The presented ideas are summarized at the next link:, however I put everything in this thread.
It is a heuristic try to give the simplest possible description of nature based on classical physics while trying to avoid disputing QM nor relativity.
I do not presume that the presented ideas are a theory. The reasons that they cannot be a theory at this level are:
* the presented ideas are still not shown to be related to nature, it just aims at showing the possibility of such relation.
* they are bold guesses (not prooven)
* there is no option today to do the calculations to falsify/proove the ideas due to high computation power required (however it is reasonable that in the future it will be possible)
Despite that, the reasons why the presented ideas should be taken seriously are:
* Theoretically, every claim can be prooven/falsify using mathematical tools (although may not be possible today)
* I think that the presented ideas are not contradictory to current observational knowledge, at least there is no proofe of contradiction
* The presented ideas do not allow fine tunning ('epicycles'). There are just 2 dimensionfull scaling constants which is the bare minimum possible for any theory. each other constant should be calculatable.
In other worlds: either it is complete description or it is nonesense.

I believe that by presenting a very simple and specific set of axioms and in trying to generalize it as much as possible, a new unexamined thread is presented.
Some of the major merits of classical physics such as natural support of relativity and QM violation of Bell inequality are addressed by this manuscript.
In the generalization process many conjectures are presented without proof, however the question which should be asked at this scope is not if they are true but if they are possible.
The main motivation for introducing a model with many unproven conjectures is the rare chance to suggest a discussion that can lead to the calculation of all physical constants by using a very compact formulation.
Regardless of this the presented ideas can be used as a classical analogy to QM and they can help to refine the ongoing discussion about QM interpretations.

The Model
* 3-d euclidean space and classical simultaneous time are assumed
* There are numerous identical size-less dot particles
* Each dot particle is attracted to all other dot particles by inverse square law:

These axioms are the only ones, no other interactions are assumed, no other properties of the dot particles are assumed and no other particles are assumed.

Starting Conditions
Consider infinite ’sea’ of dot particles with exact statistical behavior everywhere, uniform density and the same velocities distribution.
The system is assumed to be in equilibrium.
The complete system may be finite but for current discussion it is better to ignore boundary conditions.
The timescales discussed are very large in compare to two dot particles close encounter timescale so the system is a collisional one with gaussian velocity distribution.

Wave Properties
In this collisional framework, waves are assumed to propagate non-dispersively with constant speed C which depends on the density and on the ’constant’ g, both are dimensionful scaling factors.
By scaling reasons C needs to be proportional to .

Stable Standing Waves
Consider a small deviation from .
Slow changes of density across long distances in compare to the average distance between the dot particles are assumed so the discretization of the dot particles can be neglected and smoothed.
In order to look for localized stable standing waves spherical symmetry is assumed.
Average density in infinite is .
The basic formula will treat the infinitesimal energy density change across infinitesimal length:

Consider the acceleration/force that act upon group of particles in infinitesimal volume.
If density would be constant everywhere than the average force would be zero.
The superposition principle can be used together with spherical symmetry assumption as follow:
• spherical shell with lower than average density contributes opposite sign than higher than average density shell.
• a(r) is independent on density at r > r similar to a well known fact that gravity inside spherical shell is zero.
• a(r) for r < r for spherical shell is the same as all excess density is located in the center.
Considering all that, we get:

The average of the velocity squared is proportional to . Let the proportionality factor be k.

Numerical computation of the above formula under the starting conditions of:
• ρ(0) = + dρ
• ρ (0) = 0
gives the following spherical density graph

Click image for larger version. 

Name:	fig1.jpeg 
Views:	48 
Size:	21.9 KB 
ID:	24199

Within the calculation accuracy, the gaps of average density crossing are equidistant and are independent of dρ.
We will mark the average density crossing distance as D. D should depend on the density and on g as C does.
To be more specific, D should depend only on ρ ∞ as long as there are interactions, since if we change time scaling g will change but D shall not.
This can be obeyed if g is proportional to the average speed of the dot particles v squared as can be seen in the equations and should be expected by similar scaling reasons.
By the formula, the swaves seems to extend to infinity, however it cannot extend further than the area of density change of order of few dot particles.

