What evidences of relativity do you find the most compelling

[TheAntiRelative]

Just like to get an idea what most other people find to be the most important evidences. GPS, MMX, Stillwell-Ives, Pound-Rebka, Perihelion of Mercury?

Go ahead and list a few of your favorites but rank them from most to least important in your mind. SR GR... You can separate them if you want but I was thinking in broad terms...

 

[Perspicacious]

The most compelling

The greatest evidence for special relativity is that it can be derived only from Newton's first law of motion and the homogeneity of time.

http://www.everythingimportant.org/relativity

 

[LeonhardEuler]

Well, I really don't know much about GR, but as for SR, here is what convinces me:
1. The inconsistancy of Maxwell's equations without relativity
2. The Michelson-Morely experiment
3. The various technologies that depend on calculations from SR to work and do
4. Hafele and Keating's experiments with muons.
Those things pretty much clear any feeling of doubt in SR I had before studying it. I never actually believed that SR was wrong, but I could never really convince myself that all its weird predictions were true before I learned about those things.

 

[Nereid]

SR: QED (the most accurate theory we have, as in - the most detailed observations match theory ... to x decimal places, where x >12).

GR: orbits of neutron star binaries (loss due to gravitational radiation ... detected from objects that are so impossibly far away, as measured by any distance scale that any human can reasonably claim to grasp, intuitively).

 

[jtbell]

Just like to get an idea what most other people find to be the most important evidences. GPS, MMX, Stillwell-Ives, Pound-Rebka, Perihelion of Mercury?

The fact that many many many experiments involving high-speed particles have been done at places like Fermilab, CERN, and SLAC, all using relativistic equations for mass, energy, and momentum, and producing consistent results for properties of electrons, protons, muons, etc. I would be astonished if all these experiments could be analyzed consistently using non-relativistic equations.

 

[Chronos]

Pound-Rebka, hands down. GR is the only viable explanation. Nereid's example is also compelling. Only GR offers a good explanation for the decay of binary neutron star's orbits. PR is superior, IMO, because it rules out any weird cosmological effects. jt has the best example in favor of SR. Particle accelerators reconfirm SR daily. They do not, however, confirm GR as firmly as PR or binary neutron stars. Bear in mind SR is a special case of GR.

 

[quasar987]

Could you please briefly describe what Pound-Rebka is? Thx.

 

[selfAdjoint]

Could you please briefly describe what Pound-Rebka is? Thx.

From http://archive.ncsa.uiuc.edu/Cyberia/NumRel/EinsteinTest.html :

Earthbound Redshift
In 1960, Robert V. Pound and Glen A. Rebka demonstrated that a beam of very high energy gamma rays was ever so slightly redshifted as it climbed out of Earth's gravity and up an elevator shaft in the Jefferson Tower physics building at Harvard University. The redshift predicted by Einstein's Field Equations for the 74 ft. tall tower was but two parts in a thousand trillion. The gravitational redshift detected came within ten percent of the computed value. Quite a feat!

Solar Redshift
In the 1960s, a team at Princeton University measured the redshift of sunlight. Though small, given the Sun's mass and density, the redshift matched Einstein's prediction very closely.

 

[Garth]

All the Pound-Rebka experiment has measured is that there is a red shift and this red shift is equal to the change in Newtonian gravitational potential. This is consistent with GR but it may be consistent with other explanations too, such as photons losing PE in a pseudo-Newtonian theory.

Gravitational red shift in GR is a time-dilation effect caused by the curvature of space-time. This time dilation affects photons but the question remains as to what effect it might have on atoms as well.

In GR, which treats fundamental particles as having constant proper mass, time dilation has no effect on atoms, therefore the red shift is a confirmation of the existence and amount of time-dilation as predicted by GR.

