Relativity of Science

[Farsight]

It's no presumption James. You measure the local speed of light to be the same regardless of your motion. That's the evidence, and the essence of special relativity. Mathematical expressions like 1/√(1-v²/c²) are correct, but not for any mysterious reason. The reason is simple, and it's obvious, because the supporting evidence is there in pair production and annihilation. We are in essence "made of light", much as Close says with his matter waves in The Other Meaning of Special Relativity. This is the telling point, on page 15:

"What has not been generally recognized is that special relativity is a consequence of the wave nature of matter and is entirely consistent with classical notions of absolute space and time".

[James S Saint]

It's no presumption James. You measure the local speed of light to be the same regardless of your motion. That's the evidence, and the essence of special relativity. Mathematical expressions like 1/√(1-v²/c²) are correct, but not for any mysterious reason. The reason is simple, and it's obvious, because the supporting evidence is there in pair production and annihilation. We are in essence "made of light", much as Close says with his matter waves in The Other Meaning of Special Relativity. This is the telling point, on page 15:

But what does any of that have to do with the paradox situation? The mechanics of the proposed paradox has to be examined so as to point out at what point something would not "be right". Up til now, other than you, all have merely said, "oh but the flashers would not be simultaneous". And their only excuse is, "Einstein said". Just as you have pointed out with many other examples, Einstein didn't really say what they are thinking. Simultaneity issues do not really apply and if someone thinks they do, they really need to prove why they would.

"What has not been generally recognized is that special relativity is a consequence of the wave nature of matter and is entirely consistent with classical notions of absolute space and time".

I 100% agree with that. Again, it is merely due to no one actually thinking, but rather just seeing an equation and plugging it in to every hole until they go blind.

[Calrid]

Then you haven't seen the experiments and are in no position to comment.

Oh, and you have?

Clocks placed on tall buildings go out of synch. Clocks placed on fast moving planes go out of synch. Global positioning systems have to be adjusted to special and general relativistic concerns or they go out of synch. Explain to me why this is the case?

Actually I did already. I suspect you are too impetuous to read all of the posts.

No you didn't you have yet to explain why time dilation appears to be born out in experiment and absolute time seems to be at odds with all experiment.

Experiments like yours that experience lack of simultaneity in co moving vehicles are in accordance with special relativity. The Michelson Morley experiments which have been done countless times dispute aether theoreis.

"And there were dozens of witnesses that SAW Jesus walk on the water and walk out of the garden."

That's not an answer to the experiment, that is merely an evasion, why then do aether theories fair so badly in experimental testing? No one saw Jesus walk on water, they are all dead but the Michelson-Morley experiment has been run hundreds of times and in all set ups it disputes your theories. This isn't a matter of faith its a matter of scientific evidence. Yours is lacking, hence your suppositions are merely faith not the other way around.

I've gone thorugh the logic as it relates to both theory and real world experiment

Absolute bull.

I have and so have others, the fact you choose to ignore reality in favour of something that doesn't fit it means your assumptions are logically flawed.

Calrid, try to realize that your brain is actually designed, by whatever means, to do far more than merely run your mouth.

Get on that thread and show YOUR step by step logic that would require that the two clocks MUST experience asynchronous flash. Quoting holy scriptures and prophets or appealing to testimonials does nothing to help your brain do what we call "thinking". Try it (over there). It is supposed to be SCIENCE, not faith or religion. Can you spell that word, "S-c-i-e-n-c-e"? You might learn to enjoy the experience.

If only you would practice what you preach and actually refute the empirical evidence instead of saying the same thing over and over in the face of it as if what you are saying was actually born out by the real world.

The only conclusion I came to was that all things being equal two frames would experience simultaneity, I explained why in accordance with a rotational transform, apparently though although differences in frames produces a discrepancy this simple empiricism is beyond your grasp. Your problem is you are denying reality and all real world experiment without showing any experiment that could refute relativity. Your train experiment simply says nothing more than that all things being equal relativistic equations should produce a simultaneity, which they do. The only way you distinguish your ideas would be to set up an experiment where all things weren't equal and then observe the results. Since doing this tends to lead to discrepancies in clocks as shown in the above experiments (which you claim to have never heard of despite them all being easy to find on almost any web page on the subject or in any magazine or journal you'd care to name). Thus your logic is flawed, your axioms are demonstrably false and worse don't distinguish themselves at all in your set up.

