On 5/18/21 8:06 AM, Luigi Fortunati wrote:
[...]
This depends on what model you use for gravitation. Today the two most
common models are Newtonian mechanics (NM) and General Relativity (GR)
-- I'll answer for both.
I presume the man is inside the elevator, nominally standing on its
floor, in a building built on the surface of the earth (I stipulate this
last so I can distinguiah between a floor of the building and the floor
of the elevator).
Here the elevator is held stopped at some floor of the building.
It is correct to say that in the elevator stopped at the floor
(1) an electromagnetic force acts between the man and the elevator
NM: yes, the elevator floor pushes up on his feet.
GR: yes, the elevator floor pushes up on his feet.
(2) a gravitational force acts between the Earth and man
NM: yes, this force is equal and opposite to (1)
GR: no, there is no gravitational force, the man is diverted from his
geodesic path by the EM force of (1).
(3) a gravitational force acts between the Earth and the elevator
NM: yes, it is equal and opposite to the force on the elevator exerted
by the mechanism holding the elevator stopped at the floor of the
building.
GR: no, there is no gravitational force, the elevator is diverted from
its geodesic path by the force from the mechanism holding the elevator
stopped at the floor of the building.
(3) no gravitational force acts between the elevator and the man?
NM: no, there is a force, but it is unmeasurably small [#]
GR: yes, there is no gravitational force
[#] if the elevator is appropriately constructed, this minuscule force
could be arranged to cancel to zero.
Now we consider the elevator in free fall.
It is correct to say that in the elevator in free fall
(1) a gravitational force acts between the Earth and man
NM: yes, this force accelerates the elevator down
GR: no, there is no gravitational force, the man follows his geodesic
path.
(2) a gravitational force acts between the Earth and the elevator
NM: yes
GR: no, there is no gravitational force, the elevator follows its
geodesic path.
(3) no gravitational force acts between the elevator and the man.
NM: no, there is a force, but it is unmeasurably small [#]
GR: yes, there is no gravitational force, both follow their geodesic
paths.
(4) no electromagnetic force acts between the elevator and the man?
NM: yes
GR: yes
Note in all cases, in GR the geodesic paths are accelerating downward at
9.8 m/s^2.
Tom Roberts
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