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%% 5.1   Quantum mechanics
% The quantum-mechanical double-slit experiment
% Electrons in a vacuum tube, for example, are only indirectly observable, appearing as blackening on a photographic paper or as a flash of light on a detector screen. If the electron beam is passed through a double-slit aperture, one still observes individual events on the screen, which are assigned to individual electrons. However, many such events form an interference pattern on the screen that clearly indicates a wave phenomenon. This cannot be explained by the effect of single (objective) electrons.
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% Observation of an electron beam in a vacuum tube. Individual points of light appear on the detector screen, like individual electrons.
% Upon prolonged observation, many of these individual events form an interference pattern, like a wave.
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% Wave–particle duality
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% Double-slit with which-way detector (WWD)
% The electron beam in the vacuum tube as an electrical current is the source of a magnetic field. This can be detected by a probe. This way, the 'path' of the electron can be determined through the aperture .
% In 50% of the events, the electron is detected at the lower slit, and in 50% at the upper slit. The interference pattern on the detector screen disappears. Many electrons form a shadow of the aperture.
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% This influence of a detector on the phenomenon is neither compatible with the motion of material particles nor material waves. In the Copenhagen interpretation of quantum mechanics, reference is made solely to the observation at the electron source (filament) and at the detector. The causal relationship is established by the propagation laws of the action and the preservation of the measurement probability.
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% (5‑1)
% The probability density for the response of a detector includes many possible positions. In the double-slit experiment, for example, these are the interference fringes. In the single measurement, one of these possibilities manifests itself.
% In the double-slit experiment with WWD, the electron is observed at one slit. The probability contribution of the other slit disappears, and thus the interference pattern on the screen is reduced to a shadow image of the aperture.
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%% The role of the observer
% The WWD has no physical effect on the system, it only extracts information. Nevertheless, it essentially influences the system's behavior.
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% (5‑2)
% Nonlocality
% The response or non-response of the WWD instantaneously changes the amplitude of the probabilities of measurement throughout the system, also far away from the WWD.
% It is worth noting that: for events at the top of the aperture's shadow, the WWD did not respond. Without WWD, some of these events are suppressed by destructive interference.
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% (5‑3)
%% Corrections to classical physics
% Classical physics provides us with the basis and concepts for our physical understanding of the world, particularly the strict distinction between content and motion. This distinction is resolved in three steps. With these three steps, we are entering an area of reality that we can no longer consciously grasp. In physics, these steps were first necessary to describe the thermal radiation of black bodies and atomic spectra. They became the foundation of our modern information society. They can help us to see the reality in a new light.
% Trajectory → Density of the measurement probability
% The measurement density replaces the notion of bodies or objects. There is a probability that one detector at a specific location at a certain time responds.
% 1. Probability density for the response of a detector
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% The change in density \dot\rho in an area is equal to a current \rho p_{\perp} through the boundary
%  (5‑4)
% 2. Unification of content and motion
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% (5‑5)
%  3. Quantization
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% (5‑6)
% The energy relationships in the HJE now depend on the measurement probability! If one observes the line spectrum of an atom, for example, it has discrete energy eigenvalues. If one observes the same atom in a scattering experiment, the eigenvalues are continuous. This difference affects the HJE or the law of conservation of energy. Without specifying the type of measurement, the energy of the atom is not defined and thus no statements about the atom can be made. It does not exist independently of the measurement!
%% Quantum mechanics
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%  (5-7)
%% Interpretations
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%  (5-8)
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%  (5-9)
% Does the dice exist under the cup?
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%  (5‑10)
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