Gravitational Index of Refraction

Fascinating topic, and beautifully illustrated. Thanks for making this!

I actually recall someone model a black hole in Blender by putting spheres of greater refractive index around it

Grant's @3blue1brown video on refractive index is one of the best I've seen. His microscopic view of individual synchronized oscillations really hits home with how light is observed at the macro level. This takes his work up a major notch. Thank you!

1:47 made me laugh. "ACHTUNG: Schematics are Not to Scale." So hilariously funny! Subscribed.

Incredible. The very way of thinking is new to me, like suddenly being teleported to a new realm. Thank you sir.

You are certainly one of the best persons to explain complex thins in simple words. After Richard Feynman of course. Not even getting into quantum mechanics. Even Huygens–Fresnel simulations are mind blowing for one that tries to visualise it. Thank you so much for the sharing of your work Sir.

Fascinating presentation and theories. I can't help getting the feeling that you're holding back, based on your last statement. I think you are really on to something bigger. Go for it! Best of luck.

Very good video! My instinctive explanation for why the light seems to slow down when going towards the source of the gravity is that due to the space-time curvature there's just more space than there ought to be if the local spacetime was flat, that means the light must take longer to get to the destination which looks to outside observers as if it was slower

My preferred way of understanding gravitational lensing is in terms of Huygens' wavefront hypothesis. I will discuss that in two stages: - First in terms of an early exploratory theory by Einstein (1907), that already had curvature of time, but not yet curvature of space. - Second in terms of the fully fledged GR. Einstein's 1907 explorator theory proposed that deeper in a gravitational well a smaller amount of proper time elapses. So: according to that 1907 exploratory theory: deeper in a gravitational well the locally measured speed of light will be slower. For celestial objects moving at non-relativistic velocity: this curvature-of-time theory reproduces newtonian gravity. Also, the 1907 exploratory theory was already sufficient to account for the (much later conducted) Pound-Rebka experiment. My understanding is that Einstein explored what the effect would be on a Huygens wavefront grazing the Sun. The wavefront would undergo a slight turn, in accordance with the difference in speed of light as a function of radial distance. Einstein arrived at a value of something like 0.8 arc-sec, about half the value that the fully fledged theory predicts. In the years after 1907 Einstein sussed out that the theory needed curvature of space too. One of the clues to that was the Ehrenfest paradox; for a rotating disk the ratio of radius and circumference is not exactly 2pi; there is something non-euclidean going on. In terms of the fully fledged GR: around a source of spacetime curvature the ratio of radius and circumference is not exactly 2pi. As a condition to be satisfied by the theory: the radius/circumference difference is to be such that it precisely matches the gravitational time dilation, such that at any distance to the source of spacetime curvature the same speed of light obtains. That means that for a Huygens wavefront grazing the Sun there is a double whammy. Even when not counting a gravitational time dilation effect: there is a space curvature effect that result in a turning of the orientation of the wavefront. The overall effect is a deflection of 1.75 arc-sec. For light the curvature-of-time aspect of spacetime curvature has a comparatively small effect, because light is moving so fast. There is not enough time; the curvature-of-time effect has very little opportunity to make a difference. It is only for light that the aspect of curvature of space contributes a significant proportion of the total effect. By contrast: for the planets of the solar system the contribution of the curvature-of-space aspect is extremely small; the motion can almost entirely be accounted for in terms of the curvature-of-time aspect. The precession of the perihelion of Mercury correlates with the curvature-of-space aspect, that gives an indication how small that contribution is. I want to emphasize that I am totally onboard with the idea of thinking in terms of index of refraction of a gradient index lens; the spacetime curvature is acting as a gradient index lens.

great video again! it is always fun to see a semi-familiar concept through a different... "lens" 😸

Years have I waited for someone to explain as I've frailly understood the fundamental behaviors of wave theory. Your insight also reinforces the idea of resonant effects concerning the apparent observed phenomena of light slowing through a Bose Einstein condensate from laser synchronization of atomic state to and from the chaotic environment we live from day to day. Light as a particle cannot explain that. Thanks for filling in some of the missing key components so many confuse and for expounding my own thought. If I can understand it so clearly, it's not that difficult. You bring order to chaos.

I loved the visualizations so much! ❤ I'm right now working on my physics degree final project about the bending of light around black holes. The idea of the gravitational index of refraction is not new, but it isn't very well known. This is the first video I see on the topic.

The simulations appear beautiful as they do very well illustrate the intuitive sense we have of how gravitational lensing would distort light, allowing for the problems depicting something this vast on a small screen, and I strongly believe they are useful. Nice work!

We don't use refractive indices in gravitational physics as the refractive index is a function of the coordinates, i.e. every point in space has a different value for n(r). This is in contrast to some medium, e.g. flint glass, that has a constant refractive index of say n=1.58 for some choice of wavelength (also note another difference in that the gravitational field is not dispersive).

There's a nice journal article floating around the internet "F = ma for Optics" by James Evans and Mark Rosenquist that relates potential energy to index of refraction. The potential ~ -n^2 / 2. They go through several elementary examples such as a plane dielectric interface and the case with cylindrical symmetry.

