Which is why I've been trying to understand Gulliver and sokarul's position; admittedly, I'm still struggling with it. I'm usually willing to give Engy the benefit of the doubt on these arguments, but something doesn't seem right... that's the reason why I've been asking if there's a source that says it's impossible for acceleration to cause that kind of gravitational lensing. Is that an assumption based on how Gulliver and sokarul think things should be, or is there documented reason for thinking that?
I'm not sure if anyone has come up with a reference which explicitly says that gravitational lensing is not possible in a uniform gravitational field, but it can easily be inferred from how gravitational lensing works and how light bends in an accelerating reference frame.
Here are two graphs which show the path taken by light rays, first in an inertial reference frame, and second in an accelerating reference frame.
You can see the equations - they're accurate if the accelerating reference frame has constant acceleration in an inertial reference frame, which isn't quite the case with the FE model, which has constant acceleration as felt by people on its surface. However, the change in velocity as the ray travels over the portion of the graph you can see here is small compared to the speed of light, so the graph is close to accurate. The .04 is more or less arbitrary, as it depends on the choice of units - the .04 was chosen so that the curvature is enough to be visible but not so much to violate the assumptions under which the graph is essentially accurate over the visible range.
In the second image, you see that things appear higher than the actually are, because the incident light is at a higher angle relative to the viewer than the object viewed. So more or less, everything merely appears to be higher up than it really is, and only things directly above or below the viewer appear in the same place. These objects appear smaller (if they are directly above) or bigger (if they are directly below) but this effect is very minor because the closer things are to directly above or below the viewer, the smaller the displacement is.
This is therefore unable to explain observed gravitational lensing, such as during a solar eclipse, because during a solar eclipse the sun, while above the observer, appears larger rather than smaller (as it would in a reference frame accelerating towards it) and it only appears larger when it is directly behind the moon, and not otherwise. It is also completely unable to explain something like the animation we saw above.
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Change in the direction of an object is definitely just ordinary acceleration, of the usual d
v/dt variety. Light can and does accelerate, in the usual way, in a gravitational field. Its speed is constant, but its direction changes, which is in fact an acceleration in the usual sense (in fact, it means the acceleration is orthogonal to the direction of travel). Of course, this is not in accordance with Newton's laws of motion, but Newton's laws of motion fail when relativity comes into play, so when we're talking about photons moving at the speed of light, it's to be expected. And the "objects" being accelerated are the photons which make up light.