However if time-dilation does have an effect on fundamental particles as well then this effect will be canceled out when a time-dilated atom measures the energy of a time-dilated photon. In that case there must be another expanation for the red shift such as the atomic particles also gaining mass through gravitational potential energy. Not a red shift by the photon but a 'blue shift' by the atom. Of course this is not standard theory as that would violate the equivalence principle and a consistent theory to handle this would be required. The published and testable Self Creation Cosmology does just this.

Garth

 

[quasar987]

Hasn't there been an experiment where they mount a clock on a plane, make it fly, and after it lands back, compare the time on plane w/ time on earth, and the separation matches special relativity's prediction very well?

 

[Nereid]

All the Pound-Rebka experiment has measured is that there is a red shift and this red shift is equal to the change in Newtonian gravitational potential. This is consistent with GR but it may be consistent with other explanations too, such as photons losing PE in a pseudo-Newtonian theory.

Gravitational red shift in GR is a time-dilation effect caused by the curvature of space-time. This time dilation affects photons but the question remains as to what effect it might have on atoms as well.

In GR, which treats fundamental particles as having constant proper mass, time dilation has no effect on atoms, therefore the red shift is a confirmation of the existence and amount of time-dilation as predicted by GR.

However if time-dilation does have an effect on fundamental particles as well then this effect will be canceled out when a time-dilated atom measures the energy of a time-dilated photon. In that case there must be another expanation for the red shift such as the atomic particles also gaining mass through gravitational potential energy. Not a red shift by the photon but a 'blue shift' by the atom. Of course this is not standard theory as that would violate the equivalence principle and a consistent theory to handle this would be required. The published and testable Self Creation Cosmology does just this.

Garth

Would you like to contribute your favourite answer(s) to the OP's question Garth?

 

[Garth]

Would you like to contribute your favourite answer(s) to the OP's question Garth?

Yes indeed!

Of course we cannot prove relativity but rather perform experiments that are consistent with its predictions, the more hoops it 'jumps through' the more compelling the 'evidence' establishing it as the accepted model. A good scientific theory is one that not only has great explanatory power but one that can be falsified, both SR and GR can be falsified.

I will not go into the no-aether/aether debates on these Forums about SR, which I take as well tested and of profound and robust foundations within its sphere of validity.

My interest lies in GR, which also has passed through many 'hoops', not only at the time of its conception; the precession of the perihelion of Mercury and the deflection of light at the total eclipse of 1919 but of many others since, tested to a high precision, some by space technology that didn't exist in the first half of the last century.

However most of these tests predict an effect that can be broken into a space-curvature component and a time-dilation component; which in GR are equal, each contributing half of the total effect. The deflection of starlight/radio waves passing close to the Sun is a prime example. However, it is possible that another theory may exist in which the space-curvature and time-dilation components contribute different proportions of the same overall prediction as GR.

As a number of these tests have the same combination of equal space-curvature and time-dilation components it is not surprising that a theory that passes one test passes the others as well.

The interesting thing about the geodetic precession of the Gravity Probe B gyros is that in that precession the space-curvature component contributes 2/3 and the time-dilation component only 1/3 of the total. Thus an alternative theory that passes the first set of tests would not also pass this one.

Therefore I will find the Gravity Probe B geodetic precession measurement the most compelling evidence supporting the General Theory of Relativity.

I cannot finish before adding that in Self Creation Cosmology in these tests the space-curvature effect is ½ that of GR while the time-dilation effect is 3/2 that of GR. Thus in the first set of tests (all those to date) the total prediction is [(½ x ½ + 3/2 x ½)GR] equal to GR whereas in the GPB geodetic measurement it is [(½ x 2/3 + 3/2 x 1/3)GR] = 5/6GR. i.e. 5.5120 arcsec/yr rather than the GR value of 6.6144 arcsec/yr. We wait and see!

Garth

 

[Aether]

Special relativity is empirically equivalent to an ether theory taking into account time dilation and length contraction but maintaining absolute simultaneity.

So, aren't all of these "evidences of relativity" really evidences of something slightly more general than relativity per se?

