[Farsight (OP)]

Far, my understanding is that frame dragging occurs only if an object or particle is spinning. If the Earth had no rotation, an object placed anywhere on a sphere two hundred thousand kilometers from the Earth would experience the some magnitude and direction of acceleration as an object placed anywhere on that sphere.

That's my understanding too, Ron. I said it was like frame dragging. It isn't quite the same thing, but it is caused by spin. However this spin is in two dimensions, like a rotating steering wheel combined with a smoke ring:


From "Is the electron a photon with a toroidal topology?", Williamson and van der Mark, Annales
de la Fondation Louis de Broglie, Volume 22, no.2, 133 (1997), see
http://www.cybsoc.org/cybcon2008prog.htm#jw for a copy.

Elf, Einstein spent the last thirty years of his life trying to unite electromagnetism and gravity. Some materials will block certain frequencies of the EM spectrum but no material, we know of, will block infrared. The best thermos bottle ever made, even with a complete vacuum, will have some infrared EM. There is no place in the Universe, man made or natural, where there is no radiation.

Agreed, Ron. Bodies radiate, and we all know that X-rays and gamma rays are very penetrative. Good Elf said "usually blocked" and I expect he was trying keep things simple. It's sometimes rather difficult to keep things simple.   

[PhysBang]

I would ask one question of Phys, can he show us one cubic nanometer of space that does not contain radiation in the Universe? If the answer is no then it could be said that radiation is the aether of space.

It could also be said that radiation is the unicorn of space. However, none of that would mean anything.

As Einstein points out clearly in his Leyden lecture, the basic ideas of an aether as an electromagnetic theory don't match our observations. Only if we have a very odd idea of an aether can we keep an idea of an aether. This odd idea is a manifold that can be represented using a four-dimensional pseudo-Riemannian geometry.

Anyone who wants to explain gravity now has to explain how their theory translates into the language of Riemannian geometry in such a way as to reproduce the observations that we have of the behaviour of gravity.

Several times I have asked Farsight to show how anything in his theory actually back up his claims of a) the size of the universe, b) the rotation curves of galaxies, c) the orbit of Mercury. He hasn't demonstrated anything in the way of being able to match these basic results of gravity theory. As such, I cannot accept that his theory is anything resembling science.

[Good Elf]

Hi Farsight, Ron Hughes, Physbang et al,

I would ask one question of Phys, can he show us one cubic nanometer of space that does not contain radiation in the Universe? If the answer is no then it could be said that radiation is the aether of space

All radiation has a source and those sources are what you are referring to. There is no "background" of radiation acting as a kind of aether. Electromagnetic Radiation is not actually "seen" from afar ... what is "seen" is actually in your detector ... for instance your eye or the photographic plate in a telescope as an image. What is imaged there are "sources" not radiation per se... the regions from which the "light" originally came from. This process of "imaging" destroys the photons and converts them to other forms of energy.

The reason you "see" is because the photons are localized in the detectors such as your retina. In deep space where there are "virtually" no sources or sinks of radiation the radiation travels as an unconfined particle. What that means is the wave-function has "effectively" the same value everywhere in almost infinite space and when you do the sum ∫ψ²dv integrated over any reasonable volume of ostensibly empty space these values will be diminishingly small. That means the photons are phenomenologically "not there". Physics is all about phenomena and not philosophy. The phenomenon of "photons" is only near and around sinks (places where they may be absorbed) there the wave-function meets "barriers" which confine the photon and allow this function to be significantly positive... that is where it will be absorbed... especially if the site for the sink chosen is resonant with the source... It is a resonant "negotiation" between the source and sink like a transmission line.

If "light" of various frequencies is proposed as a aether and a reason for gravity then I know of no electromagnetic radiation not even gamma rays that would penetrate sufficiently into the earth to provide the impression that the earth was not hollow. Remember these "forces" must be reactive on the sources as much as on the sinks to allow for mutual "attraction". Too many photons are absorbed in the periphery of massive objects to allow EM radiation to be a candidate for "gravity". To electromagnetic radiations of every kind the earth would appear as a hollow shell because the force carriers (photons) could not penetrate sufficiently deeply to allow all the mass inside the earth to be "probed" and therefore allow the earth to be accurately "weighed". Gravity cannot be blocked (as far as we know)... not even partially... by any depth or density of material substance . That rules out electromagnetic radiation of all frequencies as a "background for the aether.

There are other forms of radiation (non-electromagnetic) such as neutrinos and they make a more plausible "aether" because of their immense ability to penetrate matter without being substantially absorbed.

