Now, let us discuss the well-known duality issue in contemporary physics, present why both “particles” and “waves” cannot be the basic elements of both matter and energy, and suggest strains (local deformations on space-time geometry) as the basic elements.

First, there is a creation problem for “particles”; a philosophical revelation as to where they come from and why they should exist does not seem possible.

Beyond philosophical concerns, the physical existence of “particles” is still questionable. They are point-like elements with ignorable physical dimensions, yet they are claimed to exist physically. Additionally, it is not possible to explain how “particles” (as point-like elements) can have so many intrinsic properties like mass, charge, spin, etc. However, all of these practically observed properties are treated as if they can be intrinsic attributes of “point particles”.

Moreover, there is also an important geometrical problem with “particles”. Simply, it is not possible to form a volume and define a space by adding and gathering points; therefore, geometrically, it is awkward that “particles” form material bodies that occupy volumes (exclusion principle).

Finally, it becomes illogical to assume that “particles” are able to deform and curve space-time geometry. Surely, matter interacts with space-time geometry as it is mathematically formulated by general relativity. However, the problem here is not with the interaction itself, but with the concept of “point particles”.

Consequently, today it is known that Nature is not formed of “point particles”, which have exact locations as it is assumed in classical physics. In fact, quantum mechanics prove that such “particles” cannot be observed (uncertainty principle).

Simply, it is useless to look for a more elementary “particle”, which is the basis of all “particles” and which can derive all other “particles”.

Wave-like properties of both matter and energy can be observed and tested experimentally. This phenomenon may suggest that quanta of matter and energy are actually kinds of waves.

On the other hand, there is creation problem for waves, too, similarly to particles. Waves need a medium that can wave, and if quanta of matter and energy are considered as waves, then the same philosophical problem appears, not for the wave itself, but for the waving medium. It does not seem to be possible to explain why and how such a medium existed in the first place.

Eventually, wave approach results in some problematic deductions; for example, it is necessary to fabricate an assumed substance (e.g. aether).

In fact, experiments (like black body radiation or photoelectric effect) have already proved that even energy is not a continuous wave, but it is released discontinuously in discrete packages.

Probability interpretation of quantum mechanics goes beyond its elements, which are illogical even by themselves. Surely, it is completely inconsistent to claim that Nature is formed of “point particles” that exist as probability “waves”.

Is it honest to assert that Nature is absurd, and it contains unreasonable dualities, because mathematical equations of quantum mechanics can precisely predict experimental results? In such a case, one should admit truthfully, as masters did, that (probability interpretation of) quantum mechanics (QED) is not able to portray Nature. In fact, the problem in quantum mechanics is not with its mathematics, but with the fact that its mathematics is applied on improper elements (probability of point “particles”). Consequently, the solution is to leave self-contradicting elements behind.

According to this paper, Nature is a constantly and continuously expanding wholeness. However, when the expansion is compressed or confined, strains are formed on the expanding space. This paper assumes that both matter and energy are geometrical strain packages on the expanding space. These strains have a spatial size, indicating their stress-energy content, although Nature is a complete continuum.

We can visualize these strains as ordinary springs, where the amount of the compression on that spring determines its energy content. In fact, our definition of energy and mass is an interpretation of Hooke’s law, which relates strain and stress. Similarly, our strains in expanding geometry also appear as packages, having a spatial magnitude, since strain is a geometrical deformation. Energy in that strain is not on a specific location; instead, it is in the entire strain package itself, e.g. a spring. On the other hand, observable deformations on the expanding geometry (e.g. vertical displacements) vary at each location at a time.

In many aspects, concept of our strains has many similarities with waves; for example, they have flowing vertical displacements, and their crests and troughs interfere each other. However, is it possible to describe these strains (buckles, wrinkles, curvatures, etc) as “waves”?

Crests and troughs of strain packages interfere eventually. The reason of this phenomenon is obvious; they are all constituents of a complete reality (continuous space-time geometry), and all vertical displacements occur on the same continuum.

On the other hand, our strain formations and waves have some critical differences. Both matter and energy are not exactly waves; hence, this paper names these deformations on space-time as strain packages in order to emphasize the nuances.

In general, waves need a medium that can wave, but in this case, the medium is nothingness (an abstract space-time continuum). Consequently, wave without a medium contradicts the definition of wave, even though it seems to satisfy the wave equation.

Additionally, strains and waves have other technical differences, too. In waves, vertical displacements are not related to the longitudinal deformations. Wave equation describes the vertical (or compression) deformation only, and it ignores the longitudinal deformation on the overall size of the medium. 

Figure 8.2 A waving medium without any longitudinal deformation-contraction,
and a strain formation where vertical and longitudinal deformations are related

Conversely, in strain formations, vertical deformation and longitudinal deformations are related to each other. Either vertical deformation causes longitudinal deformation, or vice versa. Moreover, if the elasticity of the medium is zero as it is in our abstract space-time, the geometrical magnitudes of these opposite (perpendicular) deformations directly depends on each other. As a result, magnitude of the vertical deformation defines the contraction in the overall size.

Finally, strains and waves have a major difference: Energy content of an ordinary wave is integrated and spread equally on the lengthwise direction of the wave, and each tiny section in lengthwise direction of the wave carries a tiny portion of overall energy content of the wave. However, the situation is rather different with strain packages (quantum of matter and energy). These strain packages are complete packages of energy, and if energy of a package is transferred to another package, than the whole package collapses instantaneously. (We will discuss its cause in the next section.)

Figure 8.3 Energy content of an ordinary wave is spread equally on lengthwise direction

Energy magnitude of a strain package expresses the magnitude of a local tightness (compression or confinement) on the expanding space. Tightness of a strain package (its energy content) can be transferred to other strain packages, and this dynamic process in expanding geometry is briefly the electromagnetic interaction.

As a result, quantum mechanics should be interpreted as strain mechanics, where the wave function describes a continuous strain on space-time geometry, instead of describing the probability distribution of point-particles. Additionally, effect of the strains on the overall space-time geometry is one of the most important points that should be considered to develop the mathematical formulation of quantum mechanics.

As we have discussed before, confinement volumes of the knots and the vortexes have energy content, because vertical displacements of local strains (compressions and confinements) creates longitudinal deformations on the overall space-time geometry. In other words, local confinement volumes of the knots or the vortexes create a counter stress the universal tendency to expand on space geometry.

In fact, this relationship is the basis of the mathematical formulation of the relationship between certain physical constants, which describe a state of balance in universe (e.g. Hubble’s constant, fine structure constant, etc.), and the amount of total matter content in the universe.

This paper suggests a consistent physical explanation to quantum mechanics; however, there remains the ultimate part, which is the reason why even strain packages themselves are not located in an exact single location.

Please note that it is not possible to measure the entire deformation (vertical displacement) caused by a strain package on the expanding space. The strain package that is sent by the observer interacts and affects the observed package. Therefore, the wave function of the observed package “collapses” by the energy transfer. Interestingly, this phenomenon is one of the key points that lead misinterpreting Nature as if it is a coincidence of “point particles” in uncertain locations.