 

[Nereid]

Special relativity is empirically equivalent to an ether theory taking into account time dilation and length contraction but maintaining absolute simultaneity.

Surely this begs the question, 'whence the time dilation and length contraction'?

So, aren't all of these "evidences of relativity" really evidences of something slightly more general than relativity per se?

How could you tell?

 

[Aether]

Surely this begs the question, 'whence the time dilation and length contraction'?

Yes it does.

How could you tell?

By the empirical equivalence of SR with an ether theory taking into account time dilation and length contraction but maintaining absolute simultaneity.

I do not doubt any of the above mentioned evidence, not at all...except, wrt neutron star binaries isn't there an unresolved issue of a possible unseen third object? But since these two theories are emprically equivalent, how can any of the evidence mentioned possibly weigh in favor of relativity per se?

 

[Nereid]

I think I missed it, first reading; you're talking about SR Aether, not GR?

Unless I've completely missed the boat, this is not unlike Garth's idea - there are lots of theories that give 'SR' in its domain of applicability, the 'real' question is: "which of the generalisations best matches the full set of good observational and experimental results?"

In this regard, I like the clarity of SCC - GPB will tell (unless the error bars are far, far larger than expected). (BTW, this 'tweak GR to test GR' has a long, and IMHO honourable, tradition).

However, AFAIK, there isn't any 'ether-based' alternative to GR (except, possibly, as GR formulated in a way so as to include an 'ether', but - in terms of anything determinable experimentally or observationally - no different, even in principle).

 

[Aether]

I think I missed it, first reading; you're talking about SR Aether, not GR?

Yes, for now.

Unless I've completely missed the boat, this is not unlike Garth's idea - there are lots of theories that give 'SR' in its domain of applicability, the 'real' question is: "which of the generalisations best matches the full set of good observational and experimental results?"

Perhaps "which of the generalisations can definitely be ruled out"?

In this regard, I like the clarity of SCC - GPB will tell (unless the error bars are far, far larger than expected). (BTW, this 'tweak GR to test GR' has a long, and IMHO honourable, tradition).

Let the chips fall where they may...happy hunting Garth!

However, AFAIK, there isn't any 'ether-based' alternative to GR (except, possibly, as GR formulated in a way so as to include an 'ether', but - in terms of anything determinable experimentally or observationally - no different, even in principle).

Good point.

 

[cscott]

Hasn't there been an experiment where they mount a clock on a plane, make it fly, and after it lands back, compare the time on plane w/ time on earth, and the separation matches special relativity's prediction very well?

I think this has been done quite a few times. In one instance a US Navy aircraft flew slowly in a 20-mile loop around Chesapeake Bay for fifteen hours. This was for GR, though.

 

[TheAntiRelative]

However, AFAIK, there isn't any 'ether-based' alternative to GR (except, possibly, as GR formulated in a way so as to include an 'ether', but - in terms of anything determinable experimentally or observationally - no different, even in principle).

Yeah, the aether theory that is like GR is one in which aether has varying density. Light curvature is a refraction mechanism. It's an aether absorbton theory or some such where particles all absorb aether at some rate and cause a localized rarefaction of the medium and therefore gravity becomes equivelent to bouyancy.

So yeah, in effect it's aether tailored to fit GR.

Hasn't there been an experiment where they mount a clock on a plane, make it fly, and after it lands back, compare the time on plane w/ time on earth, and the separation matches special relativity's prediction very well?

Hafele-Keating
That experiment is somewhat deprecated. GPS is better.

 

[Nereid]

Yeah, the aether theory that is like GR is one in which aether has varying density. Light curvature is a refraction mechanism. It's an aether absorbton theory or some such where particles all absorb aether at some rate and cause a localized rarefaction of the medium and therefore gravity becomes equivelent to bouyancy.

So yeah, in effect it's aether tailored to fit GR.

