Catching up a bit... On 2022-11-27 Luigi Fortunati wrote:
> In my animation
> where are the two bodies A and B.
> We can increase the mass of body B with the appropriate button (to see
> what happens to the forces) and we can highlight the two different
> conceptions of Newton and Einstein by clicking on the appropriate
> For Newton there are 4 forces: the two blue and red contact forces
> (action and reaction) and the two black gravitational forces.
> For Einstein, there are only two forces: the blue force (the one on
> body A) and the red force (the one on body B).
> Is the animation correct?
It looks correct to me.
On 2022-11-29 Luigi Fortunati wrote:
> The animation highlights the fundamental difference between Newton's
> conception and that of Einstein: the presence of the two black
> gravitational forces (Newton) or their absence (Einstein).
> I knew that in Relativity we prefer not to talk about forces,
> preferring to discuss space-time curvatures.
Not quite. In *special* relativity forces are treated just like in
Newtonian mechanics (i.e., a special-relativity version of Newton's 2nd
law still works fine), and gravity is "just another force".
In *general* relativity a suitable version of Newton's 2nd law still
works fine, but (among other differences)
(a) gravity isn't a force any more, and
(b) force-free motion (i.e., motion with no forces applied) isn't a
straight line any more, but rather a geodesic in (possibly curved)
spacetime. Geodesic motion is also known as "free-fall".
So, for example, in general relativity, if I (located near the Earth's
surface) toss a ball up and then it falls back down, we conceptualize
this motion as a geodesic in curved spacetime. That is, near the
Earth's surface geodesic motion (i.e., free-fall motion) is accelerated
downwards at about 9.8 m/s^2 with respect to the Earth's surface. Thus,
when a ball is sitting stationary on the floor, it's *not* in geodesic
motion, but rather accelereting *upwards* at 9.8 m/s^2 with respect to a
geodesic at its location. That acceleration is the result (via Newton's
2nd law) of the contact force with the floor, i.e., the floor is pushing
up on the ball.
> But I wonder (and I ask you): do space-time curvatures generate forces
> or not?
In a suitable context they can generate forces and do work.
> The reason for this question is that, if the two black forces are not
> there, body B (subjected to the red force only) should accelerate
> upwards and body A (subjected to the blue force only) would accelerate
> downwards, moving away from each other.
> And that doesn't happen.
If there were no contact forces between the two bodies, they would each
be in geodesic (free-fall) motion, i.e., they would be accelerating
towards each other. But for case shown in the animation -- where the
two bodies are touching and exert contact forces on each other, the
contact forces accelerate the bodies away from this geodesic motion, so
that the two bodies are stationary with respect to each other.
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