# Something strange with Gravity ?

#### Dicart

Registered Senior Member
Hello.

I have some question about "the gravitationnal force" because this concept seems (for me) not physicaly accurate.
At first approximation, everybody knows that the intensity of the gravitationnal force is proportionnal to the inverse of the square of the distance.
F(d)=GmM/(d*d)

Therefore at some distance everything that is at distance d will be attracted with the force F(d)
So far so good.
But this force F(d) act into the whole tridimensional volume where there is gravtitationnal activity coming from one mass.

To be consistent with the inverse squared value of gravitationnal force, the force should only act on a surface, not in a volume.
More strange : The volume is increasing at light speed ! (because gravitational field is supposed to extand at this speed, altought this point could be discussed...)
So the total intensity of the force (if we sum the force into the volume) is increasing as time passes...

To be accurate the gravitational field could behavior like the electromagnetic field... but this would mean the gravitational wave, like the light, is part of quantum mecanic (but it is not).

Anyone has an explaination to this strange behavior ?

Wow that's a mess. You are mixing bits of Newtonian gravity with parts of general relativity and a dash of hypothetical quantum gravity theories so I'm not surprised that mess makes no sense. Pick a theory and stick with it is my advice and if it turns out to be the wrong theory for the regime you are considering then pick a different one and start over.
To be consistent with the inverse squared value of gravitationnal force, the force should only act on a surface, not in a volume.
Huh? Why do you think that? And what do you mean only act on a surface? The inverse square law falls out of the flux integral over a spherical surface round a point source being independant of distance yes but that depends on all of those integration surfaces making up a 3d space and the force being defined everywhere in it.
More strange : The volume is increasing at light speed ! (because gravitational field is supposed to extand at this speed, altought this point could be discussed...)
Huh? In Newtonian gravity the gravitational field propagates instantly so it affects everywhere all at once. If you want to talk about finite propagation speeds and gravity you need to use GR but in GR gravity is spacetime curvature and not a force and your Newtonian formula is the wrong thing to be using you need to work with the Einstein field equations.
So the total intensity of the force (if we sum the force into the volume) is increasing as time passes...
Huh? What do you mean by total intensity of a force?
To be accurate the gravitational field could behavior like the electromagnetic field...
There are similarities between gravity and electromagnetism and in fact there's a weak field approximation to GR where the field equations simplify to exactly the same form as Maxwell's equations but they are not exactly the same in the full theory.
but this would mean the gravitational wave, like the light, is part of quantum mecanic (but it is not).
Where did you get the idea gravity isn't quantised? Classical gravity theory isn't quantised by definition sure but actual gravity is almost certainly quantised but nobody knows how to write the theory yet and nobody can do experiments in the kind of regime where we'd expect to see quantum behaviour yet.

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Wow that's a mess. You are mixing bits of Newtonian gravity with parts of general relativity and a dash of hypothetical quantum gravity theories so I'm not surprised that mess makes no sense. Pick a theory and stick with it is my advice and if it turns out to be the wrong theory for the regime you are considering then pick a different one and start over.

Not really.
I am aware of the specificity of theses theories.
I am here talking about Newtonian force because i think all become more clear with this theorie.
Newtonian law apply with short distances and no motion : So the problem evocated remain the same.

How can you have a 1/d2 force present at every position of a volume without having a problem with the total energy you potentialy can use ???
This is non-sense.
Newton could not know that because energetic considerations were not usual at his epoch.
But now we suppose energy can not appear from nothing.

Huh? Why do you think that? And what do you mean only act on a surface? The inverse square law falls out of the flux integral over a spherical surface round a point source being independant of distance yes but that depends on all of those integration surfaces making up a 3d space and the force being defined everywhere in it.

Because if you consider the force acting on the surface of a sphere you see that 1/(d*d) "is counteract" (in some kind) by the pi*d*d (surface) and so if you multiply 1/(d*d) by d*d you supress the variable d (the distance).
No energy gained.
But here : it is like you have an addition of infinitesimal surfaces of spheres (making a volumic sphere therefore the sum by integration) and with this you have a gain of energy.

Huh? In Newtonian gravity the gravitational field propagates instantly so it affects everywhere all at once. If you want to talk about finite propagation speeds and gravity you need to use GR but in GR gravity is spacetime curvature and not a force and your Newtonian formula is the wrong thing to be using you need to work with the Einstein field equations.

Sure.
But this is not the point.
I talked about this other "anomaly" because it can perhaps make understand the real behaviour of the gravitation (but this is more complicated).

Huh? What do you mean by total intensity of a force?

The integration of the force you can potentialy use at every point of the volumic sphere.
If you understand well, using a force somewhere dosent affect the use of the force at an other place (unlike the electromagnetic wave... wich is a quantic object).

There are similarities between gravity and electromagnetism and in fact there's a weak field approximation to GR where the field equations simplify to exactly the same form as Maxwell's equations but they are not exactly the same in the full theory.