It is an interesting point to ponder that aside from the fact that light travels at the speed of light and is simultaneously affected by electrodynamics and also by gravity and "falls" identically like a projectile along the "surface of spacetime" and is a "limiting case of material projectiles" as V -> C. This suggests there really is not action at a distance dependent on the mutual mass between particles since such a theory would mean that if one of the two "attractive" objects was of zero rest mass there would be no "attraction" at all. It is possible to demonstrate very effectively that photons have zero rest mass. So... photons "fall" like a very light stone that is traveling infinitely close to the speed of light.

Not quite, Good Elf! Maybe you were keeping it simple, but see that squared-off circle representing a single electron? It's deflected half as much as light:

  ←
↓    ↑
  →

I was keeping it simple... It is only meant to relate to General Relativity so I am not dealing with charged species like an electron. The photon bears no nett charge and has no mass... an ideal object to illustrate this principle. I also assume that the manifold in General Relativity is curved only by the masses embedded in it and there are no fields in that space... we know fields affect light so I am also ignoring that as well.. Under those circumstances photons "fall" unseen like "projectiles" through space and are a limiting case of "ordinary" relativistic projectiles where v -> C. The point to note is while the photon has momentum it has no rest mass but "falls" in an identical manner to any other object with mass. Thus mass is not an attractor as it is in Newton's Theory and Einstein was right in saying Gravity was a pseudo-force. Otherwise light would not curve around massive objects such as in Einstein's first big test of GR and also the reason behind the frequently observed phenomenon of Einstein's Rings [nofollow]. This pseudo-force is clearly all down to simple curvature and the velocity and position of the particle no matter what it is. Now there are more complex interactions involved in the creation of electrons and this theory does not deal with that issue.

I note your point though... Clearly the photon does bear "topological charge"... the twisted strip model shows one way in which this "charge" in permanently charged particles may arise. This would go a long way to realizing JA Wheeler's "dream" of geometrodynamics...

As described by Wheeler in the early 1960s, geometrodynamics attempts to realize three catchy slogans

    * mass without mass,
    * charge without charge,
    * field without field.

Already we have pretty convincingly shown that no particle in any place in our universe contains solitary magnetic monopoles so why do electric monopoles (charges) exist??  []... these entities are crucial to the current Standard Model... if no magnetic monopoles and all electric monopoles are simple topological charges then we have realized Wheeler's dream. JA Wheeler I would rate as the greatest physicist never to win a Nobel Prize. Not just for this but many great contributions... not the least of which was being RP Feynman's mentor in his crucial formative years when creating Absorber Theory... the fundamentals on which quantum electrodynamics was constructed which won Feynman a "gong".

The electron in the theory discussed in Williamson and Van der Mark's paper deals with a permanent topological charge in a very energetic optical vortex. These vortices may be created "in the wild" (recent papers have discussed the creation of these entities using simple holograms [nofollow]) and maybe they are stable quantum "resonant" entities with requisite properties of stability. It is possible to explain the charge using this model but it is more difficult to explain mass. This involves the difficult (and reversible) process of "sparking the vacuum"... creating electrons from raw photons. This has been done but it is still very difficult using present technology the electron carries a lot of energy. There is a much easier process of annihilation of the matter anti-matter "electrons" but all these events while complex are seamlessly time reversible.

Conjuring Matter From Light [nofollow]

Speculation: Mass appears to be related to the Orbital Angular Momentum of the internal photon exhibiting as an "external" mass which is linked directly to the conservation laws of CPT symmetry.

Cheers

[Farsight (OP)]

Your comments noted, PhysBang. But it isn't "my theory". All I've done is researched genuine historical material and bona-fide peer-reviewed papers. Einstein really did talk of a non-constant g_uv that causes curvilinear motion along with the aether of general relativity. The modern interpretation of general relativity genuinely seems to paint a different interpretation to Einstein's, and mathematical exercises just don't assist our discussion.   

Ron: I concur with Good Elf re electromagnetic radiation not being the "background". It's something deeper, as demonstrated by say the Aharanov-Bohm effect.   

I was keeping it simple...

Noted, Good Elf. In my experience it's something like plastering a wall. It isn't easy to make it look easy. 

I note your point though... Clearly the photon does bear "topological charge"... the twisted strip model shows one way in which this "charge" in permanently charged particles may arise. This would go a long way to realizing JA Wheeler's "dream" of geometrodynamics...

