How gravity is an emergent phenomena modeling space-time fabric gradient

I always imagined, and it could be the ultimate truth, that gravity is an emergent phenomena built by lots of subatomic particles wiggling in space-time fabric. The mathematical problem is how to account the effect of particles packed in a sphere general form (like planets or even black holes) at certain distance from the geometric center which in turn gives a sphere of iso-gravitational spherical surface with a specific field strength. If the analysis provide some kind of result without diving into complicated mathematical tools like Tensors, then bingo! Too much optimism bordering naivety but this could be the way to relate how quarks push out (either space-time fabric itself or quark-gluon plasma) just to create a gravitational field gradient. If successful, baryons, black holes and even the primeval atom are just 'bubbles of nothingness' in the space-time sea/gluon plasma is an increasing order of magnitude.

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I am a physics/mathematics enthusiast who just enjoys grappling with problems for fun.

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A video is attached below how the problem is imagined.

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e.arcurate@gmail.com

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If i understood the problem well (though i might not be sure cause i don't speak english very well). You want to solve the integral on all little particule in the sphere of the force the particule applies on point x. Sadly it is not solvable to get a closed formula. However, you can use the divergence theorem (you can look it up on wikipedia if you want). It will (roughly) tell you that the "quantity of force of the field" that gets out of the sphere of radius R (which passes by x). Is equal to the integral of the divergence of the field over the interior of the sphere, the divergence being the "quantity of force" that gets out of an infinitesimal volume. When you do the calculations, you find exactly the right formula. (because you pass from an integral in which you care where x is, to an integral on local properties of the solid sphere, which doesn't depend of x).

To explain why the divergence theorem is true simply, one could say that you let every little particule constantly send a lot of little signals in every direction, a unit signal being one unit of force. You want to know how many signal reach x (it is clearly an inverse scare law). well, you can say that the position of x doesn't change anything, as long as x is on the sphere of radius R. So we juste want to know how many signal will get out of this sphere at a time t (we will divide it by 4piR^2). However, every signal emitted always goes forward, an never stops, so we just want to know what quantity of force is emitted inside our sphere of radius R at a given time. So we juste want to know how many signals are emitted by each particule at a given time. Therefore, we do not longer care about x, and you can let the signal be emitted at the center of the sphere. This is a completely informal proof of course (to be formal, you have to use the divergence theorem), but i think it would be a good enough explanation in a video.

Thank you for taking time and write me back. I think the remaining days are few for collaboration (deadline less than a week already) but the problem is fascinating anyways. You are right that if we put a representative field generator at the center, it seems that the field intensity at X would be just a function of a spherical Gaussian surface (4πR^2) at any radius R. But is that all simple? Your approach to simplify the problem is like replacing all material of the Earth in 1cm radius sphere(blackhole) might have the same gravitational effect where you are now, theoretically. Since such scenarios are hypothetical, I don't think it is helpful to solve the problem. If you read the problem statement, what I want to model the effect of all baryonic subatomic particles as a source of gravitational field. Maybe the physics might be wrong in this part of the universe ;-) . . . . but if we dare to imagine the trapped quarks are kicking out the space-time fabric like little demons (genies), there will be a space-time wrinkle right at the outer edge of the sphere, and the wrinkle gets ironed out by distance as the cumulative beatings of the particles gets less strong. I am captivated with this perspective. I have a friend whom I asked to help out and he sent me some solutions in a way you indicated involving integrals. But X persists in the expression and couldn't see through the solution. Will share you more if you are interested. Thank you again

On Fri, Jul 29, 2022 at 1:19 PM malehe-yo @.***> wrote:

If i understood the problem well (though i might not be sure cause i don't speak english very well). You want to solve the integral on all little particule in the sphere of the force the particule applies on point x. Sadly it is not solvable to get a closed formula. However, you can use the divergence theorem (you can look it up on wikipedia if you want). It will (roughly) tell you that the "quantity of force of the field" that gets out of the sphere of radius R (which passes by x). Is equal to the integral of the divergence of the field over the interior of the sphere, the divergence being the "quantity of force" that gets out of an infinitesimal volume. When you do the calculations, you find exactly the right formula. (because you pass from an integral in which you care where x is, to an integral on local properties of the solid sphere, which doesn't depend of x).

To explain why the divergence theorem is true simply, one could say that you let every little particule constantly send a lot of little signals in every direction, a unit signal being one unit of force. You want to know how many signal reach x (it is clearly an inverse scare law). well, you can say that the position of x doesn't change anything, as long as x is on the sphere of radius R. So we juste want to know how many signal will get out of this sphere at a time t (we will divide it by 4piR^2). However, every signal emitted always goes forward, an never stops, so we just want to know what quantity of force is emitted inside our sphere of radius R at a given time. So we juste want to know how many signals are emitted by each particule at a given time. Therefore, we do not longer care about x, and you can let the signal be emitted at the center of the sphere. This is a completely informal proof of course (to be formal, you have to use the divergence theorem), but i think it would be a good enough explanation in a video.