[Calrid]

Then take the challenge. Everyone is all willing to claim how I am wrong, yet none have the courage to actually prove it with anything other than "But our scriptures say you're wrong. Witnesses SAW him walking on the water. They wouldn't LIE". Farsight, you are good at explanations. You should be able to explain the paradox.

I thought I did, James, with this post. We didn't discuss it adequately because PhysBang employed the "hostile barrage" technique to turn off other contributors.

Hmm.. why doesn't anyone understand that you CANNOT presume as premise special relativity in order to prove it for the same reason everyone complains about the religious using the Bible to prove God.

Once again, the similarity between the arguments from public Science and religion are identical in EVERY way.

We don't we say that if our hypothesis is true then it should be born out in experiment. We then set out to create and experiment where we can test absolute time against relative time. In absolute time clocks should show no discrepancies regardless of experimental set up or frames of reference, in relativistic scenarios they should be out of synch. That's it if one is true according to experiment the other must necessarily be false. All you have to do to overturn it is show one scenario where Einstein's equations don't relate to experiment, to my knowledge no one has done this, but I am all ears if you know of any. The same cannot be said for your own dearly held convictions, which apparently only require faulty axioms and arm waving. And we are supposed to believe you based on this? Why? because you say something must be how it is, even though it isn't born out by actual experiment? Your asking us to trust not our senses and our measures but some logic that appears in experiment to be contradicted by what we see and measure. This is foolish and unscientific, it's not logical or pragmatic either.

No amount of insult about me or anyone else is going to change the physical nature of reality, nor subsume the wealth of evidence there is that supports it. Science isn't about talking the talk it's about practical applications in real situations. You have provided none.

In recent times versions of the Michelson–Morley experiment have become commonplace. Lasers and masers amplify light by repeatedly bouncing it back and forth inside a carefully tuned cavity, thereby inducing high-energy atoms in the cavity to give off more light. The result is an effective path length of kilometers. Better yet, the light emitted in one cavity can be used to start the same cascade in another set at right angles, thereby creating an interferometer of extreme accuracy.

The first such experiment was led by Charles H. Townes, one of the co-creators of the first maser. Their 1958 experiment put an upper limit on drift, including any possible experimental errors, of only 30 m/s. In 1974 a repeat with accurate lasers in the triangular Trimmer experiment reduced this to 0.025 m/s, and included tests of entrainment by placing one leg in glass. In 1979 the Brillet-Hall experiment put an upper limit of 30 m/s for any one direction, but reduced this to only 0.000001 m/s for a two-direction case (i.e., still or partially entrained aether). A year long repeat known as Hils and Hall, published in 1990, reduced the limit of anisotropy to 2 × 10−13.

Einstein and special relativity

The constancy of the speed of light was postulated by Albert Einstein in 1905,[5] motivated by Maxwell's theory of electromagnetism and the lack of evidence for the luminiferous ether but not, contrary to widespread belief, the null result of the Michelson–Morley experiment.[6] However the null result of the Michelson–Morley experiment helped the notion of the constancy of the speed of light gain widespread and rapid acceptance.
[edit] Aether dragging

Initially, the experiment of 1881 was meant to distinguish between the theory of Augustin-Jean Fresnel (1818), who proposed an almost stationary aether, and in which the aether is only partially dragged with a certain coefficient by matter; and the theory of George Gabriel Stokes (1845), who stated that the aether was fully dragged in the vicinity of the earth. Michelson initially believed the negative outcome confirmed the theory of Stokes. However, Hendrik Lorentz showed in 1886, that Stokes's explanation of aberration is contradictory.[7][8]

Also the assumption that the aether is not carried in the vicinity, but only within matter, was very problematic as shown by the Hammar experiment (1935). Hammar placed one arm of the interferometer between two huge lead blocks. If aether were dragged by mass, the blocks would, it was theorized, have been enough to cause a visible effect. Once again, no effect was seen, so any such theory is considered as disproved.
[edit] Emission theory

Walter Ritz's emitter theory (or ballistic theory), was also consistent with the results of the experiment, not requiring aether. The theory postulates that light has always the same velocity in respect to the source.[9] However it also led to several "obvious" optical effects that were not seen in astronomical photographs, notably in observations of binary stars in which the light from the two stars could be measured in an interferometer. If this was correct, the light from the stars should cause fringe shifting due to the velocity of the stars being added to the speed of the light, but again, no such effect could be seen.

