Quantum mechanics

Quantum mechanics is the theory of how the atom functions.

It is associated with the theory that everything, all matter and all energy, is composed of quanta and can therefore be described as particles.

Understanding the inner workings of the atom, including its relationship to light, was one of the great challenges of the early twentieth century.

Max Planck’s work on blackbody radiation^{i} in 1901 demonstrated what is now widely recognised, that light is emitted in discrete events at specific frequencies. It also strongly suggested that the average energy of emissions – and perhaps the energy of each specific emission – is proportional to the frequency, a proportionality now known as Planck’s constant.

This came shortly after Michelson and his colleague Morley had failed to find evidence for a background medium or ether, discussed here, and James Clerk Maxwell had also made a failed attempt to describe mechanically a medium that he believed supported both light and electromagnetic phenomena, detailed here.

The importance of Planck’s findings is clear: if light is emitted in quanta of energy, then it makes the particle hypothesis all the more plausible, and particle light suggests a way around the failure of Maxwell’s ether.

This work established Planck as the founder of modern quantum theory, but he was properly cautious regarding the conclusion that many were ready to draw, that light is essentially particulate. He recognised that wave explanations also fit the data, and in particular that discrete emission and absorption of light could be a function of the atom and not necessarily of light itself. After all, if discrete emission were somehow the same as discrete existence after emission then every time a bell was struck only one person could hear it.

The assumption that particulate light can do what wave light cannot is first seen conspicuously in the paper of Einstein in 1905 on the photoelectric effect, in which he converts another formula of Planck’s from energy to momentum and argues that only particles of a minimum momentum can knock free an electron from a metallic surface.

## Critics

There were many critics amongst those in the top echelon of physicists. They included the recognition by Niels Bohr that particle light could provide no explanation for interference effects, a uniquely wave phenomenon, Max Planck, who was committed to determinism, and Robert Millikan, who argued that a localised electromagnetic disturbance was nonsensical. These and other historical critics are detailed here, more modern physicist critics are detailed here, and the wider community of critics is detailed here.

## Exceptional mathematics, with added metaphysics

The Bohr model of the atom and the idea that electrons, in some sense particle-like, orbit the nucleus dates from 1913. In 1925, Werner Heisenberg^{ii} produced a matrix-mathematical model of sub-atomic behaviour. A year later, Erwin Schrödinger^{iii} produced a very different-looking and more widely applicable version using complex numbers. Paul Dirac^{iv} added the Lorentz transformation to deal with fast moving particles. All three mathematics are adaptable to a version of the quantum principle, though none require it, being created by pure mathematical modelling, and all are in use today.

With the particle photon, as Bohr presaged, came a set of ideas and reasoning that is often described as weird.

The mathematical models of quantum mechanics are exceptional, but what most of us get to see is the metaphysics. The Schrödinger equation is dissected here, leading to a physical interpretation.

In the early years of the twentieth century, physics finally rejected the idea of a background medium, or ether, for wave light and electromagnetic phenomena. This is detailed here.

This meant that light could not be a normal wave, and led to two overlapping theories about light.

The first is that light must be a particle, an idea that has probably been around for thousands of years, and was favoured by Newton.

The second is that light has a dual nature, that it sometimes behaves as a wave and at other times as a particle. One of the key criticisms found on this site is that physics has failed to clarify and properly delineate this model, and this means that duality cannot be properly described here – it has no proper description.

A discussion of quanta is found here, and includes the following elements:

The two versions of theory are separated, as key areas of physics implicitly reject the wave part of duality. These are detailed here.

The assumption that light has a dual nature leads to a problematic set of conclusions, here.

The assumption that light is particulate, the photon, leads to a different but overlapping set of problematic conclusions, here.

## Ditching the metaphysics

The essential parts of quantum mechanics are its mathematical models, and these do not in any way rely on the descriptive parts, those that create the metaphysical complications. This is seen in many textbooks.

The popular textbook ‘Quantum Mechanics’ by Alastair Rae includes the statement:

‘For every dynamical system there exists a wave function … from which all possible predictions of the physical properties of the system can be obtained.’^{v}

In other words, all of the discussion about whether light is a wave or a particle, or possibly something with the properties of both, and whether this applies also to matter, is irrelevant to the parts of quantum mechanics that are used to make the correct predictions, i.e. the mathematical formula known as the wavefunction.

The most commonly used formula in quantum mechanics, the wavefunction of Schrödinger, is detailed and deconstructed here.

The views of Schrödinger on quantum mechanics, and whether he felt it was correct to call this equation a wavefunction, are interesting, and support a range of arguments on this site.

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i. Max Karl Ernst Ludwig Planck (1858 – 1947), Annalen der Physik: 1 (1900) 99 & 719; 4 (1901) 553.

ii. Werner Karl Heisenberg, 1901 – 1976, Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen, Zeitschrift für Physik 33 (1925) 879.

iii. Erwin Rudolf Josef Alexander Schrödinger, 1887 – 1961, Annalen der Physik (1925): 79, 361; 79, 489; 79, 734; 80, 437; 81, 109; Phys. Zeitschr. 27 (1926) 95. The first two of these are: Quantizierung als Eigenwertproblem / Quantization as a Problem of Proper Values, Parts I & II. The third is: Uber das Verhaltnis der Heisenberg-Born-Jordanschen Quantenmechanik zu der meinen. In this, Schrödinger shows how his theory gives the same results as Heisenberg’s.
In English: Collected Papers on Wave Mechanics Glasgow (1928).

iv. Paul Adrien Maurice Dirac, 1902 – 1984, Quantum Mechanics, Doctoral dissertation, 1926.
P A M Dirac, The quantum theory of the electron, Proc. Roy. Soc. A 117 (1928) 610, & Part II 118 (1928) 351
In R H Dalitz (ed) The Collected Works of P A M Dirac 1924-1948 (CUP, 1995)

v. Alastair Rae, Quantum Mechanics (McGraw-Hill, 1981) page 56