Greetings

I have been thinking about origin of gravitational force for few years
and tried to find some reply to my ideas. When I started writing down
my ponderings about four dimensional visualisations and infinities, I
came across with similarities of random walk theorem and hyperballs or
more like possibility dimensions. Like the random walk theorem stated,
when the movement is totally random, movement happens around the
starting point like a person who is lost goes around circles, because
possibility to go a specific direction is equal to going to opposite
direction. If there is a presumption that there is a particle in a
space that is totally empty excluding the particle, and the particle
is making totally random movement in infinitely small perioids of
time, the particle would stay at same position even if that particle
would be moving with speed of light. That particle would have a
hyperball or possibility dimension, which is size of a sphere which
radius is speed of light times perioid of time "r=ct". The particle
has a possibility to move anywhere inside the hyperball within the
time perioid, although it is infinitely improbable to be anywhere else
than in starting point. Because time is infinitely continuous factor,
hyperball can be infinitely large.
When another particle is added to that space, it will also have a
hyperball, that will affect to first particle and vice versa. These
two hyperballs will have overlapping areas that have higher
propabilities than opposite directions. This will cause that these two
particles start to move closer each another, since it's most probable
direction. This movement is called as gravitation force.
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My questions about this specific idea are as follows:
Is there any logical errors or incomplete definitions?
What is your opinion about this idea as an expert of the field?
Can it be taken seriously in science world?
Other possible objections and comments?

Quantum Mechanique: To even begin to be taken seriously, you will have
to be able to derive quantitatively that the force obeys the inverse
square law and is proportional to the mass of both objects.
Ultimately, you will have to show that it is consistent with the laws
of special and general relativity. If you get that far, people would
certainly take note, if it provides an interestingly different
perspective on the theory.

To be taken really seriously, you will have to predict something that
is measurable, but is different from what is already known. Otherwise,
you have simply reproduced the existing theory in a different way.

For some reason, gravitation attracts an inordinate number of people
who have theories. Most of these hope to explain some aspect of
gravitation that is important to the inventor, but fail to make
quantitative predictions at all, or simply make the same quantitative
predictions as Newton's classical theory of gravity, with vague
derivations of how we got to Newton's equations.

Since your theory is not quantitative, at least as you have stated it,
it will never get serious consideration. Also, I cannot follow your
speculations about the random walk at the speed of light. You will
need to make these arguments quantitative to have it taken seriously.
Good luck!

As far as I understood, going to in depth details would raise the
price of the question to 200$, and pointing out too many factors would
make it very time-taking. Therefore I tried to keep it as very simple
example, and only point out things that are totally necessary to
understand the idea. Your comments are very good for my purposes,
since hearing what kind of requirements critical people demand, I will
be capable to answer them later more thoroughly.
To give a better understanding what I meant with random walk, I add a
link to page that demostrates it. Check 2d box.
http://www.ki.inf.tu-dresden.de/~fritzke/research/TS/example1.html

I am well familiar with random walks, but as I understand your
proposal, you have random jumps of length L=c*T, where c is the speed
of light and T is an infinitesimal length of time. For a finite value
of T, the particle will diffuse with a diffusion constant given by D =
L^2/T = c^2*T . Rather than behaving as some "hyperball", if we start
the particle at the origin, and look for it at time t, we will find it
at a specific location, which in general will be far from the origin,
but the size of the "ball" in which we would expect to find it will
have a radius of about sqrt(Dt) = c*sqrt(T*t). That is, the ball's
radius will be the speed of light times the geometric mean of the
elapsed time and the duration of the jump. The particle will always be
found at a specific place.

What confuses me the most about what you are saying is that if I set
the duration of the jump T to zero (since you say infinitely small
periods of time), then there are no jumps at all (c*T = 0), the
diffusion constant is zero, and nothing happens except that the
particle rests at the origin.

What also mystifies me is why this helps understand gravity. You have
to hypothesize mysterious forces that cause a particle to accelerate
this way and that in order to understand a force law that can be
stated fairly simply. Why does this help.

If you like to understand gravity in terms of interacting particles,
rather than potential fields, that is certainly possible without
introducing any new physics. Feynman's approach to electrodynamics
pictures a world of virtual photons and electrons flitting into and
out of existence and the Coulomb attraction or repulsion is
accomplished by the point interactions of photons and charged
particles. The theory predicts exactly the inverse square law and
other features of the classical theory. This can be extended to
gravitation as well using the graviton as the particle that mediates
the interaction. There are difficulties with a simple field theory of
the graviton when relativistic effects are considered and this is
still one of the biggest challenges of theoretical physics, finding a
fully consistent relativistic quantum field theory for gravity.

When I mentioned hyperball of the particle, I didn't mean that it
would reflect diffusion of the particle. Hyperball was referring to
visualisation of four-dimensional space, where the radius of the
hyperball was the total length of random jumps. Possibility that a
particle would reach the shell of the hyperball would be one to total
amount of jumps times possible directions per jump. If even one factor
is infinite, that would make the calculation bit difficult. The actual
results are seen as you stated. Probability density of the hyperball
is the same as bending in the space-time continuum. If hyperball would
be thought as a trampoline which radius is the same as radius of the
hyperball, and the particle is a marble ball in the center of it.
Weight of the marble ball affects how much fabric of the trampoline is
being pulled downwards. When there is another particle, they are on
the same trampoline fabric. Because the force pulling fabric down is
stronger between the marbles than elsewhere, the fabric is lower in
between. This makes marbles to roll towards each other.

And I try to clarify more about that part when the duration of the
jump is zero. As you said length of the jump is speed of light times
the perioid of time. You speaked earlier about finite factors, but as
far as I understand, it is not disallowed to use infinitesimal
factors. Total value would become zero, as anything times zero is
zero. This doesn't mean that there wouldn't be any jumps at all. It
would mean that there is infinite amount of jumps with infinitesimal
duration to certain direction. This would cause diffusion to collapse
into zero. Particle is moving at it's origin with the speed of light.
This movement that happens at it's place is same as mass of the
particle.

Thank you again for your comments. I really appreciate it.

You lost me back at the ranch. It is easy to handle the infinities
times infinitesimals that you have described. The answer comes back as
zero. That is why I described it with a finite T and replaced T with
zero at the end. You need to progress from vigorous waving of the
hands to equations. That is the only way to compete with Newton's
great breakthrough.

P.S. I should have added:

But keep at it. There are still mysteries in the theory of
gravitation. As I mentioned earlier, one of the greatest challenges of
theoretical physics is the union of gravity and quantum mechanics.
Revolutions in science are made only by questioning the status quo.