Physics Discussion Forum

Einstein and general relativity

Einstein started with the constant speed of light as a postulate in 1905 when he was doing special relativity, but by 1911 he was getting into general relativity. That's when he wrote On the Influence of Gravitation on the Propagation of Light, where he said this:

Einstein wrote:If we call the velocity of light at the origin of co-ordinates co, then the velocity of light c at a place with the gravitation potential Φ will be given by the relation c = c_o(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". Here it is again in Die Relativitätstheorie in 1915 where 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:

Einstein wrote: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 Ausbreitungs-geschwindigkeit des Lichtes mit dem Orte variiert." I’ve got the original German version, and 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. He backed it up in his 1920 Leyden Address, where he said this:

Einstein wrote: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.

The thing to note here is that space is inhomogeneous, so light follows a curved path over time, hence curved spacetime. It's like a car veers when the near-side wheels encounter mud at the side of the road. It really is that simple.

Newton's density gradient

What's rather surprising is how similar all this is to the way Newton described it in Opticks queries 20 and 21:

Newton wrote: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?

The language is different, and the density is kind of back-to-front, 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 g_μν along with a gradient in c which causes curvilinear motion.



To many people this is unfamiliar and unacceptable. They don't appreciate that "interpretation” has changed over the years, as described by Peter M Brown’s Einstein’s Gravitational Field. They tend to overlook modern papers like Inhomogeneous Vacuum: An Alternative Interpretation of Curved Spacetime, and some even overlook scientific evidence.

Show some people two parallel-mirror light clocks at different gravitational locations, and they will refuse to believe what they see. You can employ high-powered telescopes and put the two light clocks up on a split screen, and people will still deny the evidence that’s there in plain view. They'll talk about coordinate speed and time dilation and spacetime curvature, but they can't see the obvious: in a place where the gravitational potential is lower, the light goes slower, just like Einstein said. They miss the point that light clocks clock up the motion of light, not the flow of time. When atomic clocks or light clocks "run slow" in a region of low gravitational potential, they do this because the speed of light at that location is less than it is up in space. That’s why we have the GPS clock adjustment, see the wikipedia entry for GPS and relativity. A GPS clock is an atomic clock that employs the electromagnetic hyperfine transition and microwaves. The clock runs slower because electromagnetic phenomena move slower. This is why the Shapiro delay is called what it is. It’s a delay, the light moves slower when it passes the limb of the sun. And this doesn’t just affect light. It affects everything. It affects electromagnetic things like electrons, because of what pair production is showing us: we can literally make matter from light.

How Gravity Works

People tend to think of gravity as “curved spacetime”, but that's actually the effect, not the cause. Curved spacetime is the name we apply to curvilinear motion through space. To get back to the cause you have to recall Einstein's inhomogeneous space, and look at the derivative of that curved spacetime. That's the g_μν gradient. It's a gradient in the properties of space. And it's caused in turn by the central energy locked up in the matter of a planet that “conditions” the surrounding space. It’s all to do with stress-energy and pressure, and the best way to conceptualize it is to start with an old favourite. Think about the cannonball in the rubber sheet. The cannonball is heavy, and it makes a depression that will deflect a rolling marble, or even cause the marble to circle like an orbit. It’s a nice analogy, but it relies on gravity to pull the cannonball down in the first place, so it is rather circular.



To get a better analogy, imagine you’re standing underneath the rubber sheet. Grab hold of the rubber around the cannonball and pull it down to give yourself some leeway. Now tie a knot underneath the cannonball, get rid of the cannonball, and let go. Now we’ve got a flat rubber sheet with a knot in it. The knot is a "stress configuration", and surrounding it is tension. The tension gradually reduces as you move away from the knot, so if you could measure it, you would measure a radial gradient. But note that this rubber sheet represents space, and there’s no stepping outside of it. Our “marble” has to be within the sheet, and a part of it. What we need is a ripple. A photon will do, because a photon is a transverse wave, also known as a shear wave. In mechanics a shear wave travels at a speed determined by the stiffness and density of the medium: v = √(G/ρ). The G here is the shear modulus of elasticity, to do with rigidity. The ρ is the density. The equation says a shear wave travels faster if the material gets stiffer, and slower if the density increases. You can’t directly apply material concepts to space, but in electrodynamics the equation is somewhat similar: c = √(1/ε₀μ₀). Here ε₀ is electric permittivity and μ₀ is magnetic permeability. People often don't understand these terms because they don't know about the dualism of Jefimenko's equations, or about Minkowski's wrench, which is two pages from the end of Space and Time:

Minkowski wrote:Then in the description of the field produced by the electron we see that the separation of the field into electric and magnetic force is a relative one with regard to the underlying time axis; the most perspicuous way of describing the two forces together is on a certain analogy with the wrench in mechanics, though the analogy is not complete".

