[[Mod. note -- I apologise for the delay in processing this article,

which arrived on my computer on 2024-02-15, but was mistakenly classified

as spam.

-- jt]]

*Post by Luigi Fortunati*Gravity manifests itself as gravitational force if there is an obstacle

(the stone on the wall of the well) and as gravitational acceleration if

the obstacle is not there (the same stone as before that detaches from

the wall and falls).

In the first case there is gravitational force (and there is no

acceleration), in the second case there is gravitational acceleration

(and there is no force).

When in my animation https://www.geogebra.org/m/eybpyx4d we click on the

"Detach the stone from the wall" button, the stones A and B detach from

the walls and fall.

In this phase of free fall, the two stones A and B accelerate towards

each other and, therefore, they are two mutually accelerated reference

systems: how can they both be declared inertial if they are accelerating

towards each other? Can inertia and acceleration coexist?

Note that I am talking about (gravitational) acceleration and not force.

Luigi Fortunati

Others have tried to explain this to you, but I will give it a try. You are

making it all too complex. There is always gravitational acceleration,

when viewed in a frame stationary with the gravitating mass. The

only force is the one that stops a mass from accelerating.

That does seem a bit contradictory at first, but if you think about it

correctly it isn't. When you are falling freely (i.e. no air friction) you

are in an inertial frame (at least locally). Astronauts in orbit cannot

tell if they are in orbit or moving in a straight line at uniform speed

in deep space (i.e. far from gravitating masses), unless they look

out the window. The same would be true in an elevator car falling

in a deep shaft in a vacuum.

In both cases an observer on the ground (i.e. stationary wrt the

gravitating mass) would see the orbiting or falling observer

accelerating. But the standing observer is not in an inertial

frame! He is accelerating due to the force of the earth on his

feet.

This is just like an observer on an accelerating rocket watching

someone floating free in space. To the rocket observer the

free floating person is accelerating downward. But the free

floating person is in an inertial frame, they experience no

force.

The person in a falling elevator is in exactly the same

situation. They are in an inertial frame while the observer

standing on the surface of the earth sees them as

accelerating. The person in the elevator can release an

object in mid air and it will appear to float there just

like an astronaut would see if they did the same experiment.

The observer in the accelerating rocket knows he is not in an

inertial frame because if they release an object in the air, it

will immediately start accelerating. Likewise the observer on

the surface of the earth. The observer floating in space, or in

orbit, or in the falling elevator, will know they are in an inertial

frame because if they release an object is will float in mid

air without accelerating.

The only force present in all these cases is the force on the feet

of the accelerating observer; that is, the person standing on the

ground or in the accelerating rocket watching the free falling

objects.

I suspect part of your problem getting all this is the concept

of relativity. The relativity principle maintains that physics is

the same in all inertial frames. Whether an observer sees

OTHER people accelerating is irrelevant, it is only the state

of motion of the observer that is important for their physics.

When an inertial observer sees something accelerating, then

they can attribute that to either a force or a difference in the

curvature of space-time. Which it is depends on the distribution

of mass or the presence of mechanisms that can impart a force,

such as electric charges or collisions with other masses.

For your two elevators, one at the center of the earth and the

other falling towards it, they are both in inertial frames, because

if they release an object it will appear to float mid air wrt each

observer. The reason they see the other accelerating towards

them is the distribution of mass that is distorting space-time.

If the two elevators were in empty space and were still accelerating

towards each other, there would have to be some mechanism

imparting a force on one or both elevators. In that case

one or both would no longer be an inertial reference frame,

and whichever elevator was being accelerated by a force, they

would know it because if they released an object in mid air

the object would immediately start "accelerating" wrt to that

accelerating frame.

Rich L.