gionole
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Imagine experiment is such as I drop a ball from some height vertically only.
What’s the right way to do 2nd experiment in order to check homogeneity of space.
Way 1: I move a little bit and drop the ball (same height, it’s just I moved - ball as well, but not in terms of height)
Way 2: We stay at the same place, but we drop the ball from higher height.I remember there was a constant speed moving train example and we were checking homogeneity such as we were in the train frame, drop, then we moved further in the train and drop it again from the same height. If so, then way 1 must be correct(since the experiments must be done with the same initial conditions - initial location, initial speed).
What I don’t get now is Lagrangian case for which we do for homogeneity check. For the ball, we know Lagrangian would be: ##L(y) = \frac{1}{2} mv^2 - mgy##
Then we say ##L(y+a) = \frac{1}{2} mv^2 - mg(y+a)##
How is this valid ? We definitely shift the ball upper, while we said that way 1 was correct above. Does this mean Way 2 is correct ?
What’s the right way to do 2nd experiment in order to check homogeneity of space.
Way 1: I move a little bit and drop the ball (same height, it’s just I moved - ball as well, but not in terms of height)
Way 2: We stay at the same place, but we drop the ball from higher height.I remember there was a constant speed moving train example and we were checking homogeneity such as we were in the train frame, drop, then we moved further in the train and drop it again from the same height. If so, then way 1 must be correct(since the experiments must be done with the same initial conditions - initial location, initial speed).
What I don’t get now is Lagrangian case for which we do for homogeneity check. For the ball, we know Lagrangian would be: ##L(y) = \frac{1}{2} mv^2 - mgy##
Then we say ##L(y+a) = \frac{1}{2} mv^2 - mg(y+a)##
How is this valid ? We definitely shift the ball upper, while we said that way 1 was correct above. Does this mean Way 2 is correct ?