Gravitational Index of Refraction

[@3blue1brown]

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

[@HuygensOptics]

Thanks Grant, the animations are still far from "3blue1brown level" but I'm glad you enjoyed the video.

[@sumedh-girish]

Oh boy this takes birds of the same feather flock together to a whole new level.

[@otheraccount5252]

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

[@johnnylockwood]

I want to see this

[@Yezpahr]

Back in 1999 some map maker in Unreal Tournament (Game of the Year edition) made a portal-based moving black hole for the Twin-Worlds map. The portals in the Unreal Engine couldn't be spherical but he found a work-around that ate a dozen times more CPU cycles to at least make it look spherical and have the mirror effect. (although it would break down if you approached too close, which is probably why it resided in the skybox, which ironically would be the one place where normal portals couldn't work) I presume it was done in a similar way as you describe.

[@Kram1032]

I think due to how refractive index calculations happen to work in Cycles (and most renderers), basically always assuming one side to be vacuum, you might even be able to achieve the same effect by finely stacking spheres of *the same* refractive index. This will effectively be a lens with an exponential gradient. However, presumably that's the wrong kind of gradient for replicating this sort of effect, as the effective index of refraction would surely go towards 1 at infinity, so you'd have to make the IOR weaker and weaker. I wonder how the math works out in terms of instantaneous IOR as a function of the distance of the object. And I also wonder whether frame dragging effects could be added by somehow manipulating the normals of your spheres.

[@Dryym]

@@Kram1032 That's actually close to what's done. However stacking spheres of the same IOR produces ringlike artefacts along the boundary between them. So you need to modulate the IOR by the angle of the face relative to the camera in order to make a smooth and continuous effect.

[@bob2859]

Here's the tutorial (37min): watch?v=XWv1Ajc3tfU There's a lot of node stuff going on too.

[@ezekielbrockmann114]

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

[@fredinit]

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!

[@DFPercush]

There are some lectures on QED by Richard Feynman that have made it onto youtube, where he ends up talking about lenses and diffraction gratings at the end and how it all comes together with probability. Really cool.

[@LostMekka]

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

[@KW-ir5mf]

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.

[@insu_na]

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

[@dodatroda]

That's the definition of slower.

[@Hexcede]

​@@dodatrodaNo it's really just equivalent, this is a different definition explaining the same equivalent idea

[@dodatroda]

@@Hexcede No. It's simple. If covering a distance takes more time that is the exact same thing as the speed being lower. By definition. Light doesn't *seem to* slow down, it actually does.

[@pettanshrimpnazunasapostle1992]

​@@dodatrodaimagine 2 runners on a track. One is running towards in a straight line while the other is running in a curved path. Even though both runners run at the same speed towards you, the one in the curved path, from your POV will appear to have travelled less towards you which appears slower. But they both have the same speed! Now replace the runners with photons and the paths they take as spacetime itself.

[@dodatroda]

@@pettanshrimpnazunasapostle1992 "from your POV will appear to have travelled less towards you"? Not sure what you want to say here, but the runner taking a curved path obviously covers a greater distance. We're talking about one specific distance. Distance is equal to space. Has nothing to do with spacetime.

[@aniksamiurrahman6365]

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

[@goldnutter412]

This is the way

[@ronnetgrazer362]

That is one of the best feelings. :)

[@matttzzz2]

I have no fuckin clue what in the world is happening in this video. I mean, i know all about black holes, 3D space-time, Einstein's theories, etc. but this video is confusing as hell

[@brendawilliams8062]

@@matttzzz2811/8102222…

[@renatosalles294]

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.

[@jimzielinski946]

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.

[@HuygensOptics]

You might be right there, Unfortunately I'm a bit short on math there but I will return to this subject in the future.

[@Markoul11]

@@HuygensOptics The problem with comparing light speed in free-space vacuum with light speed in a medium thus the refractive index n-=c/υ of a material is that it is falsely described in your video. Light does not slow down from c value as it approaches a massive stellar object in free space! Opposite, to its behavior when passing through a transparent optic medium like glass for example in which indeed light slows down. According to Relativity what really happens is that the speed of light in the vacuum is always fixed at c value and what actually an observer experiences is gravitational (not to be confused with kinematic DT) time dilation. Therefore the "Gravitational Refractive Index" metric and analogy cannot be used without adopting a variable speed of light in the vacuum concept. However, this has never been confirmed by experiment or astronomical observations so far and the speed of light in the vacuum is always measured at c value independent the nearby stellar mass if you are close to the Earth or close to Jupiter. So, if you assume that in gravitational lensing the speed of light in the surrounding to the stellar object vacuum is slow down then you assumption is wrong! Nevertheless, of course someone could use Gravitational Refractive index instead of gravitational time dilation to construct an effective theory for calculating gravitational lensing but this would be only an effective model and not physical thus not describing the actual observations and physical reality.

