Proving 2nd Postulate of SR: Michelson-Morley Experiment

[ratn_kumbh]

2nd postulate of SR says that speed of light is constant in all inertial frames. And it exlains all SR. but How to prove this? I have seen that michelson-morley experiment can be explained by this. Is this exp is only reason?

 

[Ich]

Have a look at http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html" .

 

[blumfeld0]

Why is it difficult to test length contraction in SR?
I don't see any experiements on that.

 

[rbj]

Why is it difficult to test length contraction in SR?
I don't see any experiements on that.

i seem to remember a mu-meson decay experiment that can be viewed as two ways. either (from our perspective) the clocks of the mu-mesons have been slowed down due to time dilation or (from the mu-meson's perspective) the distance between the Earth's surface and the bottom of the mineshaft has been decreased due to length contraction.

 

[Aether]

2nd postulate of SR says that speed of light is constant in all inertial frames. And it exlains all SR. but How to prove this? I have seen that michelson-morley experiment can be explained by this. Is this exp is only reason?

The michelson-morley experiment proves that the two-way (round-trip) speed of light is the same for every direction, but there is no experiment that can prove this for the one-way speed of light. The standard formulation of SR comprises this "2nd postulate of SR" only because it makes practical calculations very simple; and not because there is any empirical basis for it at all. The empirical content of SR is not dependent on this postulate at all.

 

[K.J.Healey]

What do you mean by "prove"? If you start with some EM equations, Maxwell's, you find the wave equation which gives you the EM wavespeed as a constant (with respect to frames).

 

[cesiumfrog]

Why is it difficult to test length contraction in SR?
I don't see any experiements on that.

The magnetic field of a wire, acting on a charge moving parallel to the wire, seems like a simple demonstration of length contraction.

Herein lies the OP's problem: it is difficult to move so fast as to transparently verify specific simple aspects of relativity; the reason physicists believe relativity is that it perfectly explains "countless" phenomena which each might not seem like "obviously" proof of anything if taken individually.

 

[Office_Shredder]

i seem to remember a mu-meson decay experiment that can be viewed as two ways. either (from our perspective) the clocks of the mu-mesons have been slowed down due to time dilation or (from the mu-meson's perspective) the distance between the Earth's surface and the bottom of the mineshaft has been decreased due to length contraction.

I think it was them entering the atmosphere... some scientists were measuring the density of mu-meson particles at different altitudes, and found that they were decaying much deeper into the atmosphere than they expected, then realized it would be explained by relativity's length contraction

Ah, this seems to explain it
http://www.egglescliffe.org.uk/physics/relativity/muons1_.html

 

[pmb_phy]

2nd postulate of SR says that speed of light is constant in all inertial frames. And it exlains all SR. but How to prove this? I have seen that michelson-morley experiment can be explained by this. Is this exp is only reason?

The invariance of the speed of light is taken as an axiom in SR, which means that we don't know why this is so and we are therefore unable to prove it. However if you, instead, posulate that the proper mass of the photon is zero then it can be proved by using Maxwell's equations. I placed the derivation of the wave equation from Maxwell's equation on my website at

http://www.geocities.com/physics_world/em/maxwells_equations.htm

Notice that the speed of light is derived from two constants which are also invariant according to SR. If a photon had mass then there would be a photon proper mass term in the result which would mean that the resulting equations would predict waves traveling at speeds less that the value of c that we obtain from measurements.

Pete

 

[Aether]

The invariance of the speed of light is taken as an axiom in SR, which means that we don't know why this is so and we are therefore unable to prove it.

There is not one shred of physical evidence that the one-way speed of light is invariant, much less explaining "why this is so". The standard formulation of SR is simply designed to simplify calculations by exploiting the fact that there is no evidence to contrary either.

The standard formulation of SR is a mixture of conventional and non-conventional concepts. Only the non-conventional concepts of SR have any empirical basis at all. The "invariance of the speed of light" is a conventional concept which can not be demonstrated empirically without contradicting the non-conventional aspects which have already been demonstrated empirically.

 

[Aether]

There is no (conceptual) problem testing the one-way speed of light. You simply send out a slow moving detector with a clock.

Wrong.

