To wit, the idea is that you cannot distinguish whether you are in an accelerated frame or in a gravitational field; alternatively stated, if you’re floating around in an elevator you don’t know whether you’re freefalling to your doom or in deep sideral space far from any gravitational source (though of course, since you’re in an elevator car and apparently freefalling... I think we’d all agree on what’s most likely, but I digress).
Anyway, what irks me that this is most definitely not true at the “thought experiment” level of theoretical thinking: if you had two baseballs with you in that freefalling lift, you could suspend them in front of you. If you were in deep space, they’d stay equidistant; if you were freefalling down a shaft, you’d see them move closer because of tidal effects dictated by the fact that they’re each falling towards the earth’s centre of gravity, and therefore at (very slightly) different angles.
Of course, they’d be moving slightly toward each other in both cases (because they attract gravitationally) but the tidal effect presents is additional and present in only one scenario, allowing one to (theoretically) distinguish, apparently violating the bedrock Equivalence Principle.
I never see this point raised anywhere and I find it quite distressing, because I’m sure there’s a very simple explanation and that General Relativity is sound under such trivial constructions, but I haven’t been able to find a decent explanation.
The first part of the argument is that for single point particles falling, the effect of gravity is the same for all particles. This suggests that we should model gravity as something intrinsic to spacetime itself, rather than as a field living on top of spacetime, which could couple to different particles with different strengths.
The second part of the argument, which is what you point out, is that gravity can have nontrivial tidal effects. (This had better be true, because if all gravitational effects were just equivalent to a trivial uniform acceleration, then it would be so boring that we wouldn't need a theory of gravity at all!) This suggests that whatever property of spacetime we use to model gravity, it should reduce in the Newtonian limit to something that looks like a tidal effect, i.e. a gradient of the Newtonian gravitational field. That leads directly to the idea of describing gravity as the curvature of spacetime.
So both parts of the argument give important information (both historically and pedagogically). Both parts are typically presented in good courses, but only the first half makes it to the popular explanations, probably out of simplification.
This point isn't raised anywhere because it's mostly a pedantic point that has nothing to do with the thought experiment. You shouldn't try and decompose thought experiments literally, otherwise you'll get caught up in unimportant details like this. Just assume the elevator is close enough to the earth such that the field lines are effectively parallel, or better yet, just pretend the elevator is in an infinite plate field.
The real principle of relativity is a bit more subtle (sometimes called the strong principle): that the effects of gravity can be explained entirely at the level of local geometry, without any need for non-local interaction from the distant body that is generating the gravitational field. To describe the geometry of non-uniform fields, we need more sophisticated mathematical machinery than what is implied by the elevator car thought experiment, but nonetheless, the elevator example is a useful launching point for that type of inquiry.
Clearly it will fail given a big enough lift to experiment in, since a big enough lift would essentially include whatever object is creating that gravitational pull (or enough to conclude its existence from other phenomena). However these effects are nonlocal, you need two different points of reference for them to work (like your two baseballs). In fact most Tidal forces are almost by definition nonlocal.
The precise definition involves describing curved spacetime and geodesics, but that one is really hard to visualize as a thought experiment. The thought experiment does offer insight though, as it is possible to imagine that, absent significant local variations in gravity, you cannot distinguish between free-fall and a (classical) inertial frame of reference without gravity. This insight provides the missing link that allows you to combine gravity with the laws of special relativity and therefore electromechanics, including the way light bends around heavy objects, which provided one of the first confirmations of this theory.
If you think it's sneaky to "implicitly" assume they're in the same direction, I would point out that this is no different from assuming they have the same magnitude. It would be kinda dumb to say "well this 1m/s^2 acceleration can't possibly be equivalent to gravity because gravity is 9.8m/s^2, so the statement is obviously wrong and they're trying to trick me!!"... same thing for direction.
I had to apologize and say that the explanation was over simplified and really it would work, say, only for some creatures living exactly on the floor of the elevator.
One of the two, at a challenging high school, made Valedictorian (surprise to her parents who didn't know she had long been first in her class) then in college PBK, got her law degree at Harvard, started at Cravath-Swain, went for an MD, and now is practicing medicine. Bright niece.
Can you please explain to me how you went from"looks like a tidal effect in the Newtonian limit" to "a gradient of the Newtonian Graviational field"?
Tidal forces occur much more due to the difference in the direction of gravity than due to the difference in magnitude.
The force that would be exerted from acceleration versus gravity is different. The force you we think of as gravity comes from a center point that changes with your position while acceleration comes from a uniform direction without regard to your position.