A solar gravitational lens will be humanity's most powerful telescope (2022)

It's the same effect as in reflections, except that speed difference between air and solid objects is much much bigger, which results in sharp turning radius.

Otoh there is no requirement for a wave front to have the same frequency as when it started. A gradient in the gravitational field can cause a gradient in the gravitational redshift and thus "parts of photon" can very well have slightly different frequencies. If you recombine the paths and have the photon to interfere with itself, the interference pattern will capture the shape of such a wave function as affected by the distortion in the gravitational field.

IIRC this is the "standard" way of thinking about what's going on although marrying quantum mechanics and general relativity is still a work in progress.

If you buy into another theory that involves a variable speed of light, I'd love to hear more about what exact theory are you talking about since it seems to me that the burden of proof is on who makes the most extraordinary claims.

Let's imagine two points in space A and B, that are let's say 10 light minutes distant from each other. A signal going straight from A to B will thus take 10 minutes.

If point A sits in a strong gravitational field (e.g. it's orbiting a very heavy star), the signal will still take 10 light minutes to reach point B. (please tell me if you disagree with this assumption).

Now, let's place another heavy star at the midpoint between points A and B.

How long will it take for a photon emitted by A to reach B? Well, it won't reach it because it will hit the start that's in between.

But another photon whose direction wasn't directly in the path from A to B will follow a longer path, be deflected around the star and reach point B.

It will take longer than 10 minutes to reach point B because it will move along a longer path.

Do you agree this is what would happen?

That is not true. The "speed of light" in vacuum is not constant for all observers in the _general_ relativity. It is constant only _locally_, Lorentz invariance is a local symmetry in GR. Special relativity thus simply becomes an edge case of GR, where the Lorentz invariance is also a global symmetry.

That's how we get lensing, regions of space near a massive object are more "viscous" and the light moves slower through them.

Now imagine that it's not a star, but a black hole with a small radius to make arguments easier. You shoot a photon slightly off the axis, and it gets deflected.

You can try to treat a photon as a moving object, and integrate the forces acting on it. Taking Lorentz transformations into account, of course.

But the thing is, your calculations will be off, and the experimental results won't match your predictions. You will need to take into account that the lightspeed near massive objects is _slower_ for distant observers.

Another example, suppose that you have a star surrounded by a massive cloud of fog. Somebody shoots a laser beam from one side of the fog bank to another, while you are far away from the star. The fog is there just to allow you to see the beam as it moves, it does not by itself slow the light.

But you will actually see the light moving _slower_ than lightspeed!

Or equivalently, you can take a clock that ticks every second. And if you lower that clock to the surface of a planet, you will see the clock ticking slower. And this is a very real effect, we have to correct for it in the GPS satellites.

The speed of light is the same in both frames of reference. What you think is going affect the speed is actually the slowing of the proper time which effectively causes the photon to redshift.

No. You can drop a ruler onto the surface of Earth and measure from the Moon the time it takes the light to travel from one end of the ruler to the other. It will be slower than the lightspeed from your point of view. This is a real effect, we've measured it.

However, it will be lightspeed from the point of view of an Earth observer.

And this effect falls out directly from the warping of space-time described by general relativity

am I understanding correctly that you claim that the warping of space-time is just a mathematical trick and that the phenomena are better explained by just postulating they light slows down in a gravity well?

Light slows down in gravity wells because the space-time is "denser" near massive objects. This is not a mathematical trick, this is actually a real effect.

It's also the reason for gravitational lensing, as the shortest path through a gravity well is not a straight line. Light can avoid the slowdown near the massive object, if it instead "goes around" it. The curved path is longer, but faster lightspeed along it compensates for the additional length.