[@educatedguest1510]

Do you know Snell's law for time dilation proven in 2021? And do you know gravity is time dilation gradient proven in 2024 (no curvature of artificial artifact needed): g = (0.5c²/D²)'≈ -c²×D', where D is time dilation (rate), and D' is time dilation gradient (derivative by location).

[@jimzielinski946]

@@HuygensOptics Einstein once said he ran out of math too, so don't feel bad.

[@jimzielinski946]

@@educatedguest1510 that's all beyond me. It's good to know that there are new avenues of study.

[@rozzgrey801]

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!

[@javierramos2915]

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.

[@fredwood1490]

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.

[@cleon_teunissen]

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.

[@tomholroyd7519]

Also, space is not a vacuum. For the most part, there are electrons, protons, metal ions, electromagnetic fields, and all the dust and crap that's accumulated over the last 13 billion years. It's a mess. It has a refractive index too.

[@BracaPhoto]

I hope you see this -- I've been toying with the idea of Pi not really being the same thing in a quantum system - I don't know where to look for others that have thought of this idea- I've have multiple thought experiments I've been doing replacing Pi as something other than 3.14 etc... I occasionally think of the quantum "sphere " as having a bulge at its "equator" - the variance from the whole number "+-0.314" is what gives the particle it's "wobble" -

[@haydentravis3348]

It's all one universe, everything has to be connected somehow. Great work illustrating that.

[@br3nto]

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

[@edcorns3964]

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.

[@bibsp3556]

I loved reading this

[@RomanVladimirovichF]

Браво!! Я очень давно ждал такого красивого представления о зависимостях скорости времени к сути материй и пространств! Благодарю! Bravo!! I have been waiting for such a beautiful idea of ​​the dependence of the speed of time on the essence of matter and space for a very long time! Thank you

[@Hey_MikeZeroEcho22P]

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

[@turun_ambartanen]

Absolutely beautiful video once again! I never thought about light following the curvature of spacetime from the perspective of the refractive index.

[@andreasboe4509]

A beautiful and clear illustration. My first reaction was that gravitational potential is reversely proportional to the square of the radius, and not simply reversly proportional to the radius, but I may fool myself. The derivative of a square is linear after all. We usually say that light entering a gravitational well maintains it's speed, but gets a smaller wavelength. That can only be true if your illustration for an external observer is correct. This compression effect is most obvious with a black hole. Objects falling into it ends up as stickers fastened to the surface of the black hole, where time is infinitely compressed. When I watch your videos I can feel that there are Nobel prize worthy discoveries hiding behind the scenery. These illustrations are powerful tools to understand the behavior of waves well enough that we can begin to make practical inventions based on them. Maybe we can create telescope mirrors and lenses that compensate for their own flaws? Maybe it can even help us resolve the current cosmological crisis?

[@__christopher__]

It's the gravitational force that is inversely proportional to the square of the radius. It wouldn't be if the gravitational potential weren't proportional to the inverse of the radius. And yes, it's related to the derivative, but the derivative of the inverse is the inverse square (the force is the derivative of the potential, not the other way round).

[@roddneyfett444]

Excellent. I remember refraction as the reason for light to bend around a gravitational body because light has no mass and no time.

[@EricKolotyluk]

WOW! That was very cool, and actually easy to follow. Thank you so much for such a refreshing insight into reality.

[@mariodistefano2973]

I ever thought you have very nice intuitions in many aspects of optics and this goes over all that, since maybe you "touched" the missing link in quantum gravity theory, FANTASTIC !!!

[@markr9640]

Another mind blowing video. Thanks for all the effort you go to. It is appreciated here on the Isle of Wight!

[@blobwatson]

Brilliant! Simplest, most intuitive, and usefully correct explanation of general relativity I've ever seen (way better than the ball on a stretchy surface)! Glad I watched to the end before commenting- half way through I was going to say "you're much closer than you think" 😅

[@Andospar]

Beautiful... (in my personal view), I always wondered how information was encoded on a blackhole. Thank you for sharing.

[@sinecurve9999]

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.

[@HuygensOptics]

Thanks, I will look into it. I just approached the subject from that of an optician and did not dive deeply into the literature.

[@removechan10298]

Absolutely fantastic video. It would be very interesting to map a large section of space, the great attractor, and farther things, so show how it all looks across a whole gravitationally bound area, AND those that are not bound, so how expansion v gravitational lensing work. (expansion not causing relativistic effects) I've watched it 4 times to really try to understand the whole idea - but first, the very idea of saying gravitational index, so succinctly, is brilliant. Scripting is brilliant, right as I am saying "ah but what about..." - you're right there answering the questions and leading us on in thinking. I've often argued on physics forums that we're already within the limits of visible relativistic effects - relative to the great attractor we're traveling at 600 km/s - which would be detectable real-world (world?) motion, with relativistic effects. Event the smallest motion is relativistic (there is no threshold, but i've heard 4% bandied around as detectable, but 0.002 could be on sensitive stuff) anyway, that's the late night grasp I have on this, amazing stuff and love the direction, BEST CHANNEL ON KZbin!