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I think one of the main ideas of idea of our current representation of the situation is that we don't need to care about masses, or particules, we can ignore them and juste say we have a certain field. if we have all local information about the field in the space-time frame, we can go back (with the field's equivalent of integral) to find where are the masses (it is basically what maxwell's equation do, but with charges). Therefore, to one field corresponds one situation, and we can juste think about space as a gravitational field. My claim then is that outside of earth, the field behaves in the same way as if all fields lines are concurrent in the center of earth, which means all the masses are in the center of earth. In that way, (if we disregard potential quantum effects i am not familiar with) We don't have to think about black holes or singularities, because our field will still work perfectly. However, you are right, there is a fun phenomena that happens right at the outer edge of the sphere : the gravitationnal field exterior to the sphere will remain the same if you place all mass on the center, however, if you are inside earth (at a radius d with d<r the radius of earth), All earth masses at a distance stricly superior to d cancel out, and the field behave in X(d) as if earth only had a radius d. Anyways, i find it quite beautiful how fields and the divergence theorems simplifies all this.

So, is intuition solving the problem easily? Locating all field contributors to a point is equivalent to distributing them uniformly is a spherical region with a finite radius as long as the point 'x' in question? Nice logic but is it so???? By the way, this approach will not reinvent the value of G or redefine the gravitational relationship between two masses more than what is already known. But, this all about how? Einstein's GR is VERY successful as Newton's theory of gravity was for 3 hundred years. So, if there is any possible WEAKNESS with GR, it will be about flaws in its inherent model of the universe. May be space-time doesn't bend/curve even though such expressions gave to incredible insight and predictions. What if we say interchangeably, 'Space thins and thickens' like some fluid due to mass and energy? As long as the predictive power is equal or better as compared to GR, then we welcome the idea. The problem is, GR is so established and its success sooo intimidating. Let's try to imagine this in artificially constructed universe of your and mine ;-)

The first thing is to set basic rules and initial universe model to start with

Basic Rules Rule #1: There is a field made up of discrete components (you are free to think of 'aether') that permeates all corners of the universe unless otherwise rule #2 Rule#2: 'Mass' and 'energy' have a tendency to displace this field creating local bubbles with varying level of success.

Consequence-2.1 Some regions are totally aether free (region within event horizon of a black hole as these regions are very much powerful to displace any trace of aether.

Consequence-2.2 Some regions are less dense (inside a less massive/energetic region as compared to a collapsed object creating BH. eg planet/asteroid/stars etc . . . .and regions which are too far from mass/energy like bootes void )

Consequence-2.3 Some regions are more dense with aether ( immediate exterior region of objects like planets/asteroids/stars and even BH outside to an event horizon)

Consequence-2.4 Mass/energy elementary components respond to density gradients of aether.

Initial universe Model to start with: Elementary components of mass/energy kick away aethers in a simpler interaction model of varying degree described as consequences above.

What would the field equation of this universe if you were their Einstein?

On Sun, Jul 31, 2022 at 3:44 PM malehe-yo @.***> wrote:

I think one of the main ideas of idea of our current representation of the situation is that we don't need to care about masses, or particules, we can ignore them and juste say we have a certain field. if we have all local information about the field in the space-time frame, we can go back (with the field's equivalent of integral) to find where are the masses (it is basically what maxwell's equation do, but with charges). Therefore, to one field corresponds one situation, and we can juste think about space as a gravitational field. My claim then is that outside of earth, the field behaves in the same way as if all fields lines are concurrent in the center of earth, which means all the masses are in the center of earth. In that way, (if we disregard potential quantum effects i am not familiar with) We don't have to think about black holes or singularities, because our field will still work perfectly. However, you are right, there is a fun phenomena that happens right at the outer edge of the sphere : the gravitationnal field exterior to the sphere will remain the same if you place all mass on the center, however, if you are inside earth (at a radius d with d<r the radius of earth), All earth masses at a distance stricly superior to d cancel out, and the field behave in X(d) as if earth only had a radius d. Anyways, i find it quite beautiful how fields and the divergence theorems simplifies all this.

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The big problem is that... Einstein is kinda right. I can only neglect relativistic corrections as long as I have a static universe, which sure isnt the case. This Model would be the same as righting maxwell's equations in electrostatic. If you won't do dynamics, you miss a lot of things and your model is false. However, if you want the equations of our "world" (which I repeat must be static), you have two of them : -The curl of the mass field equals zero

the gradient of the mass field is inverse square (which correspond to our inverse square law of gravity). However, this is going to be false, because the universe is never static.

leios / SoME_Topics