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 2
π.
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]
References:
- S. Sakkopoulos, "Newton's theory of fits of easy reflection and transmission," European Journal of Physics, vol. 9, no. 2 (April, 1988), DOI 10.1088/0143-0807/9/2/007.
- C. J. Davisson and L. H. Germer, "Reflection of Electrons by a Crystal of Nickel," Proc. Natl. Acad. Sci., vol. 14, no. 4 (April 1, 1928), pp. 317-322, https://doi.org/10.1073/pnas.14.4.317. A PDF file is available here.
- Plato, "Cratylus," from the Tufts University Perseus Digital Library Project.
- Tomonori Matsushita and Holger F. Hofmann, "Dependence of measurement outcomes on the dynamics of quantum coherent interactions between the system and the meter," Physical Review Research, vol. 5, Article no. 033064, July 31, 2023, DOI:https://doi.org/10.1103/PhysRevResearch.5.033064. This is an open access article with a PDF file here.
- Do measurements produce the reality they show us?, Hiroshima University Press Release, August 23, 2023.
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