The force of gravity

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Luigi Fortunati

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Nov 27, 2022, 5:41:36 AM11/27/22
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In my animation
https://www.geogebra.org/m/tr8jc8bt
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
checkbox.

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?

Luigi Fortunati

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Nov 29, 2022, 4:59:00 PM11/29/22
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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.

But I wonder (and I ask you): do space-time curvatures generate forces
or not?

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.

PS. If there are any errors in my animation, I am ready to make any
corrections.

xray4abc

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Dec 11, 2022, 3:54:06 AM12/11/22
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I wonder if Einstein's theory holds, if the Equivalence Principle proves
to be an artificial theoretical construction, with a very limited validity,
which I strongly believe to be the case!
I could explain why I believe that, ....though ....from experience ...
I know...for some mysterious reason, people, that is physicists in most
cases, want to avoid any unorthodox discussions .....by all ....and
any... costs!
Then, another thing...when we say "black forces" and such, obviously
(for me at least) we are referring to something related to the "black
matter", don't we?

[[Mod. note -- No, Luigi is referring to the forces shown by black
arrows in his animation. This has nothing to do with dark matter.
-- jt]]

And this matter is there..all over the Universe....so it is present
right here, even in the matter of my computer screen, even in the air,
in my body ..and so on, isn't it?
Then ..this is the place where....electric or magnetic field is said
to exist. God forbid..somebody call it ...aether or similar! ;)
Did I get it right?
Correct me if you think I am wrong about these!
Best regards, LL

Luigi Fortunati

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Dec 19, 2022, 2:58:26 AM12/19/22
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xray4abc sabato 10/12/2022 alle ore 17:54:01 ha scritto:
[Mod. note -- Quoted text trimmed. -J.T.]
> I wonder if Einstein's theory holds, if the Equivalence Principle proves
> to be an artificial theoretical construction, with a very limited validity,
> which I strongly believe to be the case!
> I could explain why I believe that, ....though ....from experience ...
> I know...for some mysterious reason, people, that is physicists in most
> cases, want to avoid any unorthodox discussions .....by all ....and
> any... costs!
> Then, another thing...when we say "black forces" and such, obviously
> (for me at least) we are referring to something related to the "black
> matter", don't we?
>
> [[Mod. note -- No, Luigi is referring to the forces shown by black
> arrows in his animation. This has nothing to do with dark matter.
> -- jt]]
>
> And this matter is there..all over the Universe....so it is present
> right here, even in the matter of my computer screen, even in the air,
> in my body ..and so on, isn't it?
> Then ..this is the place where....electric or magnetic field is said
> to exist. God forbid..somebody call it ...aether or similar! ;)
> Did I get it right?
> Correct me if you think I am wrong about these!
> Best regards, LL

Moderator's note is correct.

I've never talked about dark matter or ether (they don't interest me).

I have only tried to highlight the incompatibility between General
Relativity (which is a theory) and force (which is a physical
phenomenon measurable with a dynamometer).

Jonathan Thornburg [remove -color to reply]

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Dec 20, 2022, 2:35:07 PM12/20/22
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Catching up a bit... On 2022-11-27 Luigi Fortunati wrote:
> In my animation
> https://www.geogebra.org/m/tr8jc8bt
> 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
> checkbox.
>
> 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.

--
-- "Jonathan Thornburg [remove -color to reply]" <dr.j.th...@gmail-pink.com>
currently on the west coast of Canada
"[I'm] Sick of people calling everything in crypto a Ponzi scheme.
Some crypto projects are pump and dump schemes, while others are pyramid
schemes. Others are just standard issue fraud. Others are just middlemen
skimming off the top. Stop glossing over the diversity in the industry."
-- Pat Dennis, 2022-04-25

Luigi Fortunati

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Dec 22, 2022, 5:29:06 AM12/22/22
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Jonathan Thornburg [remove -color to reply] martedì 20/12/2022 alle ore 20:35:04 ha scritto:
> Geodesic motion is also known as "free-fall".

This thing you say is certainly true for the Moon which is in free fall
towards the Earth (or, rather, towards the Earth-Moon common center of
mass).

It is also true for airplanes and it is true for men who move on the
earth's surface always going straight.

What is the first characteristic of geodetic motion? It is that of
moving along a curve without ever passing through its centre: the Moon
never passes through the Earth-Moon center of mass, man and the plane
never pass through the center of the Earth.

The second characteristic is that the geodetic motion does not converge
towards a single point: planes and men go in any direction and there is
no one that is privileged over the others.

The third characteristic is that if the body moving along a geodesic
encounters an obstacle and stops, when we remove the obstacle, it does
not start moving again along the same geodesic as before.

In fact, if the earth were a perfect sphere of ice, a skater who goes
straight forward, and is stopped, when we free him to move, remains
stationary in place of him.

These are the three characteristics of geodetic motion.

But the famous free fall of Einstein's elevator is not a geodesic motion
at all!

In fact, it lacks even one of the characteristics of geodetic motion.

First, it doesn't go around the center of the Earth, it just goes right
through it.

Secondly, it *always* converges towards a single point: if there are a
thousand different elevators, in points very distant from each other,
all the thousand converge towards a single point: the center of the
Earth (which a thousand airplanes and a thousand people, who follow
their geodesics, do not).

Thirdly, the elevator that is stopped by a constraint, as soon as we
remove it, automatically and inevitably resumes the same geodesic motion
it had before.

Thus, the "free fall" of the Moon is a geodesic motion, the flight of
airplanes and the movement of men on the earth are geodesic motions but,
not having any of the characteristics of geodesic motion, the "free
fall" of the elevator is not a geodesic motion.
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