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.
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.