Chapter 3

The micro world

3.3 Quantisation

The previous sections show that even Heisenberg’s uncertainty principle is essentially given by the attempt to describe the particle’s wave–resonant manifestation as perceived in the macro world, through the particle’s own characteristics applicable to an observation by an observer in the micro world (position, momentum, time, energy). Here, we inevitably face the horizon of cognition, which is what causes the particle’s wave-resonant manifestation.

Now let us look at the quantisation of energy states of quantum particles. We know that if we attempt to somehow seize or enclose a particle, its stationary vibrational (energy) state starts to be quantised – it disintegrates into a discrete set of possible values (see the illustration in Fig. 3.3). This happens to electrons in an atom, for example.

Figure 3.3: A quantum particle in an infinite potential well. The equations of quantum mechanics show that while the vibrational state of a completely free particle (not limited in any way, without boundary conditions) may continuously take values, the vibrational state of a particle, which is in some way limited in its motion in space (e.g. an electron in an atom) is quantised in a stationary state (corresponding to a standing wave). Modelling the case of an infinite potential well (the potential energy in the well is zero and outside the well is infinitely large) – see a), solving the wave equation gives us a set of stationary discrete energy (vibrational) states for this particle. The particle can then be described as a superposition of these states, and rather than a particle, we are talking about a "wave packet". This may remind you of the vibrations from a guitar string. The vibrations are composed of basic and higher harmonic frequencies - see b).

When we observe a particle from the macro world, what we are actually observing is its energy-vibrational character, which manifests as its resonance, according to the experimental conditions.

We can say that in our “wave perception”, the projection of a spacetime uncertainty of the given particle “resonates” with the experimental boundary conditions and the probability of its occurrence is unevenly distributed. Yet to a proximate observer the same particle may occur at any point with the same probability and its energy spectrum (kinetic or potential energy) may take any continuous value.

The quantisation of the particle’s energy-vibrational state is thus a consequence of the existence of the horizon of cognition. It occurs as a consequence of the quantisation of spacetime – the division into interconnected intervals among which we are not able to distinguish.