Quantum Physics is not Weird. On the Contrary.. Paul J. van Leeuwen

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      Zeno did not mean to say that the arrow won't reach its target in our experience. His paradox was meant to support his message that reality must be an illusion. This idea seems perhaps far-fetched, but it will turn out that it offers an excellent road sign of how to understand and solve the difficult interpretation problems that quantum physics presents to us.

      In this connection, Democritus, a contemporary of Zeno, should also be mentioned. Democritus was a Greek philosopher who proclaimed the hypothesis that all matter consisted of very small indivisible particles, called atoms. The idea behind that was related to that of Zeno and Parmenides, namely that infinity is not a characteristic of nature. You cannot, therefore, keep splitting a piece of matter endlessly in two. This splitting will always come to an end. Therefore, Democritus is viewed as the father of the idea of the atom. Incidentally, Zeno in his turn did not wholly agree with the ideas of Democritus.

      Pierre-Simon Laplace (1749-1827)

      The influence of Newton's theory on philosophy and theology was enormous. With the right mathematical instruments everything seemed computable and God could be sidelined in his creation with regard to direct interventions. And, of course, with God everything that had to do with church and religion. Some people who did not like the position and the demands of the church preferred that idea, as did Pierre-Simon Laplace, a French mathematician and astronomer. He is the one who replaced the geometry-based classical mechanics with analytical methods which facilitated mechanics calculations considerably.

      Laplace is known for his hypothetical demon ^[11] who knows exactly the starting positions, masses and speeds of all objects in the entire universe and is able to use this knowledge to calculate the course of all events in the universe. The demon is hypothetical. He does not have to exist for the final conclusion of Laplace: all matter - including past and future - has ultimately fixed knowable properties and will therefore obey Newton mechanics for 100%. The universe becomes a gigantic clockwork from which chance is vanished. According to Laplace, coincidence as we experience it, therefore only exists for humans because they do not have sufficient information and computing power to calculate everything in advance.

      This turned coincidence and also man's free will into an illusion. People, animals and plants became nothing more than very complex machines. Which is an idea that is still strongly expressed by many in the current scientific community. Fortunately, our legal system is still based on free will, meaning that we basically assume that the offender did have a choice. The judge will not easily honor your lawyer pleading that weaving errors in your DNA caused you to take a grab out of the supermarket till. It is however striking that when something goes wrong in a company's administration, for example, when you receive a payment reminder concerning your own obituary, the computer will often get the blame. In that case we apparently grant it some free will.

      Light as little hard balls or as waves

      Newton published also a theory about light. After experiments with refraction of light by prisms, he correctly concluded that white light was a composition of colored light. Colored light could not be split further by prisms. He concluded that light, like all other matter in the universe, consisted of small hard colored balls, corpuscles. That idea explained the observation that light traveled in straight lines. It explained the reflection of light in mirrors quite well by the collision laws of his own mechanics. However, with refraction there were some problems. First of all, how was it possible that those corpuscles could so easily travel through a solid medium like glass. In addition, a French scientist demonstrated with experiments and logic that the corpuscles should travel even faster in a solid medium than in a vacuum.

      Newton, however, had an illustrious contemporary, the Dutch scientist Christiaan Huygens ^[12] (1629-1695), who contested his model of light corpuscles and his idea of absolute movement, In 1678 Huygens proposed in his "Traité de la lumière" ^[13] that light should be viewed as a wave phenomenon. Huygens also convincingly demonstrated that space and all movement within it were only relative, an idea that Einstein later applied in his special theory of relativity. Nevertheless, Newton's scientific fame and status ensured that his corpuscle model and his absolute space both went uncontested in scientific circles throughout the next two hundred and fifty years.

      How did Huygens arrive at his idea about waves? He observed how light behaved in birefringent crystals. In these crystals, for instance calcite, an incident light beam will be split into two beams that each follow a different direction. To explain this effect, Huygens assumed that light was a wave phenomenon in which the wave vibrated perpendicular to the direction of the light beam. When that vibration takes place in only one direction, the light is called polarized. Sunlight is not polarized and therefore vibrates in all directions perpendicular to the light beam. So, polarization ^[14] is the direction in which a light wave vibrates. Polarization is not limited to light waves. You could call a surface wave, as on water, more or less vertically polarized because the water particles are mainly moving in the vertical direction.

      In birefringent crystals, the propagation speed of the light wave depends on the angle the polarization direction makes with the directions of the crystal lattice. This is because the properties of a birefringent crystal lattice are different when viewed from different angles. This phenomenon is called anisotropy. The two emerging bundles therefore obtain polarizations that are perpendicular to each other.

      Figure 2.5: Birefringence: splitting the incoming wave in two different polarized waves.

      Figure 2.5 shows a simplified image of birefringence in a calcite crystal. The parallelogram represents the crystal. The incoming non-polarized wave arrives from the left on the surface of the crystal. Inside the crystal, the portion that is vertically polarized more or less retains its speed and therefore continues in a straight line. The speed of the horizontally polarized portion of the wave is however reduced, causing it to break twice, on both incidence and exit. The result is two separate parallel and perpendicularly polarized beams of light.

      Figure 2.6 shows the explanation of the propagation of light as Huygens saw it. Huygens proposed that each part of a wave front became the source of a new circular expanding wave front extending forward, something he named an elementary wave source. The new wave front could be found by drawing the tangent line along those elementary waves.

      Figure 2.6: Huygens principle of light propagation.

      Imagine yourself looking from above at a swimming pool with a deep part C₁ and a shallow part C₂. See figure 2.7. Parallel running wave fronts enter from above left - crests light gray, troughs dark gray - arriving at an oblique angle at the border between C₁ and C₂, which is here a border between deep and shallow water. Waves slow down when rolling from deep into shallow water. The wave speed in C₂, which is the shallow part of the swimming pool, will therefore be less than in C₁. So the distance between the wave crests, which is the wavelength, will have to be smaller in C₂.

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