With anything observable - even in principle - to distinguish it/them from GR?

 

[TheAntiRelative]

With anything observable - even in principle - to distinguish it/them from GR?

No not much really. Einstein is quoted many times as having some notions of his own intangible aether, aka spacetime.

The difference in concept is more with SR than with GR. Retaining the possibility of simultaneity and disregarding lightspeed constancy. The observable difference is contention over the findings of the MMX and Dayton Miller.

Non-lorentzian aether theory is based off simple fluid dynamics. Subsequent MMX-like tests are disregarded for poor setup because of entrainment. (housed in thick metal cases and performed in concrete buildings) Entrainment is explained at both a global and object level instead of object level alone. In this case stellar aberration and the water filled telescope become explicable.


It's many of the good examples in this thread that are not so easily explained in an aether model...

 

[Andrew Mason]

Yes it does.

By the empirical equivalence of SR with an ether theory taking into account time dilation and length contraction but maintaining absolute simultaneity.

I do not doubt any of the above mentioned evidence, not at all...except, wrt neutron star binaries isn't there an unresolved issue of a possible unseen third object? But since these two theories are emprically equivalent, how can any of the evidence mentioned possibly weigh in favor of relativity per se?

An aether theory that takes into account time dilation cannot maintain absolute simultanaeity. One can explain lack of time differences over what should be different length paths through the aether by length contraction, which is what Lorentz and Fitzgerald suggested. No time dilation is required.

The difference between SR and Lorentz-Fitzgerald contraction aether theory is that the latter is an ad-hoc constructive theory that does not help us to understand phenomena in terms of simpler principles, whereas SR is a very elegant principled theory that explains 'why' things occur. Neither is really 'correct'. Reality is what it is.

AM

 

[Aether]

SR is a very elegant principled theory that explains 'why' things occur. Neither is really 'correct'. Reality is what it is.

My point is that local Lorentz symmetry is what is actually supported (so far) by the experimental evidence, and that this is a slightly more general concept than SR per se. How does SR explain 'why' things occur?

 

[pervect]

I would say that SR is global Lorentz symmetry, while GR is local Lorentz symmetry.

 

[Andrew Mason]

How does SR explain 'why' things occur?

Well, the why is all relative, not absolute. It is a matter of explaining different phenomena in terms of understandable general principles.

Try explaining the extended life times of very unstable particles when traveling at high speeds using an ether based theory without time dilation. Try explaining, without SR, the highly collimated beam of synchrotron radiation given off by electrons moving at relativistic speeds.

AM

 

[Aether]

An aether theory that takes into account time dilation cannot maintain absolute simultanaeity...Try explaining the extended life times of very unstable particles when traveling at high speeds using an ether based theory without time dilation.

I have recently shown an ether theory transformation which can do this (with time dilation) and it is presented right next to the Lorentz transformation of the same example; please see the "Consistency of the speed of light" thread for the details. Lorentz ether theory (LET) is empirically equivalent to SR, and maintains absolute simultaneity. It is Lorentz symmetry that explains the extended lifetimes of particles; SR and LET are equally valid coordinate systems, but neither one explains anything of its own accord. They are tools.

Try explaining, without SR, the highly collimated beam of synchrotron radiation given off by electrons moving at relativistic speeds.

I'm sure that it can be done with LET too since SR is empirically equivalent to LET. It is not SR per se that explains such effects, it is Lorentz symmetry.

 

[Hans de Vries]

I have recently shown an ether theory transformation which can do this (with time dilation) and it is presented right next to the Lorentz transformation of the same example; please see the "Consistency of the speed of light" thread for the details. Lorentz ether theory (LET) is empirically equivalent to SR, and maintains absolute simultaneity. It is Lorentz symmetry that explains the extended lifetimes of particles; SR and LET are equally valid coordinate systems, but neither one explains anything of its own accord. They are tools.

