Can’t that person just extend his arms and feel the difference? Lets say I’ve got hyper-sensitive arms so I can measure almost exactly the force my arms feel. Since the earth is a sphere, if I extend my arms out (to my sides) my left and right hands will both feel a force with magnitude 1g, but the directions will be slightly different, since each is attracted to the center of the earth. Of course, the difference is extremely small, since the distance from hand to hand is only a few feet, and I’m thousands of miles from the center of the earth.
If I’m being accelerated to 1g with a rocket, the direction will be the same for both hands. That difference lets me figure out if I’m on a planet or being pushed.
This wouldn’t work if the earth were an infinitely large flat plane, instead of a sphere.
I used to wonder about that, too, Arjuna. The trick is that you can get that effect from an acceleration… as long as you’re not restricting yourself to Euclidian geometry. You can also produce a uniform gravitational field, as you mentioned, from a very large massive plane. In either case, the acceleration is indistinguishable from the gravitational effect.
So am I right that gravitation from a spherical planet IS distinguishable from normal acceleration? I’ve wondered about that for a while actually. Not that it disproves anything, though … just nit-picking
Okay, the link above will take you to an assortment of papers and tutorials on the subject of time and frequency. If memory serves, the experiment involving transporting clocks around the world is reported in one of these papers.
If not, a report of the experiment is found in one of the Proceedings of the Annual Frequency Control Symposium. Since there are about fifty of such Proceedings, I would suggest searching through the abstracts. The abstracts are available at the Frequency Control Society’s site, which is part of the site referenced above.
Gravity is indistinguishable from acceleration only on infinitesimal regions.
You can use acceleration to transform away a gravitational field only when the gravitational field is parallel at every point in your reference frame. This is never true of a real gravitational field in a reference frame of sufficient extent. In particular you can never transform away the gravitational field of a mass that is contained in your reference frame. If the earth is within your frame of reference, for example, you would have to accelerate in the southern direction at the North pole, but at the South pole, you would have to accelerate northward.
There is a thought experiment where you are in an elevator, and you cannot tell whether you are accelerating at 1 g or in a gravitational field of 1 g. It is assumed that you are far enough away from the source of the field that you cannot measure that the field is converging toward the source of the field. If you are close enough to the source of the field, you can use plumb bobs. If the lines get closer together toward your feet, you are in a gravitational field.
Saying that the source of the gravity is an “infinitely large flat plane” is equivalent to saying your reference fame is infinitesimal compared with the distance to the source of the gravity.
While this is true, it gets much more difficult if you aren’t trying to distinguish between “only one mass” and “only acceleration”. Your plumb bobs won’t work if I have a smaller mass above the elevator and closer than the larger mass, to cancel out the transverse portion of the gravitational field. Likewise, I could “fool” you into thinking you were some distance from a large mass using a combination of a smaller mass and acceleration.
I also suspect I could make an arbitrarily uniform field over a finite volume using a finite amount of mass.