I was delighted to see I might have been nearly right with some of my speculations and I even nearly understood about 50% of what was said. Thank you very much.

I was S O Terrible in doing Lens in my college Physics classes... This sort-of helps....so I will view this video, again.

Defining a (derived) parameter called gravitational index of refraction makes perfect sense... once you realize that what general relativity (and special relativity, as well) actually describes (as "curvature of spacetime") is really how spacetime density changes in the presence of mass (energy). You simply start with the assumption that spacetime is discrete, and made of "spatial cells" (or 4D hyperspehrical nodes)... not of constant, but rather of variable sizes (which is the same as saying that Planck length [and Planck time as well] is not constant, but variable), where size of a cell is inversely proportional to the mass/energy existing in its surroundings, and directly proportional to the distance(s) from that mass/energy. In other words, the greater the mass/energy, and the smaller the distance from that mass/energy, the smaller the size of the spatial cell. This model of variable Planck lengths gives exactly the same results as general relativity, but explains much more intuitively why light (seemingly) slows down as it approaches mass/energy. What really happens in that scenario is that photons propagate through space at constant speed (which is the [constant] speed of light for all observers in all frames of reference), and since spacetime around a massive object is denser, light approaching that massive object has to take more (discrete) steps than light going around it. Light (that is, a photon) still moves at exactly the same speed (defined as c = Planck length / Planck time, where both length and "time" [which is just another spatial dimension] change by exactly the same factor) through spacetime (regardless of spacetime's local density), and it is really the transformations (those equations from special relativity being such transformations) between frames of reference (for an observer close to the massive object and an observer far away from it) that give the illusion of light (and time) moving slower the closer it is to a massive object. I could go into more detail, and explain why spatial cells shrink in the presence of mass/energy, but the gist of it is that it has to do with constraining infinite potential of Dirac delta function (which contains all frequencies [between 0 and infinity]), and one way to do that is by limiting the (infinite) number of (discrete) frequencies by bounding the spacetime in which those frequencies can physically exist. That is, only frequencies that have periods which are whole numbers of (hyperspherical) cell's diameter can physically exist within the cell, and the smaller the cell's size, the less frequencies can physically exist inside of it. Note that there will still be an infinite number of possible frequencies within a smaller cell, but that (infinite) number will be smaller than the (also infinite) number of frequencies possible within a larger cell. I mentioned all of this once, in another channel, but (once again) another way to accomplish this constraining (of infinite potentials) is by increasing the "depth" of the "potential well" that these spatial cells are really acting as, while leaving the size of all the cells constant (exactly the same) regardless of the presence or absence of any mass/energy. Such a (hypothetical) universe would have, more-or-less, the same properties (electromagnetic, strong and weak nuclear forces) as this universe, but it wouldn't have any gravity (or, rather, any gravitational effects) in it. So... yeah, gravitational index of refraction is one way to describe the phenomenon of gravity. Another way would be to define a different (also derived) parameter that we could call 'spatial compression rate' (Scr), or something to that effect, which would describe how the size of spatial cells shrinks in the presence of mass/energy, and this parameter would (obviously) have the (normalized) value of 1 at infinite distance from any mass/energy, and some minimum value at the distance of... not zero (since spacetime is discrete, distance of zero can never be reached), but something really, really small. It should be possible to calculate the smallest possible value for Scr in a given universe, as the smallest possible value corresponds to the size (Planck Length) of the cells on the surface of a black hole which has the size (total mass) of that universe itself (where that black hole has uniform energy distribution/density across its whole surface, and is also non-rotating). We could then multiply Scr with the Planck length (and the Planck time, as both must change by the same factor to maintain the hyprespherical nature of spatial cells, and also the constant speed of light) of empty space (with no mass/energy in it) to get exactly the same "curvature" of spacetime (in the presence of mass/energy) as general relativity predicts. ... and that's where a simulation can come in very handy, indeed, because a simulation can search through the whole space of all possible (candidate) functions for Scr (including [infinite] power tower functions), and find solution that fits best all the observations (both cosmological observations and observations from quantum/gravitational experiments) in virtually no time. P.S. This model (of variable Planck lengths) also explains how a black hole that looks like it's only a couple of miles in diameter (when looked at from the outside) can contain a whole universe that (apparently) has the size of (dozens of) billions of light years across. For example, the (local) value of Scr for this black hole universe (when observed from the outside) would, therefore, be something of the order of 10^-23. Do be mindful, though, that this is Scr value (of this black hole) that's only applicable in the universe outside of this black hole, that is, the universe inside of which this black hole exists. A black hole (or any mass, for that matter) existing inside of this black hole universe (there is, apparently, a deep nesting of black holes taking place in this... "omniverse") would have a completely different (purely universe-local) value of Scr... unless one figures out the exact function for global Scr (one that would be applicable to the whole "omniverse"), but that would be "slightly" unrealistic to expect if one can't even move outside of this black hole universe (at will), much less between all of them.

Wow what an amazing video. The animations, explanations, and humour are all on point!

Thank you, your clear thinking is contagious.