LET does not predict the extended life times of unstable particles when
traveling at high speeds. Can you have a look at the formula you are using?


t\ =\ \sqrt{1-v^2/c_0^2}\ \ \ T
x\ =\ \frac{1}{\sqrt{1-v^2/c_0^2}}\ (X-vT)

Where X,T are in the absolute/preferred reference frame, x,t are in the
other reference frame and v is (in the absolute frame) the speed of the
other reference frame.

What t=\sqrt{1-v^2/c_0^2}\ T implies is that time goes fastest in the absolute
frame and slower in all the other frames. The higher v, the slower time
passes.

This simply means that unstable particles will have decreased life-
times in one direction and increased lifetimes in the opposite direction.
As said (several) times before: LET is only equivalent in the preferred frame.


Regards, Hans

 

[Aether]

LET does not predict the extended life times of unstable particles when
traveling at high speeds. Can you have a look at the formula you are using?


t\ =\ \sqrt{1-v^2/c_0^2}\ \ \ T
x\ =\ \frac{1}{\sqrt{1-v^2/c_0^2}}\ (X-vT)

Where X,T are in the absolute/preferred reference frame, x,t are in the
other reference frame and v is (in the absolute frame) the speed of the
other reference frame.

What t=\sqrt{1-v^2/c_0^2}\ T implies is that time goes fastest in the absolute
frame and slower in all the other frames. The higher v, the slower time
passes.

This simply means that unstable particles will have decreased life-
times in one direction and increased lifetimes in the opposite direction.
As said (several) times before: LET is only equivalent in the preferred frame.

Hans, please show a simple concrete example using the Lorentz transformation equations that I provided, and I will attempt to show that the LET transformation is empirically equivalent.

 

[Hans de Vries]

Hans, please show a simple concrete example using the Lorentz transformation equations that I provided, and I will attempt to show that the LET transformation is empirically equivalent.

It does not help that one can show that there is a transformation 'x' which
turns a Lorentz Transformation into an "LET" one. A simpler transformation
'y' transforms the latter into a Galilean transform. (just scaling with gamma)

This evidently doesn't prove that a LET Transform is Empirically Equivalent
with a Galilean Transform! Or as a consequence, That a Lorentz Transform
is Empirically Equivalent with a Galilean Transform...and so on.

So you will need to start with your LET transformation and prove that it
predicts observations. In all reference frames and not only in the preferred
reference frame. It's all to obvious that this can't be done.


Regards, Hans

 

[Jimmy Snyder]

As for SR, here is a quote from Bernard Schutz, A First Course in GR:

"The counter-intuitive predictions of special relativity all flow from this postulate (the universality of the speed of light), and they are amply confirmed by experiment. In fact it is probably fair to say that special relativity has a firmer experimantal basis than any other of our laws of physics, since it is tested every day in all the giant particle accelerators, which send particles nearly to the speed of light."

As for GR, Schutz is slightly less enthusiastic. He quotes S. Chandrasekar:

"The element of controversy and doubt, that have continued to shroud the general theory of relativity to this day, derives precisely from this fact, namely that in the formulation of his theory Einstein incorporates aesthetic criteria; and every critic feels that he is entitled to his own differing aesthetic and philosophic criteria. Let me simply say that I do not share these doubts; and I shall leave it at that."

 

[coalquay404]

Sorry to drag this thread up after so long but I notice that the misconception about the Pound-Rebka experiment is still quite widespread. Contrary to what many textbooks say, the Pound-Rebka experiment does not provide direct evidence in support of general relativity. The only thing that the Pound-Rebka experiment supports is a rather technical assumption about the equivalence of the locally inertial frames of special relativity with those of Newtonian theory. Of course, this is fundamentally important when one wishes to construct a space-time theory of gravitation like GR, but it *does not* support GR directly.

I still find it amazing that so few people are aware of this.