Yes, interesting bloke Wheeler. Yes, I'd say he was barking up the right tree. It's all in the geometry. But there's this subtle shift that's easy to miss. 

The electron in the theory discussed in Williamson and Van der Mark's paper deals with a permanent topological charge in a very energetic optical vortex. These vortices may be created "in the wild" (recent papers have discussed the creation of these entities using simple holograms) and maybe they are stable quantum "resonant" entities with requisite properties of stability. It is possible to explain the charge using this model but it is more difficult to explain mass.

Interesting paper, the tying light in knots. I'm confident that:

The study of knotted vortices was initiated by Lord Kelvin back in 1867 in his quest for an explanation of atoms", adds Dennis, who began to study knotted optical vortices with Professor Sir Michael Berry at Bristol University in 2000. "This work opens a new chapter in that history."

..is not a casual comment. We should discuss mass at length, perhaps in a dedicated thread. We have so much to talk about!   

Speculation: Mass appears to be related to the Orbital Angular Momentum of the internal photon exhibiting as an "external" mass which is linked directly to the conservation laws of CPT symmetry.

I don't see why you flag this as a speculation. Pair production and annihilation are bona-fide science, along with electron spin and angular momentum. We create mass from a massless photon, and we destroy it via electron/positron annihilation. You started with light travelling laterally at c conveying momentum, and you ended with light travelling laterally at c conveying momentum. In between you have inertia. Mass. The electron and positron are quite literally made from light, and the annihilation evidence says there's nothing else there. There's no evidence for any coupling with a new field. So I'd class the OAM relation where light couples with itself as the reasonable deduction, not the speculation.

[PhysBang]

Your comments noted, PhysBang. But it isn't "my theory". All I've done is researched genuine historical material and bona-fide peer-reviewed papers.

No, it really is your theory because you are making claims about experiments and observations that contradict what every scientist who uses relativity theory claims. For example, you say that relativity theory, if used "correctly", will produce the right rotation curves for galaxies. However, every scientist working in astronomy and astrophysics says that this doesn't happen.

Einstein really did talk of a non-constant g_uv that causes curvilinear motion along with the aether of general relativity.

When you say this, you are obviously ignoring what Einstein said about the aether. You even ignore what the author of the page hosting your favourite link to Einstein's address says about that address. This author writes on the page, "This address has been frequently misunderstood as positing that a return of the ether theory." Anyone who reads the address or the page must see that Einstein is clearly rejecting the standard idea of an aether theory in favour of, at best, an idea that bears only one feature of an aether theory, that of being a medium.

The modern interpretation of general relativity genuinely seems to paint a different interpretation to Einstein's, and mathematical exercises just don't assist our discussion. 

We are not talking about mathematical exercises, we are talking of the actual content of the theory. When you say that relativity theory does away with the need for dark matter, you are making a claim about actual values that are measured and actual values that are calculated. You have shown no way to reconcile these values. If you have a way to reconcile these values, you should share it. If you have no way to reconcile these values, you should retract your claims. You need to show exactly how "a non-constant g_uv that causes curvilinear motion along with the aether" produces the calculations for the rotation curve of a galaxy and how this calculation matches up with the observed rotation curve. An astronomer or an astrophysicist who makes a claim about dark matter backs up her or his claim with the relevant observations and calculations.

I note that you have retracted some of your previous claims. For example, you have removed your two calculations of the size of the universe from your public document version of your theory, two calculations that differed by several orders of magnitude. Many actual scientist retract claims when they have made an error. If your claims about dark matter are in error, it is no shame to retract them.

[Farsight (OP)]

No, it really is your theory because you are making claims about experiments and observations that contradict what every scientist who uses relativity theory claims. For example, you say that relativity theory, if used "correctly", will produce the right rotation curves for galaxies. However, every scientist working in astronomy and astrophysics says that this doesn't happen.

I'm not making claims that contradict relativity. We all know that Einstein missed the expansion of the universe, it's just a trivial matter of looking at what Einstein said about inhomogeneous space and then applying knowledge of the expanding universe. As for "every scientist", you should read Mordehai Milgrom's New Physics at Low Accelerations (MOND): an Alternative to Dark Matter at http://arxiv.org/abs/0912.2678. Note page 4 where he says:

"We see that the modification of GR entailed by MOND does not enter here by modifying the ‘elasticity’ of spacetime
(except perhaps its strength), as is done in f(R) theories and the like."

