[Bill S]

"This accelerated ... same value" is NOT THE HOLE picture", that he feels equally "as heavy" only because those internal stresses are caused by equal forces in both cases ...
Not sufficient to deduce that gravity and acceleration are the same thing ! (at least to me ...)

I'm not sure that the equivalence principle actually says they are the same thing.  My understanding is that it says one is indistinguishable from the other, in specified circumstances.

[rmolnav (OP)]

I'm not sure that the equivalence principle actually says they are the same thing

You´re right, as far as the principle itself says ... But, as I said in #10:
"You know, there are scientists who go far beyond just "equivalence" (?), when exposing their ideas on the matter. E.g., after explaining the elevator experiment:
1st scientist: "Einstein realized there is no way to tell the difference between sitting in a gravitational field and being accelerated (by the way: that is not exact, as I explained in my last post ...) They are equivalent situations".
2nd: "The fact that these two effects are the same, give the same results, means that gravity is acceleration, NOT JUST LIKE ACCELERATION , IT´S THE SAME THING".
(from a Spanish tv program I saw, "Inside Einstein´s Mind").
I think that program was from NOVA.

[Bill S]

One would then have to ask if acceleration curves spacetime.

Of course, that would be after you asked if gravity curves spacetime, or if that is just a mathematical concept.

[Colin2B]

NOT JUST LIKE ACCELERATION , IT´S THE SAME THING".

I believe this is a mistranslation/misunderstanding of the original German which means equivalent to rather than exactly the same as. The same problem occurs with mass/energy equivalence.
To an extent it is similar to extending an analogy beyond its original meaning.
As I said before, Einstein was using a uniform gravitational field in his illustration so certainly didn’t include the grav field of massive bodies.

[rmolnav (OP)]

Here you have the NOVA page with the TV program I saw.
In some countries, mine included, the video can´t be seen, due to license restrictions. But fortunately one can read the transcription ...
http://www.pbs.org/wgbh/nova/physics/inside-einsteins-mind.html

[guest4091]

The EP seed
A passage based on Einstein's autobiography 1946.

"[a thought experiment that came to him in 1907: nothing less than the definition of the equivalence principle, later developed in his general relativity theory. It occurred to Einstein – thinking first of all in visual terms, as was usual for him – that if a man were falling from the roof of his house and tried to let anything drop, it would only move alongside him, thus indicating the equivalence of acceleration and gravity. In Einstein's words, "the acceleration of free fall with respect to the material is therefore a mighty argument that the postulate of relativity is to be extended to coordinate systems that move nonuniformly relative to one another . . . ."]"
"Einstein's Third Paradise", Daedalus (Fall 2002),
© 2003 by Gerald Holton
source aip.org

Sometimes reading about the person is as interesting as their inventions.
The success of the relativity principle in SR encouraged him to apply it in GR. He did not see a need for a special reference frame, if a general one would work. The results of unification, electric and magnetic, gravitational mass and inertial mass, mass and energy, proved correct.
The elevator example.
The left example is a box accelerating upward at g, with Al (small box) at the bottom center. Al records his weight standing on a scale. A light beam enters a small hole centered on the right wall. As the light moves from the right wall to the left wall, the box moves a tiny distance y upward. Al perceives the light to strike the left wall lower than the point of entry.
The right example is an identical box resting on the ground, with Al standing on a scale, weighing the same as in the left example. If the laws of physics are the same in both frames of reference, Al should see the light beam move in a curved path moving through the box.
The effect of light moving through a g-field was verified in a 1919 solar eclipse. Similar effects are observed today as gravitational lensing.
The equivalence holds for uniform g-fields, or small space and time intervals (to avoid tidal effects).



https://app.box.com/s/0gobsjcp4ukr6kaikvli1gc966ajvztf

[Colin2B]

“if a man were falling from the roof of his house and tried to let anything drop, it would only move alongside him, thus indicating the equivalence of acceleration and gravity. In Einstein's words, "the acceleration of free fall with respect to the material is therefore a mighty argument that the postulate of relativity is to be extended to coordinate systems that move nonuniformly relative to one another . . . ."]"

The success of the relativity principle in SR encouraged him to apply it in GR. He did not see a need for a special reference frame, if a general one would work. The results of unification, electric and magnetic, gravitational mass and inertial mass, mass and energy, proved correct.
The elevator example.

The equivalence holds for uniform g-fields, or small space and time intervals (to avoid tidal effects).

I think these quotes are fundamental to understanding the equivalence principle, which is often misquoted.
For an object falling towards the earth surface, this application of reference frame for nonuniform motion does allow us to consider that (relatively) the object is stationary and the surface is accelerating towards it, but only for “uniform g-fields, or small space and time intervals”. To try and apply this in the larger scale is clearly unreasonable, however, as you say this simple thought process led to a very predictive theory.