The Sagnac experiment placed a modified apparatus on a constantly rotating turntable; the main modification was that the light trajectory encloses an area. In doing so any ballistic theories such as Ritz's could be tested directly, as the light going one way around the device would have a different length to travel than light going the other way (the eyepiece and mirrors would be moving toward/away from the light). In Ritz's theory there would be no shift, because the net velocity between the light source and detector was zero (they were both mounted on the turntable). However in this case an effect was seen, thereby eliminating any simple ballistic theory. This fringe-shift effect is used today in laser gyroscopes.
[edit] Length contraction

The explanation was found in the FitzGerald–Lorentz contraction, also simply called length contraction. According to this physical law all objects physically contract along the line of motion (originally thought to be relative to the aether), so while the light may indeed transit slower on that arm, it also ends up travelling a shorter distance that exactly cancels out the drift. In 1932 the Kennedy–Thorndike experiment modified the Michelson–Morley experiment by making the path lengths of the split beam unequal, with one arm being very short. In this version a change of the velocity of the earth would still result in a fringe shift except if also the predicted time dilation is correct. Once again, no effect was seen, which they presented as evidence for both length contraction and time dilation, both key effects of relativity.

Einstein derived the FitzGerald–Lorentz contraction from the relativity postulate; thus his description of special relativity was also consistent with the apparently null results of most experiments (though not, as was recognized at the 1928 meeting, with Miller's observed seasonal effects). Today special relativity is generally considered the "solution" to the Michelson–Morley null result. However, this was not universally recognized at the time. As late as 1920, Einstein himself still spoke of a different concept of ether that was not a "ponderable medium" but something of significance nonetheless.[10]

The Trouton–Noble experiment is regarded as the electrostatic equivalent of the Michelson–Morley optical experiment, though whether or not it can ever be done with the necessary sensitivity is debatable. On the other hand, the 1908 Trouton–Rankine experiment, which can be regarded as the electrical equivalent to the Kennedy–Thorndike experiment, achieved an incredible sensitivity.

http://en.wikipedia.org/wiki/Michelson% ... experiment

Do you dispute these experiments results? If so why and how are the experiments flawed? If you could gives us an analysis of the experiment and tell us why it does not constitute evidence I am all ears?

Note: relativity was never meant to dispute all ether theories just ones that explained the motion issues in terms of a medium that had a discernible drag effect on light. hence the use of the word ponderable medium which had an actual effect on lights speed of propagation e.g. Maxwell's Luminiferous Aether.

[Calrid]

"What has not been generally recognized is that special relativity is a consequence of the wave nature of matter and is entirely consistent with classical notions of absolute space and time".

Unfortunately this just says that relativity is a classical theory which indeed it is. It does not say anything more than that.

[PhysBang]

You propose a hypothesis to answer a question as long as the question displays logic. Apparently my question displays logic else you would be using logic to answer it (assuming you can use any logic of course.. I have yet to see the evidence).

When someone says something crazy, no amount of logic can "answer it". All one can do is point out that it's crazy.

My argument was that people doing the same physical actions at different locations and times got their results at different locations and time. You could not even understand that.

No, your argument was entirely about simultaneity and that two events could never be in sync if they were separated by "spacetime". That was the only issue on the table. Again, you skew the facts to protect EGO.

You claimed that the same physical laws could not lead to different timing for different events. I showed you that this happens all the time. I also provided you with three links that provided detailed arguments about exactly why SR leads to the relativity of simultaneity.

I quoted you a section from a chapter he wrote demonstrating the relativity of simultaneity. That's about as in-context as one can get! Did you read the chapter? I'm guessing no, since your writing continues to be absurd.

EXACTLY like a literalist quoting his misunderstanding of the Bible. And you might want to look up what "out of context" means too.

That is the craziest thing you have said yet.

I know that "my version" would not be correct for your scenario because your scenario violates special relativity with its very assumptions.

The point is for you to prove special relativity, not merely quote chapter and verse from the book being deposed (probably should look up that one too). SHOW YOUR Math/Logic.

You want me to prove SR? That's the new craziest thing you've said.

[PhysBang]

Hmm.. why doesn't anyone understand that you CANNOT presume as premise special relativity in order to prove it for the same reason everyone complains about the religious using the Bible to prove God.

Once again, the similarity between the arguments from public Science and religion are identical in EVERY way.

Because, if you were trying to produce a paradox for special relativity, then you would have to start from the assumption that SR was true. To do otherwise is really, really stupid.

[Churro the Viscous]

Hmm.. why doesn't anyone understand that you CANNOT presume as premise special relativity in order to prove it for the same reason everyone complains about the religious using the Bible to prove God.

Once again, the similarity between the arguments from public Science and religion are identical in EVERY way.