I've merely stated the obvious. Einstein told us that a gravitational field is a region of inhomogeneous space, and we all know of the raisins-in-the-cake analogy for the expanding universe. Space expands between the galaxies but not within, giving rise to another source of inhomogeneous space. According to Einstein, that's a gravitational field, with no causative matter. I really can't see why you have such a problem with this.

When you say this, you are obviously ignoring what Einstein said about the aether. You even ignore what the author of the page hosting your favourite link to Einstein's address says about that address. This author writes on the page, "This address has been frequently misunderstood as positing that a return of the ether theory." Anyone who reads the address or the page must see that Einstein is clearly rejecting the standard idea of an aether theory in favour of, at best, an idea that bears only one feature of an aether theory, that of being a medium.

I'm not obviously ignoring anything, I'm reporting what Einstein said. He talked about a non-constant g_uv that causes curvilinear motion, and he talked about the aether of general relativity. See http://www.zionism-israel.com/Albert_Einstein/Albert_Einstein_Ether_Relativity.htm. What more can I say? There it is, in black and white. 
 

We are not talking about mathematical exercises, we are talking of the actual content of the theory. When you say that relativity theory does away with the need for dark matter, you are making a claim about actual values that are measured and actual values that are calculated. You have shown no way to reconcile these values. If you have a way to reconcile these values, you should share it. If you have no way to reconcile these values, you should retract your claims.

No I shouldn't. We have free speech in science, and observations and comments are permitted. 

You need to show exactly how "a non-constant g_uv that causes curvilinear motion along with the aether" produces the calculations for the rotation curve of a galaxy and how this calculation matches up with the observed rotation curve.

As above.

An astronomer or an astrophysicist who makes a claim about dark matter backs up her or his claim with the relevant observations and calculations.

But even to this day, no astronomer or astrophysicist can provide conclusive proof for the existence of dark matter. It remains the subject of debate. And since it was first proposed by Zwicky seventy three years ago, we are surely free to discuss alternatives. People are discussing them more, and proposing experiments, see for example Testing MOND/TEVES with LISA Pathfinder by Christian Trenkel, Steve Kemble, Neil Bevis, and Joao Magueijo at http://arxiv.org/abs/1001.1303.

I note that you have retracted some of your previous claims. For example, you have removed your two calculations of the size of the universe from your public document version of your theory, two calculations that differed by several orders of magnitude. Many actual scientist retract claims when they have made an error. If your claims about dark matter are in error, it is no shame to retract them.

I haven't retracted anything. I never gave any calculations, I reported two numbers, a contradiction was pointed out, so I removed the contradiction. That was back in January 2008, see "last updates". And please can we stay on topic.

[PhysBang]

As for "every scientist", you should read Mordehai Milgrom's New Physics at Low Accelerations (MOND): an Alternative to Dark Matter at http://arxiv.org/abs/0912.2678. Note page 4 where he says:

"We see that the modification of GR entailed by MOND does not enter here by modifying the ‘elasticity’ of spacetime
(except perhaps its strength), as is done in f(R) theories and the like."

Perhaps you failed to notice that this proposes a modification of GR. Do you propose a modification of GR?

I've merely stated the obvious. Einstein told us that a gravitational field is a region of inhomogeneous space, and we all know of the raisins-in-the-cake analogy for the expanding universe. Space expands between the galaxies but not within, giving rise to another source of inhomogeneous space. According to Einstein, that's a gravitational field, with no causative matter. I really can't see why you have such a problem with this.

The widely examined and accepted cosmological models are not relevant here. I have a problem with your claims because you are denying the facts. The facts are that the rotation curves of galaxies do not work out unless we include dark matter. Please show us, and the entire scientific community including Milgrom, how standard GR can produce the rotation curves of galaxies without the need for dark matter.

I'm not obviously ignoring anything, I'm reporting what Einstein said. He talked about a non-constant g_uv that causes curvilinear motion, and he talked about the aether of general relativity. See http://www.zionism-israel.com/Albert_Einstein/Albert_Einstein_Ether_Relativity.htm. What more can I say? There it is, in black and white. 

Indeed it is. But somehow, you have it in your head that g_uv isn't exactly what everyone means when they speak of curved spacetime. It's like you are pointing at a picture from Picasso's blue period and telling everyone that the painting is done entirely in red paint.

We are not talking about mathematical exercises, we are talking of the actual content of the theory. When you say that relativity theory does away with the need for dark matter, you are making a claim about actual values that are measured and actual values that are calculated. You have shown no way to reconcile these values. If you have a way to reconcile these values, you should share it. If you have no way to reconcile these values, you should retract your claims.

