Now, we may discuss the exact definition of the concept of physical existence. In fact, there is no universally accepted definition of existence; therefore, this significant discussion not only has a philosophical aspect, but also engages itself with the real interpretation of quantum mechanics (more properly, QED).

This paper assumes that physical reality is based on an abstract geometry, which is a consequence of logical principles (Chapter 4). Significantly, we have never mentioned that Nature is formed of a medium, because existence of such a medium cannot be defined, and it remains a philosophical problem. Moreover, science of physics would be incomplete, if the reason behind the existence of such a medium is deduced mathematically.

Similarly, it would be rather problematic to assert that matter in Nature is formed of elements that exist inherently. Immediately, questions arise about where these basic blocks of matter come from or why there is something instead of nothing… Same kind of scientific and philosophical problems seem to present themselves here, too.

The basic elements of our geometry, like distance, dimension, space etc. can be assumed as real, and in our physical reality, there seems to be no problem recognizing them as such. However, these geometrical elements are a consequence of logical principles, and they cannot be accepted as entities of physical existence. Emptiness does not satisfy any definition of existence, and these elements do not have intrinsic properties that can be observed. Although, distance, dimension, space etc. is measured indirectly, it is rational to accept them as real, as they are the foundation concepts of physical reality.

Correspondingly, we have discussed before that concept of stress cannot be measured directly in general. However, the exact magnitude of stress at a strain formation can be observed by indirect measurements. This is valid, not only for mechanical stress, but also for the stress on the expansion that is described in this paper. Therefore, it would be more appropriate to accept a stress formation as real, since it is within physical reality, but not as an entity of physical existence that can be observed directly.

Now, it is clear that our definition of existence is related to the existence of a thing with an observability condition. This statement will be the basis of our concept of existence. However, the question remains, we have still not discussed what it is that is observed and what it is to observe.

According to this paper, both matter and energy are strain packages (stress deformations) on expanding geometry, and the magnitude of that strain (the tightness of the confinement volume) determines the energy content of that strain package. We will not detail these mechanisms here again, since we have discussed them before. However, strains cause observable (vertical) deformations (like buckles etc.) on expanding geometry, and this is the point where we can propose a proper definition of physical existence.

Simply, if a local deformation exists on expanding geometry, then we can assume that there exists something. Conversely, if there is no deformation, than there is nothing. Consequently, our definition of physical existence is based on the existence of a deformation (like wrinkle, curvature, buckle etc.) on fundamentally expanding geometry, because it is the deformation, which practically exists. The deformation on expanding geometry is described mathematically by curvature and torsion.

At the smallest scale, quantum mechanics exactly describes these strain formations from a different point of view. Probability interpretation of quantum mechanics defines the possibility of finding a “point particle” at a location at a time (probability density), by the wave function of that “particle”. Naturally, probability of finding that “particle” in somewhere in space should equal one, if that “particle” exists.

According to Geometric Generalization, the wave function describes the deformation (like buckling amplitude) of the strain package, and probability density defines the magnitude of the (vertical) deformation on that strain package at a location at a time. Naturally, sum of the overall deformation makes a single complete strain, since strain is a complete and continuous deformation package.

However, the magnitude of the energy of that strain is a function of the tightness of that strain, and it does not vary at each location in that strain; energy is the property of the complete strain. Moreover, complex strain formations can appear when crest and troughs of individual strains interferes.

For example, quantum of electromagnetic radiation (photon) can be visualized by wrinkles/buckles that appear on a thin sheet that is under stress. At point A, sheet is deformed vertically, and has a maximum vertical displacement (electricity). However, in reality, these strain packages are not static, and they flow constantly (like waves) in expanding geometry.

Figure 8.1 Electromagnetic radiation

Consequently, the wave function of a “particle” describes the structure of a single, complete, and continuous deformation. According to quantum mechanics, it can be stated that the possibility of being that “particle” at point B is zero; or according to this paper, it can be stated that there is no deformation (vertical displacement) at point B. Actually, in the case of a photon, the expansion follows such a path that it crosses through the real plane and forms continuous deformations that oscillate between existing and absent states.

Conversely, in the confinement volumes (strain packages like knots or vortexes), there appears a constant curvature and a constant local deformation (like a curvature of helix) on expanding geometry; therefore, according to quantum mechanics, location of that “particle” is within an uncertainty limit. In fact, we should say that a strain package has a constant deformation, and uncertainty range is the soft size of that strain package.

Eventually, according to this paper, the entire strain package, which is described by the wave function, is regarded as the basic constituent of physical reality. However, the existence of the deformations caused by the strain package on the expanding space is the physical existence.

Interestingly, readers should have realized that this paper’s proposal renders the concept of point “particles” completely redundant. Therefore, any philosophical problems on the existence of such “particles” do not surface, since existence appears as a phase of nothingness. Naturally, there are no dualities or incoherencies in Nature. Let us overview wave-particle duality now.

Physical existence (deformations on space-time geometry) does not have constant spatial locations in time, since space-time fundamentally expands and develops. In other words, in the wrinkling epoch, intersection point of oblique radial (time) directions and circumferential (spatial) dimensions constantly expand and flow away in expanding geometry. Hence, spatial coordinates of physical existence have a very complex nature.

This paper introduces a very interesting question. If concept of physical existence is defined by existence of deformations (like curvature, buckle, etc.) on expanding space, then can we consider the entire universe as a complete existence, since the universe is spatially closed and has a (very slight) universal curvature (Section 4.2)?