not because they are independent.

Einstein himself realised this and noted

Quote

1905 paper top of page 6

We now have to prove that any ray of light, measured in the moving system, is propagated with the velocity c, if, as we have assumed, this is the case in the stationary system; for we have not yet furnished any proof that the principle of constancy of the velocity of light is compatible with the principle of relativity.

It is this meticulous checking through the logic, here and elsewhere in the paper, that makes Einstein's derivation longer than most modern ones.

Naturally he then goes on to prove the compatibility of the two axioms.

 

I have ordered that 1916 Popular Exposition book you recommended in the other recent thread.

https://www.scienceforums.net/topic/120443-another-way-of-looking-at-special-relativity/?do=findComment&comment=1122355

Might I expect to find ,in that book  the same reasoning(on this particular subject)  laid out as in that 1905 paper or might it be "simplified" as the title might lead one to expect?

 

Edited November 13, 2019 by geordief

[studiot]

31 minutes ago, geordief said:

 

I have ordered that 1916 Popular Exposition book you recommended in the other recent thread.

https://www.scienceforums.net/topic/120443-another-way-of-looking-at-special-relativity/?do=findComment&comment=1122355

Might I expect to find ,in that book  the same reasoning(on this particular subject)  laid out as in that 1905 paper or might it be "simplified" as the title might lead one to expect?

 

You will get considerably more than that, depending upon the actual edition you buy.

[geordief]

Thanks.I notice where he says in the preface "Physical objects are not in space but...... spatially extended"

 

 

Look forward to the delivery of this book next week.

 

Have to laugh though at the idea of  "a few happy hours of suggestive thought".. it takes me a good week to read any book at all,let alone this one.

 

edit:it is a 1954 edition

Edited November 13, 2019 by geordief