The slow-transport method of synchrony is then examined in the light of these results and is shown not to provide an adequate method of uniquely determining the one-way speed of light.

John A. Winnie, Special Relativity Without One-Way Velocity Assumptions: Part I, Philosophy of Science, Vol. 37, No. 1. (Mar., 1970), pp. 81-99

Maybe not if you assert an Aether but this doesn't deny SR, it just introduces an external entity breaking the symmetry.)

I have neither asserted an aether, nor have I denied SR.

(as is done in GR)

How familiar are you with GR?

 

[jambaugh]

[edit] I've deleted the original post where I "put my foot in it".

Wrong.

Hmmm... I seem to have put my foot in it.

As I understand it this ambiguity is simply a matter of choice of gauge. I see your point now. Both the one-way-speed convention and the convention of assuming slow clocks remain synchronized in the limit are the same assertion and untestable. It is precisely a gauge condition.

It reminds me that you can actually "do" GR by taking the speed of light in various directions as your variable instead of (in part a definition of) the metric and/or connection. A point I had to make once to someone with his pet alternative to GR theory. It seems I'm getting forgetful in my old age.

I have neither asserted an aether, nor have I denied SR.

Pardon, though I did speak hypothetically, I implied facts not in evidence. I was biased in part by your choice of user name and in part by my memory of past arguments with various "aetherists". My most humble apologies, I consume crow with relish. I should have read more carefully.

How familiar are you with GR?

Pretty familiar. I've worked a few problems and contributed to a paper or two, e.g. :http://arxiv.org/abs/gr-qc/0009099"

Again my apologies. You are quite quite right and I quite wrong! (And rude about it too!)

Regards,
James Baugh

 

[Aether]

I was biased in part by your choice of user name and in part by my memory of past arguments with various "aetherists". My most humble apologies, I consume crow with relish. I should have read more carefully...Again my apologies. You are quite quite right and I quite wrong! (And rude about it too!)

Thank-you, but no apologies are necessary. My user name is designed to throw you off balance at first, and you righted yourself well.

Pretty familiar. I've worked a few problems and contributed to a paper or two, e.g. :http://arxiv.org/abs/gr-qc/0009099"

Cool! I will look at this paper.

 

[rbj]

There is not one shred of physical evidence that the one-way speed of light is invariant, much less explaining "why this is so".

how would you ever know any variation in c? the speed of light is always 1 Planck Length per Planck Time. always. if you think it has varied (because of a change in the number of meter sticks per clock tick), it's because of a more fundamental dimensionless value (the number of Planck Lengths per meter stick and/or the number of Planck Times per clock tick) that has changed. those are the salient quantities that, if changed by different degrees, might be perceived as a change in c.

"why this is so" means the burden of proof is on the other side. why should a vacuum whizzing past me be meaningfully differentiated from a "stationary" vacuum? if you cannot tell the difference, if there is, in fact, no meaningful difference between a moving vacuum and a stationary vacuum, then the burden of proof is on the person who claims that the speed of light (or the speed of any ostensibly instantaneous action) is different for any inertial observer, unless you have some reason to declare that this one inertial observer is at rest in an absolute sense and this other inertial observer (moving relative to the first) is in motion. if you cannot do that, there is no reason to think that the laws of physics (including the quantitative value for c) is different for the two.

so the burden of proof lies the other way: there is not one shred of physical evidence that the speed of light in vacuo varies, much less explaining why such variance could even be observationally meaningful. the variation of dimensionful constants is not only non-existant, such variation is operationally meaningless[\b]. you couldn't tell if such changed, even if it somehow did (while all dimensionless constants associated with it remaining constant). it's only the dimensionless values that count. a variation in \alpha matters, while a variation in c or G or \hbar or \epsilon_0 is meaningless. such a purportedly perceived variation is more meaningfully attributed to a dimensionless quantity varying.

The "invariance of the speed of light" is a conventional concept which can not be demonstrated empirically without contradicting the non-conventional aspects which have already been demonstrated empirically.

it cannot be demonstrated empirically at all (or falsified). that's because it's not a dimensionless quantity and every meaningful physical measurement we make, with a numerical value, is fundamentally dimensionless.

