3.4.4.2 Uncertainty Principle
In 1927, Heisenberg proved that it was impossible to determine both a particle’s position and momentum with arbitrary precision, regardless of the accuracy of the experimental tools. This theoretical limits on the ability to describe the world was later called the: “Uncertainty Principle”, which also implies that the observer inevitably affects the results of the observation at some level, because the the act of measurement changes, for example, the momentum of the system. This, however, does not have any serious consideration for large bodies, but becomes very important for microscopic systems. In 1932, Heisenberg won the Nobel Prize in Physics for his work that has considerable impact on quantum physics.
The uncertainty principle shows mathematically that the product of the standard deviation, or the uncertainty, in the position and momentum of a particle could never be less than halve of the value of the reduced Planck’s constant (
):
(3.18)
For this reason, the position and momentum are known as complementary variables. Henceforth, the complementarity principle was formulated later by Bohr; that quantum objects have certain complementary properties which cannot all be observed or measured simultaneously. In addition to position and momentum, other examples include: energy and duration, spin on different axes, wave and particle, value of a field and its change at a certain position, entanglement and coherence.
The uncertainty principle is inherent in the properties of all wave-like systems, so it arises in Quantum Mechanics simply due to the wave nature of matter particles and quantum objects, as we explained in section 4.4.1. Therefore, it should not be confused with the observer effect, that measurements of certain systems cannot be made without affecting the system. We shall also discuss the observer effect in section 4.4.5 and in chapter VI because it is one of the subtle quantum properties that cannot be explained without taking into account the reality of oneness.
In wave mechanics, the uncertainty relation between position and momentum arises because the expressions of the wave-function, in the two corresponding orthonormal bases in Hilbert space, are Fourier transforms of one another, because position and momentum are conjugate variables. A nonzero function and its Fourier transform cannot both be sharply localized.