No I shouldn't. We have free speech in science, and observations and comments are permitted. 

You aren't entirely correct; we are not in a venue of free speech. For example, I was banned from this forum for saying true things about you that are relevant to understanding your position. At the risk of further banning, I will point out that your refusal to actually acknowledge the data that exists, as you are fee to do, should be taken as a symptom that you really do not understand anything in this field and that your claims are bogus.

An astronomer or an astrophysicist who makes a claim about dark matter backs up her or his claim with the relevant observations and calculations.

But even to this day, no astronomer or astrophysicist can provide conclusive proof for the existence of dark matter. It remains the subject of debate. And since it was first proposed by Zwicky seventy three years ago, we are surely free to discuss alternatives. People are discussing them more, and proposing experiments, see for example Testing MOND/TEVES with LISA Pathfinder by Christian Trenkel, Steve Kemble, Neil Bevis, and Joao Magueijo at http://arxiv.org/abs/1001.1303.

If we look at that paper, we see attempts to reconcile different theories to the various observations though comparisons of predictions and measurements. This is, again, something you refuse to do. This is what makes it plain that your position is not a scientific one but one not far from fiction.

I note that you have retracted some of your previous claims. For example, you have removed your two calculations of the size of the universe from your public document version of your theory, two calculations that differed by several orders of magnitude. Many actual scientist retract claims when they have made an error. If your claims about dark matter are in error, it is no shame to retract them.

I haven't retracted anything. I never gave any calculations, I reported two numbers, a contradiction was pointed out, so I removed the contradiction. That was back in January 2008, see "last updates". And please can we stay on topic.[/quote]
This is very much on topic, as your refusal to acknowledge the facts here highlights your refusal to engage the science in an honest and open manner. You certainly derived one value, writing, "The universe is larger than the Compton wavelength of a proton by a factor of 10^40. That’s why gravity is weaker by a factor of 10^40." Here you were attempting to use the matching of mathematical results to support your theory, something you refuse to do with your claims about dark matter. When if became obvious that you contradicted yourself by several orders of magnitude, you removed the statement and now you say that you haven't retracted anything. Either you still endorse this derivation or you have retracted this derivation. Either you accept that mathematical results are important in science or you do not.

[Ron Hughes]

The widely examined and accepted cosmological models are not relevant here. I have a problem with your claims because you are denying the facts. The facts are that the rotation curves of galaxies do not work out unless we include dark matter. Please show us, and the entire scientific community including Milgrom, how standard GR can produce the rotation curves of galaxies without the need for dark matter.

There is one way Phys, if the equation F = ma is not the same in all frames of reference.

[Farsight (OP)]

Perhaps you failed to notice that this proposes a modification of GR. Do you propose a modification of GR...

Not at all. I report Einstein's statements: a gravitational field is a region of inhomogeneous space caused by a concentration of energy tied up the matter of a planet, which in turn causes the curvilinear motion that is described as curved space-time. I don't deny the facts of general relativity, I report them. They're as described by Einstein, and they are validated by experiment. I'm sorry they're not as you wish them to be, and I'm sorry that the non-uniform expansion of the universe clearly offers another causative agent for inhomogeneous space which dispenses with the need for dark matter. I know it's distressing to you, but after 77 years without validation, dark matter has had its day, and science must progress.

I would urge you to consider Einstein's inhomogeneous space in the light of this statement:

"We see that the modification of GR entailed by MOND does not enter here by modifying the ‘elasticity’ of spacetime (except perhaps its strength), as is done in f(R) theories and the like."

[PhysBang]

I report Einstein's statements: a gravitational field is a region of inhomogeneous space caused by a concentration of energy tied up the matter of a planet, which in turn causes the curvilinear motion that is described as curved space-time.

Einstein did not write or say this anywhere.

I don't deny the facts of general relativity, I report them.

When you say that GR can account for rotation curves without dark matter, you are denying the facts. Anyone who reads the links about MOND you have provided can easily tell this. You could easily prove that all the authors you cite are incorrect with a few calculations. Your refusal bears on your behaviour in general and the character of the theories you offer.

[litespeed]

I like this thread and hope no one gets banned from it. As a practicing lay-person myself, I find such exchanges useful, if not always edifying. Can I throw a pebble into the pond and to see if any interference patterns evolve?

