In this chapter, we discuss how our expanding space geometry generates basic physical concepts of mass and energy.

This paper considers basic elements of mass (elementary “particles” with mass) as strain packages like knots or vortexes in the fundamentally expanding space, instead of a “point particle” with no geometric dimensions.

The knots or the vortexes can be interpreted as circulating energy packages, where the expansion is confined into localized volumes. We will name these soft volumes as the confinement volume, which can be interpreted as the size of the knot or the vortex. The confinement volume is the volume, where the expansion is confined and it circulates locally.

As a result, formulation of mass is also based on geometrical deformation (strain) and stress relation (an interpretation of Hooke’s law), since mass is a form of energy. Simply, the mass of a strain package (elementary “particle”) depends on the tightness of its confinement volume. In other words, if the compression in the confinement volume increases, then the mass (energy) content of that package will increase too.

We can formulate magnitude of mass of a single strain package (elementary “particle”) as a function of the radius of its confinement volume:

E 5.3

This simple equation is surely not complete, and it needs to be correlated with our unit system (SI), similar to energy packages, which are described as a function of its wavelength.

E 5.4

In fact, the tightness of the confinement volume can be interpreted as the wavelength of the confined energy package (mass). In other words, we can simply formulate mass by equalizing E=mc² and the equation of energy above, since we consider mass (elementary “particles” with mass) as a confined and localized energy package.

E 5.5

According to this paper, equivalency of mass and energy is fundamental, and (c) emerges in the equation (E=mc²) because of the inconsistent unit system, which is organized by neglecting fundamental principles of Nature unwittingly. In Chapter 11, we will suggest a Universal Unit System, which eliminates such constants like the constant of speed of light by fixing them to one (1).

Additionally, if we can assume that the circumference of the confinement volume represents the wavelength of the energy package, then mass of any type of elementary “particle” can concretely be defined according to the radius of its confinement volume.

E 5.6

Unfortunately, this correlation between wavelength and mass is already well known, but not appreciated because of the atomist-materialist viewpoint, which considers mass as a property of point “particles”. It has been used for calculation of the Compton Wavelength, which can be thought of as a fundamental limitation on measuring the position of the “particle” in the probability interpretation of quantum mechanics.

E 5.7

Compton wavelength is the wavelength of the energy, which is equal to the rest mass of that “particle”. For electron, it is 2.4x10^-12m, and it exactly gives the energy of the rest mass of electron (0.511MeV). Simply, wavelength of the confined energy is equal to the circumference of the confinement volume, and it is equal to the Compton wavelength of that “particle”.

At this point, we should emphasize that the confinement volume is not a hard solid volume. (In fact, existence of such solid volumes (atoms) can simply be disproved logically.) Conversely, our confinement volume is a soft volume; it is an interpretation of the uncertainty range in Heisenberg’s uncertainty principle:

E 5.8 (Please notice that p=mv=mcβ, where β is a dimensionless ratio of v/c)

In other words, the possibility range of locations that a “point particle” can be at a time is the confinement volume itself. We will discuss quantum mechanics in Chapter 8; simply, this paper treats the wave function itself as the description of the constituent of reality.