Two bodies in remote space

[Luigi Fortunati]

In my animation

https://www.geogebra.org/m/dfv4bsrw

there are two bodies next to each other, standing still without pushing
each other (and the dynamometer proves it).

They don't push each other because nothing pushing body A to the right
and nothing pushing body B to the left.

But if the two bodies A and B have electromagnetic charge (as seen by
clicking on the "Electromagnetic interaction" button), the external
force that pushes body A to the right and body B to the left, is there.

In this case there is an external action (the blue electromagnetic
attraction between the two opposite charges) that pushes the two bodies
towards each other and all this generates an opposite internal red
reaction (in the contact zone) direct in the opposite direction to
contrast the approach of the two bodies.

Red forces exist as a reaction to blue forces and would not exist
without them.

Is it correct to say that the situation is completely analogous to the
one seen by clicking on the "Gravitational interaction" button, where
the reciprocal red force (of action-reaction between bodies A and B)
exists only thanks to the blue gravitational force?

[Luigi Fortunati]

Post by Luigi Fortunati
In my animation

https://www.geogebra.org/m/dfv4bsrw

there are two bodies next to each other, standing still without pushing
each other (and the dynamometer proves it).
They don't push each other because nothing pushing body A to the right
and nothing pushing body B to the left.
But if the two bodies A and B have electromagnetic charge (as seen by
clicking on the "Electromagnetic interaction" button), the external
force that pushes body A to the right and body B to the left, is there.
In this case there is an external action (the blue electromagnetic
attraction between the two opposite charges) that pushes the two bodies
towards each other and all this generates an opposite internal red
reaction (in the contact zone) direct in the opposite direction to
contrast the approach of the two bodies.
Red forces exist as a reaction to blue forces and would not exist
without them.
Is it correct to say that the situation is completely analogous to the
one seen by clicking on the "Gravitational interaction" button, where
the reciprocal red force (of action-reaction between bodies A and B)
exists only thanks to the blue gravitational force?

Too bad I didn't have any answers, for me the question is very
important.

I will try to simplify question.

In my animation

Post by Luigi Fortunati

https://www.geogebra.org/m/dfv4bsrw

clicking on "Gravitational interaction" we see two bodies without any
electric charge exerting a compressive force in the contact area,
measured by the dynamometer.

Here is the question: is the force that compresses the contact zone
between the two bodies, whether due to Newton's gravity or Einstein's
spacetime curvature, real (it always exists) or is it apparent (and
disappears under certain conditions)?

[Richard Livingston]

Post by Luigi Fortunati

Post by Luigi Fortunati
In my animation

https://www.geogebra.org/m/dfv4bsrw

there are two bodies next to each other, standing still without pushing
each other (and the dynamometer proves it).
They don't push each other because nothing pushing body A to the right
and nothing pushing body B to the left.
But if the two bodies A and B have electromagnetic charge (as seen by
clicking on the "Electromagnetic interaction" button), the external
force that pushes body A to the right and body B to the left, is there.
In this case there is an external action (the blue electromagnetic
attraction between the two opposite charges) that pushes the two bodies
towards each other and all this generates an opposite internal red
reaction (in the contact zone) direct in the opposite direction to
contrast the approach of the two bodies.
Red forces exist as a reaction to blue forces and would not exist
without them.
Is it correct to say that the situation is completely analogous to the
one seen by clicking on the "Gravitational interaction" button, where
the reciprocal red force (of action-reaction between bodies A and B)
exists only thanks to the blue gravitational force?

Too bad I didn't have any answers, for me the question is very
important.
I will try to simplify question.
In my animation

Post by Luigi Fortunati

https://www.geogebra.org/m/dfv4bsrw

clicking on "Gravitational interaction" we see two bodies without any
electric charge exerting a compressive force in the contact area,
measured by the dynamometer.
m
Here is the question: is the force that compresses the contact zone
between the two bodies, whether due to Newton's gravity or Einstein's
spacetime curvature, real (it always exists) or is it apparent (and
disappears under certain conditions)?

Luigi,

This is largely a question of terminology rather than physics. You can
certainly consider that the two objects experience an attractive force
towards one another if you want.

However, the point that I and others have tried to make is that in general
relativity the natural path for each object near the other is one that
accelerates towards the other, as viewed in this center of mass frame.
Satellites in orbit "feel" no force. In the paradigm of general relativity
they are following a geodesic path through space-time just like any other
free object not subjected to an external force. The apparent curved path
is due to the curvature of the geometry of space-time.

