According to the equivalence principle, no experiment should exist that one can perform to determine whether one is in an accelerating elevator, or in a gravitational field. I will outline two scenarios that will differ depending on whether you are in an elevator or in a gravitational field, and thus provide an experiment one can determine to differentiate the two.
Scenario 1:
Suppose I am standing in an elevator which is accelerating upwards at g and also suppose I am holding one ball in each hand.
Now with my right hand, I do nothing but release the ball, but with my left hand, I throw the ball perfectly horizontally, with a velocity v.
Now we know that in this situation, the elevator will strike both balls simultaneously because the vertical velocity of both balls is equal to 0 and it is only the lift that is moving up.
Scenario 2:
This time, suppose I am standing on the Earth, and acceleration due to gravity is exactly g. Now again I simply release the ball in my right hand, but throw the ball in my left hand perfectly horizontally, with a horizontal velocity v. Imagine I measure that the ball on the right falls to the ground after 1 second.
Now as shown in the answers to this question, as a result of time dilation, we measure the moving ball on the left striking the ground after not 1 second, by $\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$ seconds.
That is, the ball on the left in this scenario will take longer to hit the ground.
Summary:
Therefore, if I experience a "gravitational pull" I can determine if it is from a gravitational field, or due to an accelerating elevator, by throwing one ball out horizontally, and dropping another. If they hit the ground at the same time I am in a lift, otherwise I am in a gravitational field.
How can this apparant violation of equivalence principle be resolved?
No comments:
Post a Comment