## Chapter 3

# The micro world

## 3.1 The duality of particles in the double-slit experiment

The French physicist Louis de Broglie studied the wave–particle duality and proposed the wave–particle duality principle [31], which won him the Nobel Prize in 1929 [32].

According to this principle, the wave properties of particles can be described with the following equation:

*λ = h/p = h/(mv) * (3.1)

where *λ* is the wavelength, *h* Planck’s constant, *p* momentum, *m* particle mass, *v* particle velocity. At high speeds, we substitute the mass (*m*) for relativistic mass.

where *m _{0}* is the rest mass,

*v*is the relative velocity and

*c*is the speed of light in a vacuum.

Note: Quantum mechanics is not considered relativistic. Only when describing relativistic particles, is quantum mechanics extended by the theory of special relativity, and this has given rise to the quantum field theory. The quantum field theory is relativistic and is also called the second quantisation. However, so far, no theory has been able to unify the quantum world phenomena with gravity.

Contemporary quantum mechanics in its basic form does not work with the term spacetime. Yet we previously justified that it is the quantised spacetime that lies behind the above mentioned wave manifestations of particles.

We noted that when observing objects into the micro world, at the horizon of cognition, spacetime disintegrates (crumbles) into a set of interconnected nondisconnect able intervals in our observation. Each of these intervals inevitably also has an opposite counterpart. These intervals then line up one after the other and, in our observation, the particle oscillates between them (to us, all possible occurrences exist at once).

For a moving particle, these intervals propagate in space like a wave, and its wavelength is expressing the spacetime curvature at the horizon of cognition. We can talk about a wavelike character of spacetime itself as a consequence (manifestation) of our observation.

Now imagine sending just a single particle during the double-slit experiment. In our model situation (an object at the horizon of cognition) it will be a single point (quantum) with a non-zero rest mass.

However, in our observation, we cannot talk about a particle anymore, but about a “projection of a spacetime uncertainty of a point”, propagating in spacetime. This is illustrated in Fig. 3.1.

Figure 3.1: Moving particles at the horizon of cognition. The source sends a single particle that is near the horizon of cognition in our observation. If we do not experimentally measure or limit the particle in any way, it is a free particle that indistinguishably occurs/propagates in a set of interconnected spacetime intervals (intervals with both positive and negative polarities are alternating). If the particle passes the narrow slit, the wavefront of the corresponding wave is circular.

And now we send this object through the plate with two slits.

Due to the impossibility to distinguish (recognise) caused by the horizon of cognition, the interference, i.e. summation individual “waves” from both slits, holds (a particle observed from a distance can only occur in positions where we do not recognise its actual trajectory). The probabilistic waves of our projection are summed over both slits – and in the network of interconnected intervals of opposite signs, they strengthen or cancel each other out.

The interference after passing through both slits is illustrated in Fig. 3.2.

Figure 3.2: Explaining the double-slit experiment. If we place a plate with two slits in the way of our ”projection of a spacetime uncertainty of a particle”, the projection will pass through both slits simultaneously (with all the consequences implied, including its forces effects in both places at once). It continues propagating beyond the plate, while to us the unobservable particle itself keeps indistinguishably oscillating among all possible states of the quantised spacetime (a set of interconnected intervals of opposite signs). Next we place a screen at a suitable distance behind the plate with the two slits. As a consequence of the indistinguishability, at the points where the particle impacts the screen, an interval of a positive sign corresponding to a trajectory through one slit must/has to meet with an interval of a positive sign corresponding to a trajectory through the other slit – therefore, constructive interference can only occur in certain directions depending on the wavelength and the experiment’s geometry.

Yet if a detector is used to observe which slit the particle passes through, we are observing it close up = the observer’s position has been moved into the particle’s own spacetime (!). For us, at that moment, the particle is not at the horizon of cognition and classical Newton mechanics applies. The interference and diffraction effects related to the uncertainty of its projection disappear.

If we were to move towards the particle, not with a step, but gradually (imagine us simply shrinking – note: we are considering an object with non-zero rest mass – it would not be possible for us to move towards light photons in such a manner), we would perceive the particle as gradually increasing in size and its rest mass would increase (a consequence of the spacetime curvature). This would simultaneously change the time scale of our observation. A consequence of this gradual change of parameters – the relation (3.1) *λ* = *h/p* = *h/(mv)* would still hold - would be the gradual shortening of the corresponding particle’s wavelength *λ.* The particle would then behave according to classical Newton mechanics more and more (as in our observation it was leaving the horizon of cognition).

We can find analogies all around us, and in the case of quantum mechanics, there is an analogy with the rippling of liquids. And not just classic waves on the surface of water. Yves Couder and Emmanuel Fort from the university “Paris 7” [33] and Daniel Harris from MIT [6] carried out experiments where a liquid droplet bounced on a vibrating fluid bath, driven by the waves originating in its own collisions. Although the resulting movement of the droplet was chaotic, it was exactly analogical with the observed behaviour of quantum particles.

Considering all possible states, among which the particle inherently oscillates in our observation, spread in time and space, we can imagine that there is some kind of resonance with boundary conditions given by the experimental setup, and so there is an analogous "continuous" mechanism, as with the liquid droplets described in [33] and [6].

We can imagine the projection of a particle observed from a distance as a chaotic oscillator. Spacetime becomes a non-linear resonator that adopts the characteristic physical parameters of an oscillator, affecting its apparent movement and occurrence. And this is where the analogy with the movement of the droplet in a vibrating fluid bath comes in.

The perception of the wavelike character/nature of spacetime may remind us of the formerly used aether theory, which even ancient Greek philosophers included in their reflections. [34].

We are now ready to investigate if the above-mentioned philosophical observations could help us clarify the mystery of typical quantum effects in the micro world.

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