[@HuygensOptics]

You are correct, there really isn't any threshold, effects just get very small, often too small to measure (even with atomic clocks). Thanks for your comment, I think you will like the upcoming video too, since it will be on a related subject.

[@removechan10298]

@@HuygensOptics some back of the envelope maths (that's latin for chatgpt) says 1m/s change in velocity could be measured via relativistic effects with a nuclear clock, and 1m of altitude change could be measured by a nuclear clock (in a given gravity field - obviously close to an earthish mass) but what are the lower bounds of relativistic effects that can be measured with atomic or nuclear clocks - and what do they look like, and do we account for them across all measurements? and the axis in the CMB is related to our motion, how do we account for that... hrm.

[@PerpetualScience]

The refractive index is more accurately modeled by n=e^(-V_g/c^2). Source is the Wikipedia page on gravitational time dilation. I'm also a physicist. Regarding 18:50, I tried to see if I could reproduce GR with a generalized version of Lorentz Ether Theory(LET). It worked great for light, but unfortunately failed horrifically for literally everything else. There was nothing to set the scale of particles, and therefore no way to dictate the volume of a region of spacetime. As such, a clock could shrink by n and run n times faster. In order to fix this, a scale parameter had to be added. At this point though, I was just representing the metric tensor in an exceedingly cumbersome way with no benefits, so I deemed this attempt a dead end. It was like that VSL stuff you see sometimes on KZbin, but with frame dragging. Not sure if those guys have gotten that far yet(it really isn't that far, pretty trivial).

[@htwt]

Awesome! Very intuitive. I like your analogies!

[@ralfg9194]

Thank you for your efforts. Wonderful work, clear explanations. Thanks from Germany.

[@mishun]

6:38 analogy between classical mechanics and variable refractive index was actually very popular idea for school physics olympiads around 2 decades ago. Indeed, if you look at toy problem of particle with kinetic energy K hitting border between two volumes in which it's potential energy differs by U then resulting formula looks precisely like Snell's law with refraction index ratio of \sqrt{1 - U/K}. Analogy can be further extended from here to arbitrary potential fields, and gravity is especially convenient since you can factor out particle mass. Although, these physics problems usually worked other way around by reducing some weird optics to mechanics. 14:15 light doesn't slow down, but wavelength decreases as one would expect. 14:49 speed of light isn't the most important constant since it's more-or-less fully determined by our system of measurement choice :)

[@Google_Does_Evil_Now]

This is such a good way to show that C speed of light is constant. 15:00 is the "ah ha" moment for me. And Samantha is measuring relative to her, in a very heavy gravity, so the rocket is accelerating very hard to counter the heavy gravity, 1/2 of C. So for her to measure C as the same C everywhere, which it must be because it's a constant, then that means Time is different for her, relative to us. And her Time speed is Time/2 if she uses a clock visible on Earth. This means across the universe that Time is moving at a different speed everywhere. Even if only slightly different, but sometimes it's massively so. This is a much clearer way to explain space, gravity, time and speed of light. Thank you.

[@ed.puckett]

Thank you, your clear thinking is contagious.

[@BiswajitBhattacharjee-up8vv]

Very good, Generally gravitational potential is a good representation in today's practice. I myself derived few good equations for mass and the index. You have carefully avoided the negative (-) value for reflective index but now in high intensity laser this is no more negligible. We all wish good from you.

[@AftabAlam-jk7de]

Great work! Thank you for this extraordinary theory and simulations. Appreciate!

[@davidregen1358]

Very enlightening and thought provoking. Thanks.

[@stephanieherman2861]

3Blue1Brown is fantastic! Unbelievably good!

[@jasonpenzo8624]

Thank you for making these videos.

[@DudaJarek]

Very nice! Such gravitational bending through Fermat principle was proposed by Robert Dicke as "Variable speed of light"

[@DrDeuteron]

well it is variable, for distant observers, but its always 'c' locally.

[@DudaJarek]

@@DrDeuteronIn special relativity indeed. However, in general it is more complicated - the standard view for light bending is travelling through geodesics, which are bent by spacetime intrinsic curvature. Mathematically it can replaced with Fermat principle - assuming that gravitational field slows down EM propagation, also explaining gravitational time dilation.

[@farhadtowfiq6767]

​@DrDeuteron the variability is equivalent to the time dilation and the space metrics (curvature). However, in the general relatively it is exactly two times to that of Newton's gravity, one time for time dilation and and one time for geometry dilation.