 

[Aether]

Pretty familiar. I've worked a few problems and contributed to a paper or two, e.g. :http://arxiv.org/abs/gr-qc/0009099"

I am looking at this paper, but it will be next week before I can get a copy of ref. 2; do you have a link to that paper anywhere online?

Unimodular relativity is a theory of gravity and space-time with a fixed space-time volume element the modulus, which we suppose is proportional to the number of microscopic modules in that volume element.

In view of the Beckenstein bound where the information entropy of any black hole is proportional to the area of the event horizon, and not the volume it encloses, have you considered that (in the case of a black hole at least) the modulus may be proportional to the area of the event horizon rather than the volume enclosed?

 

[Aether]

[add]

There is not one shred of physical evidence that the one-way speed of light is invariant, much less explaining "why this is so".

...the burden of proof is on the person who claims that the speed of light (or the speed of any ostensibly instantaneous action) is different for any inertial observer...

In this case pmb_phy said that "we don't know why this is so and we are therefore unable to prove it" which is wrong; we do know why this is so, it is so because we defined it so.

It seems clear that pmb_phy thinks that he is talking about an empirically established fact, e.g. that the one-way speed of light is invariant, and that we don't know why nature is this way. Therefore, the burden of proof is on him. My objection is to his implicit assumption that the invariance of the speed of light is an empirically established fact; it is not, it is a postulate.
[/add]

so the burden of proof lies the other way: there is not one shred of physical evidence that the speed of light in vacuo varies, much less explaining why such variance could even be observationally meaningful.

I don't necessarily disagree with you. Remember, I also said this:

The standard formulation of SR is simply designed to simplify calculations by exploiting the fact that there is no evidence to contrary either.

...the variation of dimensionful constants is not only non-existant, such variation is operationally meaningless. it's only the dimensionless values that count. a variation in \alpha matters, and a variation in c or c or \hbar or \epsilon_0 is meaningless. such a purportedly perceived variation is more meaningfully attributed to a dimensionless quantity varying.

We are on the same page here.

...it cannot be demonstrated empirically at all (or falsified). that's because it's not a dimensionless quantity and every meaningful physical measurement we make, with a numerical value, is fundamentally dimensionless.

Measurements of the (an)isotropy of the speed of light are always dimensionless quantities. For example, the Michelson-Morley experiment compares the travel times of two light rays and yields a dimensionless (typically null) result.

 

[cesiumfrog]

There is not one shred of physical evidence that the one-way speed of light is invariant [...] The "invariance of the speed of light" is a conventional concept which can not be demonstrated empirically without contradicting the non-conventional aspects which have already been demonstrated empirically.

At the last conference I went to, I saw several talks reporting on tests of the one-way speed of light; why the scaremongering ("not one shred")?

 

[Aether]

At the last conference I went to, I saw several talks reporting on tests of the one-way speed of light;

Please cite those papers. There are papers out there claiming to have made measurements of the one-way speed of light, but these can all be shown to be either outright wrong, or meaningless coordinate-system dependent measurements.

...why the scaremongering ("not one shred")?

Because there really is not one shred...it is not possible to measure the one-way speed of light in a coordinate-system independent way without contradicting the non-conventional content of SR, not even in principle. Any vaild claim to the contrary would amount to an empirical disproof of SR.

 

[rbj]

In this case pmb_phy said that "we don't know why this is so and we are therefore unable to prove it" which is wrong; we do know why this is so, it is so because we defined it so.

yeah, but there could be an issue of whether we can simply define it so, by fiat. (i agree that we can, though.)

It seems clear that pmb_phy thinks that he is talking about an empirically established fact, e.g. that the one-way speed of light is invariant, and that we don't know why nature is this way. Therefore, the burden of proof is on him. My objection is to his implicit assumption that the invariance of the speed of light is an empirically established fact; it is not, it is a postulate.

i think that the, given a symmetry regarding the two opposite directions that light moves back and forth on the M-M inferometer, that if the two-way speed of light is invariant, there is no apparent reason for such speed to be different in one direction vs. its opposite and you are measuring the change of the means of two different speeds.

it is empirically inferred from M-M that there is no measurable consequence of any notion of aether, because you would expect the Earth to be passing though it at a speed roughly that of its orbital speed, at least during some season of the year. so with that expectation, then there is empirical support, if not decisive proof that there is no aether that serves as the medium for which light (and other EM) propagates in. but, as Einstein has been heard to say (or write), it's not as if God had any choice in the matter (paraphrased from memory). Einstein knew of M-M, but i think he would have been greatly disconcerted if M-M had turned out the other way (a noticable fringe shift when turned 90 degrees at some season of the year.)