Because, if you were trying to produce a paradox for special relativity, then you would have to start from the assumption that SR was true. To do otherwise is really, really stupid.

PhysBang is correct here, James S Saint.
The post in question wasn't an attempt to prove relativity, it was an attempt to show you that your disproof was incorrect.
You had to assume relativity in order to show how it was inconsistent with reality or with itself.
The response to you was just a debunking of your debunking.
Nothing illogical on anybody's side but yours there, James.

[Farsight]

"What has not been generally recognized is that special relativity is a consequence of the wave nature of matter and is entirely consistent with classical notions of absolute space and time".

Unfortunately this just says that relativity is a classical theory which indeed it is. It does not say anything more than that.

The paper says far more than that Calrid. You should read it: The Other Meaning of Special Relativity. All the mathematics is the same, and it still matches all the experiments, but this employs space with waves running through it. Setting gravity aside, some go straight (light), some follow closed paths (massive particles), and some are in between (neutrinos). Hard evidence like pair production and magnetic dipole moment back this up, and it logically explains why massive particles can never reach c and we always measure c to be the same locally. I'm thinking it's fairly close to what James would advocate, but it's still special relativity. It's a different interpretation of special relativity employing wave/particle duality in absolute space. And since the universe is pretty absolute, and we can determine our motion through the universe from the CMBR, it all seems reasonable. I think Einstein would have liked it.

[Farsight]

But what does any of that have to do with the paradox situation?

It removes it. What you think of as "the time" is merely your cumulative measure of wave motion, which is altered by your own motion. Irrespective of that, and irrespective of where and when they were emitted, two photons either meet at the same location at the same time according to the station clock, or they don't. The motion of outside observers and what they deem to be simultaneous has nothing to do with it.

The mechanics of the proposed paradox has to be examined so as to point out at what point something would not "be right". Up til now, other than you, all have merely said, "oh but the flashers would not be simultaneous". And their only excuse is, "Einstein said". Just as you have pointed out with many other examples, Einstein didn't really say what they are thinking. Simultaneity issues do not really apply and if someone thinks they do, they really need to prove why they would.

It's something of a grey area. Einstein didn't quite get his clock synchronisation right, and from 1911 was challenging his own postulate, but people who feel themselves to be knowledgeable in SR don't seem to know about these things.

"What has not been generally recognized is that special relativity is a consequence of the wave nature of matter and is entirely consistent with classical notions of absolute space and time".

I 100% agree with that.

And it's still SR. Same maths, same predictions, same experimental proof... but with a wave/particle duality interpretation. What's not to like?

[Calrid]

"What has not been generally recognized is that special relativity is a consequence of the wave nature of matter and is entirely consistent with classical notions of absolute space and time".

Unfortunately this just says that relativity is a classical theory which indeed it is. It does not say anything more than that.

The paper says far more than that Calrid. You should read it: The Other Meaning of Special Relativity. All the mathematics is the same, and it still matches all the experiments, but this employs space with waves running through it. Setting gravity aside, some go straight (light), some follow closed paths (massive particles), and some are in between (neutrinos). Hard evidence like pair production and magnetic dipole moment back this up, and it logically explains why massive particles can never reach c and we always measure c to be the same locally. I'm thinking it's fairly close to what James would advocate, but it's still special relativity. It's a different interpretation of special relativity employing wave/particle duality in absolute space. And since the universe is pretty absolute, and we can determine our motion through the universe from the CMBR, it all seems reasonable. I think Einstein would have liked it.

I'll take a look later. What I meant was that James was probably reading something into it that was not implied. If he whole heartedly agrees with that statement there should be no problem with accepting relativity without some "paradox" therefore.

Special relativity has no trouble mixing it up with other classical theories such as optics or electromagnetism, it never really has, it doesn't have any real problem mixing it up with non classical theories even like certain aspects of quantum field theory for example.

[PhysBang]

What you think of as "the time" is merely your cumulative measure of wave motion, which is altered by your own motion. Irrespective of that, and irrespective of where and when they were emitted, two photons either meet at the same location at the same time according to the station clock, or they don't. The motion of outside observers and what they deem to be simultaneous has nothing to do with it.

If one actually describes the scenario in the reference frame of the train, then what one frame takes to be simultaneous is absolutely required. Otherwise, the mathematical descriptions of the events to not match up.

Einstein didn't quite get his clock synchronisation right, and from 1911 was challenging his own postulate, but people who feel themselves to be knowledgeable in SR don't seem to know about these things.

Einstein thoroughly rejected his 1911 work, as those knowledgeable in General Relativity know.

