Tuesday, November 27, 2012

An arguable misnomer in physics: the term “quantum mechanics”

Analog or digitaluninterrupted or pixilated, continuity or discontinuity, field or particle? These pairs of opposing adjectives and nouns often occur in texts and discussions about physical reality and theoretical modeling. The periodic table of discrete chemical elements with their characteristic numbers and spectra directs scientists towards a quantum view of matter. As an example: the solution of Schrödinger's equation for the hydrogen atom provides us with quantum numbers (n, l, and m), which are integers [1]. Important: these integers are coming forth from solving an equation formulated with continuous variables for physical quantities that encode electron movement and potential. Thus, quantum mechanics models reality on the basis of continuity. Discrete values result from the approach in which the theoretical model is treated and solved; but may not be nature-inherent.

Intrigued by cosmological challenges and debates over the fundamental laws of the physical world, David Tong—a theoretical physicist at the University of Cambridge—is giving the continuity-discontinuity interrelation a closer look. He writes that the term “quantum mechanics” could said to be a misnomer for a theory that formulates its equations in terms of continuous quantities [2].  He cites Leopold Kronecker's proclamation “God made the integers, all else is the work of man.” and counters with “God did not make the integers. He made continuous numbers, and the rest is the work of the Schrödinger equation.” [3].  Tong explains the latter in detail:

Integers are not inputs of the [quantum] theory, as Bohr thought [Danish physicist Niels Bohr “implemented” discreteness at the atomic scale]. They are outputs. The integers are an example of what physicists call an emergent quantity.  In this view, the term “quantum mechanics” is a misnomer. Deep down, the theory is not quantum. In systems such as the hydrogen atom, the processes described by the theory mold discreteness from underlying continuity. 

Quantum phenomena are these days demonstrated and animated in educational as well as entertaining videos. The Zeitgeist-driven perception: What I simulate and animate, is what I see and believe in. Yet, living in a digital age does not automatically imply living in a digital universe.

Keywords: physics, philosophy, quantum theory, physical world, pointillist universe, emergent integers.

References and more to explore
[1] Quantum Mechanics: Solving Schrödinger's equation [users.aber.ac.uk/ruw/teach/237/hatom.php].
[2] David Tong: The Unquantum Quantum. Scientific American, December 2012, 307 (6), pp. 46-49 [www.nature.com/scientificamerican/journal/v307/n6/full/scientificamerican1212-46.html].
[3] Quoted at axeleratio.tumblr.com: axeleratio.tumblr.com/post/36680758289/god-did-not-make-the-integers-he-made-continuous.


  1. Somebody seems to have forgotten that it's not just the theory. One of the first indications that the universe may not be continuous was the finding that measuring the excitation spectrum of hydrogen found a series of discrete emission lines, an experimental (empirical) result. A theory was then needed to explain that experimental result. Several were proposed.

    Other experiments were conducted in different areas of physics, that also could not be explained by a model of the universe that only contained continuous phenomena, the photoelectric effect, for example. Another was the impossiibility of explaining blackbody radiation from any model that assumed that light was continuous.

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