Picking on Einstein

Physics.Org ^ | 01 April 2005 | Staff

[Grut]

Two objects released at the top of the car will fall at a uniform acceleration and parallel to each other if the car is being accelerated uniformly. But if the acceleration is due to gravity, they will fall at a nonuniform rate and on converging lines.

As far as I can see (and I'm a perfect duffer, here) in order for these expected differences to disappear, clocks would have to run slower in a gravity well and parallel lines would have to converge... which seems to be what General Relativity calls for. But I really don't see that the differences would disappear.

[donh]

Two objects released at the top of the car will fall at a uniform acceleration and parallel to each other if the car is being accelerated uniformly.

The two objects will not fall. I don't think you understand the elevator story.

Try this. You have awakened naked in featureless cube of an elevator which is free-falling toward a large airless planet. You know that the elevator has gyroscopes mounted in the wall to keep it upright. You have a big soft mattress to protect you from the fall--how do you know which wall is the floor upon which to place the mattress? Ans. You don't. You have no way to tell.

But if the acceleration is due to gravity, they will fall at a nonuniform rate

if you are accelerating, you are traveling at a "non-uniform rate", regardless of the source of the acceleration. From this statement--I sort of suspect you have the notions of acceleration and velocity a bit merged in your mind; I'll hazard a guess that you are assigning acceleration to gravity force, and vaguely mistaking changes in velocity for velocity.

and on converging lines.

I've not a clue as to what this might mean.

The elevator dilemma is that, for denizens of the elevator, the force due to gravity operating on the elevator to accelerate it toward the ground in freefall, is exactly matched, moment for moment, by the force due to the acceleration. Hence, the passengers feel no acceleration. They are weightless in freefall. Later-day experiments unambiguously show that this thought experiment was on the money.

Einstein sez: either this is a remarkable coincedence, or there is some underlying relationship between force due to gravity, and force due to acceleration.

[Grut]

Well, I'm confused but not that confused. Let me try again.

Objects falling towards a mass fall towards the center of that mass; 'down' is in exactly opposite directions on opposite sides of the Earth.

Also, because the force exerted by gravity is a function of distance, the deeper you fall into a gravity well, the greater the acceleration you're subject to.

What I remember of the elevator experiment compared the acceleration experienced by scientists inside the car as it was pulled along by its cable in free space at a constant one g with the acceleration they would experience if it was suspended by that cable at the Earth's surface. The assumption was that they would not be able to tell the difference.

But the acceleration in free space is uniform: the top and bottom of the car are both subject to one g; while the acceleration on the car at the surface is not uniform. The top of the car is subject to slightly less acceleration than the bottom because it is farther from the Earth's center of mass. Therefore, it will take slightly longer for an object to fall the length of the car in a gravity well than in free space.

Likewise, if we release two objects at the top of the car in free space they will 'fall' (i.e., remain stationary in space while the car is pulled by them) without converging, while two similar objects released inside the surface car will fall towards the Earth's center of mass, i.e., converge towards that distant point.

That was the basis of my earlier comments and I apologize for not making myself clearer.

Now, what to do with your matress? Simple. Just put it against the wall that's shredded first by tidal forces. OK, that's a little whimsical but if the well's deep enough the wall that's deepest in will come apart first and therefore it ought to be possible to measure the stresses within each wall, determine which is most stressed and say "there's down."

Or just measure the tidal forces directly.

[donh]

Here is a fairly straightfrorward explanation the elevator experiment.

http://www.astronomynotes.com/relativity/s3.htm

And here is one of the latest refinements, accurate down to an error of about one part in 10 to the 15th:

http://cfa-www.harvard.edu/equiv/

It's true that if the earth were to suddenly become a black hole during this experiment, the top of the elevator would decompose slower than the bottom, but that isn't because of discrepencies between the force due to gravitational pull and the countervailing force due to the resulting acceleration; it is due to discrepencies in gravitational force between the top and bottom of the elevator. It remains the case the ball don't fall, no matter where it is in the elevator.

I will give you credit, that if the earth were a black hole, the guy in the elevator could tell which way was down (well, if he hadn't already been squashed like a bug), however, that doesn't refute the principle of equivance, it just means the elevator experiment is only an easy-to-understand way of stating the issue for limited cases where gravitational force can be sensibly approximated as a constant.