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are manifestations of objects far removed from their internal structure. The advancement of physical experiments in the internal structures of elementary particles at the beginning of the 20th century brought properties of matter to the surface, which revolutionised science at the time.

      Inductive physics: surprised by quantum phenomena

      These properties could no longer be explained by reference to everyday concepts and experiences; instead of the expected, ever smaller tiny spheres of matter that behaved in the same way as their larger counterparts, matter proved impossible to define within known limits. Experiments showed:

      –There is no rest in the smallest particles, but constant movement;

      –Particles are scattered like light waves;

      –Regardless of the mass of a revolving particle, its angular momentum always has the same value or a multiple of it;

      –Particles overcome energy barriers even though they have too little energy to do so;

      –Interactions can only be ascribed probability, they cannot be predicted;

      –Radiation can only have certain frequencies.

      Atoms demonstrated inexplicable behaviour:

      –Despite the electrical repulsion of the protons, the nuclei do not burst apart;

      –The electrons e- remain at very precise distances from the nucleus;

      –Atoms attract one another and bond together to form molecules, although they are electrically neutral (the same number of electrons and protons);

      –Protons p+ and neutrons no can be brought into an “excited energy state”, which means that they themselves have an internal dynamic, in particular a composition.

      Helium atom*

      The major theory of physics that encapsulates these phenomena mathematically is called quantum mechanics and consists of:

      –The quantum of action, or Planck’s constant, ħ, formulated in 1900 for discrete energy;

      –The de-Broglie-Einstein relations for the link between energy and frequency, formulated by Einstein in 1905 for photons, by de Broglie in 1924 for electrons;

      Max Planck, 1858–1947; Louis de Broglie, 1892–1987; Erwin Schrödinger, 1887–1961; Werner Heisenberg, 1901–1976

      –The Schrödinger equation, 1926, for the calculation of all probabilities and states;

      –The uncertainty principle, formulated by Heisenberg in 1927 to describe the impossibility of knowing the position and momentum of a particle simultaneously.

      From the finding that events in the atomic dimension can only be predicted in terms of probabilities, the pioneers of quantum mechanics concentrated on calculating these probabilities and declared the corresponding formulae to be fundamental laws of nature. They responded to sceptics such as Einstein—“God does not play dice”—to the effect that the processes were objectively uncertain.

      Quantum mechanics in this spirit

      –allocates to every object a wave with frequency and wavelength (dependent on velocity, de Broglie-Einstein);

      –interprets the intensity of the wave as the probability of the whereabouts of the object;

      –calculates stable states with the “black box” of the Schrödinger equation—extremely precisely; to a hair’s breadth in comparison with the distance between New York and Los Angeles;

      –keeps the standard model of elementary particle physics together,

      –but cannot derive any of its axioms and laws.

      Richard Feynman,

       1918–1988

      Richard Feynman, one of the founders of elementary particle physics, wrote: “Because atomic behavior is so unlike ordinary experience, it is very difficult to get used to and it appears peculiar and mysterious to everyone, [even] to the experienced physicist … We cannot explain the mystery in the sense of ‘explaining’ how it works. We will tell you how it works.”

      Deductive physics: quantum phenomena are inevitable

      Because mass dynamics radiate (emit waves), at atomic distances a superposition of waves develops, giving rise to interference waves. These correspond to the statistical waves of quantum mechanics. They are transmitted through the continuum like sound waves through air (a wave crest being equal to positive pressure, a wave trough to negative pressure, in comparison with the rest state).

      The understanding of the elementary behaviour of waves opens the doors to all quantum phenomena. These have nothing to do with the idea of “atomos” (indivisible), but only the interference of radiation. The most obvious interferences encountered in everyday life are in musical instruments, for example the organ pipe: a sound wave seeks to escape from the pipe and is thrown back. As disorder in the pipe would need more energy than order, the incoming and outgoing waves oscillate synchronously, at the same wavelength and so that their nodes are at the same point. The result is a standing wave: the wave must fit in the pipe * —and this is the quantum effect!

      A wave can be represented mathematically by a sine function. The calculation of the superposition of two such waves requires a simple trigonometrical relation2, which shows that two waves combine to form a single one, the product of a sine multiplied by a cosine. The sine is an envelope (not dependent on time): the abstract frame for the cosine, which actually oscillates within it in time.

      If, unlike in an organ pipe, two interfering waves are differently formed, the interference wave does not remain standing. If the wave package in the envelope has velocity v , simple mathematics shows that the envelope only moves at v/2. 3

      This fact alone can be used to derive fundamental laws of quantum mechanics:

      –The de-Broglie-Einstein relations;4

      –The rest frequency5 of a mass (Dirac 1928);

      –Uncertainty.6

      The following are also explained:

      –The quantum of action7, the hydrogen atom8 and the harmonic oscillator9 are explained by the resonance of mechanical and quantum mechanical frequencies (similar to the resonance of a poorly-balanced wheel when its rotation frequency and the natural frequency of the wheel bearing are the same);

      –Zero-point movement is explained from radiant energy being cancelled out by interference and transformed into kinetic energy;10

      –The Schrödinger equation, from the superposition of the Lorentz contraction of relative velocity and potential field;11

      –The Dirac equation from the rest frequency and the conservation of the energy and spin on each spatial axis;12

      –Nuclear forces from the cancellation of field energy by the interference of particles at wavelength intervals.13

      –Quantum entanglement (Einstein’s “ghostly remote effect”) arising from the fact that everything is connected via the continuum.14

      Paul Dirac,

       1902-1984

      Quantum phenomena only seem puzzling

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