I 100% agree with that.

And it's still SR. Same maths, same predictions, same experimental proof... but with a wave/particle duality interpretation. What's not to like?[/quote]
SR is completely compatible with quantum mechanics and it always has been.

Robert Close is simply regurgitating mistakes about SR that are about 100 years old. Here's his own words:
"Thus we see how Lorentz transformations can be obtained by using sonar or any other type of wave to measure time and distance. Lorentz invariance is not a property of time and space per se. Rather it results from the methods used to measure time and distance. If the above-mentioned sailors were to rendezvous to share their data and some vodka, they might conclude after a few drinks that absolute time and space in moving underwater reference frames are related by Lorentz transformations using the speed of sound in water. After sobering up, however, they would realize that sonar is not the only way to measure time and distance and that their measurements are not evidence of any non-Euclidean properties of underwater time and space. "

Robert Close wants us to forget that there is a big difference between the sonar case and SR: sonar is only one way to measure, whereas SR applies to all means of measuring. He wants us to neglect that we have no evidence for his preferred, absolute reference frame whereas we do have a preferred frame for our sonar applications.

In SR, we might excuse this by using some mathematical chicanery, as Close does, to suggest that something about physics hides the real absolute reference frame from us. he might also suggest that unicorns and fairies work to carry electrons from place to place and then remove all trace of their work. This might work for SR, but when we get to general relativity, we can no longer accept this. GR gives us absolute freedom in picking a system of coordinates and putting physics to work in that system. And we cannot accept the frame co-moving with the bulk of the background radiation as an absolute reference frame because we rely on GR to analyze that radiation and to analyze the anisotropies in that radiation. These anisotropies are the relics of places where there were changes in the density of the background radiation and thus they have a different co-moving reference frame (and different proper times) from the rest of the background radiation. Do present the background radiation as an absolute reference frame, one has to produce analysis on these anisotropies that recover all the information from these regions that we get from GR.

[Farsight]

I'll take a look later. What I meant was that James was probably reading something into it that was not implied. If he whole heartedly agrees with that statement there should be no problem with accepting relativity without some "paradox" therefore.

I'm hoping he'll read it too, and then appreciate that special relativity ought not to be the target here.

Special relativity has no trouble mixing it up with other classical theories such as optics or electromagnetism, it never really has, it doesn't have any real problem mixing it up with non classical theories even like certain aspects of quantum field theory for example.

Agreed. There's a rather simple way to extend this to gravity too. For the life of me I don't know why Einstein didn't nail it. Take a look at http://arxiv.org/abs/physics/0204044 and http://iopscience.iop.org/0256-307X/25/5/014 sometime, and do read that Leyden Address.

[Farsight]

Einstein thoroughly rejected his 1911 work, as those knowledgeable in General Relativity know.

He didn't reject c varying with gravitational potential. He repeated it year after year. See the GR section of this article which says the modern interpretation rejects it, not Einstein.

SR is completely compatible with quantum mechanics and it always has been.

So take note of the other interpretation.

Robert Close is simply regurgitating mistakes about SR that are about 100 years old. Here's his own words: "Thus we see how Lorentz transformations can be obtained by using sonar or any other type of wave to measure time and distance. Lorentz invariance is not a property of time and space per se. Rather it results from the methods used to measure time and distance. If the above-mentioned sailors were to rendezvous to share their data and some vodka, they might conclude after a few drinks that absolute time and space in moving underwater reference frames are related by Lorentz transformations using the speed of sound in water. After sobering up, however, they would realize that sonar is not the only way to measure time and distance and that their measurements are not evidence of any non-Euclidean properties of underwater time and space."

He's right. Apply wave/particle duality, and it's obvious. Everything is made of waves.

Robert Close wants us to forget that there is a big difference between the sonar case and SR: sonar is only one way to measure, whereas SR applies to all means of measuring. He wants us to neglect that we have no evidence for his preferred, absolute reference frame whereas we do have a preferred frame for our sonar applications.

There is no difference, and the CMBR dipole anisotropy is the evidence for the preferred frame.

In SR, we might excuse this by using some mathematical chicanery, as Close does, to suggest that something about physics hides the real absolute reference frame from us. He might also suggest that unicorns and fairies to carry electrons from place to place and then remove all trace of their work.

Don't bother me with garbage like chicanery and fairies. The paper is sound.