Specifically, General Relativity seems to predict infinite singularities in black holes, but infinities do not exist in our universe. I do not see this as all that alarming. After all, the same sort of thing happened to Newton regarding the weird orbit of Mercury. Now we have another weird phenomenon to think about.

Opinion requested: is (are) additional dimensions outside of, but including, space time considered reasonable possibilities for examination? I am thinking of Vehn diagrams. A single dimension is included in two dimension which is included in three dimensions which is included in four dimensions etc.

[Farsight (OP)]

litespeed: general relativity itself doesn't predict the central black hole singularity. Instead the Misner/Thorne/Wheeler "geometrical interpretation" does. See http://www.mathpages.com/rr/s7-02/7-02.htm and note this bit:

Incidentally, I should probably qualify my dismissal of the "frozen star" interpretation, because there's a sense in which it's valid, or at least defensible. Remember that historically the two most common conceptual models for general relativity have been the "geometric interpretation" (as exemplified by Misner/Thorne/Wheeler's "Gravitation") and the "field interpretation" (as in Weinberg's "Gravitation and Cosmology"). These two views are operationally equivalent outside event horizons, but they tend to lead to different conceptions of the limit of gravitational collapse. According to the field interpretation, a clock runs increasingly slowly as it approaches the event horizon (due to the strength of the field), and the natural "limit" of this process is that the clock just asymptotically approaches "full stop" (i.e., running at a rate of zero) as it approaches the horizon. It continues to exist for the rest of time, but it's "frozen" due to the strength of the gravitational field. Within this conceptual framework there's nothing more to be said about the clock's existence. This leads to the "frozen star" conception of gravitational collapse.

I'd say additional dimensions are OK so long as they're dimensions of measure rather than dimensions that offer freedom of motion. For example we have three dimensions of space through which we can move, but we aren't free to move through the time dimension.
 

Physbang: see http://www.zionism-israel.com/Albert_Einstein/Albert_Einstein_Ether_Relativity.htm

"According to this theory the metrical qualities of the continuum of space-time differ in the environment of different points of space-time, and are partly conditioned by the matter existing outside of the territory under consideration. This space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that “empty space” in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials gμν).."

Einstein said this in 1920, and he talked about curvilinear motion in The Foundation of the General Theory of Relativity in 1916. The theory I offer is Einstein's relativity. I'm not denying the facts.

[PhysBang]

Physbang: see http://www.zionism-israel.com/Albert_Einstein/Albert_Einstein_Ether_Relativity.htm

"According to this theory the metrical qualities of the continuum of space-time differ in the environment of different points of space-time, and are partly conditioned by the matter existing outside of the territory under consideration. This space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that “empty space” in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials gμν).."

Einstein said this in 1920, and he talked about curvilinear motion in The Foundation of the General Theory of Relativity in 1916. The theory I offer is Einstein's relativity. I'm not denying the facts.

This is another example of you cherry-picking quotations. Academics tend to call such behaviour dishonest.

Let's begin with the first sentence of the paragraph, the sentence that you failed to copy:

"Mach’s idea finds its full development in the ether of the general theory of relativity."

This makes it clear that what Einstein is talking about in his paragraph is an idea of Mach, in particular, that that aspect of physics that imparts the properties of inertia to objects is also influenced by these objects.

You are also cherry-picking by ignoring the actual cosmological models designed and endorsed by Einstein throughout his life. You are trying to make the point that it is wrong to ever consider anything to be homogeneous and isotropic in GR, but by ignoring all of Einstein's science and focusing on a single passage from an address out of context, you merely promote ignorance.

If you think that there is a case for GR to account for dark matter, then make the case with the actual observations and calculations of the science, don't cherry-pick statements from Einstein taken from a popular lecture and paste them out of context.

[Farsight (OP)]

I'm not cherry picking, PhysBang. You said Einstein didn't say that stuff about inhomogeneous space etc. But he did. I'm not promoting ignorance, I'm promoting knowledge. I've given you the link, and out of context just doesn't wash. He said what he said.

[demografx]

PhysBang, let's keep ad hominems out of the forum. Such as accusations of dishonesty and promoting ignorance.

Talk to the facts, and only the facts, such as those on public record. Offer your interpretation, if you wish, be specific, then let the readers decide for themselves if there is any distortion going on.

Thank you.

[PhysBang]

PhysBang, let's keep ad hominems out of the forum. Such as accusations of dishonesty and promoting ignorance.

