Einstein's elevator : factor 2 missing between SR and GR Reading Semon et al. (2009) (https://doi.org/10.1119/1.3088883), I have found this:
"The reason the historical approach
is not generally used in advanced texts is that although
the examples of a uniformly accelerating elevator and
a rotating material disk were instrumental in the development
of Einstein’s thought as he was creating the theory of
general relativity, the examples are problematic when analyzed
with the mathematical formalism of the completed
theory. For example, using the accelerating elevator to predict
the bending of light in a gravitational field leads to a
result that differs by a factor of 2 from that predicted by the
field equations of general relativity (and verified by experiment
)."
Do you understand what the author is saying ? I would really appreciate to compare the calculations and see the missing factor 2. And understand why apparently it is not a problem.
Thank you !
Francois
 A: There is the equivalence principle, so observers in an accelerating elevator and observers in a uniform gravity field will make identical observations.
Let us observe the accelerating elevator from the outside. And let us concentrate on the momentum of light that is moving between the floor and the ceiling of the elevator.
From the outside we notice such effect that the number of photons moving up at one moment is increasing, while the number of photons moving down at one moment is decreasing. Other way to say that is that the photons hit the floor at higher frequency than the ceiling. Those 'extra' hits cause the light to exert some 'extra' force on the elevator.
An observer inside the elevator says that the two frequencies are the same.
Now let us observe a small chamber standing on the surface of the earth, we observe it from a satellite on a geosynchronous orbit. There is again light moving around in the chamber. Equivalence principle tells us that an observer in the chamber observer same kind of things as our observer in the elevator observed.
What does the observer in the satellite observe? The theory of gravity tells us that she observes twice the deflection of the light compared to the person in the chamber. Or the change of momentum of the light is twice as large.
So the observers inside the containers observe the same things. Observers outside disagree with the inside observers in a similar way. Both outside observers say that the light has some 'extra' weight that the inside observer does not observe.
When we observe light passing near the sun we are outside observers. At least if we are on earth. So we observe some 'extra' deflection.
A: "The reason the historical approach is not generally used in advanced texts is that although the examples of a uniformly accelerating elevator and a rotating material disk were instrumental in the development of Einstein’s thought as he was creating the theory of general relativity, the examples are problematic when analyzed with the mathematical formalism of the completed theory. For example, using the accelerating elevator to predict the bending of light in a gravitational field leads to a result that differs by a factor of 2 from that predicted by the field equations of general relativity (and verified by experiment )."
That above paragraph is silly. We have developed advanced equations and now we use them, that's all.
Let's say a small laboratory is hovering near the sun. A ray of light comes in through a small hole on the wall. A physicist in the lab compares the path of the ray to a straight rod. He says the ray curves x degrees.
Another physicist on the earth measures how much that same ray curves, she gets two times larger number. She explains the difference by saying that the rod in the lab is not straight.
The curvature of space-time is the reason that the rod is not straight. All rods in the lab are non-straight, that is why the physicist in the lab can't find out the 'real' curving rate of the light ray.