[@mistersircode]

I love how other people have the same correlations as I do lol... literally a couple weeks ago I was attempting to simulate black holes in a renderer with a gradient-controlled index of refraction with mildly good results. So cool to see a video on this exact idea... Hopefully this might give me some insight to make my simulations a bit more accurate

[@user-cb3qr9dt2k]

You always have interesting videos, Sir. I worked in the fiber optics industry for 9 years (some 14 years ago) Some of this is nostalgia for me, so to speak. I loved that job. Thank you Sir. After about 12:00 you get into the physics I like, Now I have to see if you have done a video on the physics of the planned Star Shade.

[@eewls]

your videos taught me to think of light as waves

[@DougMayhew-ds3ug]

This approach to the line of inquiry about refraction and electromagnetic waves is a prudent one. Nobody can write off gravitational lensing effects, so it’s a good way to anchor the pathway to more speculative hypothesis you may have in mind to explore. The realization that the rules or “formula” of physics or constants may change for each instance of a series within a nested stack of discontinuities, seems to be the view that keeps marking its appearance in my research travels, and resonates with similar ideas. One similar idea is the extended set of Riemannian manifolds, where seemingly linear euclidian space and related local action is subsumed within a larger non-linear space or manifold, which fools the investigator into thinking the local space is all there is, because the subsuming geometry is not always measurable or determinable from the linear perspective, because it passes through a singularity. If a system has singularities, there is a higher principle at work, and when “captured” can linearize them, such as Gauss remapping the square root of negative numbers onto the complex plane. The poles are the areas where greatest rate of change is occurring. The related issue of qualative change, as opposed to quantitative change, is important when looking at non-linear models. In the former, you sometimes have to throw out the system formula because the major rules change for each newly added principle, giving such a system an unpredictable nature sometimes, the mathematicians worst nightmare. I still suspect there is a non-linear aspect that electrodynamics overlooked, that only shows up to play at extremely high frequencies, to form particles. That idea still lingers. Perhaps it would be like a refraction shock-wave that morphs into a closed torus, but only at very high frequencies. Some kind of reflective bubble must form to make a particle, or that essentially is the particle, the interplay between a wave and space time at extreme frequencies, a self-generated resonant cavity composed of spacetime itself. Looking forward to see the path lit. Fine work!

[@HuygensOptics]

About your last alinea: I've actually been stating something similar at the end of my video called "this is not a wave". That mass is just high frequency vibrational energy that has "precipitated" and cannot easily return to the vacuum because it is confined by the properties of space. It would require a high non-linearity in the elastic properties of space combined with a form of spatial inertia that is due to the overall (baseline) energy density of space. Which by the way, does not have to be the same everywhere in the universe.

[@DougMayhew-ds3ug]

The difference between identical events that unfold serially or in parallel can be thought of as ocean waves on an ideal beach. From a line perpendicular to the shore, the waves are in series, but from a line parallel to the shore, the waves are unfolding simultaneously, or parallel. Something tells me this orthogonal relationship, and the similar orthogonal relation of electric and magnetic fields, has lovely secrets to tell, that a higher magnitude ordering principle is hiding beyond this orthogonal relation.

[@alex79suited]

I thought it was very good to be honest, but I love the science, so most videos I find to be great. Thanks again. Peace ✌️ 😎.

[@andymouse]

Fascinating and thought provoking, great viewing !.....cheers.

[@smizmar8]

I've thought about this so much! My supposition is that around the photon sphere of a blackhole, there should be a rainbow either side, or a blackholebow if you will. Thanks for this video!

[@HuygensOptics]

there seems to be no dispersion in gravitational lensing, meaning that all wavelengths bend equally.

[@smizmar8]

@@HuygensOptics yeah, I've heard that, but the way you just said it finally made sense to me.. damn.

[@douginorlando6260]

This approach looks like a straightforward way to model gravitational lensing around a galaxy cluster using brute force Finite Element Analysis calculations on a computer.

[@douginorlando6260]

The trick of it would be to start the model based on 3 D placement of estimated galaxy masses using fundamental observations of galaxy red shift distances and angular locations. Then compare resulting calculated warped lens effect with the actual image. Then systematically adjust locations and masses to better match observed lens effect. Also time delays should be matched (a supernova was detected in one refracted image of a galaxy, then observed again months later in another refracted image of that same galaxy). One overlooked parameter is the speed of light reduction in a slight non vacuum, especially through a million Lightyears of space with ions per cubic meter. Military aircraft radar see around the curvature of the earth as if the earth radius was significantly larger (this is different than bouncing off the ionosphere). The ionosphere reflects/refracts radio waves back towards earth because ionization has a large effect on light deflection which in some circumstances is similar in result as refraction I always had doubts about the accuracy of Eddington’s measurement of refraction of starlight grazing the sun (the evidence supporting general relativity over alternative theories). The plasma gradient in the corona must affect the refraction of light for hundreds of thousands of km as the light grazes the sun. Low density plasma must change the permeability & permittivity of a vacuum and therefore change the speed of light

[@ozne_2358]

Interesting simulation. As an optics expert, you should be able to calculate the type of optical system capable of forming a proper image from the gravitational lens of the sun in order to create the biggest telescope ever. I remember reading that such telescope should be capable of seeing car around hypothetical planets around Alpha Centauri.