To commit an ad hominem is to perform an ignotario elenchi argument. That is, it is to bring up facts irrelevant to the matter at hand. I have done no such thing. It is relevant to understanding Farsight's claims that one understand that he is presenting a small subset of the available literature, out of context, in such a way that a reader might be mislead. It is also relevant for a reader to know that Farsight has been made aware of the misleading nature of his presentation and that he continues to present his claims in this manner.

Talk to the facts, and only the facts, such as those on public record. Offer your interpretation, if you wish, be specific, then let the readers decide for themselves if there is any distortion going on.

Part of addressing the facts is to actually show how these facts are presented. In this case, I have to somehow demonstrate that what Farsight is offering is not actually relevant to the points that he wants to make. If Farsight would offer something to work with, namely scientific arguments to back up his scientific claims, then I could engage in an analysis of the facts.

[demografx]

By ad hominem, I simply refer to your character attacks, again, such as your referring to his "dishonesty and promoting ignorance", or "you really do not understand anything in this field."

You did a good job of largely avoiding that in your reply directly above, which expresses and re-states your technical objections, but without the mudslinging.

[Farsight (OP)]

Physbang: I'm afraid it isn't a small subset of the available literature. In 1911 Einstein wrote a paper "On the Influence of Gravitation on the Propagation of Light" where he said "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).". See http://www.relativitybook.com/resources/Einstein_gravity.html for an online version. 

In 1912 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". I’ve got this page as a PDF image, I’ll have to check where it’s from. Similarly in 1913 he wrote "I arrived at the result that the velocity of light is not to be regarded as independent of the gravitational potential".

In 1915 he wrote "However 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."  This is on page 259 of Doc 21.

I’ve already given information from chapter 22 of Relativity: The Special and General Theory written in 1916 where Einstein refers to the postulate of special relativity. I’ve got a page showing the original German, where Einstein says die Ausbreitungsgeschwindigkeit des Lichtes mit dem Orte variiert. Get a German friend to translate it and he will confirm the google translation the speed of light varies with the locality. It’s backed up by the actual scientific evidence of for example the GPS clock adjustment. A GPS clock employs microwaves. That’s light. The clock runs slower because the light moves slower. There’s also the Shapiro delay. It’s a delay, the light moves slower when it passes the limb of the sun. The wiki article on the Shapiro delay even includes the quote from Chapter 22: 

"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)."

All you have to do is look at the original material to understand that the modern interpretation of relativity is different to Einstein’s, and appreciate that this then causes misunderstanding. As an example of this, read Is The Speed of Light Constant? on the Baez website by Gibbs and Carlip, and look at the section on General Relativity. You see the chapter 22 quote again along with the comment “Since Einstein talks of velocity (a vector quantity: speed with direction) rather than speed alone, it is not clear that he meant the speed will change, but the reference to special relativity suggests that he did mean so. This interpretation is perfectly valid and makes good physical sense, but a more modern interpretation is that the speed of light is constant in general relativity.” Lower down the article says “ Finally, we come to the conclusion that the speed of light is not only observed to be constant; in the light of well tested theories of physics, it does not even make any sense to say that it varies.”. Hence the article says Einstein’s variable speed of light makes sense, and doesn’t make sense. 

All of this isn’t out of context, it’s conclusive.

demografx: thank you for your moderation.   

[PhysBang]

Physbang: I'm afraid it isn't a small subset of the available literature. In 1911 Einstein wrote a paper "On the Influence of Gravitation on the Propagation of Light" where he said "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).". See http://www.relativitybook.com/resources/Einstein_gravity.html for an online version. 

Why, if you want to defend a point about general relativity, are you looking at things Einstein wrote before general relativity?

Since you seem to want to use the 1911 theory as representative of Einstein's theory, please show us using this theory where Einstein uses an aether. Additionally, please show us how one can use the 1911 theory to calculate the rotation curves of galaxies. It would be nice if you could also show how this use gets rid of the measurements of the amount of dark matter.

All you have to do is look at the original material to understand that the modern interpretation of relativity is different to Einstein’s, and appreciate that this then causes misunderstanding.

OK, so please demonstrate how, using the 1911 theory or the later theory, the rotation curve of a galaxy doesn't produce a measurement of dark matter.

Hence the article says Einstein’s variable speed of light makes sense, and doesn’t make sense. 

