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Einstein’s remarkable insight was that a man falling freely experiences no gravity and his experiences are identical in some sense to a man far away in free space.

But the man falling is increasing speed every second. This wouldn’t have happened without gravity. So how are these two scenarios identical in the sense Einstein viewed it?

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    $\begingroup$ What kind of speed are you measuring? $\endgroup$ Commented Aug 15 at 1:16
  • $\begingroup$ Sorry this is not a trick question or anything. The usual speed of the man falling wrt earth $\endgroup$ Commented Aug 15 at 1:22
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    $\begingroup$ @sku, A slightly more detailed version of Einstein's insight starts with the man inside a closed box, with no way to get information from outside. In that case, until he hits an atmosphere or a rocky surface, there is no experiment he can perform inside the box that will tell him whether he and his box are falling toward a nearby planet, or whether they are "drifting" somewhere out in intergalactic space. $\endgroup$ Commented Aug 15 at 1:28
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    $\begingroup$ I see. I get it. It is in this sense the two scenarios are equivalent. Thank you $\endgroup$ Commented Aug 15 at 1:31
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    $\begingroup$ @SolomonSlow Well explained - you could consider promoting your comment to an answer. $\endgroup$ Commented Aug 15 at 1:35

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An important word in your question that is missing is local.

Einstein was saying that based on observations in their own immediate surroundings, a freely falling observer would not measure a local acceleration (even though they are accelerating in a gravitational field). That is, locally, a freely falling frame of reference in a gravitational field is identical to a frame with no gravitational fields.

Like Solomon Slow stated in the comments, if you assume the man was in a closed capsule and cannot see nor receive any information from the outside of it, if he is falling to earth (ignoring all resistive forces), then there is no experiment he could perform locally that will allow him to distinguish whether he is in deep space or freely falling in a gravitational field.

The remarkable insight in Einstein's reasoning was that all physical experiments performed inside a small$^1$, freely falling lab, will yield identical results if performed in a lab in free space with no gravitational fields$^2$. This is called the principle of equivalence and laid the basis for the general theory of relativity.

$^1$ Small enough so that tidal effects are negligible.

$^2$ A frame with no forces. i.e., an inertial frame of reference.

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  • $\begingroup$ I am amazed that nobody has explicitly mentioned Einstein's Equivalence Principle up to this point. en.wikipedia.org/wiki/Equivalence_principle $\endgroup$ Commented Aug 15 at 9:03
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    $\begingroup$ @m4r35n357 Amusingly, that is a good point. I'd assumed that everyone knew we were talking about it. Okay, I'll edit. thx $\endgroup$ Commented Aug 15 at 9:37
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Imagine the man is just chilling in a windowless spacecraft in outer space when suddenly a planet materializes out of thin air nearby and the spacecraft starts drifting towards it.

The man in the spacecraft cannot tell that he's all of a sudden "falling" towards a planet. As far as the man is concerned, he's still chilling in outer space until suddenly he hits the surface of the planet.

The man's experience inside the spacecraft did not change one bit before and after the planet materialized; that's why the two scenarios are identical. This is called the equivalence principle.

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    $\begingroup$ "out of thin air" --- extremely thin $\endgroup$ Commented Aug 15 at 19:40

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