Yes but gravity doesent weaken as used.

Where did you get the idea gravity isn't quantised? Classical gravity theory isn't quantised by definition sure but actual gravity is almost certainly quantised but nobody knows how to write the theory yet and nobody can do experiments in the kind of regime where we'd expect to see quantum behaviour yet.

I dident say gravity can not be quantised (graviton is a quantisation)

I said it doesent fit the quantum mechanic because using a quantum of the field somewhere do not weakens the field at other places.
Gravity uses graviton but graviton dosent expand like other particles (this is what i say).

Not really.
I am aware of the specificity of theses theories.
Then why bring up other bits of other theories if you want to talk about Newtonian gravity? OK whatever let's talk Newtonian gravity.
How can you have a 1/d2 force present at every position of a volume without having a problem with the total energy you potentialy can use ???
How are you planning on using that energy?
Because if you consider the force acting on the surface of a sphere you see that 1/(d*d) "is counteract" (in some kind) by the pi*d*d (surface) and so if you multiply 1/(d*d) by d*d you supress the variable d (the distance).
No energy gained.
But here : it is like you have an addition of infinitesimal surfaces of spheres (making a volumic sphere therefore the sum by integration) and with this you have a gain of energy.
This is just nonsense. The flux integral over the surface is constant but it isn't an energy or a force and nor would you get an energy or a force by integrating in the radial direction and I've no idea what you think you'd achieve by doing that since it's just multiply counting the flux.
The integration of the force you can potentialy use at every point of the volumic sphere.
Why would you integrate force?
I said it doesent fit the quantum mechanic because using a quantum of the field somewhere do not weakens the field at other places.
I think you're just confused between static force fields and the wave field changes propagate which are not the same thing and I think you need to think very carefully about what you mean by "using" a field and how you're going to do it.

This is just nonsense. The flux integral over the surface is constant but it isn't an energy or a force and nor would you get an energy or a force by integrating in the radial direction and I've no idea what you think you'd achieve by doing that since it's just multiply counting the flux.
Ok. Try again.

You have a mass M centered in the vacuum (why not).
Now you try to answer : What force will act on a mass from this center point ... toward infinity.
A force will have an action (probably here an acceleration).

OK.

Now i fill all the vacuum with some mass m.

You know the formula : F=GmM/(d*d)

How can you summ these forces without adding energy ? (think about the infinity...)

... What force will act on a mass from this center point ... toward infinity.
... A force will have an action (probably here an acceleration).
... How can you summ these forces without adding energy ? (think about the infinity...)

Just go read a book or two so you can at least start asking meaningful questions.

Ok. Try again.

You have a mass M centered in the vacuum (why not).
Now you try to answer : What force will act on a mass from this center point ... toward infinity.
Gravity does not act just on a center point. That's why there are tides.
A force will have an action (probably here an acceleration).
Nope. In a rigid body, a force will produce no action if the NET force is zero. In a semi-rigid body the force will produce limited action (i.e. once again - tides.)
How can you summ these forces without adding energy ? (think about the infinity...)
Gravity alone denotes potential energy, not kinetic energy.

Gravity does not act just on a center point.

But this is a (very... because mathematical ) correct approximation for usual astronomic objects.
WIkipedia said:
In classical mechanics, the shell theorem gives gravitational simplifications that can be applied to objects inside or outside a spherically symmetrical body. This theorem has particular application to astronomy.

Isaac Newton proved the shell theorem[1] and stated that:

1. A spherically symmetric body affects external objects gravitationally as though all of its mass were concentrated at a point at its center.
2. If the body is a spherically symmetric shell (i.e., a hollow ball), no net gravitational force is exerted by the shell on any object inside, regardless of the object's location within the shell.
https://en.wikipedia.org/wiki/Shell_theorem

That's why there are tides.

You mean there is a variation of 10 meters deformation of water within a 40 000 000 meters diameter object ?
Impressing...
So we should take in account these deformations when computing astronomical trajectories ?

Nope. In a rigid body, a force will produce no action if the NET force is zero. In a semi-rigid body the force will produce limited action (i.e. once again - tides.)

And with a gaz object ?
You dident understand we are dealing here with the mathematic problem.

Gravity alone denotes potential energy, not kinetic energy.

It only depends on what you want to demonstrate.
Both are correct

But this is a (very... because mathematical ) correct approximation for usual astronomic objects.
Right. It is a reasonable APPROXIMATION when looking at, say, planetary orbits. Not when looking at tides, or (for example) orbits of low Earth satellites.
You mean there is a variation of 10 meters deformation of water within a 40 000 000 meters diameter object ?
That is possible due to tides, yes.
So we should take in account these deformations when computing astronomical trajectories ?
We do, all the time.
And with a gaz object ?
I assume you mean "gas." Yes, you will see tides deform gaseous planets as well.
It only depends on what you want to demonstrate.
Both are correct
Nope. Gravity plus mass gives you potential energy. Speed plus mass gives you kinetic energy. They are different.