In the paradigm of general relativity the only force in your simulation is
the one pressing against each mass preventing it from getting closer to
the other. The result of this force is the acceleration of each mass away
from the other, away from the free path, the geodesic path, that the mass
naturally wants to follow.

The objects exert a force back on the dynamometer because they have mass.
They "want" to continue going along the geodesic path, but because they
have mass they resist. Thus the dynamometer measures a force.

I think part of the confusion is that general relativity is an explanation
of gravity one layer further down than Newtonian gravity. In Newtonian
gravity the objects experience a "force" remote from the object causing
that "force". There is no explanation for how the force appears. In
general relativity that "force" is explained by, is caused by, the
non-Euclidian geometry of space-time. The non-Euclidian geometry is not
itself a force, but it causes effects that we interpret as a force.

It is possible that some future theory of electromagnetism might offer a
similar deeper understanding and we might then consider EM not a force but
{some deeper thing}. Time will tell.

Rich L.

[Luigi Fortunati]

Post by Richard Livingston
Luigi,
However, the point that I and others have tried to make is that in general
relativity the natural path for each object near the other is one that
accelerates towards the other, as viewed in this center of mass frame.

Meanwhile, I want to specify that the two bodies "accelerate" towards
each other in space but not in space-time where the forces (and the
consequent accelerations) do not exist.

Look at my animation
https://www.geogebra.org/m/pzts2ks7
set in space-time.

When you press "Start", the two bodies move towards each other,
following (as you say) their natural path (not accelerated, I say)
towards the center of mass.

But when, after the inelastic collision, the two bodies *stop*
approaching each other, their old geodesics no longer exist!

From that moment on, the two bodies become a single body following a
single geodesic (see what happens at the end of the animation).

There are no longer two "natural paths" but only one.

Post by Richard Livingston
And that despite there is in fact a correspondence in magnitude
between all the forces involved due to the fact that the two bodies
press on each other by the same exact amount that the two bodies
are attracting each other.

The two bodies attract each other because they follow their different
"natural paths" and that's okay.

But why do they keep attracting each other even when they stop getting
close to each other and become one body with a single "natural path"
instead of two?

[Luigi Fortunati]

Post by Richard Livingston
Luigi,
However, the point that I and others have tried to make is that in general
relativity the natural path for each object near the other is one that
accelerates towards the other, as viewed in this center of mass frame.

Meanwhile, I want to specify that the two bodies "accelerate" towards each other in space but not in space-time where the forces (and the consequent accelerations) do not exist.
Look at my animation
https://www.geogebra.org/m/pzts2ks7
set in space-time.
When you press "Start", the two bodies move towards each other, following (as you say) their natural path (not accelerated, I say) towards the center of mass.
But when, after the inelastic collision, the two bodies *stop* approaching each other, their old geodesics no longer exist!
From that moment on, the two bodies become a single body following a single geodesic (see what happens at the end of the animation).
There are no longer two "natural paths" but only one.

Post by Richard Livingston
And that despite there is in fact a correspondence in magnitude
between all the forces involved due to the fact that the two bodies
press on each other by the same exact amount that the two bodies
are attracting each other.

The two bodies attract each other because they follow their different "natural paths" and that's okay.
But why do they keep attracting each other even when they stop getting
close to each other and become one body with a single "natural path"
instead of two? 1

In English

https://www.geogebra.org/m/gpv6f5pn

[Luigi Fortunati]

Post by Luigi Fortunati
In English

https://www.geogebra.org/m/gpv6f5pn

Cubic bodies

Post by Luigi Fortunati
https://www.geogebra.org/m/ne77y6j4

[Julio Di Egidio]

Post by Luigi Fortunati

Post by Julio Di Egidio
And that despite there is in fact a correspondence in magnitude
between all the forces involved due to the fact that the two bodies
press on each other by the same exact amount that the two bodies
are attracting each other.

The two bodies attract each other because they follow their different
"natural paths" and that's okay.

You actually acknowledge nothing and just come back with
even more complication, here as elsewhere, which is how
the whole things remains simply and totally unproductive:
you are not learning.

Post by Luigi Fortunati
But why do they keep attracting each other even when they stop getting
close to each other and become one body with a single "natural path"
instead of two?

There are two *extended* bodies there, and while you can
attach resulting forces to the respective centers of mass (or
of charge), the point remains that the two distinct bodies
(particle by particle) keep attracting each other as long as
they do not simply compenetrate each other; while, assuming
no bouncing, of course (the center of) the combined system
does follow a "single path": but this is all utterly obvious and,
I must say, apparently pointless... indeed I will give up.