This might work for SR, but when we get to general relativity, we can no longer accept this. GR gives us absolute freedom in picking a system of coordinates and putting physics to work in that system. And we cannot accept the frame co-moving with the bulk of the background radiation as an absolute reference frame because we rely on GR to analyze that radiation and to analyze the anisotropies in that radiation. These anisotropies are the relics of places where there were changes in the density of the background radiation, and thus they have a different co-moving reference frame (and different proper times) from the rest of the background radiation. To present the background radiation as an absolute reference frame, one has to produce analysis on these anisotropies that recover all the information from these regions that we get from GR.

No problem. It's an SR paper. And in a place where gravitational potential is lower the energy density is higher. In a place where the energy density is higher, the light goes slower. It's as simple as that.

[PhysBang]

Einstein thoroughly rejected his 1911 work, as those knowledgeable in General Relativity know.

He didn't reject c varying with gravitational potential. He repeated it year after year. See the GR section of this article which says the modern interpretation rejects it, not Einstein.

A) The actual science is the modern interpretation, so it doesn't matter what Einstein thought. B) He did reject the variable speed of light. You always like to produce his 1911 speculative piece, but you have no other reference for Einstein ever entertaining a variable speed of light.

Robert Close wants us to forget that there is a big difference between the sonar case and SR: sonar is only one way to measure, whereas SR applies to all means of measuring. He wants us to neglect that we have no evidence for his preferred, absolute reference frame whereas we do have a preferred frame for our sonar applications.

There is no difference, and the CMBR dipole anisotropy is the evidence for the preferred frame.

No, the anisotropy is evidence of a difference between a frame co-moving with the average of the solar system movements and a frame co-moving with the average of the CMBR. There is no one CMBR frame, there is only a frame that we can identify with the average. Additionally, we have no physical means of measurement that identifies any frame as special. All we have is one means that measures the difference between one average and another average.

In SR, we might excuse this by using some mathematical chicanery, as Close does, to suggest that something about physics hides the real absolute reference frame from us. He might also suggest that unicorns and fairies to carry electrons from place to place and then remove all trace of their work.

Don't bother me with garbage like chicanery and fairies. The paper is sound.

It is only sound insofar as it is able to recapture the basics of SR, basics known for 100 years. It is not sound to use sonar as an analogy, since we do not have any physical means of measurement that violates SR, while we do have many that violate Close's sonar.

No problem. It's an SR paper. And in a place where gravitational potential is lower the energy density is higher. In a place where the energy density is higher, the light goes slower. It's as simple as that.

If it's no problem, then let's see you model anything in physics with your theory. You have had what, six years to do this?

[Farsight]

A) The actual science is the modern interpretation, so it doesn't matter what Einstein thought.

Dismiss Einstein if you wish, I'd rather pay attention to what he actually said. And the "actual science" isn't in the modern interpretation, it's in the evidence like Shapiro and the GPS clock adjustment. Clocks go slower in a region of low gravitational potential, and some of those clocks are light clocks.

B) He did reject the variable speed of light. You always like to produce his 1911 speculative piece, but you have no other reference for Einstein ever entertaining a variable speed of light.

You're in denial, and mathematical demands will not distract from the evidence or from what Einstein said. Here it is again:

People say the speed of light is constant, and Einstein said it. But it isn't exactly true. Yes, Einstein started with this as a postulate in 1905 when he was doing special relativity, but by 1911 he was into general relativity. That's when he wrote On the Influence of Gravitation on the Propagation of Light. He kind of got this back to front because his ideas were still evolving, but there's nothing wrong with this:

If we call the velocity of light at the origin of co-ordinates c0, then the velocity of light c at a place with the gravitation potential Φ will be given by the relation c = c0 (1 + Φ/c²).

This is the speed of light varying with gravitational potential. It wasn't a one-off, because in 1912 he said it again when he wrote "On the other hand I am of the view that the principle of the constancy of the velocity of light can be maintained only insofar as one restricts oneself to spatio-temporal regions of constant gravitational potential". He repeated this in 1913 when he said: "I arrived at the result that the velocity of light is not to be regarded as independent of the gravitational potential. Thus the principle of the constancy of the velocity of light is incompatible with the equivalence hypothesis". This wasn’t just some early thought that he later discarded, because there it is again in Die Relativitätstheorie in 1915 when he says " the writer of these lines is of the opinion that the theory of relativity is still in need of generalization, in the sense that the principle of the constancy of the velocity of light is to be abandoned." That’s on page 259 of Doc 21, see the princeton bibliography for a list. He says it again in late 1915, on page 150 of Doc 30, within The Foundation of the General Theory of Relativity. Einstein says "the principle of the constancy of the velocity of light in vacuo must be modified." He really spells it out in section 22 of the 1916 book Relativity: The Special and General Theory. What he says is this:

In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position. Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid in the dust. But in reality this is not the case. We can only conclude that the special theory of relativity cannot claim an unlimited domain of validity; its results hold only so long as we are able to disregard the influences of gravitational fields on the phenomena (e.g. of light).

