Luigi Fortunati il 18/04/2023 18:49:41 ha scritto:
In my animation
https://www.geogebra.org/m/ggqgaeeb
there is an elevator that works with electromagnetic force and not with=
gravity.
How does it differ from Einstein's elevator when it is restrained and
when it descends in free fall?
[[Mod. note -- *IF* the ratio electromagnetic_force / mass is the
same for the elevator and the test mass ("robot"), then this is indeed exactly analogous to an Einstein elevator. If this ratio differs, then
the weight force won't be zero when the constraint is removed (i.e.,
when the elevator is free-falling).
For gravity, Einstein's (weak) principle of equivalence says that the corresponding ratio gravitational_force / mass is indeed the same for
*all* objects, so Einstein's elevator automatically gives zero weight
when its constraint is removed (i.e., when the elevator is free-falling=
).
-- jt]]
The analogy I was referring to is the following.
Einstein says: "In the elevator stopped at the floor there is the force
of gravity that pushes the man against the floor. I prove you that it
is not a real force. And the proof is this: if the cable breaks and the elevator goes into free fall, in this accelerated reference the force
of before is no longer there and, therefore, it was a fictitious
force".
In the case of my animation, in the elevator stopped at the floor there
is the electromagnetic force that pushes the robot against the floor. I
prove to you that it is not a real force. And the proof is this: if the
cable breaks and the elevator goes into free fall, in this accelerated reference the force from before is no longer there and, therefore, it
was a fictitious force.
Is this statement the same as Einstein's?
[[Mod. note -- Einstein's statement implicitly assumed the weak
equivalence principle, i.e., it is based on the observation that in
a uniform gravitational field, *all* objects free-fall at the same
rate (and thus there is no relative motion between the free-falling
elevator and the free-falling objects in the elevator). It's this *universality* of free-fall that's the key precondition for Einstien's argument.
*IF* it were the case that all objects had the same ratio
electromagnetic_force / mass , then the electromagnetic-elevator
situation would be exactly analogous to the Einstein-gravitational-
-elevator situation.
But, in reality different objects have very different
electromagnetic_force / mass ratios (e.g., consider objects made of
copper vs objects made of wood vs objects made of iron). This means
that in a free-falling electromagnetic elevator there may still be
(a lot of) relative motion between different objects, i.e., "free fall"
in an electromagnetic field is *not* universal.
-- jt]]
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