Minkowski's wrench is referring to a screw mechanism. It goes back to Maxwell’s On Physical Lines of Force see page 53. In essence the electric field is like the twist in the screw, and the magnetic field is like the rotation that comes with it. So permittivity is telling you the "twistability" of space, and permeability is telling you how good it is at making things turn. Hence they're similar to stiffness and density, and the photon is similar to a ripple in a rubber sheet. But this rubber-sheet analogy still isn't perfect, because in the rubber sheet, the speed increases as we approach the knot. For space, speed doesn’t increase as we approach our central stress. Instead it reduces, because the pressure is outward rather than inward. It’s like pushing your fingers into a taut rubber sheet and then spreading them. The energy conditions the surrounding space to create a negative tension gradient, a pressure gradient. And of course we live in three dimensions not two, so we need to move on from a rubber sheet to something like a clear transparent jelly squeezed into a glass box. And then we need to bring in vacuum impedance, which is Z₀ = √(μ₀/ε₀). Impedance is like resistance, but for alternating current rather than direct current. You might wonder why alternating current is important here, but it's very simple. That's what a light wave is:



There's an electromagnetic field variation, first one way, then the other, and you just can't have this field variation without some form of current. It isn't conduction current, it's displacement current. And impedance to this current increases as we approach the central matter/energy stress, and that results in a lower velocity because c = √(1/ε₀μ₀). Hence when a photon passes a massive body, it's travelling through inhomogeneous space where there's a gradient in c across the photon wave-front. Hence it veers towards the body a little. The result is the refraction we call gravitational lensing. Here’s the crucial point: our real world is like ghostly transparent block of rubber containing ripples of stress, some of which are tied into knots called matter. And we are a part of it, we are ripples and knots too. We are painted into the bulk of the "rubber" that is space. Like Flatlanders, we stretch with it. We are made out of this insubstantial fabric. We are so totally immersed in it and so much a part of it that we cannot directly measure any change in vacuum impedance. And nor can we directly measure any change in the velocity of light, because we calibrate our rods and clocks using the motion of light. And because of what pair production is telling us: anything that affects the speed of light affects electrons, and we can say the same for protons and neutrons. It affects all processes. That's why we can’t measure the change in c locally. But we can measure it from afar, by comparison. It’s there in the gravitational time dilation, programmed into our GPS, in the Shapiro delay, and in gravitational lensing. Gravity doesn't make "time to go slower". There's a gradient in vacuum impedance and hence a gradient in c, and that's why things fall down.

Let’s take a look at an electron to see why things fall down. It has spin angular momentum and a magnetic dipole moment, and since we can make an electron out of light, think of it as light going round and round. Stick a circle of light that looks like this: O, into a gravitational gradient. What’s going to happen? Divide the circle into four flat quadrants to make it even simpler:

..←
↓....↑
..→

Starting from the left and going anticlockwise, at a given instant we have a photon travelling down like this ↓. There’s a gradient in c from top to bottom, but all it does is make the photon look blueshifted. A little while later the photon is moving like this → and the lower portion of the photon wave-front is subject to a slightly lower c than the upper portion. So it bends, refracts, curves down a little. Later it’s going this way ↑ and looks redshifted, and later still it’s going this way ← and bends down again. These bends translate into a different position for our electron. The bent photon path becomes electron motion. The electron falls down:

○
↓

The reducing speed of light effectively bleeds rotational motion out into linear motion. But only half the cycle got bent, so only half the reduced c goes into kinetic energy aka relativistic mass. That’s why light is deflected twice as much as matter. And that’s why gravity is not some magical mysterious action-at-a-distance force. There are no hidden dimensions, there's no blizzard of gravitons sleeting between the masses. It’s just a gradient in the properties of space caused by the central energy density, pretty much as Newton and Einstein said.

