Tikalon Blog by Dev Gualtieri

Quantum Uncertainty

October 23, 2023

Although television existed in the United States before World War II, it greatly expanded after the war. If you've ever wondered why there's no television channel one, it's because its frequencies were useful for other purposes, and it was more convenient just to delete channel one than shift the number designations of all the other channels downwards. In order to maximize the number of VHF television stations, the Federal Communications Commission (FCC) decided to reallocate channels in the 1950s. This necessitated a channel change of my hometown television station, WKTV, from channel 13 to channel 2 in 1959.

One television commercial of my early years was for Certs mints, famous for each having a "golden drop of Retsyn," a formulation of partially hydrogenated cottonseed oil, copper gluconate, and flavoring. In the television commercials, two teenagers are arguing over whether Certs are candy mints or breath mints. An off-screen announcer would interject by saying, "Stop! You're both right! Certs is two, two, two mints in one!" A similar situation occurs for quantum entities, which act as both particles and waves.

Isaac Newton (1642-1727) expressed this idea when he wrote that light consisted of corpuscles that propagated in fits.[1] Early in the 20th century, Nobel Physics Laureate, Niels Bohr (1885-1962), stated the idea of quantum complementarity that quantum entities will show either wave or particle properties depending on the particular experiment. While the wave nature of light was observed for centuries prior to that time, it wasn't until Arthur Holly Compton (1892-1962) demonstrated the momentum of light in 1923 that its particle nature was proven. Compton won the Nobel Prize in Physics in 1927 for this discovery.

Electrons, known as particles from their discovery by Joseph John "J.J." Thomson (1856-1940), were shown to have wave properties in the 1927 Davisson-Germer experiment conducted by Clinton Davisson (1881-1958) and Lester Germer (1896-1971) while working at Bell Labs. They demonstrated the wave property of electrons by diffraction of an electron beam by a nickel crystal.[2] Davisson was awarded the 1937 Nobel Prize in Physics for this discovery.

People of the same era seem to share a particular look. This observation can be verified by viewing images of the principal female characters in "rom-coms" over the decades. Compare the photograph of Edgar Allan Poe (1809-1849) on the left with that of J.J. Thomson (1856-1940) on the right. Edgar Allan Poe and J.J. Thompson images sources for Edgar Allan Poe and J.J. Thompson via Wikimedia Commons.

About the same time as the confirmation of the wave-particle duality of quantum entities was the 1927 theoretical observation by German physicist, Werner Heisenberg (1901-1976),called the uncertainty principle that states that a simultaneous accurate observation of some pairs of measurements on a quantum system is not possible. Example are the pairs, position, x, with momentum, p; and energy, E, with time, t. This principle is expressed as an inequality, as follows:

ΔpΔx ≥ ħ

ΔEΔt ≥ ħ

in which the constant, ħ, called the reduced Planck constant, is the Planck constant h divided by 2π.

While the Heisenberg uncertainty principle expresses a particular uncertainty in measurement of such pairs of canonically conjugate variables, there's another measurement uncertainty, called the observer effect, with which all experimenters can relate. This is the error introduced by the measuring instrument's disturbing the physical system that's being measured. Examples in my own electronics workshop are a voltmeter's changing a voltage reading by resistive loading of a circuit, or an oscilloscope reading a slightly different frequency when the capacitance of its probe changes an oscillator resonance.

The pre-Socratic Ancient Greek Philosopher, Heraclitus (c. 500 BC), discerned the observer effect long before modern physics. His work survives only through a few fragments, and through summaries by other philosophers, such as the portion of passage 402a from the Cratylus of Plato (c.425-348 BC) shown above.

The translation of this is "Heracleitus says, you know, that all things move and nothing remains still, and he likens the universe to the current of a river, saying that you cannot step twice into the same stream." This is summarized as the adage that "You can't step into the same river twice." since stepping into it causes a change in the river.

(Greek text from "Plato. Platonis Opera," John Burnet, Ed., Oxford University Press, 1903. English translation from "Plato. Plato in Twelve Volumes, vol. 12 , Harold N. Fowler, Trans., Harvard University Press (Cambridge:1921). Both from the Tufts University Perseus Digital Library Project,[3] licensed under a Creative Commons License.)

I generally dislike papers with too much mathematics; but, when the topic is quantum mechanics, mathematics is unavoidable. A recent open access paper by two quantum physicists from Hiroshima University (Hiroshima, Japan) in Physical Review Research analyzed the dynamics of the interaction between a physical property and the change in state of the meter used for its measurement.[4-5]

The researchers approached the fundamental problem of quantum measurement by combining information about the past of the system with information about its future in a description of the system dynamics during the measurement interaction.[5] They demonstrated that the measured value of a physical property depends on the dynamics of the measurement interaction through which it is observed.[5] As explained by study co-author, Holger Hofmann, a professor at Hiroshima University,

"There is much disagreement about the interpretation of quantum mechanics because different experimental results cannot be reconciled with the same physical reality... In this paper, we investigate how quantum superpositions in the dynamics of the measurement interaction shape the observable reality of a system seen in the response of a meter. This is a major step towards explaining the meaning of 'superposition' in quantum mechanics."[5]

The authors conclude that the physical reality of an object cannot be separated from the context of all its interactions with the environment, past, present and future.[5] Says Hofmann, there's "strong evidence against the widespread belief that our world can be reduced to a mere configuration of material building blocks."[5]

Quantum Uncertainty

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