[@warriorsabe1792]

The thing is, the light still *does* move in a straight line - what happens is the very concept of a straight line *itself* is changed. That's what it means to curve spacetime, straight lines now do things you wouldn't expect from flat, uncurved space, such as diverge then reconverge. So there's no need to slow down the light going by, even in a pseudo-sense like with a lens, because there's no refraction going on, just the straight lines it was already going in happening to converge somewhere

[@Tobe.Energy]

This is mind blowingly awesome.

[@bhuvaneshs.k638]

This is good. I remember doing derivations on these where how gravitational lens effect the refraction for JEE Advance physics problems. Were snells law constant becomes a function of gravitation potential

[@dmatscheko]

13:45 The light has to travel furter, because the mass is bending (or rather expanding) space (see the image at 5:12). So light does not really slow down from our perspective, there is only more space.

[@stephaneduhamel7706]

Indeed, the usual illustrations for the curved spacetime of General Relativity are displaying gravitational potential rather than actual spacetime curvature, which is very ironic, because gravitationnal potential is a purely Newtonian concept.

[@craig7350]

Interesting topic, thanks for this!

[@cleon_teunissen]

About attribution of time dilation: I think the following consideration is very much relevant: Compare two different ring accelerators for particles. Let the accelerator rings be used for muons. The two rings have in common that they have the muons going around at the same velocity. But the two rings have different diameter. For the smaller diameter ring accelerator: in order to sustain the circumnavigating motion a stronger centripetal acceleration is required. That is, in order to have the muons go around at the same velocity as in the larger ring the smaller ring is subjecting the muons to larger acceleration. We have that the difference in amount of elapsed proper time correllates with the *velocity* of the muons. By contrast, the difference in amount of elapsed proper time does *not* correlate with the amount of acceleration that the muons are subject to. I believe the following thought demonstration is very interesting: A wheel shaped space station, the space station is rotating, so that the inhabitants of the space station experience acceleration. Let the space station have several occupation layers, at various distances to the axis of rotation. For levels that are further away from the axis of rotation the G-load is higher. Levels further away from the axis of rotation are circumnavigating at a larger tangential velocity. That is: the levels at larger distance to the axis of rotation travel a larger distance than the levels closer to the axis of rotation. For a measurement setup inside an enclosure at any distance to the axis of rotation: a local measurment cannot distinguish between velocity time dilation and gravitational time dilation. For clocks located at larger distance to the axis of rotation a smaller amount of proper time will elapse, but locally there is no way to decide whether to attribute that to velocity time dilation or gravitational time dilation. As a matter of principle: in terms of General Relavity the phenomena of velocity time dilation and gravitational time dilation are intrinsically related. Recommended reading: 2004 article by Andrew J. S. Hamilton and Jason P. Lisle 'The river model of black holes' (The article is not specifically about black holes, but about spacetime curvature in general) (I can't give a link, messages with a link in them disappear.) The river model is not a new theory. Rather, it describes a heuristic. The heuristic provides a way to think of velocity time dilation and gravitational time dilation in relation to each other.

[@GooogleGoglee]

Can you make a TL:DR version of your comment?

[@cleon_teunissen]

@@GooogleGoglee GR is a subject that sees more babylonian confusion than any other subject in physics. Communication with language is massively dependent on the participants having a shared understanding. Yeah, I prefer to communicate more efficiently, but with GR there is just very little reliably shared understanding.

[@Alexander_Sannikov]

If the influence of a black hole's gravitational space warping could be described by a refraction index, then a light beam aimed straight at the black hole would slow down (due to some positive refraction index near it), however, the space around a black hole accelerates towards it (accelerating light towards the black hole as well).

[@Peibolia]

The video actually discusses that

[@andrewmcfarland57]

Fascinating presentation.