I don't necessarily disagree with you.

yeah, i figgered that out, now. sorry for thinking otherwize.

 

[pervect]

There is not one shred of physical evidence that the one-way speed of light is invariant, much less explaining "why this is so".

This is rather misleading, at minimum. There exist some unusual and non-standard defintions of speed which make the one-way speed of light different in differing directions. (Technically, this would be a non-isotropic speed of light).These unusual definitions of "speed" amount to using non-standard (i.e non-isotropic) clock synchronizations.

However, these sorts of definitions aren't actually useful. For instance, these definitions are incompatible with the common sense requirement that two objects of equal mass moving in opposite directions "at the same speed" must have zero total momentum. These definitions are rather like saying that an airplane that leaves chicago at 6am and arrives at Los Angeles at 8am has a "speed" of 820 miles/hour. (Check out united 101 for example). If one uses a "fair" (aka isotropic) clock synchronization (rather than pst and cst), or uses a rapidity measurement (time elapsed on the airplane) rather than a speed measurement, , the actual trip time is 4 hours, and not 2, and the speed is half the above value. The "speed" computed in this non-standard manner is very non-physical, it for instance has no particular relationship to momentum.

Besides not being very useful, these unusual definitions aren't standard. For instance, Will talks about one-way speed tests of light http://prola.aps.org/abstract/PRD/v45/i2/p403_1, as some posters have mentioned. (Will uses "slow clock transport" as a non-light based means of clock synchronization).

 

[Aether]

This is rather misleading, at minimum.

Do you think that the article quoted below is misleading, or that I am misinterpreting it in some way?

...this situation reveals a structural feature of the Special Theory, and thereby of the universe it purports to characterize, which not only makes the one-way speed of light indeterminate, but reveals that its unique determination could only be at the expense of contradicting the nonconventional content of the Special Theory...

John A. Winnie, Special Relativity Without One-Way Velocity Assumptions: Part I, Philosophy of Science, Vol. 37, No. 1. (Mar., 1970), pp. 81-99

There exist some unusual and non-standard defintions of speed which make the one-way speed of light different in differing directions. (Technically, this would be a non-isotropic speed of light).

I am not talking about non-standard definitions here, I am talking about physical evidence.

These unusual definitions of "speed" amount to using non-standard (i.e non-isotropic) clock synchronizations.

However, these sorts of definitions aren't actually useful.

I have given examples in other threads for unusual definitions of speed and non-standard clock synchronizations, but I haven't claimed that there is any physical evidence for those either.

For instance, these definitions are incompatible with the common sense requirement that two objects of equal mass moving in opposite directions "at the same speed" must have zero total momentum...The "speed" computed in this non-standard manner is very non-physical, it for instance has no particular relationship to momentum.

One-way speed is not an objective physical quantity, so momentum is not an objective physical quantity either. Our "common sense" notions of momentum require us to assume isotropic speeds, but that only helps us to set up a convenient coordinate system; it does not constitute physical evidence.

Besides not being very useful, these unusual definitions aren't standard. For instance, Will talks about one-way speed tests of light http://prola.aps.org/abstract/PRD/v45/i2/p403_1, as some posters have mentioned. (Will uses "slow clock transport" as a non-light based means of clock synchronization).

Tests using "slow clock transport" apparently do not provide any useful physical evidence though:

The slow-transport method of synchrony is then examined in the light of these results and is shown not to provide an adequate method of uniquely determining the one-way speed of light.

John A. Winnie, Special Relativity Without One-Way Velocity Assumptions: Part I, Philosophy of Science, Vol. 37, No. 1. (Mar., 1970), pp. 81-99

 

[jambaugh]

Wrong.
I have neither asserted an aether, nor have I denied SR.

