The Mathematical Principles of Quantum Mechanics

Francis T. S. Yu

Since quantum mechanics is one of the pillars of modern science, this chapter discusses one of the most intriguing principles in quantum mechanics, the uncertainty principle. In this it examines Heisenberg's principle was based on a diffraction limited observation, instead of upon a “nature” of time, developing his principle. There is a profound relationship between science and mathematics, in which people have seen that without mathematics there would be no science. In other words, science needs mathematics but mathematics does not need science. Although science is mathematics, mathematics is not science. Since an empty subspace has “no time”, all particles within the subspace collapse or “superimpose” instantly all together at t = 0, because time is distance and distance is time. This is precisely what the “simultaneous and instantaneous” superposition principle does in quantum mechanics. One of the most intriguing principles in quantum theory must be Heisenberg's uncertainty principle.

David A. Edwards

F. J. Duarte

Quantum mechanics is based on the concepts of indeterminacy , indistinguishability probability amplitudes , probabilities , reversibility , superposition , and uncertainty . And yet that is only part of the essence of quantum mechanics. Using the words attached to the concepts just described provides only a partial description of what quantum mechanics really is. The other part is provided by a set of physical and mathematical principles annexed to the mentioned concepts. The beauty is that quantum mechanics becomes workable and functional just by observing its mathematical principles. There is no need for any particular interpretation. Not even the orthodox interpretation. Here, fifteen mathematical-physical principles of quantum mechanics are listed and succinctly explained.

Edwin C. Kemble

Hou Yu-de

Through comparing Planck's trouble in the hypothesis of energy quantum with the first crisis of mathematics, the essence of them becomes much clearer. This shows the importance of the historical method in scientific research. This article also briefly illustrates that identity principle is the first principle of quantum mechanics.

Hilbrand Johannes Groenewold