[@syukranhakimbinnorazman7430]

I had a similar thought experiment (i.e., bridging relativity into microscopic optics) during my Ph.D. years. My research was on applied optics and imaging, so I didn't have much time nor expertise to explore further. It's good to see a well-explained video on this topic. On the other hand, I'm interested in knowing if this concept can be used to explain diffraction (or unify refraction and diffraction into a single general concept). I know that we can use Huygens' principle to describe how diffraction works. However, the explanation of why it happens doesn't really satisfy me, especially at the aperture boundary. What if the light was diffracted due to space being bent at the aperture boundary? If that were the case, would different materials give different diffraction patterns (because they have different masses)? We know that's not true because the diffraction pattern only depends on distance, wavelength, and aperture size. The material of the aperture does not matter. Or does it? I don't know. Has it been rigorously tested/measured? I was looking for an analogy by exploring how water waves diffract. If I'm not mistaken, the math for water diffraction also uses a similar equation by Sommerfeld (i.e., optics). Water has viscosity (which I assume plays a part in water diffraction). But light has no such properties. I'm pretty sure I'm 99.9% wrong here. But if someone can shed some light on this (pun intended), it would be much appreciated.

[@HuygensOptics]

In fact, the material does have a slight influence on diffraction, which is due to the phase shift that is introduced at the boundary. It's related to the phenomenon that is observed in the phase shift in reflection on different metals / materials, which is not exactly 180 degrees for all materials / metals. The effect is generally small and I think in the order of 5% of the total phase shift. It's also sometimes referred to as complex refractive index.

[@DrDeuteron]

circa 11:00, if you look at the Schwarzschild metric, n=c/(dr/dt) goes as (1-1/r) with r in units of Schwarzschild radius, so you picked the right form.

[@deltalima6703]

This video is quite good. I would be interested in seeing the details nailed down for a real cluster as best as possible instead of just swept under a rug. The concept looks very interesting. 👍

[@NeuroScientician]

Can you reconstruct images shifted by gravitational lensing? |Eg, can you effectively look behind stuff?

[@johnmorrell3187]

Yes, and in fact gravitational lensing has successfully been used to resolve images of objects which would otherwise be way too far away and faint to see with modern telescopes.

[@BrilliantDesignOnline]

14:04 Since the light is 'bent' by the object, wouldn't it bend toward the leading edge of the object, an upstream 'acceleration' gradient?

[@kylelochlann5053]

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).

[@minipiman]

That is why he gives the example of the gradient index lense, so it has spatially varying refractive index.

[@nulliusinverba4942]

It's not dispersive because it is not bending light. It's only time that slows down under gravity (GR).. light always travel at the same speed (SR) --> c = frequency x wavelength

[@kylelochlann5053]

@@nulliusinverba4942 The coordinate speed of light in general frames can be anything, it's only the local vacuum speed of light that's approximately constant. Gravitational lensing is not dispersive because there's no frequency dependence.

[@DrDeuteron]

1:30 you need to publish a paper about types of "gravitational aberrations" ...classify them, name them, etc.

[@piwi2005]

The "refractive index" of space not only depends on the gravitational potential, but depends on the impact parameter of the light rays. For example, if you want to simulate how light bends around a black hole by replacing the black hole with a spherical glass of variating index n(r), you will find this doesn't work. You will need n=n(r,a) with a the impact parameter, so as to match black hold deviation angles as fonction of a.

[@SamuelLiJ]

Yes, I just verified this numerically. There is no choice of n as a function of r which reproduces the correct trajectories in general.

[@JoeDeglman]

The refractive index only depends upon the density of the plasma, matter, or magnetic flux in an atmosphere near such objects, not on the mass. The Earth, for example, has a larger refractive index in its atmosphere, about 1000-fold that of the Sun's plasma brim. The Sun only bends light at 1.75 arcseconds, the Earth 30 arcminutes. In contradiction of the General Theory, the Sun only "bends" light in its plasma brim, and not at 2,3,4,... solar radii as the General Theory predicts. No one has ever observed the "bending" of light in the vacuum of space, only through the lensing effects of an atmosphere around such objects.

[@PerpetualScience]

@@SamuelLiJ Actually, you can use the refractive index there. You just have to use the matrix version as opposed to the scalar version, as the corresponding refractive index is anisotropic.

[@SamuelLiJ]

@@PerpetualScienceYes, that does work. In general, I suppose that a tensor-valued index can reproduce any central potential as long as the trajectories are not self-intersecting. But it does take away some of the elegance.

[@Markoul11]

The problem with comparing light speed in free-space vacuum with light speed in a medium thus the refractive index n-=c/υ of a material is that it is falsely described in your video. Light does not slow down from c value as it approaches a massive stellar object in free space! Opposite, to its behavior when passing through a transparent optic medium like glass for example in which indeed light slows down. According to Relativity what really happens is that the speed of light in the vacuum is always fixed at c value and what actually an observer experiences is gravitational (not to be confused with kinematic DT) time dilation. Therefore the "Gravitational Refractive Index" metric and analogy cannot be used without adopting a variable speed of light in the vacuum concept. However, this has never been confirmed by experiment or astronomical observations so far and the speed of light in the vacuum is always measured at c value independent the nearby stellar mass if you are close to the Earth or close to Jupiter. So, if you assume that in gravitational lensing the speed of light in the surrounding to the stellar object vacuum is slow down then you assumption is wrong! Nevertheless, of course someone could use Gravitational Refractive index instead of gravitational time dilation to construct an effective theory for calculating gravitational lensing but this would be only an effective model and not physical thus not describing the actual observations and physical reality. .

