How Variable Speed of Light Explains Gravity

A little more technical account how GR tests are describes by VSL and how Newton's law is recovered.
14:18: c* is the lower speed of light IN the gravitational field, not OUTSIDE. Same for frequencies and wavelengths.
16:42: 1,75'' was not yet found by Einstein in 1911, but in 1915.
18:00 Discussing the blueshift wen photons fall into the gravitational field. The redshift occurs of course when the photons come out.

[howardlandman]

Einstein wasn't the only one considering VSL. For example, Ishiwara wrote in 1912 that
"if the speed of light varies in space and in time, then these variations lead to the appearance precisely there of a gravitational field." [Ishiwara, J., Zür Theorie der Gravitation, Phys. Zeitschrift 15, 1189-1193 (1912), translated by Barbour in Vizgin, Unified Field Theories in the First Third of the 20th Century, Birkhäuser Verlag, Switzerland (1994)]

[GreylanderTV]

Hi, I have not watched all your videos yet, but variable speed of light is something I have often pondered. Something that seemed pretty obvious to me early on in studying GR, but in part due to a hint given by one of my professors, is that you can reformulate general relativity in terms of a variable speed of light which depends on both space and direction. In essence you exchange the metric tensor, g, with an inverse "speed of light" tensor C given by g = c/C (treat /C as tensor inverse, with c just a scalar constant). Furthermore, we restrict ourselves to coordinate systems in which the metric does not mix space and time. This is always possible because there are 4 degrees of freedom in choice of coordinate system, meaning the metric tensor only has six physically meaningful degrees of freedom. The spatial components of g and C each form a 3 tensor, g3 and C3 respectively. These are the physically meaningful fields for GR. Note that we can interpret g3 as a tensor generalization of "index of refraction": C3=c/g3. You get the speed on light in a particular direction from C3*dx, where dx is a spatial vector.

We can rewrite any physical equation in terms of C rather than g. And all experimental predictions of physics remain unchanged. We are simply re-writing and re-interpreting the equations. Et voila! Variable speed of light.

Nothing forces us to accept the geometric interpretation. Or we could even allow that g3 and C3 could depend on both "geometric" and "index of refraction" components. Either way the physics does not change. It might be argued that this formulation is less elegant, but I think it dispenses with unnecessary assumptions. It also avoids a great deal of misleading physical intuition that results from playing around with coordinate systems that mix space and time coordinates, something which is physically meaningless.

Thoughts?

[idan]

Dear Alexander,

Around 1911 Einstein proposed to incorporate gravitation into a modified version of special relativity by allowing the speed of light to vary as a scalar from place to place in Euclidean space as a function of the gravitational potential. This "scalar c field" is remarkably similar to a simple refractive medium, in which the speed of light varies as a function of the density. Fermat's principle of least time can then be applied to define the paths of light rays as geodesics in the spacetime manifold. Specifically, Einstein wrote in 1911 that the speed of light at a place with the gravitational potential Δφ would be c'=c0(1+Δφ/c^2), where c0 is the nominal speed of light in the absence of gravity. In geometrical units we define c0 = 1, so Einstein's 1911 formula can be written simply as
c' = 1+Δφ. However, this formula for the speed of light – indeed, this whole approach to gravity – turned out to be incorrect. In the general theory of relativity, completed in 1915, the speed of light in a gravitational field cannot generally be represented by a simple scalar field of c values in Euclidean space, due to the intrinsic curvature of spacetime. In terms of some quite natural coordinate systems, the speed of light varies not only from place to place, but also in different directions at any given place (even though the speed of light always has the invariant value c in terms of local free-falling inertial coordinates, consistent with the equivalence principle). For example, near a spherically symmetrical and non-rotating mass, we can define stationary coordinates in which the speed of light is isotropic, but in these coordinates the circumference of a circular orbit of radius r is not equal to 2πr. On the other hand, we can define stationary coordinates in which a circular orbit of radius r does equal 2πr, but in terms of these coordinates the circumferential speed of light differs from the radial speed. The former is given by the same formula as in Einstein’s 1911 paper, but the latter differs from the 1911 formula by a factor of 2 on the “potential” term: c'=c0(1+2Δφ/c^2) or again, c'= 1+2Δφ (In geometrical units)..

To explain this in detail, we must first consider how the Schwarzschild metric is derived from the field equations of general relativity. To deduce the implications of the field equations for observable phenomena Einstein originally made use of approximate methods, since no exact solutions were known. These approximate methods were adequate to demonstrate that the field equations lead in the first approximation to Newton's laws, and in the second approximation to a natural explanation for the anomalous precession of Mercury. However, these results can now be directly computed from the exact solution for a spherically symmetric field, found by Karl Schwarzschild in 1916. As Schwarzschild wrote, it's always pleasant to find exact solutions, and the simple spherically symmetrical line element "let's Mr. Einstein's result shine with increased clarity".

Thank you,

[SuperMagnetizer]

It seems plain to me that just as light is refracted when entering glass or water, so is it also refracted when entering stronger fields of gravity, and for the same reason. The speed of light is reduced in both cases, which has nothing to do with curved spacetime.

[nealesmith]

I've been interested in this for at least 30 years but never saw it discussed before. Very interesting!

