To paraphrase: If you’re in a box, there’s no experiment you can do on the inside that can tell the difference between sitting on the surface of a planet and accelerating through deep space.
Except, can’t you? What am I missing?
The Problem In Time
Couldn’t you tell with really precise clocks? On a planet, they would run slower at the floor than the roof. But accelerating through space, the whole box would experience the same acceleration in the direction of motion, so there would be no difference. Right?
The Problem in Space
Near a black hole, you are elongated in the “down” direction – Stephen Hawking called it “Spaghettification.” But if you are accelerating, you are compressed in the “down” direction. If you can be ripped apart by spaghettification, shouldn’t you be able to measure the shear forces responsible? Shouldn’t there be shear forces if you are accelerating, also? Shouldn’t they be perpendicular to the ones in a gravity well? Couldn’t you measure that?
I asked ChatGPT about shear forces under relativistic acceleration, and the answer seemed logical until I got to this statement:
However, it’s important to note that these shear forces are relative. They depend on the observer’s frame of reference. From the object’s own rest frame, the object does not experience any force because it is at rest in its own frame. The shear forces are apparent only when viewed from an external reference frame in which the object is moving at relativistic speeds.
ChatGPT
What the hell does that mean? How can an external observer measure a force on an object that the object itself doesn’t feel? That implies either that gravity and acceleration are radically different, or that the guy on the ship in Interstellar would see McConaughey get torn to pieces if he fell in the black hole, but Matt himself would feel fine the whole time. That’s an even worse paradox than Schrödinger’s cat. It can’t be right. But it’s exactly the sort of hallucination that I’ve been running into myself while trying to make sense of this stuff.
Anybody know any GR whizzes that can answer these questions for me? They are starting to get under my skin.
Afterthought
I think my space problem is confounded by my conflating acceleration with relativistic velocity. I’m not sure how to sort it out, but the compression due to velocity resulting in phantom shear forces part remains. Maybe it’s a qualitatively different problem, but it’s still something GR seems both to allow and forbid at the same time.