 

[clj4]

Sorry to drag this thread up after so long but I notice that the misconception about the Pound-Rebka experiment is still quite widespread. Contrary to what many textbooks say, the Pound-Rebka experiment does not provide direct evidence in support of general relativity. The only thing that the Pound-Rebka experiment supports is a rather technical assumption about the equivalence of the locally inertial frames of special relativity with those of Newtonian theory. Of course, this is fundamentally important when one wishes to construct a space-time theory of gravitation like GR, but it *does not* support GR directly.

I still find it amazing that so few people are aware of this.

Really? Can you prove your statement?

 

[Garth]

coalquay404 is correct.

As other theories, such as http://en.wikipedia.org/wiki/Self_creation_cosmology#Gravitational_red_shift , also predict the same outcome for gravitational red shift, the Pound-Rebka experiment is a necessary but not sufficient test for GR.

Garth

 

[pervect]

I agree with Garth that the Pound-Rebka experiment doesn't test all aspects of GR, i.e. it doesn't distinguish GR from all alternate theories. On the other hand, I would say that the experiment does provide direct experimental support for GR, which is what the OP appears to be trying to deny.

 

[Meir Achuz]

Just like to get an idea what most other people find to be the most important evidences. GPS, MMX, Stillwell-Ives, Pound-Rebka, Perihelion of Mercury?

Go ahead and list a few of your favorites but rank them from most to least important in your mind. SR GR... You can separate them if you want but I was thinking in broad terms...

I got to this thread late in the game, so I hope I don't repeat an earlier answer.
For SR, I consider the verification of p=mv\gamma thousands of times each day the best proof.
For GR, I think the jury is still out. All the effects you mention can follow from the equivalence principle, SR, and some ingenuity. E's equation R=T is reasonable and neater, but not necessary for those effects.

 

[robphy]

The binary pulsar results are compelling
http://relativity.livingreviews.org/Articles/lrr-2006-3/articlesu17.html

 

[clj4]

I agree with Garth that the Pound-Rebka experiment doesn't test all aspects of GR, i.e. it doesn't distinguish GR from all alternate theories. On the other hand, I would say that the experiment does provide direct experimental support for GR, which is what the OP appears to be trying to deny.

Yes, this makes sense, thank you.

coalquay404's post is formulated in a misleading way as well.

 

[Garth]

The binary pulsar results are compelling
http://relativity.livingreviews.org/Articles/lrr-2006-3/articlesu17.html

Yet the system consists only of bodies orbiting in vacuo. Theories that are conformally equivalent to GR in vacuo, such as http://en.wikipedia.org/wiki/Self_creation_cosmology , also predict the same gravitational radiation flux from binary pulsars.

Garth

 

[Aether]

For SR, I consider the verification of p=mv\gamma thousands of times each day the best proof.

This is proof for a physical theory that is more general than just SR. SR is coordinate-system dependent, and the experimental evidence is not.

 

[clj4]

This is proof for a physical theory that is more general than just SR.

What would that theory be?

SR is coordinate-system dependent, and the experimental evidence is not.

What is the relevance of the above statement?
You know perfectly well that there are coordinate independent formulations of SR (as well as coordinate dependent experimental proofs). Do you still harbor the secret hope of disproving SR? Are you still interested in re-running the Gagnon experiment? I offered you the theoretical data...never heard back from you on my offer.

 

[Aether]

What would that theory be?

SR and GGT (aka, Lorentz ether theory) are the same physical theory in different coordinate systems. I refer to this more general physical theory as "Lorentz symmetry"; if anyone else has a better suggestion for a name, then I would like to hear it.

SR is coordinate-system dependent, and the experimental evidence is not.

What is the relevance of the above statement?

This shows how SR is only a subset of the physical theory proven by the referenced experiments.

You know perfectly well that there are coordinate independent formulations of SR (as well as coordinate dependent experimental proofs).

Please show a coordinate-system independent formulation of SR.

Are you still interested in re-running the Gagnon experiment? I offered you the theoretical data...never heard back from you on my offer.