[@farrier2708]

Some years ago I watched a vid' that seemed to resurrect the theory of Luminiferous aether. I commented then, about the possibility of space having a refractive index and, if it did, how would that result in the way we interpret red shift and other data collected from spectra. Thank you for this vid'. It explains my thoughts in more detail than I ever could and has also convinced me that I am not a complete lunatic. 😎👍

[@br3nto]

12:49 what you’re showing is an viewer with the mass and the light source. But it seems the viewer would also have a good view of the light source on either side of the galaxy too. Later in the video you mention the effects wouldn’t be as pronounced in reality, but I can imaging these patterns could create some intriguing artefacts that would be difficult for astronomers to resolve.

[@physbuzz]

Cool! I'm trying to remember... there's the deflection of light around the sun according to Newtonian mechanics, then special relativity, then general relativity. I think the Newtonian case has effective refractive index involving sqrt((E_0-U)/2), special relativity should be fine with a wave equation (c/n)^2 d^2 phi/dt^2=grad^2 phi, and IIRC you need general relativity to get the deflection of light around the sun correct (Eddington's 1919 experiment, the previous predictions are wrong by a factor of ~two). This amounts to having another term in our wave equation, (c/n)^2 d^2 phi/dt^2=grad^2 phi + Gamma^mu d phi/dx^mu. So without a coordinate transformation we can't just account for this term by choosing an effective refractive index n, we need that extra 1st order term. I think this means that the model presented in the video can't correctly account for the Eddington 1919 experiment, not even with a better choice of n! I'd have to double check my statements though, but it could be interesting to compare these three different theories, and how they can agree or disagree in the low gravity limit.

[@HuygensOptics]

Thanks for this comment. As I said in the video, I just don't know enough about any non-linear effects that might be there. So that is why I used a very simple relationship between ng and Vg in the simulations.

[@petermferguson]

At 12:40 - Detectors placed at the top and bottom of this image on the paths highlighted, would ‘see’ the emitter in two ways and therefore in two positions. So for every gravitational lensing we observe there are at least two ghost images which are observable from elsewhere. In which case, our observations can be subjected to the same ghost image artefacts. How many observed galaxies are duplicates?

[@michaelkaliski7651]

It was established more than a century ago that gravitational lensing occurs as light passes close to the surface of the Sun from some distant object. During a solar eclipse it was observed that objects that should have been occluded by the Sun/Moon became visible slightly earlier than was mathematically predicted if light always travelled in a straight line. So gravitational lensing is an established fact. It is also apparent that light passing close to any massive object in space must also be subjected to some gravitational distortion or lensing and this effect will become more apparent looking further out towards the visible limits of the Universe, simply because of the increasing likelihood of light originating so far away encountering some massive object on its’ way to Earth. Is there a universal coefficient of diffraction that can be applied as a general principle to light travelling from progressively further distances from Earth? Sadly the answer has to be no because the density of matter distribution in space and therefore the gravitational fields are not constant, although over a sufficiently large distance perhaps a rough average value could be assigned. While this would not be directly related to gravitational lensing, it might provide the means for a correction factor that would allow us to make sense of some of the more controversial results being delivered by the latest space telescopes.

[@AlexErmoshenko]

Excellent as always!

[@guillermo_de_quevedo]

There are blind spots. Places where we should be able to see the emisor, but the lensing effect moves all light away. It is like the radar blindspots in submarines because of the salt gradient in the sea. Remember this from a video series regarding submarines of Smarter Everyday channel

[@456MrPeople]

14:26 Special relativity says the speed of light is constant in all inertial frames of reference. When you are accelerating, you are not in an inertial frame of reference, so the speed of light only constant locally, not globally.

[@radomane]

I try to not think about this topic unless it’s near an eclipse, so I was really planning on not thinking about this until 2061 and you’re fucking up the plan.

[@deltalima6703]

"Everyboby has a plan..." -Mike Tyson

[@pufthemajicdragon]

15:32 Hey, that's Sam Carter! Has she made general yet?

[@slam_down]

There's so few of us who noticed that, but its a really nice touch. Who knows? She's probably Admiral General of the space force by now, with Teal'c as bodyguard 🤷

[@Scrogan]

Really cool. Take the equation for time dilation as a function of radius from the mass and see if it matches up with your 1-k*Vg equation.

