We consider gravitational potentials, which let planets orbit around the sun. This view implies a remote non-local impact of the sun on the planets and vice versa.
But in fact, the gravitational fields have an energy density, which is present locally. The energy density E quadratically depends on the field strength and is given by E=-g²/(8πG), g=MG/r². G is the gravitational constant, r is the distance to the centre of mass M, which generates the gravitational acceleration g.
With the locally available energy density, the gravitational force also becomes a local force.
The gravitational force on an object, which contributes to the gravitational field, is given by the derivative (gradient) of the total field energy in respect to the position of the object.
This force is an interaction between gravitational fields. The energy density of the gravitational field of the object decays with the distance d from the object to the fourth (~1/d4). The interaction of the local gravitational field of the object with the omnipresent background field, therefor is a local interaction.
The idea of a remote gravitational interaction on a distance is a blatant chimera!
The highlighted relation between energy density and force applies to all kinds of force fields.
Wolfgang Konle I agree with your conclusion that gravity is local. I would say that Newton thought gravity to be non-local and he was puzzled by this “action at a distance “ which seemed to act instantaneously .
Now we know that gravitational acceleration is an effect of Spacetime curvature. If we were to instantaneously halve the mass of the sun then we would not detect this change for about 9 minutes which is the time it would take for the gravitational effect to propagate.
Of course it is not possible to destroy mass/energy so this effect never happens. The closest we come to such mass destruction is in black hole or neutron star mergers and in this case we get gravitational waves travelling at the speed of light.
So we can say that nothing travels faster than the speed of light not even gravity.
I also take the view that quantum entanglement effects do not travel faster than the speed of light.
Richard
I am sure you know, our Universe has over trillions of suns.
I am sure you know, there is over trillions of solar systems.
My question...which sun are we talking about?
second question...what is local or none local in the universe?
I'm sure you know, Sir. Newton in 1700s did not know anything about our vast size of the universe. Then what is local or non-local for his perception?
thanks
Javad Fardaei "My question...which sun are we talking about?"
Any sun which has planets.
"what is local or none local in the universe"
Local means "short distance", non-local means "long distance".
If we talk about an object in a gravitational field, local means within the range of the gravitational field of the object (e.g. of the planet), non-local means within the distance to the source of the gravitational field (e.g. to the sun).
Zachary Knutson
"gravity warps space-time so action at a distance is a discrepancy to be solved..."The rule:
"The gravitational force on an object, which contributes to the gravitational field, is given by the derivative (gradient) of the total field energy in respect to the position of the object."
provides a short range solution of this discrepancy, because the background field energy is present locally at the position of the object.
Wolfgang Konle
There is no gravity force or field exist in space, that is why our astronauts call it zero-gravity.
If there was any gravity force exist, after several billions of years all the planets, suns, moons would go to gravity force, and eventually stop.
If our sun that made over 98% lightest element H had any gravity, all the comments, asteroids, never been rejected by sun flare. there is no single gravity force exist in space.
there is no single mathematic calculation exist to describe nature of the universe.
This is my theory, our universe is a complete entity that our flat static mathematic is wrong tool describe nature.
To my understanding, prediction of any kinds, or modeling nature is not science.
I know you are disagree with everything I say, but the truth always win. There is no single argument with my statements, and you knw it too.
Javad Fardaei "There is no gravity force or field exist in space, that is why our astronauts call it zero-gravity."
Astronauts feel no gravity because they are in free fall!
Javad, what you are posting shows that you are absolutely clueless about that issue. (comments/comets??) Why are you posting about things, you do not understand?
Only two explanations are possible:
(1) You do not know that you don't understand.
or
(2) You know, but you are a troll and you want to annoy people.
Both possibilities are bad for you and for all who read your nonsense.
It is the concept of spacetime itself that challenges non-locality. In complex spacetime, Euclidean horizons arise to demarcate regions of distinct curvatures (closed, flat and open). While scaling varies in proportion to associated mass densities, and conforms to General Relativity, additional effects such as non-locality can be effected through the imaginary components of complex spacetime.
John BUERS Awuor
There is no evidence that spacetime might have imaginary components.
A confirmation of evidence depends on a viability of a possibility and the means to access its actualization., if any. By the concept of dimensional orthogonality, no dimension is a solo generator of any other, and complex numbers are deemed as equivalent to vectors. This connection provides the sense in which extra dimensions; the imaginaries, are implied in my statement on complex spacetime. A mathematical follow-up provides for an expanding universe with accelerations at ranges beyond its Euclidean horizon. That constitutes implied evidence.
John BUERS Awuor "complex numbers are deemed as equivalent to vectors"
No, this is wrong. Vectors have equitable components, complex numbers have different components. In electronics, Laplace transform, the real part means frequency, the imaginary part means damping or decay properties.
I have not got the sense in which '..vectors have equitable components...' Kindly clarify.
That '....complex numbers have different components' is ok though partial, in that, differences are often geometrized by orthogonality that guarantees product relations; yet the complex notation is a sum!
Preston Guynn "Gravity is a description of the interaction between masses."
No, gravity is a description of the interaction between gravitational fields.
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