Quantum: the wave packet
the photon illustrated as a wave packet: a quantum of light
The quantum upset Isaac Newton’s binary universe and invented a new metaphor for reality. The quantum is ambivalent, uncertain, relative. It refuses to be pinned down with a single identity, being a tidy yet mischievous packet that behaves like conjoined twins, acting simultaneously as a unitary particle and as a bundled wave. Perhaps the best informal description of the quantum was made by the great physics teacher Richard Feynman who called it “a lump of energy.”
Max Planck is credited with conceiving the idea of the self-contained bundle of light-energy which he named the energy element.
the energetic elemental
“… it is necessary to interpret [light] not as a continuous, infinitely divisible quantity, but as a discrete quantity composed of an integral number of finite equal parts. Let us call each such part the energy element ε …” —On the Law of Distribution of Energy in the Normal Spectrum*, M. Planck, 1901
Albert Einstein gave the first sneak peek of the energy element’s dual nature. He renamed it das Lichtquants, the light quantum.
“…the emission or conversion of light can be better understood on the assumption that the energy of light is distributed discontinuously in space. According to the assumption considered here, when a light ray starting from a point is propagated, the energy is not continuously distributed over an ever increasing volume, but it consists of a finite number of energy quanta, localised in space, which move without being divided and which can be absorbed or emitted only as a whole…” —On a Heuristic Point of View about the Creation and Conversion of Light*, A. Einstein, 1905
light imaged as both particle and wave
Niels Bohr quantized matter when he applied Plank’s quantum theory to a “planetary” model of the atom. Electrons, Bohr said, orbited the nucleus just as planets orbited the sun, except that an electron might leap from ring to ring by emitting or absorbing a quantum packet of energy.
There is “a general acknowledgement of the inadequacy of the classical electrodynamics in describing the behavior of a system of atomic size. … it seems necessary to introduce in the laws in question a quantity foreign to the classical electrodynamics, … the elementary quantum of action.” —On the Constitution of Atoms and Molecules*, N. Bohr, 1913
Bohr’s leaping electron
Werner Heisenberg experimented with orbit hopping electrons and decided that, actually, there were no orbits at all, at least not solar-system type rings. Newton’s reliable laws defined planetary paths, but the same math didn’t work when applied to circling electrons. Physicists had been excusing such inconsistencies as “a deviation from classical mechanics,” but Heisenberg called it instead, “a complete negation of classical mechanics.”
“…one cannot think of there being an absolute validity of classical mechanics even for the simplest quantum-theoretical problems. From this state of affairs, it seems more advisable to give up completely on any hope of an observation of the hitherto unobservable quantities (such as the position and orbital period of the electron) … [We must] attempt to construct a quantum-theoretical mechanics that would be analogous to classical mechanics.” —On the Quantum-Theoretical Reinterpretation of Kinematical and Mechanical Relationships* , W. Heisenberg, 1925
From orbits to “orbitals”: models of various atomic orbitals. The solid bodies enclose the volume wherein a 95% probability places an electron. The exact location of the electron within that space is unknown. Colors show the phase of the wave function.
Heisenberg came up with matrix mechanics, a system for describing the dual behavior of the quantum. At first he didn’t know what he’d done. A colleague figured out that the results could be transcribed into mathematical matrices. Two years later, this insight led Heisenberg to an idea no one could have predicted and yet, one that in hindsight seems inevitable — the famously eponymous Heisenberg's uncertainty principle.
Erwin Schrodinger quantized everything, every particle in the universe, with his “undulatory theory of mechanics.” Independently of Heisenberg and in the same year, Schrodinger traveled a purely mathematical route to arrive at an elegant formula also destined to become eponymous, Schrodinger’s equation. It describes the same peculiar truth as data-derived matrix mechanics. Suddenly all light waves get mighty particular, and all particles begin waving, and none of this activity happens in any way that makes sense as we traditionally experience the world. Schrodinger himself hedged, admitting in his paper what an “extreme conception” he put forth.
Animation of a wave-packet solution of the Schrödinger equation.
“The point of view taken here … is rather that material points [particles] consist of, or are nothing but, wave-systems. This extreme conception may be wrong…
“[Consider] the very striking fact, of which we have today irrefutable knowledge, that ordinary mechanics is really not applicable to mechanical systems of very small, viz. of atomic dimensions. …. [T]he equations of ordinary mechanics will be of no more use for the study of these micro-mechanical wave-phenomena… —An Undulatory Theory of the Mechanics of Atoms and Molecules*, E. Schrodinger, 1926
Einstein, among many other physicists, found these developments troubling and debatable. Today, the Heisenberg and Schrodinger discoveries are incorporated into what’s called The Standard Model,* an understanding of the sub-atomic world based on experiment and observation. Ferocious arguments continue over just what this dual-nature quantum realm is and how it works.
Science, like its forebearer Alchymy, is messy, incremental, and non-linear, and generates terrible quarrels. The quantum leaps of scientific advancement become obvious only in the long view. Reality’s momentum makes locating it uncertain.