I will simulate the addition and subtraction of some sine functions to test your claims in the other thread and then get back to you.

 

[clj4]

SR and GGT (aka, Lorentz ether theory) are the same physical theory in different coordinate systems. I refer to this more general physical theory as "Lorentz symmetry"; if anyone else has a better suggestion for a name, then I would like to hear it.

Nonsense. SR has no preferred frame, GGT does. After the hundreds of exchanges on this site, you should know at least that. GGT is a subset of RMS and they are both aether theories that disagree with SR.

This shows how SR is only a subset of the physical theory proven by the referenced experiments.

Incorrect, since you are basing this on the false premise refuted above.

Please show a coordinate-system independent formulation of SR.

Gladly, here is one of the many:

http://www.physics.sfsu.edu/~lea/courses/grad/705notes-1.PDF

There are literally hundreds of such formulations taught in colleges.

I will simulate the addition and subtraction of some sine functions to test your claims in the other thread and then get back to you.

"Simulate"? How? You don't even have the correct formulas. The stuff that the "sock puppets" wrote is incorrect and you couldn't calculate a valid formula for the Gagnon experiment.
So what do you plan to "simulate"?

 

[Aether]

SR and GGT (aka, Lorentz ether theory) are the same physical theory in different coordinate systems. I refer to this more general physical theory as "Lorentz symmetry"; if anyone else has a better suggestion for a name, then I would like to hear it.

Nonsense. SR has no preferred frame, GGT does.

This is simpy a difference in coordinate-systems, and that's all.

Gladly, here is one of the many:

http://www.physics.sfsu.edu/~lea/courses/grad/705notes-1.PDF

There are litterally hundreds of such formulations taught in colleges.

You were supposed to "show a coordinate-system independent formulation of SR", but you didn't do that. Notice how in Sec. 2.2 The Lorentz transformation, the discussion is about "coordinates", and section 2.5 begins "The set of transformations of coordinates in spacetime...".

"Simulate"? How? You don't even have the correct formulas. The stuff that the "sock puppets" wrote is incorrect and you couldn't calculate a valid formula.

This belongs in the other thread. Why don't we both delete this discussion from this thread, and move it to the other thread?

 

[Hurkyl]

You were supposed to "show a coordinate-system independent formulation of SR", but you didn't do that. Notice how in Sec. 2.2 The Lorentz transformation, the discussion is about "coordinates", and section 2.5 begins "The set of transformations of coordinates in spacetime...".

"Coordinate-system independent" means that the formulation does not depend on the choice of coordinate system. It does not mean that the formulation eschews the use of coordinates entirely.

That said, it IS easy enough to formulate SR without any reference to coordinates. The simplest I can imagine starts with Euclidean 4-space, postulates the existence of a single "null-cone", and then uses that cone to define a new notion of length and angle, thus arriving at Minowski space. The rest is just elementary calculus.

 

[Aether]

"Coordinate-system independent" means that the formulation does not depend on the choice of coordinate system. It does not mean that the formulation eschews the use of coordinates entirely.

That said, it IS easy enough to formulate SR without any reference to coordinates. The simplest I can imagine starts with Euclidean 4-space, postulates the existence of a single "null-cone", and then uses that cone to define a new notion of length and angle, thus arriving at Minowski space. The rest is just elementary calculus.

This would be a coordinate-system independent formulation of SR?

 

[coalquay404]

"Coordinate-system independent" means that the formulation does not depend on the choice of coordinate system. It does not mean that the formulation eschews the use of coordinates entirely.

That said, it IS easy enough to formulate SR without any reference to coordinates. The simplest I can imagine starts with Euclidean 4-space, postulates the existence of a single "null-cone", and then uses that cone to define a new notion of length and angle, thus arriving at Minowski space. The rest is just elementary calculus.

