In this chapter, we examine Geometric Generalization’s philosophical consequences, summarize its conclusions, and expand our hypothesis into its full meaning. Additionally, in this chapter, we will discuss the “Exact Meaning of Relativity and Connecting Gravity with Quantum Mechanics”.

According to Geometric Generalization, physical reality is a consequence of an expanding closed spatial dimension. This expansion is continuous, omnidirectional, and isotropic; it is the most fundamental integral act of Nature.

However, expanding space wrinkles and collapses onto itself from the inflationary epoch up to Hubble’s expansion, and the expansion strains universally (Section 5.2). While the expansion strains universally, local deformation packages (like wrinkles, ripples, buckles, etc.) are formed on expanding geometry. These deformations are quanta of matter and energy (Section 5.3), and they cause the expanding space to wrinkle by their knot-like or vortex-like structures.

Distance is the only fundamental quantity in geometry. In Chapter 11, we will set up a Universal (Natural) Unit System, where all other physical quantities are a function of spatial distance.

Actually, deformation packages in expanding geometry indicate a local compression or confinement in expanding geometry. Energy, in its largest meaning, is the magnitude of the compression of confinement in expanding geometry as an interpretation of Hooke’s law, which relates strain and stress. Even though, energy can be practically measured by spatial distance (wavelength of photon), energy magnitude of a package expresses the proportion of the compression of confinement. Therefore, both quantum of matter and energy should be named as strain packages or strains, instead of “particles” or “waves”.

Figure 9.1 Quantum of energy and mass are strain formations on the expanding space-time geometry

, and

E 9.1

E 9.2 (h is the Planck constant, c is the constant speed of light, and λ is the wavelength of the energy –mass quantum)

Strain packages cause local deformations in expanding geometry (like vertical displacement of buckles, wrinkles etc.). Geometric generalization accepts the strain package itself as the basic constituent of physical reality, and the wave function describes the deformation (curvature or torsion) at a location at a time, instead of probability of “point particles” at a location at a time (Section 8.2).

With the universal strain on the expansion, the expansion is partially confined into local knot-like or vortex-like structures, which flow within the wrinkled expansion. The soft confinement volume of a strain package with mass is the volume, where quantum mechanics asserts that the location of a “point particle” is uncertain. In fact, the range of uncertainty of a “particle” defines the strain package itself in expanding geometry, and strain package that is defined by its wave function should be considered as the basic constituent of physical reality. Therefore, it is more proper to call quantum mechanics as strain mechanics.

On the other hand, in practical terms, physical existence is the existence of a deformation on expanding geometry caused by a strain package at a location at a time.

As a result, quantum (strain) mechanics should be developed by considering below points, which were discussed in previous chapters:

a) Wave function describes the (vertical) displacement of a strain formation in continuous and expanding space, instead of a describing the probability of finding a point-particle at a location at a time (Section 8.2).

b) Light cone represents the local expansion of a location in universally strained (wrinkled) space, instead of describing the propagation of a point-particle in static space (Section 8.4).

c) The intrinsic circulation mechanism (zitterbewegung) at the constant speed of light in the confinement volumes of the knots and the vortexes (Chapter 3).

d) The (circumferential) directions of the wave-like vertical deformations of spatial strains that are formed around knots (Section 7.2).

e) The relationship between vertical displacements and longitudinal deformations-contractions. Strains, instead of probability waves (Section 8.3).

Now, we can expand our hypothesis into its full meaning, and suggest the briefest description of laws of Nature:

“Physical reality is a complete and continuous flux of expanding closed spatial dimensions. Hence, in the wrinkling epoch, all physical existence (deformations of all kinds of strain packages) flows the equivalent distance within the expansion (at the speed of light) constantly and continuously, whether the expansion is locally confined into the knots or vortexes (matter) or compressed (energy).”

Figure 9.2 Light cone and circulations in confinement volume

According to Geometric Generalization, we can clarify the two different meanings of time:

Time as a dimension is a geometric direction, which is perpendicular to spatial dimension, and it emerges because of the curvature in spatial dimension. Hence, the distance towards time dimension is the difference of the radiuses of curvatures of two points in space-time.

On the other hand, time as the quantity of clock-ticks is a consequence of the inner circulations in knot-like or vortex-like formations, and it is the property of the knot, which varies relatively according to the stress in that knot.

Additionally, with the formation of strain packages in the expanding space-time geometry, we can concretely define the spatial distance metric as a function of the size of these strains.

Tightness of a strain package determines its energy content (strain-stress relation). When compression or confinement on expanding geometry increases, energy content of a strain package increases.

Tightness of a strain package (its energy content) can be transferred to other strain packages. In other words, strain packages that flow within expanding geometry absorb or emit other strain packages, and this dynamic process in expanding geometry is briefly the electromagnetic interaction.

Strain packages that form matter are formations like knots or vortexes, where the expansion is confined locally. Inner structures of these knots determine the formation principles of elementary “particles”, and inner stresses in the knots are the nuclear (strong and weak) forces.

Finally, the mutual relationship between the gathering and heaping of the knots and the universal strain in overall the expanding space-time geometry is the gravitation.