In Summary

Imagine a swimming pool. Every morning you swim from one end to the other in a straight line. But one day in the dead of night I truck in a load of gelatine powder and tip it all down the left hand side. This starts diffusing across the breadth of the pool, imparting a viscosity gradient from left to right. The next morning when you go for your swim, something's not right, and you find that you're veering to the left. If you could see your wake, you'd notice it was curved. That's your curved spacetime, because the pool is the space round a planet, the viscosity gradient is Einstein's non-constant g_μν, and you're a photon. As to how the gradient attracts matter, consider a single electron. We can make an electron along with a positron from light, via pair production. Since the electron also has spin, think of it as light trapped in a circular path. So if you're swimming round and round in circles, whenever you're swimming up or down the pool you're veering left. Hence you find yourself working over to the left. That's why things fall down.

See http://ag-physics.org/gravity/ for an article by Albrecht Giese. Edit: I should add that I didn't work this out for myself. I got the picture from reading R F Norgan's 2004 material. Reg talks about aether, and whilst I'm not keen on the word myself, Einstein did talk about the aether of general relativity in his 1920 Leyden Address. And besides, what's the Higgs field anyway? See Is The Vacuum Empty? The Higgs Field And The Dark Energy and http://www.aether-theory.co.uk/.

That was actually quite pleasent to read.

Farsight wrote:and http://www.aether-theory.co.uk/.

From the book website:

Is Space a substance?
Come again?

Modern Physics is based on the premise that Space is not an Aether.
Really? Why?

But if Space is not an Aether then what keeps the stars and galaxies separated from each other?
Holy cow! Our galaxy shows that it cannot keep the stars separated (black hole). Charlatans!

How does light travel across empty Space
Are they crazy? The moment light travels, empty space is no more. Besides, light does not travel across space, it travels in space.

and what determines its very precise velocity through that Space?
Well, not a substance as we all know. Light propagates not through space, but in space. Dammit, just get that right, dammit.

The Aether provides the answers - so why is it still rejected.
Maybe because worshiping an "Aether" like a god is not a solution?

I beg you pardon.

Thanks GD. Don't be so hostile Martin. I'm just giving the guy due credit. If you don't agree with somebody or something, no problem, you're free to say so and say why. But please don't include words like crazy or worship. There's too much of that sort of thing out there on the internet, and in the end it prevents discussion.

Vey interesting article.

As you say Newton was not far off the mark and you can actually translate Einstein back into Newton [1].

In fact we can do this by including the gravitational potential energy in algebraic format in the Newtonian equations. But because we lose tensor calculus in the process, we also lose those nasty little singularities. It turns out that dark matter can also be explained as an effect of the extreme gravity of a supermassive black hole.

It is also possible then to formulate advanced quantum gravity in such a way that also explains "dark energy", which is effectively none other than the old aether [2].

Available online

1.An advanced dynamic adaptation of Newtonian equations of gravity. Physics Essays 21: 222-228.
http://dx.doi.org/10.4006/1.3027501


2. String quintessence and the formulation of advanced quantum gravity. Physics Essays 22: 364-377. http://dx.doi.org/10.4006/1.3182733

Thanks HQT.

HQT wrote:As you say Newton was not far off the mark and you can actually translate Einstein back into Newton [1]. In fact we can do this by including the gravitational potential energy in algebraic format in the Newtonian equations. But because we lose tensor calculus in the process, we also lose those nasty little singularities. It turns out that dark matter can also be explained as an effect of the extreme gravity of a supermassive black hole. It is also possible then to formulate advanced quantum gravity in such a way that also explains "dark energy", which is effectively none other than the old aether [2].

Sounds promising. I dislike point singularities, particularly since they emanate from Misner/Thorne/Wheeler rather than the original general relativity. At the same time I note Einstein's Leyden Address, and yet I've long thought it's not that complicated, surely there must be a better way to express it? Hence I am mindful of Dark Energy: Back to Newton. I have to say though that I don't like the sound of string quintessence and advanced quantum gravity, but more importantly when I try the links to see if this is mere "same elephant" terminology I find I can't read the papers without paying. This is a bit of an journal issue, along the lines of we are the custodians of knowledge and we are running our business on the back of it. But that's not for this thread, let's talk about that offline.

Good point, but for those readers who may be interested in reading the papers, you can of course get free membership of that journal for one year, and then read the paper for free.

But I am now in any case more in favour of publishing in open access journals.