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I've been doing a fair amount of research of original material, and the picture of general relativity that I get seems to be very different to what I was taught.
For example, people tend to say the speed of light is constant, and Einstein said it. But it isn't true. Yes, he started with this as a postulate in 1905, but in 1911 he wrote On the Influence of Gravitation on the Propagation of Light, where we can see his ideas evolving as he talks about c = c0 (1 + Φ/c²). Then in 1916 in section 22 of Relativity: The Special and General Theory he talks further: "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)".IMHO people tend to see the word velocity in the 1920 translation without seeing the context. Many skip over his reference to "one of the two fundamental assumptions", and don't see that he's talking about a serious issue with the SR postulate of the constant speed of light. Many do not realise that Einstein didn't speak English in 1916, and what he actually said was die Ausbreitungsgeschwindigkeit des Lichtes mit dem Orte variiert. This translates into the speed of light varies with the locality. He was saying the speed varies with position, hence the reference to that postulate. And what he also said, is that this causes the light to follow a curvilinear path like a car veers when the near-side wheels encounter mud at the side of the road.
People often react badly this.
People think Einstein told us about curved spacetime, but when you read The Foundation of the General Theory of Relativity, incredibly, it's just not there. Yes, he talks about geometry and curvature and space-time, but he's giving the equations of motion, through space.
He doesn't talk about "motion through spacetime" like people do these days.
But perhaps the signal most important thing most people don't know, is that whilst aether is a taboo word which is most definitely out of the mainstream, Einstein's gave his Leyden address in 1920. And the title is Ether and the theory of relativity. There's Einstein, talking about space and calling it an aether: "Mach’s idea finds its full development in the ether of the general theory of relativity. 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), has, I think, finally disposed of the view that space is physically empty".
What's especially surprising is how similar it is to the way Newton described it in Opticks:Doth not this aethereal medium in passing out of water, glass, crystal, and other compact and dense bodies in empty spaces, grow denser and denser by degrees, and by that means refract the rays of light not in a point, but by bending them gradually in curve lines? ...Is not this medium much rarer within the dense bodies of the Sun, stars, planets and comets, than in the empty celestial space between them? And in passing from them to great distances, doth it not grow denser and denser perpetually, and thereby cause the gravity of those great bodies towards one another, and of their parts towards the bodies; every body endeavouring to go from the denser parts of the medium towards the rarer?" queries 20 & 21The language is different, but the underlying concept is the same. The energy tied up as the matter of a planet "conditions" the surrounding space to create a non-constant gμν along with a gradient in c which causes curvilinear motion. To many people this is unacceptable, because it isn't what they've been taught. It doesn't matter that it comes from Einstein and Newton and is supported by experimental evidence, they refuse to believe it.
Show them two astronauts carrying parallel-mirror light clocks at different locations, and they will refuse to admit what the different readings on those light clock is telling them.
Why is it that people seem unable to see what Einstein actually said, or the evidence that supports it?
Claiming that my mathematics or education is lacking or that I've been repeatedly banned doesn't make up for sincere discussion of this important matter.
It's quite clear what Einstein said, and my astronauts example is fully supported by the GPS clock adjustment and the Shapiro time delay.
All: see http://arxiv.org/abs/physics/0204044 for Einstein's Gravitational Field by Peter M Brown. It's a very interesting paper, well worth reading:
Refraction is the change in direction of a wave due to a change in its speed. This is most commonly observed when a wave passes from one medium to another at an angle. Refraction of light is the most commonly observed phenomenon, but any type of wave can refract when it interacts with a medium, for example when sound waves pass from one medium into another or when water waves move into water of a different depth...Wikipedia: Refraction [nofollow]
There is a local expression of forces (evanescent field) and a distant expression of forces (far field). The local expression of forces are in the near field and are associated with the notion of "virtual particles" in which the fluxes of "field lines" associated with the sources are not "detached from their sources"
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.
Gravity is deemed "symmetric" (unipolar) while electromagnetism is "anti-symmetric" (bipolar). We often discuss "forces" when we deal with these two different phenomena but the theory of forces cannot account for this alone since "forces" are actions at a distance while everything appears to point to an explanation due to the interaction between "particles" which depends on their mutual interactions. I would point out "a particle" is also a paradigm that might be hindering our ideas about "forces".
