“Quantum Mechanics” is neither quantum, nor mechanics

Definitions

Let’s start from considering the very definition and etymology of the words used:

“Mechanics”

mechanics (n.)

“the theory of machines,” also, “the mathematical doctrine of the motions of particles and systems (especially rigid bodies) under the influence of force and constraints,” 1640s, based on Late Latin mechanica, from Greek mekhanike, mekhanika (see mechanic (adj.)); also see -ics.

Online Etymology Dictionary https://www.etymonline.com/search?q=mechanics&ref=searchbar_searchhint

machine (n.)

1540s, “structure of any kind,” from Middle French machine “device, contrivance,” from Latin machina “machine, engine, military machine; device, trick; instrument” (source also of Spanish maquina, Italian macchina), from Greek makhana, Doric variant of Attic mēkhanē “device, tool, machine;” also “contrivance, cunning,” traditionally (Watkins) from PIE *magh-ana- “that which enables,” from root *magh- “to be able, have power.” But Beekes, on formal grounds, objects to the connection to words in Germanic and Slavic. He finds the Greek word isolated and is convinced that it is Pre-Greek.

Online Etymology Dictionary: https://www.etymonline.com/search?q=machine

When we say “mechanics” we therefore understand a more or less systematized, more or less theoretical (more about this word later) body of knowledge pertaining to the description, design, operation, of “machines”.

We can then draft a definition of “machine” as follow: a (usually complex) device, instrument, tool, which enables the potential user to achieve results and effects which are difficult or even impossible to achieve without the said device, instrument, tool itself.

“Quantum”

quantum (n.)

1610s, “sum, amount,” from Latin quantum (plural quanta) “as much as, so much as; how much? how far? how great an extent?” neuter singular of correlative pronominal adjective quantus “as much” (see quantity).

The word was introduced in physics directly from Latin by Max Planck, 1900, on the notion of “minimum amount of a quantity which can exist;” reinforced by Einstein, 1905. Quantum theory is from 1912; quantum mechanics, 1922. The term quantum jump “abrupt transition from one stationary state to another” is recorded by 1954; quantum leap “sudden large advance” (1963), is often figurative.

Online Etymology Dictionary https://www.etymonline.com/search?q=quantum

So, when we use the word “quantum” we talk about a quantity which comes into discrete, individual, countable pieces. Some examples being money in the form of dollars (or euros) which is made up of cents, rice which is made up of individual grains of rice, a handful of gravel which is made up of individual little stones.

Mathematical structure

The mainstream textbook philosophy presents the mystical object named “wave function” (Psi) as the one and only protagonist of the story. This rather strange object lives in a space which is multidimensional (Hilbert space) and to make things worse the number of dimensions of such space is problem-dependent: one particle in 3D space needs to be represented by a Psi living in a 3-dimensional Hilbert space, two particles need to be represented in a 6-dimensional Hilbert space and so on… In general n particles need to be represented in a 3n-dimensional Hilbert space.

More precisely, the so-called “wave function” is a complex-valued distribution with support in the configuration space (OR in the momentum space) of the system. Guess what: the “wave function” is not a wave: it is in fact not a periodic perturbation of a 2-dimensional or 3-dimensional substratum (sound in air, gravity waves in air-sea interface, electromagnetic waves in the Aether, compression or shear waves in the Earth’s interior etc.) propagating through the substratum and evolving in time. It is more a kind of signal reconstructed from the measurements on the physical system which evolves in time until a new measurement (a new information transfer from the system to the observer) resets its values to a new starting point. This last statement could be a way out of the paradoxical “wavefunction collapse” and more will be written about it later.

An outline of the mathematical structure of the metatheory encompassing Schrödinger and Heisenberg concepts is given in the diagram below, which was constructed with information available on standard Quantum Mechanics textbooks [1][2].

The “quantum” in “Quantum Mechanics” has its origin in the works of Planck (1900) when the discretization of absorption and emission of electromagnetic energy was introduced in the context of the effort to precisely describe the interaction between matter (in the form of the inner walls of an oven) and thermal-visible-ultraviolet radiation to correctly find a model for the black body spectrum.

In this context, the discretization of light emission and absorption processes was regarded as a hypothesis which helped in building quantitatively precise models of the black body spectrum.

The “wavefunction” as a mathematical instrument was crafted by Schrödinger in 1925-1926 (25 years after the Planck’s “Quantenhypotese”), as he was tinkering with the Hamilton-Jacobi formulation of classical mechanics which, by the way, was invented in the 1820s-1830s with the declared aim of unifying the mechanics of point-particles and the propagation of wavefronts (aka “Hamiltonian analogy”) [4] (does this sound familiar?).

At the same time (also in 1925-1926) Heisenberg was working on his “Matrizenmechanik”, that is the abstract manipulation of “states” represented by a complex-valued vector in a Hilbert space by means of operators. In this representation, once a basis of the Hilbert space is chosen, the vectors are represented by a n-tuple of complex numbers and the operators by matrices (whence the name of the model).

