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Can the differential in the speed of time between the far side and the near side of a Photon in relation to a large mass explain the bending of light?

"re-phrased to make it clearer or more precise"

Unfortunately I can only explain things in very simple layman's terms. These are things I have thought out with only elementary understanding of the relativity theory.

I imagine a dimensional photon passing by a dense mass whereby the near side of the photon travels at a slower timespeed than the far side of the photon. This has the effect of making the photon path bend towards the dense mass i.e. lensing effect.

I imagine the same thing happening as light enters a transparent medium. As one side 'hits' the medium it slows down while the other side rushes on, again causing it to bend it's path. This effect is larger with relatively higher frequencies with the separation of color frequencies as a result.

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    $\begingroup$ Am I mistaken or has there been a sudden flurry of questions referring to the "speed of time"? And if so, where is it all coming from? Will the next flurry be about "the height of altitude"? $\endgroup$
    – WillO
    Commented Dec 10, 2019 at 18:19
  • $\begingroup$ By the way, the answer to the question is "no." Gravitational light bending is because light follows a geodesic. $\endgroup$
    – puppetsock
    Commented Dec 10, 2019 at 18:38
  • $\begingroup$ @puppetetc This is an answer nor a comment. It just substitutes bending of light by bending of a geodesic. $\endgroup$
    – my2cts
    Commented Dec 10, 2019 at 18:43
  • $\begingroup$ Gravity causes light to bend and time to slow. What causes gravity is the question. $\endgroup$
    – Bill Alsept
    Commented Dec 12, 2019 at 1:20

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The question could be re-phrased to make it clearer or more precise, but the gist of it is clear enough. The OP is asking whether relative clock rate, which changes with distance from a gravitating mass, is sufficient to explain gravitational lensing.

It's not useful to say "No, a light ray follows a geodesic in curved space", because the change of relative clock rate with distance directly corresponds to space curvature. So the correct answer to my rephrasing of the OP's question is "Yes, the relative clock rate variation vs distance does cause the curvature of a light beam's path."

But the OP's question has another component that should be addressed as well. He is imagining that a photon has a spatial extent, and that if the clock rate on one side of the photon is a bit different than the clock rate on the other side, the photon will be deflected toward the side with slower clock rate. His intuition is basically correct. See this paper, "Comparison of the Phenomena of Light Refraction and Gravitational Bending". Clock rate variation due to gravitation can be modeled as a variation in a quantity analogous to refractive index.

The model is not quite correct (because refractive index does not affect a light wave's frequency, whereas gravitational redshift does), but by analogy, for photons one can think of space as having a higher refractive index where gravitational potential is lower (closer to a gravitating mass). If a photon is thought of as a wavefunction rather than as a particle, the wavefunction is indeed spread out in space; and it propagates very much like a classical light wave. Much like a light wave passing through a gradient index lens, the photon's wavefunction will be distorted as it passes through the region around a gravitating mass. This is an analogy, not quite a correct model -- but it can be useful.

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  • $\begingroup$ " So the correct answer to my rephrasing of the OP's question is "Yes, the relative clock rate variation vs distance does cause the curvature of a light beam's path." The curvature is caused by gravitational stress-energy, time dilation is caused by the gravitational potential (OK both are caused by gravity itself). But there can be zero curvature, and still time dilation, like the center of a star (and between another point somewhere else with different gravitational potential). That is why you feel weightless at the center, though there is still time dilation. $\endgroup$
    – Árpád Szendrei
    Commented Dec 10, 2019 at 20:45
  • $\begingroup$ The bending of light around massive objects is ultimately caused by the bending of spacetime (gravitational lensing). $\endgroup$
    – Árpád Szendrei
    Commented Dec 10, 2019 at 20:46
  • $\begingroup$ physics.stackexchange.com/users/183212/s-mcgrew. Thank you very much for your answer. Nice to know I am not completely crazy. $\endgroup$
    – Oliver Van Der Togt
    Commented Dec 11, 2019 at 23:27
  • $\begingroup$ If I understood your question correctly, how about editing the question to make it more clear? $\endgroup$
    – S. McGrew
    Commented Dec 12, 2019 at 2:26
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You are asking about gravitational lensing. It has been experimentally proven several times.

A gravitational lens is a distribution of matter (such as a cluster of galaxies) between a distant light source and an observer, that is capable of bending the light from the source as the light travels towards the observer.

https://en.wikipedia.org/wiki/Gravitational_lens

In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. Importantly, the world line of a particle free from all external, non-gravitational forces is a particular type of geodesic. In other words, a freely moving or falling particle always moves along a geodesic. In general relativity, gravity can be regarded as not a force but a consequence of a curved spacetime geometry where the source of curvature is the stress–energy tensor (representing matter, for instance). Thus, for example, the path of a planet orbiting a star is the projection of a geodesic of the curved four-dimensional (4-D) spacetime geometry around the star onto three-dimensional (3-D) space.

https://en.wikipedia.org/wiki/Geodesics_in_general_relativity

Contrary to popular belief, light follows a null geodesic. This means that the spacetime distance between emission and absorption is 0.

Now the reason objects with a lot of stress-energy (it is not mass) like heavy stars can bend the path of light, is they do curve spacetime. We use the phrase gravity bends spacetime.

What does this mean?

enter image description here

This means that the geodesic around the massive object becomes the shortest path, and light basically just follows this bent path.

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  • $\begingroup$ OK do the geodesic is bent. Can that be explained by.... Etc. $\endgroup$
    – my2cts
    Commented Dec 10, 2019 at 19:58
  • $\begingroup$ @my2cts The curvature is caused by gravitational stress-energy, time dilation is caused by the gravitational potential (OK both are caused by gravity itself). But there can be zero curvature, and still time dilation, like the center of a star (and between another point somewhere else with different gravitational potential). That is why you feel weightless at the center, though there is still time dilation. $\endgroup$
    – Árpád Szendrei
    Commented Dec 10, 2019 at 20:47
  • $\begingroup$ @my2cts The bending of light around massive objects is ultimately caused by the bending of spacetime (gravitational lensing). $\endgroup$
    – Árpád Szendrei
    Commented Dec 10, 2019 at 20:47
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If you consider a plane electromagnetic wave passing near a large mass, the part of the wave front which is closer to the mass will move slower.

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