In the present day, it is well known that both matter and energy behave like both waves or particles. Matter and energy emerge in discrete packages, and they are said to be quantized. Although, probability interpretation of the theory of quantum mechanics may seem to be suspicious logically, it (QED) is mathematically the most precise theory ever, with its theoretical calculations and experimental data in perfect agreement. This paper assumes that the reader has a basic knowledge of quantum mechanics.

Geometric generalization develops many aspects of quantum mechanics. In this chapter, we will present the physical (geometric) interpretation of quantum mechanics. In fact, quantum mechanics is a set of multiple concepts, which we will argue in order of complexity. This section discusses uncertainty.

From the beginning of this paper, matter and energy have not been treated as either “particles” or “waves”. In the previous chapters, it has been discussed that physical reality is based on fundamentally expanding geometry (Chapter 4), and both matter and energy are the local strains formed against compression or confinement of this tendency to expand (Chapter 5).

Therefore, each quantum of matter or energy has a basic magnitude, which indicates the amount of local squeeze (strain) on the expansion. This magnitude is described by the function of spatial distance (in fact, strain is a proportion), and it defines either the size of the confinement (Compton wavelength for matter quanta) or the size of the compression (wavelength of energy quanta).

In order to visualize the correlation between distance and magnitude of matter and energy, we may remember our balloon example. A portion of the surface of our balloon that is tied into a knot symbolizes matter quanta in our example. Notice that the size of the tied surface defines the energy magnitude in that knot. Similarly, this paper assumes that magnitude of both matter and energy is the tightness of the confinement or compression of the expansion. This tightness varies for relative observers, and it is the basis of relativistic transformations.

We have discussed these in depth before, but now it is time to take note of another interesting aspect. Although, Nature is formed of constant and continuous expansion, both matter and energy appear as packages, like the knots on the continuous surface of our balloon. Please note that the amount of energy content itself is not quantized, but the matter and energy appear in packages that have a variable size (for relative observers).

In fact, Heisenberg’s uncertainty principle indicates and proves the correlation between spatial magnitude of strain and the energy content of a single quantum. To be more precise, it defines the size of our soft confinement volumes of strain packages. Actually, this point is very important, and it forms the basis of this paper’s universal unit system.

At this point, experienced readers should have realized that our definition of mass (Section 5.3) that is based on the tightness of the soft confinement volume is a version of Heisenberg’s equation.

, and

E 8.1 (Please notice that p=mv=mcβ, where β is a dimensionless ratio of v/c)

Consequently, our definition of mass covers relativistic variations, since the tightness of the confinement volume varies for relative observers. Essentially, Heisenberg’s equation also describes this correlation.

On the other hand, there is constant and continuous action, taking place in the confinement volumes, which we will soon discuss. However first, we should clarify the notion of probability, and discuss what those things that are claimed to exist within uncertainty are?