Well, the fundamental form of the equivalence principle is all about freefalling frames in GR being compared to inertial frames in SR, and in both cases no external structure is needed. But like I said, if you can imagine a smaller box inside your inertial/freefalling box, which accelerates/stays at rest in a gravitational field using some structure external to itself but internal to the larger box (say, using rockets on its bottom), then it's a trivial extension of the "everything must look the same inside an inertial/freefalling box" principle to show that everything must look the same inside these smaller boxes (since they are part of the inside of the larger boxes, both accelerating towards the ceiling at the same rate and in the same way). But the principle of equivalence is really fundamentally about comparing the freefalling frame to the inertial frame, it only says that the at-rest-in-a-gravitational field lab must be equivalent to the accelerating-in-space lab to the extent that you can show why this follows from the freefalling/inertial equivalence.ubavontuba said:No refunds! :rofl:
Besides, technically the structure is important to the experiment. It is the key to the fundamental difference between gravity and acceleration, that I am exploiting.
Remember, I said it was a "loophole," not a "fundamental discovery."
This loophole is applicable on all sorts of scales though. Therefore it really is a fundamental difference (even if it's not a paradigm changing consideration).
Frankly, I'm surprised that Einstein didn't address it. Apparently it didn't occur to him (or anyone else?) in regards to his paper... or he didn't think it worthy of mention.
Of course, the larger freefalling box need not have actual physical walls, it's just supposed to be a local region moving along with freefalling objects, so you can imagine falling past something like a smaller box on a rope attached to a crane and drawing an imaginary box around you as you fall. But then you'd have to ignore everything outside the imaginary freefalling box, and fix the boundary conditions on the imaginary walls, and then reproduce those same boundary conditions on the imaginary walls of an imaginary inertial box moving past an accelerating box-on-a-crane in empty space. So however the shaking of the small box (due to a tiny gnome inside dancing around, perhaps) affects the parts of the crane on the boundary of the freefalling box, you have to make sure the parts of the accelerating crane on the boundary of the inertial box are moving in exactly the same way. One way to do this would might be to imagine attaching the crane to an object of equal inertial mass as the earth but ignore the gravitational effects of this mass as I suggested, another way would be to have thrusters on the sides of the crane on the portions outside the imaginary box which insure that the parts of the crane on the boundary move the same way as in the gravitational field. As long as you fix those boundary conditions, everything that happens inside the imaginary box should look the same whether the box is freefalling past a crane attached to the earth or whether it's moving inertially past a similar crane that's accelerating in empty space.