## Chapter 3

# The micro world

## 3.4 Tunnelling

Another typical manifestation of the quantum world is tunnelling. Thanks to this phenomenon, the quantum particle can pass through a seemingly unsurpassable obstacle, as it is shown in Fig. 3.4.

Figure 3.4: Quantum tunnelling. The difference between classical and quantum mechanics is that if we place barrier in the way of a ”classical” material object, and the barrier has a higher potential energy than the kinetic or potential energy of the object, the object will not be able to pass the barrier and will bounce off it (picture a small gap of air or a sheet of paper between two conductive objects of different charge). A quantum particle, however (depending on the relative energy difference and barrier width), is able to pass the barrier and continue propagating with no energy loss (!). How is this possible? Again, the position of observer plays a part. Quantisation of spacetime cannot be limited in the perception of a distant observer, because if this were possible, we would be able to define and localise the particle through its spacetime manifestation. This is, however, not possible in principle, as a consequence of the horizon of cognition. We can imagine that even the oscillation of spacetime has its time and spatial inertia. This could be proven, for example, by the fact that if we added a sensitive quantum detector to this system (similar to the double-slit experiment) the tunnelling would entirely disappear (!).

How is it possible that the oscillation of spacetime has its inertia? Let’s imagine a particle (in our observation, a projection of a spacetime uncertainty of a point) that reaches a potential barrier that is higher than the particle’s energy. At that moment a resonance occurs between the particle (our projection) and the barrier. In our observation, this resonance causes a change to the vibrational characteristics of spacetime, both of the particle and even the barrier (spacetime is a unity of interconnected intervals that has no discontinuity under regular circumstances). However, the particle itself cannot enter the barrier and in our observation thus appears on “its own” side of the barrier. But due to the resonance of the continuous spacetime, the particle’s vibrational imprint does enter the barrier (in physics we call this an evanescent wave, see [36]. It is a standing wave that changes its phase only along the barrier but not in the direction into the barrier and its amplitude decays exponentially in the direction into the barrier). If the barrier is not too wide or high (with regards to the energy-wave characteristics describing our projection), this vibrational imprint can be non-zero even on the other side of the barrier. At that moment, another “transfer” of this imprint (as there is no discontinuity) occurs and so the spacetime is quantised even on the other side of the barrier. Our projection of spacetime uncertainty can thus occur in front of and beyond the barrier (it can jump across the intervals on both sides).

Even in the case of just a single particle, we are able to observe its manifestations on both sides of the barrier simultaneously (analogous to passing through both slits in the double-slit experiment). However, the probability amplitude of the oscillations (manifestations) in front of and beyond the barrier is different, depending on the experimental setup.

And again, the tunnelling effects disappear if the observer is moved close to the particle.

The latest experiments (from 2015) [37] show that this is the case. Scientists from Cornell University observed that rubidium atoms that had been cooled down to a temperature close to absolute zero no longer showed the tunnelling phenomenon and did not behave according to Heisenberg’s uncertainty principle if observed “close up”. This is known as the quantum Zeno effect – if we observe atoms directly, they do not show quantum effects. As we explained earlier, this is a direct consequence of moving the observer near the particle.

We can also look at this from the perspective of the law of duality – each law must also encompass its own violation (otherwise it would not be able to exist, just as one magnetic pole cannot exist without the other). Each particle must therefore also have the possibility to pass through a barrier that is “unsurmountable” for it. However, it is not possible to observe this phenomenon close up, i.e. in the particle’s spacetime. Such an event happens very, very rarely. When observing from afar, the particle’s own time is so accelerated in comparison to the observer that this phenomenon is actually recorded as tunnelling. If we move the observer to the particle, into the particles time and space (see the abovementioned experiment where the particle’s time was slowed down by cooling it down to a temperature close to absolute zero) then it becomes inherently (in the particle’s own time it obviously occurs extremely rarely) impossible for us to record it.

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