A discerning reader should note that the authors write, "In general relativity, the appropriate generalisation is that the speed of light is constant in any freely falling reference frame (in a region small enough that tidal effects can be neglected).  In this passage, Einstein is not talking about a freely falling frame, but rather about a frame at rest relative to a source of gravity.  In such a frame, the speed of light can differ from c, basically because of the effect of gravity (spacetime curvature) on clocks and rulers." Thus one notes that the authors are pointing out that in the particular passage of Einstein that they quote, Einstein is using an improper generalization. What makes one generalization proper and the other improper is that the proper generalization recognizes the role that light has in determining the causal structure of events. AS the authors note, the constant speed of light is fundamental to the way that general relativity determines causal structure. Thus it is conceptually more fundamental than the time it takes for light to cross a certain distance in a certain time in a certain particular system of coordinates. This is particularly true since the correct description of any physical system in any well-formed set of coordinates in general relativity must maintain this causal structure.

The most well known system of coordinates in general relativity with what one might call a variable speed of light is that associated with the Friedmann equations. These equations provide a solution to the Einstein field equation and the form the basis of a family of cosmological models preferred by Einstein after 1929 and survive in a modified version in contemporary cosmology. In these solutions, light can travel faster than light, because over time the distance between where the light left and where the light is received can get larger. However, one should recognize that this is not a way to measure speed that is representative of the causal structure of the universe and when one takes that into account properly, one finds the speed of light as constant. Despite working with, and accepting as approximately correct, the Friedmann models, cosmologists do not run around saying that the speed of light is variable.

All this is clear from not simply cherry-picking particular parts of the document and from looking at the authors' claims in context.

[Farsight (OP)]

Why, if you want to defend a point about general relativity, are you looking at things Einstein wrote before general relativity?

To demonstrate that I'm not cherry picking. We see Einstein repeatedly telling us the speed of light is variable.

Since you seem to want to use the 1911 theory as representative of Einstein's theory, please show us using this theory where Einstein uses an aether.

I don't. Plus I've already shown you the 1920 Leyden Address where Einstein talks of the aether of General Relativity.

OK, so please demonstrate how, using the 1911 theory or the later theory, the rotation curve of a galaxy doesn't produce a measurement of dark matter.

I politely decline on the grounds that such a laborious exercise is unnecessary in the light of Einstein's description of a gravitational field as inhomogeneous space, along with our current knowledge of the expansion of the universe. Space expands between the galaxies, not within. The result is inhomogeneous space, and that's a gravitational field with no causative matter. 

...As the authors note, the constant speed of light is fundamental to the way that general relativity determines causal structure.

It is at odds with Einstein, who described the central concentration of energy tied up in as the matter of a planet causing a conditioning of the surrounding space described via a non-constant g_μv which causes a variable speed of light that then causes the curvilinear motion that is described as curved spacetime. I've paraphrased, but read the original material, and you will find that I am correct. 

Thus it is conceptually more fundamental than the time it takes for light to cross a certain distance in a certain time in a certain particular system of coordinates. This is particularly true since the correct description of any physical system in any well-formed set of coordinates in general relativity must maintain this causal structure.

No, I'm afraid it isn't. What's conceptually more fundamental relates to what we actually observe. We don't observe time passing, our seconds are defined using the motion of light. Thus when our second changes, it's because the rate of motion of light has changed. 

The most well known system of coordinates in general relativity with what one might call a variable speed of light is that associated with the Friedmann equations. These equations provide a solution to the Einstein field equation and the form the basis of a family of cosmological models preferred by Einstein after 1929 and survive in a modified version in contemporary cosmology.

Noted.
 

In these solutions, light can travel faster than light, because over time the distance between where the light left and where the light is received can get larger. However, one should recognize that this is not a way to measure speed that is representative of the causal structure of the universe...

No, of course not. There are galaxies receding from us at more than c due to the expansion of the universe, but we do not consider them to be actually moving at more than c.   

..and when one takes that into account properly, one finds the speed of light as constant.

I'm afraid one doesn't. One only "finds the speed of light to be constant" when one employs the motion of light to define one's seconds and metres to then measure the speed of light. It isn't constant, Einstein said it, gravitational time dilation is scientific fact, and our best clocks are atomic clocks which count microwave peaks. Those clocks run slower when the light moves slower. The scientific evidence is there, and "when one takes that into account properly" in no way counters it.   

Despite working with, and accepting as approximately correct, the Friedmann models, cosmologists do not run around saying that the speed of light is variable.

But I'm afraid some do. See for example http://en.wikipedia.org/wiki/Variable_speed_of_light and http://arxiv.org/PS_cache/arxiv/pdf/0705/0705.4507v1.pdf where Magueijo and Moffat responded to Ellis. Its constancy has become a tautology.