Short-Range Interactions Between Standing Waves
To a first order approximation we can assume that the shapes of the standing waves do not get distorted by the interaction.
This approximation may be reasonable if the centers of the two standing waves are not so close to each other relative to the average density crossing distance D.
1. Two Standing Waves Interactions
It can be argued that two standing waves will have stable equilibrium positions at either aligned peaks along the line leading from one center to the other or anti aligned or both.
At each such equilibrium position if exists, we can consider small displacements along the line leading from one center to the other as harmonic oscillator like behavior.
The next graph describes numerical results of simulating two swaves under the ’rigid body’ approximation where each swave does not change its shape.
Positive force means attraction and negative force means repulsion.

Click image for larger version. 

Name:	fig2.jpeg 
Views:	45 
Size:	28.9 KB 
ID:	24200

If two standing waves are bound to each other, it is reasonable to claim that they are orbiting each other on a fixed plane in the ’center of mass’ frame similar to classical point particles.
It can be reasoned using the ’rigid body’ approximation by rotation symmetry around the axis connecting the two centers (z).
Because of this symmetry, no force can exist in the θ direction (considering cylindrical coordinate system) and any force in ρ direction will be accommodated by it’s inverse to be cancelled leaving only forces along the z axis.
Assuming two such standing waves are orbiting one another, since each standing wave is constructed from lower and higher densities than average and those deviations accelerate,
we can assume that propagating waves will radiate in general direction opposite of the accelerations which as assumed laid on a plane.
The propagating waves will be longitudinal and their net momentum may be zero. Moreover, the direction of the propagation of the waves in this scenario is assumed to be bounded to a plane.
For those reasons we will discuss bonds of three standing waves which are not restricted to a plane.

2. Three (or more) Standing Waves Interactions
Interactions between three bound standing waves are not limited to a plane and it involves more than centric interactions which may be very complicated to analyze,
however it can be argued that propagating waves with angular momentum can be sustainable.
This can happen if the standing waves centers trajectories have combined non zero average torsion.
From now on we will assume that this is the case.

Consider two groups where each group consists of three standing waves.
Assuming that those two groups are separated by distance much larger than the distance between standing waves within each group,
we can argue that the dominant interaction between the groups is via the hypothetical angular momentum waves generated by each group.
The propagating waves do not have spherical symmetry with regard to the group center because of the structure of the group,
however for general motion of the group if we average the propagation over time we can approximate it to have spherical symmetry.
The flux of the waves is proportional to the inverse square of the distance.
The groups can be tagged by the angular momentum sign along the propagation direction.
This can be related as stated before to the average torsion sign.
The propagated waves keep the same sign of torsion as that of the originating sources trajectories.
This can be seen easily if we take as example a helix source of which the waves are propagated as helix with changing radius but with the same orientation.
A repulsion force is expected to occur between two groups with same sign since there will be high correlation between the waves and the group trajectories and by that each group will act by the momentum transfer of the waves.
An attraction force is expected between two groups of opposite sign due to low correlation between the waves and the group trajectories which can cause each group to effectively feel unbalanced velocity distributions in the opposite direction of the wave propagation.

Special Relativity
In trying to give classical interpretation to the invariance property of the speed of light, Lorentz had an ’artificial’ argument that lengths are contracted in each direction to exactly compensate the speed relative to ’the absolute aether’.
In the presented model this argument is naturally fulfilled if one assumes that the main forces are mediated by waves,
it is just that the only way to measure the speed of light is by using the speed of light.
Since there is no way to measure the absolute velocities distribution of the dot particles within this framework, both assumptions of Special Relativity are obeyed.

(part 2 and final to be followed)