HTH and best luck,

Julio

[Richard Livingston]

Post by Luigi Fortunati
The two bodies attract each other because they follow their different
"natural paths" and that's okay.
But why do they keep attracting each other even when they stop getting
close to each other and become one body with a single "natural path"
instead of two?

The same question can be asked of each atom in each of the bodies:
Why do they not accelerate toward the center of mass of the body?
The answer is electromagnetic forces, the same ones that keep your
feet from sinking into the earth. These EM forces cause the atoms to
accelerate w/in the curved space-time generated by all the mass
in the objects. and the result is the common motion of the combined
mass.

Rich L.

[Luigi Fortunati]

Post by Richard Livingston
Why do they not accelerate toward the center of mass of the body?

They don't accelerate (I think) because there's another atom below
blocking it.

And the atom below does not accelerate because that another atom even
further below that blocks it.

And so on.

As in my drawing
https://www.geogebra.org/m/n9fdyenp

[Tom Roberts]

Richard Livingston gioved=C4=97 29/09/2022 alle ore 17:44:00 ha scritto=

The same question can be asked of each atom in each of the bodies:=20
Why do they not accelerate toward the center of mass of the body?=20
The answer is electromagnetic forces, the same ones that keep your=20
feet from sinking into the earth. These EM forces cause the atoms
to accelerate w/in the curved space-time generated by all the mass
in the objects. and the result is the common motion of the combined
mass.

=20
They don't accelerate (I think) because there's another atom below=20
blocking it.

You both are using too imprecise terminology, with a PUN on "accelerate"
here -- WHAT TYPE of acceleration do you mean?

Luigi is clearly thinking of coordinate acceleration relative to
coordinates at rest with respect to the body in question.

But Richard is thinking of each atom's proper acceleration. relative to
the atom's instantaneously co-moving locally inertial frame. Such
locally inertial frames, of course, are always falling due to the local
gravity, and here the EM forces make the atoms accelerate relative to
such (falling) frames.

In GR, proper acceleration is physical, while coordinate acceleration
can be merely an artifact of the coordinates used (as happens here for
Luigi's choice [#]). Gravitation never generates proper acceleration,
but real forces, such as EM, always do.

[#] Luigi chose coordinates relative to which the
accelerations of atoms are zero, even though their proper
accelerations are nonzero.

Tom Roberts

[Luigi Fortunati]

Post by Tom Roberts
You both are using too imprecise terminology, with a PUN on "accelerate"
here -- WHAT TYPE of acceleration do you mean?

Richard Livingston had asked: "Why do they not accelerate toward the
center of mass of the body?" and, therefore, the acceleration is that of
every single atom in the reference of the center of mass of the body.

Every single atom is stationary with respect to the center of mass
because it is blocked by the other atoms.

There is no single bond for everyone, every single atom is a bond for
the others and the other atoms are a bond for him.

Including the atom that is in the center of the mass.

Post by Tom Roberts
[#] Luigi chose coordinates relative to which the
accelerations of atoms are zero, even though their proper
accelerations are nonzero.

It is true, in my design
https://www.geogebra.org/m/n9fdyenp
I had chosen a single reference frame, the only one present in that
context where everything was still and not even a leaf moved.

But now I have proceeded to add a body in motion over everything else.

Animation is this
https://www.geogebra.org/m/zvjvwtef

There are two references and not just one.

We can choose which of the two to put ourselves in to observe what
happens.

If we put ourselves in the reference frame of the Earth (button "Free
fall of the body P"), the body P (which could be an atom, an asteroid or
even a planet) is in free fall with respect to the Earth.

If we put ourselves in the body reference frame P ("Free fall of the
Earth" button), the Earth is in free fall with respect to P.

Are the two points of view (the two references frame) equivalent to each
other?

Luigi Fortunati

[Robert Komar]

Post by Tom Roberts
In GR, proper acceleration is physical, while coordinate acceleration
can be merely an artifact of the coordinates used (as happens here for
Luigi's choice [#]). Gravitation never generates proper acceleration,
but real forces, such as EM, always do.

As someone who has never studied GR, this is an eye-opener for me.
If gravity is not a real force, is there a need for gravitons? Perhaps
trying to unify gravity with the other three forces in a grand unified
theory is a misguided adventure? I'm asking as someone who is
largely ignorant in these fields.

