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**Abstract:** It is shown that if space is modeled as an elastic medium where spherical, scalar quantum-waves traverse, then the constants of this medium relate to the scalar compression length of space based on the rest-energy of the particle, where a particle is shown to be the interaction of scalar quantum waves. The speed of the scalar waves in this medium is derived to be the speed of light, `c`.

The purpose of this paper will be to derive the constants of an elastic-space model, where particles are modeled as the combination of spherically-symmetrical quantum waves, with the particle being defined at the center of the interaction of a set of “IN” and “OUT” spherical waves. The waves will be shown to be travelling at the speed of light based on cosmological parameters of the Universe.

The interaction of two, spherical quantum waves have been shown to describe the quantum and relativistic effects of the electron^{[1]}. In this model, the “IN” waves which arrive from a distant point in our Universe, combine with the “OUT” waves which leave the center of what we see as a particle, to create spherical shells of interference. The first maxima of this interference pattern is the wave center and the defining boundary of what we see as a particle. Although this model has been explored extensively, the questions that remain pertain to the speed of the waves and the elasticity of the medium in which they travel. This will then tell us more about the medium and it’s properties.

Albert Einstein first developed the concept of mass changing the density of local space which then warps the path of light. The same concept in reverse is part of the elastic space model: that the compression of space produces mass. The characteristic-compression length of space, `x`, will be shown to be related to the rest-energy of the particle in question. As the solution to a spherical, standing wave equation produces scalar values, we may simplify the formula for elasticity to one dimension as follows:

- Formula 1

Where `F` is the force of compression, `x` is the characteristic-compression length, and `k` is the elastic constant of space which is constant in all directions. Integrating {1} with respect to `x` reveals the *potential energy* in this relation, which we also set equal to the *rest-energy* of the particle which it creates:

- Formula 2

Where `m` is the mass of the particle, wave-center. From this relation we can derive `k` from known quantities as follows ^{[2]}. For `m` = the mass of the Universe, 1.44 × 10^{53} kg, and for `x` = radius of the Universe (`R _{u}`), 10

- Formula 3
`k`= 7.18 × 10^{17}Newtons/meter

For `m` = mass of proton, 1.67 × 10^{-27} kg and `x` = estimated range of strong nuclear force (2 × 10^{-14} meters), we obtain `k` = 7.18 × 10^{17} Newtons/meter. For `m` = mass of electron, 9.11 × 10^{-31} kg and `x` = classical electron radius of 2.82 × 10^{-15} meters, `k` = 2.0 × 10^{16} Newtons/meters. Based on the numbers tabulated, the preferred choice for `k` is 7.18 × 10^{17} Newtons/meter.

The formula for elasticity in {1} and {2} was simplified to one axis based on the spherical nature of the standing quantum waves. We can also simplify other basic formulas such as the speed of these standing quantum waves in the space fabric. The one-dimensional formula for the speed of standing waves in an fabric of elasticity `k` is:

- Formula 4

Where `k` = 7.18 × 10^{17} Newtons/meter as previously determined from {3}, `x` is the displacement of the space-fabric by the wave energy, and ` is the mass-per-unit length of the space-fabric. Applying our model of elastic space to Mach’s principle results in a Universal force that is the pulling force of all masses in the Universe on any other object. This force is determined by substituting ``x` = radius of Universe into {1} to obtain:

- Formula 5
`F`=`k``x`=`k``R`=_{u}`k`(10^{26}meters) = 7.18 × 10^{43}Newtons

We now desire to determine the speed of waves in the space-fabric that result from this Universal pulling force in {5}. We know what that the term in {4} for the speed of the waves has been determined in {5} as 7.18 × 10^{43} Newtons. Now we examine , or the linear mass-per-unit length of the space-fabric. If we take the average mass of the Universe found from critical and average density determinations as 1.44 × 10^{53} kg, and the distance of the Universal force acts over as 10^{26} meters, we find as:

- Formula 6
- = 1.44 × 10
^{53}kg / 10^{26}meters = 1.44 × 10^{27}kg/meter

Substituting the value for ` from {6} and the value of ``k` `R _{u}` from {5}, we find the speed of the quantum standing waves from {5} due to the Universal pulling force (Mach’s principle) as:

- Formula 7
- meters/second

Which is seen to be very nearly `c`. Also note that seconds^{-1} which is Hubble’s constant. Then the familiar Hubble relation, is revealed from {7}.

It has been shown from the model of elastic space-fabric and by assuming scalar formulations of elastic force and wave speed in this fabric, that the speed of the scalar quantum waves in the space-fabric is the speed of light. Also, the rest-energy of the wave-centered “particles” that we see can be equated to the potential energy of compression in this fabric, with the characteristic-compression length of the fabric for each particle being equal to the range over which the associated force acts over.

- Wolff, Milo. "Exploring the Physics of the Unknown Universe.", Technotran Press, pp. 179-187, Copyright 1990
- Harney, Michael. "Quantum Foam", Journal of Theoretics Vol. 6-5 Comments Section Oct/Nov. 2004. www.journaloftheoretics.com

- Books of Milo Wolff