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I'm reading about the (very near) equivalence of gravitational mass and inertial mass in my undergrad GR course, and the text (Lambourne) describes this equivalence as the inspiration for Einstein's falling elevator thought experiment. (i.e. one cannot tell the difference between free-fall and lack of gravity/upward acceleration and presence of gravity).

What was the significance of this thought? Surely physicists understood that the gravitational force caused things to accelerate before this, and therefore were aware of this kind of equivalence of motion and gravitation. Why was understanding gravity as an acceleration so big for Einstein (and physics as a whole)?

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According to science historians Galileo's 1 pound weight vs 10 pound weight falling at the same rate was never tested but he did it as a thought experiment. His correct conclusions might indicate people did understand relative frames. But your question is probably not one that can be answered definitively. Newton and others understood how to model gravity (force, etc.) but we are still trying to understand gravity itself. Einstein certainly took our understanding much further as a property of space-time geometry. – user6972 Nov 24 '13 at 4:38
    
I'm not sure (hence a comment rather than an answer) but I think the main significance of the elevator gedankenexperiment is that light must be accelerated by gravity. More generally, Einstein turned the equivalence from a (known) fact about massive bodies into a general principle that applies to all physical laws. – Nathaniel Nov 24 '13 at 8:20
    
@Nathaniel I think the core of the issue was to show that one may not be able to tell gravity for any other form of acceleration in some circumstances. I can't remember right now whether Einstein considered geodesic deviation or not. – user34134 Nov 24 '13 at 15:47

Clearly, physicists thought gravity caused masses to accelerate. However, Einstein's thought experiment gave way to the reasoning that perhaps there is no difference between a constant gravitational field and a constant acceleration. The significant importance is that this allowed him to speculate that perhaps gravity affects massless objects, like photons.

Think about it. Assuming a constant gravity field is no different than a constant acceleration, then if a beam of light bends downward in an accelerating elevator, it must bend downward in an elevator in a gravity field. That's the breakthrough! We can easily understand a beam bending downward due to acceleration, but if gravity is causing a massless object to change direction just as if it had mass, then Newton's law of gravitation isn't complete. Under Newton, light with no mass experiences no force from gravity and thus doesn't bend.

With this new concept running around, it allowed physicists to speculate that gravity is more than just a force, but perhaps a result or a property even of the geometry of space. Perhaps massive objects cause space itself to curve, which allows even massless things like light to fall towards them.

Naturally one can see where that might lead... To a revolutionary way of considering the geometry of spacetime. That is why this one little notion was so massively important to our understanding of the universe

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About..

  1. locally measured your time never differ, aka, 'c' relative your wristwatch for example, although some might want to argue that a acceleration is different there, which I don't agree too. But we can keep it to uniform motions and then also conclude that this fact is what makes 'repeatable experiments' work, as well as constants. Assume this wrong, and I would expect us to start living in 'interesting times'.

As for " Surely physicists understood that the gravitational force caused things to accelerate before this"

That is according to Einstein frame-dependent, gravity is transformed away for you when you're in a 'free fall'. So how people thought about it before Einstein is different from now. That a far away observer might define you as accelerating is a result of observer dependencies to me, different frames of reference.

Furthermore it's no longer a 'acceleration', that as you become 'weight less' in it. What he did was to define a equivalence between a planetary gravity (Earth), and a constant, uniform acceleration, aka, your rocket at one gravity.

You will always know a real acceleration, or gravity. That's when you find yourself gaining weight, without eating.

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This is exactly backwards. Einstein's epiphany wasn't that gravitating objects cause nearby objects to accelerate, or that gravitating objects cause nearby photons to accelerate as much as matter does. Einstein's epiphany was the opposite of that, namely that gravitating objects do not cause nearby objects to accelerate!

An object in free fall doesn't experience any proper acceleration. A free-falling object only appears to accelerate, if you use a non-inertial frame of reference. That is, if you choose to use a non-inertial frame of reference, gravity will appear in the form of a purely fictitious force.

In a version of Einstein's "elevator" thought experiment, free-falling objects (or light) inside an accelerating rocket in space undergo no proper acceleration. However, the free-falling objects mathematically behave similar to accelerating objects, if for convenience reasons you choose to describe the objects using an accelerating frame of reference in which the rocket's spatial coordinates don't change with time. Completely equivalently, free-falling objects inside the rocket undergo no proper acceleration if the rocket is sitting on its launch pad on Earth. They merely mathematically behave similarly to accelerating objects, if you choose to describe the objects using a frame of reference in which the spatial coordinates of the rocket, and the Earth's surface that the rocket is sitting on, don't change with time. A coordinate system "attached" to the Earth's surface is not an inertial frame of reference, it's an accelerating frame of reference whose origin accelerates "upward" (away from the Earth's center).

From the perspective of gravity as a fictitious force, of course photons will appear to accelerate in an accelerating frame of reference, with the same "acceleration" value as a bit of matter, because the "acceleration" has nothing whatsoever to do with any consideration of whether or not photons interact with a "gravitational field". The apparent acceleration is entirely due to choosing to use a non-inertial coordinate system.

One can't really be blamed for using a non-inertial coordinate system near gravitating objects, because it isn't possible to use an inertial frame of reference that covers all of a region of spacetime around the gravitating object. A global inertial frame of reference like that does not exist, due to the gravitation object causing curvature in the spacetime around it. (You can, however, use inertial frames locally near an event, or approximate all of spacetime under appropriate conditions as involving a small perturbation tensor field on a flat spacetime background.)

Gravitating objects not causing nearby object to accelerate isn't simply a matter of perspective. In general relativity, there's a physical difference between using an accelerating frame of reference, and modeling the situation with a proper force that accelerates everything. Using an accelerating frame of reference results in gravitational time dilation, which has indeed been observed.

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English mathematician Sir Isaac Newton published Principia, which hypothesizes the inverse-square law of universal gravitation. He deduced that the forces which keep the planets in their orbs must be reciprocally as the squares of their distances from the centers about which they revolve. If he was reasoning this way about forces (F), he was also doing so for Masses (M) and Acceleration (A) since Newton was obviously aware that Force was related to Mass multiplied with Acceleration (F = MA).

The innovation Einstein brought to this was to consider the frame of reference (in this case the elevator) bringing it to extremes, such as accelerating the frame at the speed of light.

A couple of things came of this:

  1. The Cartesian frame of reference Newton presupposed turns out to be much more dynamic than Newton or anyone imagined (space bends). Newton's Cartesian space was static and rigid.
  2. Time's dimensional relationship to space was proven (time slows as acceleration increases)
  3. All things being equal, Newton's gravity was pretty good except as the boundary conditions were approached (extreme acceleration, etc)

So yes, prior to Einstein physicists did understand things accelerated due to gravity, at least since Newton who formulated an equation to describe this.

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This neither answers the question nor clearly explains the motivations and consequences of general relativity. – Jerry Schirmer Dec 24 '13 at 15:59

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