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The Equivalency Principle

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Posted by Tim on April 13, 2003 23:58:22 UTC

hi Don
permitt my quote sir,
"Using what he called a thought experiment, Einstein reasoned that if you were in an elevator remote from a gravitational field rising with constant acceleration, the force you would experience would be indistinguishable from the force of gravity.

In a similar thought experiment it is possible to reason that the acceleration vectors would be parallel to the direction of motion. The gravitational vectors would be concentric at the center of the mass providing the gravity. The two would be distinguishable and not the same."

the two thought experiments you describe are dissimilar in one crucial property. first of all i believe your description of Einstein's thought experiment is a wee bit off.

Einstein's experiment provided a situation in which the observer could not tell if he was moving or at rest. all he knows is that he is enclosed in an elevator and attracted to the floor.

the second thought experiment you allude to requires that the observer knows that there is motion and the direction of the motion.

the point being, in the first experiment if you don't know the source of your apparent attraction to the floor of the elevator albeit a stationary elevator resting on the surface of a massive object or an elevator in deep space that is being accelerated then you can't determine what is the cause of your attraction to the floor, gravity or acceleration.

the second thought experiment that you describe is analogous to an observer watching the elevator albeit a stationary elevator resting on the surface of a massive object or an elevator that is in deep space and being accelerated.
there are a number of options for this observer.

the observer could be standing on the massive object observing the elevator and the poor soul inside of it. in this case the observer would "see" gravity. but some further thought about this observation might change our conclusion, one might also percieve that the massive object and the elevator and the observer inside it are all falling, falling at the same rate, hence staying together. the whole system may be percieved as falling with respect to some other massive object unseen. with this in mind one might suspect that acceleration is playing a part here.

the observer could be out in space moving at the same rate with respect to the massive object. again the observer "sees" gravity. how ever thinking about Newton's first law of motion, one might also suppose that the massive object is moving according to inertia and that the elevator is also moving with its own inertia. also one needs to realize that if any thing in the universe is accelerating anywhere then it can be said that the observed massive object and it's elevator are in the process of acceleration even if a given observer can't detect that acceleration. this being so because there can be no universal frame of referance. in other words anything can be considered as being in a state of acceleration.

the observer could be out in space "accelerating" with respect to the massive object. but wait a minute, since motion is relative the observer could just as well consider himself at rest and the massive object "accelerating". now in this case the observer would "see" a massive object with an elevator "on" it either falling towards or falling away from the observer. but wait again, is the elevator "on" (through gravity) the massive object or is it just falling at the same rate as the massive object maintaining its position relative to it? (rememmber a marble and a bowling ball fall at the same rate.) in this case the observer can't objectively tell why the elevator stays on the massive object or why the guy in the elevator is attracted to the floor, is it because of gravity or acceleration?

the conclusion, gravity and acceleration obey the equivalency principle.

regards, tim

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