People tend to see the word velocity in the translations and tend to think vector quantity. They tend to miss the way he refers to c, which is most definitely a speed. It's pretty obvious he's talking about speed because he’s repeatedly referring to “the principle” or "one of the two fundamental assumptions". He was talking about the special relativity postulate, which is the constant speed of light. And it's even more obvious if you go back to the original German. What he actually said was die Ausbreitungsgeschwindigkeit des Lichtes mit dem Orte variiert. I’ve got the original German version, and I got a German friend to translate it for me. It translates into the speed of light varies with the locality. The word “velocity” in the translations was the common usage, as in “high velocity bullet”, not the vector quantity that combines speed and direction. He was saying the speed varies with position, hence the reference to the postulate, and hence it causes curvilinear motion. The space is inhomogeneous, so light follows a curved path. like a car veers when the near-side wheels encounter mud at the side of the road.

[PhysBang]

Dismiss Einstein if you wish, I'd rather pay attention to what he actually said. And the "actual science" isn't in the modern interpretation, it's in the evidence like Shapiro and the GPS clock adjustment. Clocks go slower in a region of low gravitational potential, and some of those clocks are light clocks.

OK, these phenomena are modelled by the "modern interpretation" of GR. Please provide a model of these phenomena without the "modern interpretation" of GR. You have had years to do this.

You're in denial, and mathematical demands will not distract from the evidence or from what Einstein said.

The mathematical details are all the details. The constancy of the speed of light is a statement about the speed of light in a free-falling coordinate system. Your quote mining does nothing to hide that you haven't addressed the facts of the mathematics.

[Farsight]

No. See Inhomogeneous Vacuum: An Alternative Interpretation of Curved Spacetime for the mathematics. And note that the mathematics isn't the facts. The scientific evidence is the facts. Things like the GPS clock adjustment. A light clock goes slower near the surface of the earth, because the light goes slower, and that's it. Einstein said it, and the Shapiro delay is proof positive. The coordinate time diverges because we define the second using the motion of light. The wikipedia article even includes the Einstein quote. The word in the translation is velocity, but the word in the original German is geschwindigkeit. That means speed, and it's crystal clear it really did mean speed because Einstein talked about one of the postulates of special relativity. He previously talked about c on this matter, and c is not a vector quantity. See the NIST caesium fountain clock and the definition of the second:

"Since 1967, the second has been defined to be the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. This definition refers to a caesium atom at rest at a temperature of 0 K (absolute zero), and with appropriate corrections for gravitational time dilation."

Lasers and a microwave cavity are employed to cause hyperfine transitions, which are electron spin-flips within caesium atoms. Electrons are literally made from light in pair production, and the hyperfine transition is an electromagnetic phenomena, as are the emitted microwaves. Microwaves are light in the wider sense. There’s a peak "frequency" in the emitted light, which is found and measured by the detector, but get this: the "frequency" is measured in Hertz, which is defined as cycles per second, and the second isn't defined yet. So what the detectors essentially do, is count incoming microwave peaks. When they get to 9,192,631,770 that's a second. Hence the frequency is 9,192,631,770 Hertz by definition. And did you catch the gravitational time dilation? If you were to take this clock and place it in a region of low gravitational potential, it would be like pressing a slow-motion button. All electromagnetic and other processes then occur at a reduced rate, including the hyperfine transition and the motion of the resultant light towards the detector. However regardless of this, when the detectors get to 9,192,631,770, that's a second. Only this 299,792,458 m/s is not the same as previously, because the second is bigger, because the light goes slower. The patent evidence is as obvious as the nose in front of your face, and you would have to be suffering from something resembling a religious conviction to dismiss both it and Einstein.

[PhysBang]

No. See Inhomogeneous Vacuum: An Alternative Interpretation of Curved Spacetime for the mathematics.

I have seen and read it. It accounts for a single phenomena and there is no evidence that it is consistent with the remainder of GR. It is published in an obscure journal of dubious editorial standards and I doubt that you have ever actually read that paper. If you disagree, use that paper to calculate the perihelion advance of Mercury or the rotation curve of any galaxy.

And note that the mathematics isn't the facts. The scientific evidence is the facts. Things like the GPS clock adjustment.