Cheers,
Rob Komar

[Richard Livingston]

Post by Robert Komar

Post by Tom Roberts
In GR, proper acceleration is physical, while coordinate acceleration
can be merely an artifact of the coordinates used (as happens here for
Luigi's choice [#]). Gravitation never generates proper acceleration,
but real forces, such as EM, always do.

As someone who has never studied GR, this is an eye-opener for me.
If gravity is not a real force, is there a need for gravitons? Perhaps
trying to unify gravity with the other three forces in a grand unified
theory is a misguided adventure? I'm asking as someone who is
largely ignorant in these fields.

[Moderator's note: Pun intended? --P.H.]

Post by Robert Komar
Cheers,
Rob Komar

I've wondered the same question. While I have studied GR, I am far from
an expert, so my opinion is probably of little value. But I've also
wondered if gravity should be quantized like the other "forces".

On the one hand, the current theory of gravity provides the space- time
geometry within which QM operates. Can you have a quantum theory that
operates within a quantum space-time? I really don't know.

On the other hand, gravity does transfer energy from place to place, and
that is clearly within the purview of quantum mechanics.

One thing that I have studied extensively is how well special relativity
and quantum mechanics actually play together and reinforce each other.
There is no conflict between special relativity and QM. It is really
quantum field theory that has a problem with GR.

Again, while I have studied quantum field theory, I am again far from an
expert. But there are several aspects of the current theory that I am
suspicious of and wonder if the problems quantizing gravity actually
have to do with mistaken concepts in field theory? Again, my opinion on
this is probably of little value.

Rich L.

[Julio Di Egidio]

Post by Luigi Fortunati
In my animation

https://www.geogebra.org/m/dfv4bsrw

there are two bodies next to each other, standing still without pushing
each other (and the dynamometer proves it).
They don't push each other because nothing pushing body A to the right
and nothing pushing body B to the left.
But if the two bodies A and B have electromagnetic charge (as seen by
clicking on the "Electromagnetic interaction" button), the external
force that pushes body A to the right and body B to the left, is there.
In this case there is an external action (the blue electromagnetic
attraction between the two opposite charges) that pushes the two bodies
towards each other and all this generates an opposite internal red
reaction (in the contact zone) direct in the opposite direction to
contrast the approach of the two bodies.

Your blue forces should be attached to the centers, indeed they
are not "external"... That said, IMHO, the main reason why you are
not getting answers is that you keep repeating the same mistakes.

Post by Luigi Fortunati
Red forces exist as a reaction to blue forces and would not exist
without them.

No, the red forces exist because the two bodies get in contact, and
these, microscopically speaking, are in fact electromagnetic repulsive
forces that prevent the two bodies from penetrating each other (i.e.
as long as they are not as strong as to break the molecular bonds,
then it's another regime). The point is you still miss what is action
and reaction: the two blue forces are each the reaction of the other,
while the two red forces, on the other hand, are each the reaction of
the other, not the mix of red and blue you do above and elsewhere!
And that despite there is in fact a correspondence in magnitude
between all the forces involved due to the fact that the two bodies
press on each other by the same exact amount that the two bodies
are attracting each other.

Let my try and put it this was: imagine you are pushing on a bolder
that in turn pushes by contact on a second boulder: you exert force
A and *by reaction* bolder 1 replies with -A on you, in turn bolder 1
is pushing on 2 with force B and *by reaction* bolder 2 pushes back
on 1 by a force -B... and that is about the 3rd principle, despite it is a
matter of the collinear setup that A and B will necessarily have the
same magnitude. Indeed, notice that, as soon as the pushing is not
all just collinear, the magnitudes are not anymore simply the same.

Post by Luigi Fortunati
Is it correct to say that the situation is completely analogous to the
one seen by clicking on the "Gravitational interaction" button, where
the reciprocal red force (of action-reaction between bodies A and B)
exists only thanks to the blue gravitational force?

Modulo the corrections mentioned above, and having assumed the
specificities of GR don't count in this small experiment, yes, the two
situations are completely analogous.

That said, you have meanwhile also asked if the red forces are "real":
1) of course they are, just put a hand in between the two bodies,
wouldn't you feel the pressure?! 2) as long as that question still
revolves around the meaning of "apparent forces", I thought it had
meanwhile amply been explained how that "apparent" does not mean
those forces do not exist. And why should anybody be interested in
repeating things already said, to you, recently, and more than once...

HTH,

Julio