### Heisenberg Uncertainty Principle

The most famous uncertainty relation is between location and momentum of a particle. It denotes that one cannot determine the exact location and momentum of a particle at the same time. In classical physics, momentum is defined as the product of mass (m) and velocity (v) of an object.

P = mv

Simply speaking, momentum is the impact felt by a boxer receiving the opponent’s tossed feast. The relation between the momentums of an object in regards to its spatial position (x) are obtained by:

P_{a} = a / ax^{a}

Where a is a constant. If our object is a subatomic particle then we need to add imaginary number (i) and Dirac constant (ħ) to the equation,

P_{a} = i ħ a / ax^{a}

The Dirac constant is a reduced Planck Constant (h/2π). The presence of i indicates that the momentum of a subatomic particle is governed by a complex function. Therefore, the momentum of subatomic particles is periodic (see the complex number chapter). The Assertion C2 in complex number chapter assumes that the value of the momentum has to hit zero at each period.

The presence of ħ also points out that momentum is directly related to Planck constant. In wave-function chapter, we have assumed that the particle itself disappears and reappears in space-time within each wavelength. We can relate the intermittent blinking of momentum to the intermittent appearing and disappearing of the particle into the space-time. Moreover, in the Mass & Gravity chapter we have assumed that the Planck Constant is the amount of kinetic energy carried by the particle upon its arrival into the space-time. In following paragraphs, we will review the quantum mechanical phenomena while keeping the above conjectures in mind.

According to Werner K. Heisenberg, the famous German physicist, we cannot simultaneously determine the precise position and momentum of a particle. This kind of correlation between two properties is called a complementarity relation. The equation is written as,

*Δ X ∆P ≥ h/ 2π*

Where Δ stands for uncertainty. When the position uncertainty (Position's potential Δ X) approaches zero, the momentum uncertainty (Momentum's potential_Δ P) is equal or greater than* h/ 2π x 0* . This implies that if we pin point a particle’s location, its momentum can vary widely up to infinity.

Therefore, quantum theory tells us that we cannot track a particle by any method whatsoever. The particle just appears and disappears. Can we assume that, we cannot detect particles because they lose their mass and leave the space-time? Maybe we have to change the sentence as "we cannot track a particle by any method whatsoever in *objective world*. The problem arises when we are expecting to see the whole picture in just one arena, (the rational number arena). Irrational numbers occupy a much bigger arena. These numbers prevent us from being optimally exact.

As an analogy, please note that we cannot follow and understand a three dimensional motion in it’s entirely in a two dimensional world. Evan Walker says: “… Heisenberg used matrices (whole array of numbers) to represent the positions and motions of an atomic particle.^{[1]}

In his calculation to create the matrix he used the symbol i which stands for square root of –1, the so called, imaginary number. He had to choose a number, which is out of the domain of our real number system. We cannot ignore the quantity i and call it imaginary. We have to accept that it stands for a kind of reality. Therefore, we have to expand the science domain to include territories other than familiar space-time. If mathematics so precisely is predicting the mysterious world of quantum physics, we have to value its elements. We have to trust that its unexplained or intangible measures have an actual meaning.

Let us revisit the location /momentum uncertainty. Please note that one of the elements is spatial and the other is energy related. We can interpret the principle as; when locality gets blurred the energy is more defined. This was further documented in the Boundaries Chapter. There are other complimentarity relations such as time and energy uncertainty in a system.*ΔE Δt ≥ h/ 2π*

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