But these facts are useless unless we can describe them in a way useful to physics. GR describes events that we observe or predict by using the specifics of a spacetime manifold--this is entirely mathematical. If you have some other way to do this, then please provide the details. Please describe in detail that we can asses either the perihelion advance of Mercury or the rotation curve of any galaxy.

So far, you have a lot of talk, but no game. Let's see your theory do anything.

[Farsight]

You know I've read the paper, I've quoted sections to you. Here's another:

In this Letter, we emphasize the strong similarities between the light propagation in a curved spacetime and that in a medium with graded refractive index. These similarities suggest that an inhomogeneous vacuum may be the physical reality of the curved spacetime. We provide a general method to derive exactly the corresponding graded refractive index of the vacuum in a static spherically symmetrical gravitational field both for outside and inside the gravitational matter system, and point out that the refractive index profile is simply a unified exponential function of the gravitational potential for a weak gravitational field. We show that even the long puzzling central image missing problem in gravitational lensing[34] can now be solved clearly with the use of the obtained refractive index profile.

But you dismiss it, along with Einstein, and the scientific evidence. You're in denial PhysBang. All you can do is attempt to erect a smokescreen of mathematical demands and call it "your theory". Don't you get it yet? It isn't my theory. It's Einstein's.

[James S Saint]

When speaking of the consistency of the speed of light, shouldn't you be distinguishing whether you mean with gravity fields or without? Einstein later realized that gravity affects the speed of light. But when speaking of SR, it is assumed that there is a uniform gravity field (as in "none") merely for the sake of discussion.

[James S Saint]

What I am seeing in the Paradox thread is that I am the "Atheist" arguing the logic in the "Bible" with the "Christians" PhysBang and Carleas defending the faith while the "Jews", Maddy and Churro are still using the Torah.

The primary issue is merely the interpretation of their "Bible", very much as Farsight pointed out. And although Farsight is hardly alone in his plea that interpretation is "the issue", I still see logical error in every current perspective.

The Paradox merely displays the issue of relativity of simultaneity by presenting a case wherein we would know which frame of reference didn't see correctly. But rather than logic being used to defend the faith, the defense thus far has been, "but our scriptures say..", even when that isn't what they meant by what they said (the exact scenario of religious people who argue over doctrine - and with the same lack of progress).

If the Torah had included a dictionary from the beginning, the entire world would be very different and there probably would be no separation between Christian and Jew. And a commonly heard phrase among the Arabs would be "Mohamed who?!?".

[Farsight]

When speaking of the consistency of the speed of light, shouldn't you be distinguishing whether you mean with gravity fields or without? Einstein later realized that gravity affects the speed of light. But when speaking of SR, it is assumed that there is a uniform gravity field (as in "none") merely for the sake of discussion.

Sorry. Yes, when speaking of SR we assume no gravity, and people talk of a constant speed of light. There is however an oddity to this however related to Einstein's clock synchronisation. Imagine you're in the middle of a "motionless" mirrored box which serves as your frame of reference. (You can't be sure it's truly motionless, but you know what I mean). You send a pulse to the front of the box, it bounces back, and you mark the time of its return. You assume that the speed of light is the same both out and back. Now repeat this in a fast-moving box.

[James S Saint]

Sorry. Yes, when speaking of SR we assume no gravity, and people talk of a constant speed of light. There is however an oddity to this however related to Einstein's clock synchronisation. Imagine you're in the middle of a "motionless" mirrored box which serves as your frame of reference. (You can't be sure it's truly motionless, but you know what I mean). You send a pulse to the front of the box, it bounces back, and you mark the time of its return. You assume that the speed of light is the same both out and back. Now repeat this in a fast-moving box.

And what are the presumed results?

In my world, the speed of light is not an observed constant. But I can explain why it has appeared so.

[Calrid]

Sorry. Yes, when speaking of SR we assume no gravity, and people talk of a constant speed of light. There is however an oddity to this however related to Einstein's clock synchronisation. Imagine you're in the middle of a "motionless" mirrored box which serves as your frame of reference. (You can't be sure it's truly motionless, but you know what I mean). You send a pulse to the front of the box, it bounces back, and you mark the time of its return. You assume that the speed of light is the same both out and back. Now repeat this in a fast-moving box.

And what are the presumed results?

In my world, the speed of light is not an observed constant. But I can explain why it has appeared so.

Not mathematically or logically so anyone can understand it. Explaining how something out of kilter with reality works is really explaining nothing except the root of your misconceptions.