Is free fall NOT the same as floating in space?

[James Demers]

For many, many years (don't ask), I've been running into the classic example of the local reference frame: the man in the box who can't tell if he's floating free in space, or falling into a gravity well.

It occurs to me that if one is in a falling box, a mass released at the top of the box will be subject to a wee bit less gravity than a mass released at the bottom of the box. A sensitive enough instrument would be able to detect a force pulling them apart. (This is nothing exotic: it's the tidal force.) Thus, the experiment would tell you that your box is not floating free, but is accelerating toward another mass. (A worrisome discovery, I would think.)

Is this just a matter of a poor choice of example, one that's persisted for about a century? Or is there something actually different between the two boxes?

 

[sophiecentaur]

, a mass released at the top of the box will be subject to a wee bit less gravity than a mass released at the bottom of the box.

This is true and the same difference can be detected in the Microgravity in an orbiting space vehicle. To avoid this effect, you really would need to be "floating" at a great distance from even the Sun.

 

[PeroK]

For many, many years (don't ask), I've been running into the classic example of the local reference frame: the man in the box who can't tell if he's floating free in space, or falling into a gravity well.

It occurs to me that if one is in a falling box, a mass released at the top of the box will be subject to a wee bit less gravity than a mass released at the bottom of the box. A sensitive enough instrument would be able to detect a force pulling them apart. (This is nothing exotic: it's the tidal force.) Thus, the experiment would tell you that your box is not floating free, but is accelerating toward another mass. (A worrisome discovery, I would think.)

Is this just a matter of a poor choice of example, one that's persisted for about a century? Or is there something actually different between the two boxes?

Exactly. The two are only approximately equivalent. If your experiment lasts a sufficiently long time, you will see differences between, say, orbiting the Earth in the space station and drifting out in space somewhere.

And, obviously, someone in free fall towards the Earth may eventually collide with it!