[jimmyzhao]

Someone should write a formal paper on this theory and win a *Nobel Prize*

[garrythorp]

Replacing distance with time at c gives a (newG/massp) about equal to (upqk/totalqk) in p.

[GamesBond.]

Afaik the only known cause for light refraction is related to a change in the propagating medium. So in space I think it refracts mostly because of the medium made of plasma gas which surounds the sun, and the galaxies. As soon as it leaves that medium and enters another medium free of plasma it will change its speed and refract. Galactic redshift could also be caused by charged plasma gas (but not only by it), as apparently there is a phenomenon called `plasma redshift`. Light waves loose energy when traveling through charged plasma because it collides with electrons and there is an energy transfer. Since E=hf, a drop in energy is equivalent to a drop in frequency, which causes a redshift effect.

[jeromemalenfant]

I don't understand how a variable speed of light theory explains the gravitaitonal red shift if only the wavelength but not the frequency of light changes when the light slows down near a massive object. As an analogy, light slows down in water comparted to air, but if you're standing at the bottom of a pool the light coming down to you from a source above the pool does not appear redder. That's because our eyes respond to the frequency of the light, not the wavelength, and the frequency of the light doesn't change as it goes from air to water.

Also, I thought that Einstein's first attempt at a theory of gravity, namely a 'variable-speed-of-light' theory, gave the wrong answer for the deflection of light by the Sun; i.e. the same value as Newton's theory, but half of what Einstein's later, complete theory of general relativity predicted.

And does a VSL theory explain frame dragging due to a rotating massive object, an effect predicted by GR and confirmed by the Gravity Probe B mission?

[m.j.r.technologyreveiws]

Nice! A mathematical explanation of my perceived thoughts on the matter. Our perception from within our earths and solar systems and galaxies gravitational field is that everything we see farther and farther outside our gravity well is more and more redshifted. Meaning it only looks to us like it’s accelerating away.

[ChrT]

Einstein's general relativity correctly predicted gravitational waves which have since been proven to exist (indirectly, then directly). Gravitational waves cannot be explained simply by a variable speed of light. Obviously, black holes also cannot be explained by VSL since if just the speed of light is varying, the light path will always be reversible. And in recent times, we have made a picture of a black hole.

So VSL is at best an approximation to GR for slowly changing and weak gravitational fields.

[philoso]

The equation on page 11:44. Try a substitute c*c for 1/e0/u0. This is a door behind which we can get a deeper understand of g and this universe.

Once we open this door it is easy to understand why I declare that g is derived from e0 and u0, and hence Aether.

Aether was ruled out from our ignorance. It is not too late to reincarnate it.

[hjstd]

This dovetails nicely with Rupert Sheldrake's idea that constants we expect in the Universe are not constant.

[makeitreality]

Good summary in the beginning. Variable speed of light (VSL) provides an alternative to viewing General Relativity (GR) spacetime as warped or skewed, in either or both space and time axes. This video demonstrates that formulas can be turned around to make light speed the variable quantity. But the interpretation robs Peter to pay Paul. Consider speed as distance over time. If the speed is variable, either or both space (distance) and time axes. The formulas are saying the same thing in different ways! (Which is exactly what to expect when solving for C). But where does this give us any new insight for harnessing or controlling gravity?

[paul_gradenwitz]

Very interesting consideration. Variable speed of light is what we experience in the increased travel time of light that grazes heavy masses as is tested with the Shapiro delay. But since we have with a variable propagation delay that the speed is different for different directions we have to describe that propagation speed as a tensor. I would love to discuss more about that.

[pinchopaxtonsgreatestminds]

The misunderstanding of gravity comes from the Cavendish experiment which does not show mass attracted to mass, it shows ab object moving towards another object, and that's all it shows. you can't see the mass, because mass is resistance to movement, and we weigh stuff. You weigh a sponge, and you weigh a smaller sponge, and you are weighing mass, and you put the big sponge in some water by the small sponge, and water floods into the big sponge, and moves the small sponge towards it.. you have a correlation that the big mass moved the smaller mass towards it.. but it wasn't the mass that moved the smaller sponge, it was the holes in the mass. There is a relationship to mass, and holes in mass, and you can make it a 100% relationship by having the centre of a particle as a hole in space. Now the mass is the weight which is the spin inside the hole, and mass moves towards holes in mass, and gravity spins in the hole. The spin is resistance to movement, because when something is spinning it is not going anywhere apart from the local hole, and the holes are what gravity moves towards, not the spins. Therefore mass is not attracted to mass... and that's going to mess you up every time you use m1 m2. Then a black hole does not need any mass, it just needs to be a hole in space. Then you get new ideas about Dark Matter.

[lantonovbg]

c is constant but G is variable, depending on the local mass density

[reframer]

Great video! Looking forward to see the next one :)

[supercobra]

Hi! I'm working on a theory and my formulas could be interpreted as yours. I'm talking about sum of m over r.
m comes from the quantity of "units of matter" in radius r. Basically, it's volume over radius in the scale of light and that's how you get c squared.

[Naomi_Boyd]

This is a very complicated video for such a simple concept. There are really only 2 propositions that need to be considered.
1. Light always travels at a constant velocity in a vacuum.
2. Light always measures as having the same velocity in a vacuum regardless of the reference frame of the observer.
If gravity dilates time, these propositions are mutually exclusive. They can not both be true.