Actually, there are countless elegant and esoteric coordinate-free formulations of SR. My favourite involves considering a manifold of conformorphisms - three-dimensional Riemannian metrics modulo conformal transformations and three-dimensional diffeomorphisms - and taking GR to be a theory of extremal curves on this manifold (it's not really a manifold, the technical name for it is a stratified manifold). You can derive the entire light cone structure of general relativity and special relativity in a manifestly coordinate-free way, effectively deriving spacetime as a fundamental concept.

Ergo, anyone who claims that coordinate-free approaches to SR do not exist really doesn't know what they're talking about.

 

[Hurkyl]

This would be a coordinate-system independent formulation of SR?

Not only is coordinate-system independent (which it automatically is, since it's a formulation of SR), but it's done without any reference to coordinates, whatsoever.

I'm sure that there's a nice system of axioms for Minowski space that are analogous to Hilbert's axioms for Euclidean space, but I don't know what they are.

Actually, there are countless elegant and esoteric coordinate-free formulations of SR. My favourite involves

Hehe! Of course, I couldn't exactly say "easy enough" in the same breath as that...

 

[Aether]

Ergo, anyone who claims that coordinate-free approaches to SR do not exist really doesn't know what they're talking about.

What I am claiming is that SR is empirically equivalent to Generalized Galilean Transform (GGT), aka Lorentz ether theory, and that they are both the same physical theory using different coordinate systems.

Not only is coordinate-system independent (which it automatically is, since it's a formulation of SR), but it's done without any reference to coordinates, whatsoever.

Every formulation of SR is automatically coordinate-system independent?

Do these coordinate-system independent formulations of SR define the one-way speed of light as a constant?

 

[coalquay404]

What I am claiming is that SR is empirically equivalent to Generalized Galilean Transform (GGT), aka Lorentz ether theory, and that they are both the same physical theory using different coordinate systems.

Every formulation of SR is automatically coordinate-system independent?

Do these coordinate-system independent formulations of SR define the one-way speed of light as a constant?

There's a subtle but devastating difference between coordinate-independent and coordinate-free. I think that's where your confusion stems from. Special relativity is automatically (indeed, by construction) coordinate-independent, although the original formulation is not coordinate-free. I'm unaware of what the GGT you speak of is, but your mention of the aether makes my eyes glaze over in resignation. What's more, the claim that "they are both the same ... theory using different coordinate systems" sounds, to people who understand the wording, ridiculous. If they are equivalent modulo choice of gauge then your GGT is *not* distinguishable from special relativity and hence should be discarded.

 

[Hurkyl]

Every formulation of SR is automatically coordinate-system independent?

SR is a coordinate-independent theory, therefore any formulation of it will be coordinate-independent.

Most formulations will not be "manifestly" coordinate-independent: they will formulate SR in a way that apparently depends on the choice of coordinate system. But it is then later proven that if we had started with a different coordinate system, we would still arrive at the exact same theory.

Do these coordinate-system independent formulations of SR define the one-way speed of light as a constant?

Ah, but 3-velocity is not a physical quantity! The coordinate-free formulations wouldn't say anything at all about 3-velocity, since the very notion of 3-velocity depends on a choice of coordinates (which is one reason why it's called the "coordinate velocity").



There are all sorts of coordinate systems you can put on Euclidean space, and you can do Euclidean geometry in any of them. But the Euclidean geometry has a "nicest" class of coordiante systems: the orthonormal ones, right?

The same is true in Minowski space: the geometry picks out a "nicest" class of coordinate charts, and those are what we often call the "inertial reference frames". Those do, indeed, have a constant one-way (coordinate) speed of light. But other affine coordinate charts on Minowski space do not have constant one-way speed of light. The curvilinear charts, of course, don't even have light traveling along a coordinate-line!


Doing SR in a "skew" coordinate system does not change it into another theory -- it's still SR. (Just like Euclidean geometry done in a skew coordinate system is still Euclidean geometry)