[@salmiakki5638]

I like Samantha Critoforotetti Cameo and bravery at display 😂😊

[@Yuri_Panbolsky]

0:20 Professor Francis Yu - kzbin.info/www/bejne/bISbiqukl6eYY7M NASA laser optics engineer - kzbin.info/www/bejne/Z3e0qWqPbplro6c

[@NWRefund]

Do cosmologists take effects like this into account when calculating distance from red shift?

[@NWRefund]

Could this cause a dispersive effect? It’d have to be incredibly small such that it only really comes into effect at cosmological distances.

[@ror3D]

Just a small typo at 5:10 : G is 6.67*10^-11, the exponent is negative, not positive

[@HuygensOptics]

Well spotted! I find with so many images, there is always an error somewhere.

[@lartsevevgenii6640]

fantastic explanation! thank you sir!

[@ttararin]

Simple and elegant!!! 👏🏻

[@catcatcatcatcatcatcatcatcatca]

It would be REALLY COOL to see that black-hole lens in real life. Even if the ridiculous propotions probably affect its behaviour greatly, and the shape seems ridiculously hard to manufacture even if broken to multiple lenses. I just can’t help but wonder what would it even look like and how would it show the world. My intuition also says that one would need a traditional lens before it to focus the light to a plane. Additionally, if the ”black hole” in the lens didn’t cover the whole ”image” projected by the traditional lens, you would hopefully see a ”black-hole” distorsion over part of the image, while the rest are (more or less) undistorted.

[@dandeeteeyem2170]

Dude, your videos are always brilliant. You would have made the best physics teacher had you taken a different career path 😅

[@marcellovignoli8083]

Thanks for the nice clear thinking.

[@joepike1972]

14:41 The average speed of light going towards and returning back to the observer is what is constant. The experiments conducted to do measure light going one way without the return.

[@andrewharrison8436]

The alternative approach is to think in terms of geodisics - the "shape" of space means that the shortest distance is now a curve or even an orbit. Note that the shortest distance now depends on velocity. So for me moving at a relatively low velocity my geodisic is an orbit that takes me down near the earth's core and back, fortunately the continuous push of my chair keeps me on the surface of Earth. Moving quite a bit faster we have the space station zipping around with out being accelerated in low earth orbit. Light is moving above escape velocity but if I point a laser beam horizontally it will follow a geodisic that is affected by the Earth's mass. Increase the mass to black hole amounts and there exist orbits for light.

[@KingJAB_]

I’ve always wondered if it would hypothetically be possible to model how a black hole bends light using a ball of material with a gradient of refractive index, and this video further convinces me that it should be possible if we manufacture materials with arbitrarily high refractive indexes

[@xenontesla122]

This reminds me of one time I found a site giving the equation for the equivalent index of a black hole. If I ever get around to learning blender I want to make an accurate black hole render.

[@abvanoosten]

Actually the most general form of the dielectric 'constant' is a fourth rank tensor just like the Riemann tensor and it has the same symmetry properties.

[@Ratzfourtyfour]

Sometimes I see outrageous sciency video titles and know right away that's just bait. Not this time around.

[@masayukiizutsu4270]

So a periodic array of masses may provide us a negative gravity like photonic crystals, it's marvelous.

[@HuygensOptics]

I'm not sure how that would create negative gravity or what that would even mean.

[@dominicestebanrice7460]

The fact that even the most extreme vacuum conditions in deep space contain at least a million atoms per cubic meter, combined with the functionally inconceivable distances and timescales involved, surely points to something like an "effective" refractive index for space. My question is how different wavelengths of EM radiation would respond; we know X-Rays don't refract the way 400-700nm visible light does for example on entering glass and so this adds another fascinating dimension. The time seems ripe however for an overthrow of the old "certainties" concerning gravitational lenses, Doppler-shift etc.

[@HuygensOptics]

Just a small correction: the vacuum of intergalactic space only contains about 1 atom per cubic meter on average, not a million.

[@howaboutataste]

The light affected by gravitational lensing IS traveling a straight line, at velocity c. It is space-time that diverges, not the path of the waves.

[@HuygensOptics]

The result that we observe is the same.

[@MrLewooz]

well..... I generally throw up when I see an equation... (i clean toilets in a guest house as a day job) but what nice explanation and a flippin' idea!

[@trumanhw]

Very very cool. And thank you (as always) for your efforts into pedagogy. Does speed of light not just determine how clocks tick..? Eg, in a vacuum, the time a photon needs to travel 299,792,458m defines a local second..?

[@dennisbrown5313]

While gravitational waves likely travel at C (to best guess - not yet proven), in any case, these are dependent solely on 'space' displacement. Space expansion will certainly slow the waves (for the distant observer). Further, this wave isn't carried via photons (best current experimental knowledge) so is not necessarily restricted to always travel at C. While it certainly can't travel faster (w/o violating known laws) there is no innate reason a slower 'speed' is not possible.