That "primary force" of gravity and the "primary force" of electromagnetism (charge and magnetism) do not appear to be primarily the result of the exchange of "force carriers" or due to continuous accelerations in the matter or charge sources. Einstein thought of gravity as a pseudo-force and is explained by his local theory of spacetime curvature.. his "General Theory of Gravatation" (ED: spacetime was a concept Minkowski invented not truly Einstein's own original idea but "near enough").
This was summed up by John A. Wheeler as "Matter tells space how to curve, and space tells matter how to move".
Action at a distance for these "gross effects" is not required. A simplistic view of this concept is like a skateboard in a skateboard park.. the board moves according to it's velocity and the curvature directly under it's wheels at each instant in time and does not require the concept of a "distant source of force" attracting the skateboard be needed to explain it. That was another visual analogy so do not think too much about that simple notion.
Likewise gravity "appears" to not require distant forces to motivate the gross motion of planets of the rotation of galaxies... it gets it "moving orders" from the local curvature of spacetime. The complementary particle to the photon... the graviton would then play the same role as a photon in electromagnetism and would involve "real" gravitons but gravity... that we measure mass by using a set of scales... plays the same role as the electromagnetic forces we see in magnets electric motors and moving charges of various types... the mass "fluxes" (like the electromagnetic fluxes) remaining attached to the "sources" (whatever they are)and neither "primary force" requires propagating light or propagating gravitons. what I mean by this in the case of gravity curved spacetime explains the motion of celestial bodies while in electromagnetism charged particles (and magnetism) and their quasi-stationary fields explain the "forces" between charges. Each of these phenomena might appear to be separate and acting on different "manifolds" but a theory of combing these manifolds was Einstein's dream and is the base motivation for current String Theory today. The distant influence of both gravity and light due to carriers of force require the idea of accelerations in the sources generating these particles. There are some problems with all these theories.
I am not "undervaluing" the influence of light since almost everything in the universe we can sense is the effect of either quantum electrodynamics or of gravitation. The other forces (weak, strong forces) are not essential for the things we appreciate (may also be even detrimental) on a day to day basis and are involved with "nuclear radiations" of various kinds... so "light" and therefore photons in all their forms are very important to the way our world works... both real photons and virtual photons in all the forms of the motion of sources of the apparent permanent charge. Of course matter also plays a role in there as "mass" and as "matter waves" but this is not explained by QED.
Now returning to the core issue... Regarding the curvature of spacetime in the General Theory of Gravatation it might be "directly compared" with the property of optical diffraction in refractive materials. So instead of speaking about curved spacetime and Einstein had spoken in terms of a "gravitational refractive index" then this would effectively embed "matter" in an unseen medium whose property was to alter the speed of light rather than "warp some kind of unseen membrane" which we currently identify as "mass". The optical refractive index of a medium is a reflection of the speed of light through the medium and the speed of light in a vacuum.
With gravity we cannot see any medium so we usually do not invoke a material medium to "conduct" gravity. None has ever been detected. Still... as a pure paradigm it "might be useful" to consider this property as if it did exist. This phenomenon exhibits "optically" as Einstein's Rings and we might like to consider spacetime curvature having a variable gravito-optical density reflecting and paralleling the idea of warping of a membrane. But are refractive index and a hypothetical gravito-optical density the same... No... But why not? That is a very interesting question.
We actually cannot verify the existence of either a "physical spacetime" or a vacuum refractive index altering material properties existing in the empty space around matter... That might be interpreted as a vacuum energy density in some way. This really is not a required part of the Einstein's Theory since all theories have their paradigms and they are taken up or discarded when required. What is important is we all realize that, while the paradigm assists us in visualizing the phenomena, it should not be thought of as the only way of understanding it and the future of science will change it's paradigms more often than some may want. The mathematical description of the theory should be attempting to describe this "mental picture" we have developed of these "forces" but do not be surprised when an experiment changes the results of some of the theory the paradigm is radically modified to account for these perceived conceptual anomalies.
As an additional point... There is very little differentiating "virtual" photons from "real" photons since photons can be created on demand and a sufficiently energetic process can produce these "real" photons from a source embedded in "virtual" photons... A radio transmitter is a source such as this... even the transitions in an atom can produce photons from virtual photons.
On the other hand it is still to be shown experimentally that gravitons really exist to enable the analogy between the photon and electromagnetism and the graviton and gravity to be extended into an overall paradigm.