How familiar are you with GR?

James, there is a 24hr grace-period for deleting posts; if you want you can delete your posts in this thread and then I'll delete my replies. In any case, I will delete this part of this post by tomorrow.

Since you suggest it I shall. I did feel I shouldn't deny my goof by deleting it too quickly but rather own up to it. The rest of my soapbox speech w.r.t. group deformation may be of interest to some so I'll save it to post elsewhere.

I am looking at this paper, but it will be next week before I can get a copy of ref. 2; do you have a link to that paper anywhere online?

I'm sorry no, nor do I have ready access to a copy right now. The title was:
"Cosmological Constant and Fundamental Length"
You can read the abstract or buy a copy at: http://scitation.aip.org"

In view of the Beckenstein bound where the information entropy of any black hole is proportional to the area of the event horizon, and not the volume it encloses, have you considered that (in the case of a black hole at least) the modulus may be proportional to the area of the event horizon rather than the volume enclosed?

I recall when we were discussing this that we defined invariant volumes as the intersection of the future light-cone of one event and past light-cone of another later event with the proper-time between the two events defining the invariants. The 4-th power of this proper time is proportional to the volume and the boundaries remain light-cones in all frames.

The problem with the event horizon is that it is a null surface. I'm not sure there is a way to get the type of proportionality you are suggesting. So I don't know if the two ideas will "meet up" anywhere.

But I recall Dr. Finklestein worked out a nice extension to the idea of the Plank scale by considering the problem of measuring a field over many cells simultaneously. You get a relationship between the number of cells and their resolution before quantum uncertainty in the energies leads to formation of an event horizon. Let me see if I can find a reference.

Regards,
James

[Edit] PS I think we are diverging from the topic of this thread...should we move this elsewhere?

 

[RandallB]

The standard formulation of SR is a mixture of conventional and non-conventional concepts. Only the non-conventional concepts of SR have any empirical basis at all. The "invariance of the speed of light" is a conventional concept which can not be demonstrated empirically without contradicting the non-conventional aspects which have already been demonstrated empirically.

What does that mean? Sounds like double speek.
What “non-conventional aspects” of SR (and how have they been demonstrated empirically?) are contradicted by the “conventional concept” that the measured speed of light is invariant??

 

[RandallB]

The standard formulation of SR is a mixture of conventional and non-conventional concepts. Only the non-conventional concepts of SR have any empirical basis at all. The "invariance of the speed of light" is a conventional concept which can not be demonstrated empirically without contradicting the non-conventional aspects which have already been demonstrated empirically.

What does that mean? Sounds like double speek.
What “non-conventional aspects” of SR (and how have they been demonstrated empirically?) are contradicted by the “conventional concept” that the measured speed of light is invariant??

 

[Aether]

I think we are diverging from the topic of this thread...should we move this elsewhere?

I will try to get a copy of ref. 2 next week, and then think some more about this then. If it is something that you are still interested in, you could start a new thread on the subject since the paper has been published. If you don't do that, then I'll PM you with any further comments or questions that I have about it.

 

[jambaugh]

RandallB,

If I may interject. What Aether is saying (possibly could have said more clearly?) is that we cannot measure a distance without adopting some convention as to the speed of light or equivalently to adopting some convention of simultaneity of of events in a given inertial frame.

It can be shown that any distance measurement reverts back to a radar ranging measurement which thus requires you know the speed of light in both directions. You can't then use this distance measurement to empirically confirm the speed of that light beam. This is why in particular c is a defined constant and not a measured quantity. This was the mistake I made earlier.

You can't know that say traveling in the x-direction linearly sets your clock back by a proportional amount which is reversed when you bring the clock back to you. Since this changes the timing of the event when the light pulse whose speed you wish to measure reaches a distant marker it affects your definition of its speed. We adopt the assumption of isotropy in space but it can't be empirically confirmed with regard to this type of hypothetical effect.

What is happening is one is hypothesizing all of the Lorentzian transformational effects of an aether without actually referring to the aether directly. You get a skewed form of SR which predicts the exact same observable phenomena but with a skewed ontological modeling of said phenomena.

