From quantum physics to probability theory and back

E. B. Davies

Andreas Schlatter

The Born-rule, which assigns probabilities to measurement outcomes, is one of the fundamental axioms of quantum physics. It dates back to the time of the establishment of the formalism of quantum physics in the first half of the 20th century. From the beginning, and particularly in connection with the development of different interpretations of the theory, there has been a desire/need to better understand the true nature of the Born-probabilities. Are they classical/epistemic of origin or are they irreducible and of on tic stature as a kind of intrinsic propensities of physical systems? We show that, by only using the mathematical formalism of the original theory, we find a possible answer.

Barry Loewer

Andrei Yu. Khrennikov

In this chapter the contextual measurement model (CMM) is employed forprobabilistic structuring of classical and quantum physics. We start with CMM framing of classical probability theory (Kolmogorov 1933) servingas the basis of classical statistical physics and thermodynamics. Then weconsider the von Neumann quantum measurement theory with observablesgiven by Hermitian operators and the state update of the projective typeand represent it as CMM. The quantum instrument theory is a generalizationof the von Neumann theory permitting state updates of the non-projectivetype and it also can be represented as CMM. We also show connectionof the generalized probability theory with the space of probability measureswith CMM. Finally, linear space representation for contextual probabilityspace is constructed by using the construction going back to Mackey.

Wim Vegt

Photon-photon Interaction has already been described in 2005 and measured in 2011. By D. Englund e.o. in Ultrafast Photon-Photon Interaction in a Strongly Coupled Quantum Dot-Cavity System (2) . This manuscript explains the origin and the mathematical approach in Maxwell’s theory to explain this quantum mechanical effect. To understand, to describe and to calculate this unique phenomenon, we have to go back in time. Before the famous 1927 Sovay Conference to the time before Maxwelll published his famous set of 4 Electromagnetic Equations. To create a new path in Classical Physics to explain Modern Quantum Physics. The famous 1927 Solvay Conference was considered a turning point in the world of Physics. The scientific realists like Albert Einstein had lost and the instrumentalists like Niels Bohr had won the fundamental conflict. Since then Physics has followed the path of the instrumentalists in which Quantum Physics has been determined by the concept of Elementary Particles and Probability Waves. Until May 2013, when for the first time a photo had been made of the Probability Waves Inside the Hydrogen Atom . It should be impossible to make a photo of a non-existing complex probability wave with mass zero But the fact could not be denied anymore that scientists had succeeded to make the “complex” and the “non-existing” quantum mechanical “Probability Wave” visible. Since the Copenhagen Interpretation there is still no clarity about the physical interpretation of the Quantum Mechanical “Probability Wave Function”This Manuscript describes a third unknown interpretation of the Quantum Mechanical “Probability Wave Function”. A fundamental physical interpretation that will change the generally accepted Copenhagen Interpretation. This Manuscript will answer the fundamental question: Does an alternative theory exist in which the existence of this particular photo, of the Quantum Mechanical Probability Wave within the Hydrogen Atom, could be explained. And that the famous photo of the Hydrogen Atom can be explained in a logical and a simple way. To find the answer, we have to go back in time. Back 300 years in time to the moment when Isaac Newton discovered the beauty and one of the many secrets of the light. The moment when science walked away from light. And we return to the fundamental question: “Is it possible to build Matter out of Light (confined electromagnetic waves)?” To answer the fundamental question: Is it possible to create Matter out of Light?, we first have to answer the question how we have come to this world of Probability Waves and Elementary Particles and Quantum Physics.Louis de Broglie described in 1924 in his PhD thesis the wave properties of matter. Erwin Schrödinger published in 1926 the well-known Schrödinger wave equation with the characteristic spherical and elliptical wave solutions. To describe these material waves, the immediately and first explanation was: “There is only one possibility. These are “electromagnetic waves”. De Broglie waves are ” Light Waves”. Because these were the only waves, known in the world of Physics. But there was a fundamental problem. These material waves, discovered by Louis de Broglie and mathematically described by Erwin Schrödinger could never be solutions of the well-known 4 equations of James Clerk Maxwell. The material waves were spherical and elliptical solutions and that was impossible for the solutions of the Maxwell Equations. According to the Maxwell Equations, light always travels along a straight path. A second problem was that the model of the atom of Bohr could not hold. How could an electron be everywhere at the same time in a kind of a spherical shell surrounding the nucleus. And be a particle at the same time. And Bohr found a compromise to declare the “De Broglie” waves to be the probability waves. Two problems were solved. Bohr’s planetary model could hold. And there was a name for the unknown material waves, discovered by Louis de Broglie and mathematically described by Erwin Schrödinger. The theory of “Probability Waves, Elementary Particles and Quantum Physics” had been created. To find a possibility, to create matter out of light we have to go back to the Equations of James Clerk Maxwell. The only possibility to declare the probability waves, discovered by Louis de Broglie, to be electromagnetic waves, to be light, and to be the building element of our universe, is to find evidence that he Maxwell Equations are not complete and that it is possible to confine light (electromagnetic waves) in spherical and elliptical shapes. A new equation has to be found. In this article it has been claimed that this missing equation is equation (5). Because the Theory of General Relativity has been built on the Einstein-Maxwell Equation, a new equation has to be found that describes in a generalized way the interaction between light and matter. This missing equation is equation (5-a).

Peter Milne