In both models, the states can be represented either in configuration space or in momentum space and one can switch back and forth between the two dual representation by applying a Fourier transform to the “signal” represented by either the complex distribution (Schrödinger) or by the state vector (Heisenberg)

It was later discovered that evolving the complex distribution and its corresponding “Hamilton principal function” with the rules of a modified form of Hamilton-Jacobi mechanics and repeatedly applying the “time evolution operator” to the “vector” in the “Matrizenmechanik” was numerically equivalent.

This meta-theory encompassing Heisenberg’s “Matrizenmechanik” and Schrödinger’s modified form of Hamilton-Jacobi mechanics, coupled with the anti-ontology of Bohr (Copenhagen School – particle trajectories do not exist, things do not have ontological value before being measured) is what is still in use today to calculate the outcomes of experiments involving the transmission of small amounts of electromagnetic radiation or matter from a source to a receiver and to model the atomic and molecular spectra.

Neither Quantum…

So, where is the original meaning of “quantum”? Well, it survives in two ways:

1) the discrete stationary energy levels of the atoms and molecules
2) the discrete occurrence or non-occurrence of a photon-detection or electron-detection event.

This first kind of “quantization”, however has to do with boundary conditions imposed on “something which is vibrating”, of which the complex distribution in configuration space (or the associated complex-value vector in Hilbert space) are a representation of.

This however, has nothing exclusively “new” or “post-Planckian” to it: classical mechanics (quantitative description of 3-dimensional material systems evolving in time) is a wonderful tool for dealing with this situations. The most intuitive example is given by a guitar string: it is well known that the boundary conditions give rise to a discrete set of possible modes effectively “quantizing” the spectrum.

The second kind of quantization (seemingly purely stochastic appearance of a particle at a specific spot on a detector at a specific point in time) is, I think, the true mystery, but it is not “quantum” in itself. I argue that the seemingly random appearance of photons or electrons modulated by the square modulus of the complex-valued distribution is intimately connected with the Principle of Least Action, and implies some deep reasoning about time, causality, and free will, which accompany physics since its very beginnings in Hellenistic times (about 3rd Century BC) and throughout all its history (more will be said about this here).

…nor Mechanics

In what sense is the so-called “Quantum Mechanics” in its contemporary form (which arose from the fifth Solvay Conference on Physics of 24th-29th October 1927) not a “Mechanics”?)

In fact, it is not the positions and velocities of individual particles (“mass points”) and/or the state of deformation, rotation or stress of time-continuous objects spatially localized in 3-dimensional space (properties which can with no doubt be assigned to components of a machine and which can, if we want, be re-grouped and ab-stracted into a state living in configuration space as in Lagrangian formalism or a state living in a phase space as in Hamiltonian formalism) which are analyzed, quantified and used to make prediction about the immediate future or to produce design rules for yet-to-be built machines.

What we are dealing with instead, does not give us any 3-dimensional description of a system evolving in time, therefore no picture, therefore no design, therefore no machine! In this very sense the post-1927 “Quantum Mechanics” is not a Mechanics neither in the etymological nor in the practical sense.

What should “Quantum Mechanics” be called

I propose to call the metatheory encompassing the models of Heisenberg and Schrödinger “Delocalized position-momentum signal analysis” as it operates on an object (the “quantum state” in any of its possible representations) which is not localized in space but represents some properties of a physical 3-dimensional system evolving in time (that is, whatever experimental apparatus is being observed together with all the matter and radiation exchanged between sources and detectors) without a clear specification of the correspondence between the abstraction and the physical referents of the variables treated.

Conclusions

“Quantum Mechanics” is an unfortunate misnomer which has been given to a mathematical metatheory with unclear ties to 3-dimensional objects evolving in time (therefore it cannot be called a “Mechanics”).

The quantum hypothesis invoked by Planck in 1900 reveals itself to be not new and not strictly necessary for “saving the phenomena” observed in the laboratory, a closer investigation either leads back to classical mechanics or to the metaphysics of the PLA, both of which existed well before the modelization of cavity-radiation thermodynamics. For these reasons, the adjective “Quantum” as a form of distinction from “Classical” is misleading and should be avoided.

A new, more fitting name for the Schrödinger-Heisenberg metatheory is proposed: “Delocalized position-momentum signal analysis”.

References

[1] “Meccanica Quantistica: nuova introduzione (Ristampa 2009)” – Kenichi Konishi, Giampiero Paffuti (Edizioni Plus – Pisa University Press) ISBN 978-88-8492-318-9

[2] “Meccanica quantistica, teoria non relativistica (Traduzione italiana della terza edizione originale russa del 1973, edizione italiana del 2010) – Lev D Landau, Evgenij M. Lifsits (Editori Riuniti University Press) ISBN 978-88-6473-208-4

[3] “From Classical to Quantum Mechanics through Optics” (2009) – Jaume Masoliver, Ana Ros (https://arxiv.org/abs/0909.3258)

[4] “Third Supplement to an Essay on the Theory of Systems of Rays” (1831) – William Rowan Hamilton (The Transactions of the Royal Irish Academy, Vol. 17 (1831), pp. v-x, 1-144 (150 pages)) (https://www.jstor.org/stable/30078785)