I think of it best as a gauge degree of freedom within the formulation of GR. What Aether is calling a "convention" I would call a "gauge constraint". Recall that in GR for flat space-time there are still gauge degrees of freedom in the (usually zero) connection. Apply a gauge transformation making the Christoffel symbols non-zero and you get one of those skewed forms of SR I mentioned.

(I think) It is equivalent to putting the entire universe in a uniform constant gravitational field. There is no way to empirically detect it as there are no tides. You don't even get the usual horizon due to this "acceleration".

Philosophically speaking it is silly not to adopt the constant c "convention" within SR but operationally speaking it is a gauge condition and not an empirically testable hypothesis. And especially when you move into GR and relativistic quantum theory it it is vital to recognize this distinction e.g. so you don't introduce non-physical divergences in your calculations by integrating over non-physical variables.

Regards,
James Baugh

 

[Aether]

What Aether is saying (possibly could have said more clearly?) is that...Philosophically speaking it is silly not to adopt the constant c "convention" within SR but operationally speaking it is a gauge condition and not an empirically testable hypothesis. And especially when you move into GR and relativistic quantum theory it it is vital to recognize this distinction e.g. so you don't introduce non-physical divergences in your calculations by integrating over non-physical variables.

Many people have a hard accepting this. I tried to choose my words so that they would be clear, concise, and correspond as closely as possible to the terminology used in John A. Winnie's paper. A forum consensus on how to say this best would be great.

 

[Aether]

What does that mean? Sounds like double speek.

This is the terminology used in these two papers:

John A. Winnie, Special Relativity Without One-Way Velocity Assumptions: Part I, Philosophy of Science, Vol. 37, No. 1. (Mar., 1970), pp. 81-99

John A. Winnie, Special Relativity Without One-Way Velocity Assumptions: Part II, Philosophy of Science, Vol. 37, No. 2. (Jun., 1970), pp. 223-238

What “non-conventional aspects” of SR (and how have they been demonstrated empirically?) are contradicted by the “conventional concept” that the measured speed of light is invariant??

Every aspect of SR which can be demonstrated empirically is a "non-conventional aspect" of the theory; isotropy of the two-way speed of light for example, this has been demonstrated empirically using Michelson interferometers. The "relativity of simultaneity" is a conventional aspect of the standard formulation of SR.

 

[Aether]

Aether you seem to be fixated on co-ordinate systems disallowing oneway tests to be viable.

This thread is about how to prove the SR postulate about the invariance of the speed of light, wisp. Many people think that this can been done with experiments, but it can't be done with experiments without falsifying SR in the process.

If SR turns out to be wrong, which is very likely, then science will look pretty stupid.

SR is a "special" case of GR, wisp. It is "special" because gravity has been neglected; all you have to do to prove that SR is "wrong" is to say, hey, look, there's some gravity over here! The point about SR is that we can set up some very special (never really quite perfect though) conditions, neglect gravity, and make some other assumptions, and then we can do high-speed engineering calculations that really work without needing to use all of the heavy machinery of GR.

Anyway, we can discuss that in another thread if you want.

 

[blumfeld0]

I'm sure those involved in this discussion know most of the details outlined in this article but just for those who are beginners: http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html

A few relevant quotes:

At the 1983 Conference Generale des Poids et Mesures, the following SI (Systeme International) definition of the metre was adopted:
The metre is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second.
This defines the speed of light in vacuum to be exactly 299,792,458 m/s. This provides a very short answer to the question "Is c constant": Yes, c is constant by definition!
However, this is not the end of the matter. The SI is based on very practical considerations. Definitions are adopted according to the most accurately known measurement techniques of the day, and are constantly revised. At the moment you can measure macroscopic distances most accurately by sending out laser light pulses and timing how long they take to travel using a very accurate atomic clock. (The best atomic clocks are accurate to about one part in 1013.) It therefore makes sense to define the metre unit in such a way as to minimise errors in such a measurement.
Another assumption on the laws of physics made by the SI definition of the metre is that the theory of relativity is correct. It is a basic postulate of the theory of relativity that the speed of light is constant. This can be broken down into two parts:

* The speed of light is independent of the motion of the observer.
* The speed of light does not vary with time or place.