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Wave-Particle Duality

March 11, 2024

Television was generally monochrome (black and white) until the mid-1960s. While color television had been demonstrated using various technologies decades earlier, there was a desire for a method that would be backwards-compatible with existing television receivers; that is, color transmissions would appear as black and white on existing receivers. The end result was a system that represented color as a small additional signal detected with reference to a local oscillator stabilized by a signal pulse between image frames.

There was a memorable series of black and white television commercials in the 1960s that featured teenage twins debating about whether Certs was a breath mint or a candy mint.[1] This question was resolved by an announcer declaring Certs to be both a candy mint and a breath mint; viz.,
Twin No. 1 - "Certs is a candy mint!"
Twin No. 2 - "Certs is a breath mint!"
Announcer - "Stop! You're both right! New Certs is two mints in one!"

Certs twins

Certs twins.

In 1999, the United States Customs Service decided that Certs was a candy, and it placed it into the highly taxed tariff class 2106.90.99.

Warner-Lambert, owner of Certs at that time, won an appeal to the Court of Appeals for the Federal Circuit that Certs should be placed in tariff class 3306.90.00, "Preparations for oral or dental hygiene;" so, Certs is legally a breath mint.[2]

(Still image from a YouTube video. Click for larger image.)

A similar debate about the nature of electrons happened decades earlier. This debate was whether electrons, and other matter, were particles or waves. That debate had the same resolution - They're both particles and waves depending on how you measure them. This principle was first hypothesized by French physicist, Louis de Broglie (1892-1987), formally, Louis-Victor-Pierre-Raymond, Seventh duc de Broglie.[3] De Broglie knew, from the work of Hermann Minkowski (1864-1909) and Max Abraham (1875-1922) that the vacuum wavelength λ of a photon is the Planck constant h divided by its momentum p; that is,
λ = h/p
You can see how this is possible by equating the photon energy from the Einstein equation for mass-energy equivalence with the energy in the Planck relation; viz.,
E= mc2 = hν

λ = c/ν

λ = h/mc
The term mc is the photon momentum p. Generalizing this to particles other than phonons replaces the speed of light c in the momentum relation with the velocity v.
λ= h/p = h/mv

French physicist, Louis de Broglie (1892-1987, Louis-Victor-Pierre-Raymond, Seventh duc de Broglie) in 1929.

French physicist, Louis de Broglie (1892-1987) (formally, Louis-Victor-Pierre-Raymond, Seventh duc de Broglie) in 1929.

De Broglie might have been lost to science, since he received his first degree in history. However, he became interested in mathematics and physics and was awarded a Ph.D. in 1924 for the thesis, "Recherches sur la théorie des quanta" (Research on the Theory of the Quanta).[3] This thesis introduced his concept that matter has wave properties.

(Modified Wikimedia Commons image.)

The wave nature of electrons was just an hypothesis until proven by a definitive experiment on electron diffraction in 1927 by Clinton Davisson (1881-1958) and Lester Germer (1896-1971) at Bell Labs. Davisson and Germer scattered electrons from the surface of a crystal of nickel to display a diffraction pattern in an analogy of X-ray diffraction by matter instead of electromagnetic waves. De Broglie was awarded the 1929 Nobel Prize in Physics "for his discovery of the wave nature of electrons."[4] Davisson shared the 1937 Nobel Prize in Physics for the discovery of electron diffraction, but Germer was notably slighted.

The quantum nature of matter has been experimentally proven for electrons (mass = 9.11 x 10-28 grams) and particles up to 10-20 grams.[5-6] Physicist generally believe that larger masses will demonstrate quantum effects. However, such effects are very small, and they are harder to determine experimentally, since a larger mass has many interactions with the environment that will collapse its quantum state.[6] There is no apparent mass limit to quantum mechanics, but, as yet, no definitive experiment to confirm the quantumness of an arbitrarily large mass.[5-6]

One promising experiment has been proposed in a recent article in Physical Review letters by a team of physicists from University College London (London, United Kingdom), the Bose Institute (Kolkata, India), and the University of Southampton (Southampton, United Kingdom).[5] The proposed experiment seems to have the capability of testing the quantumness of an object, regardless of its mass or energy.[6] The proposed experiment uses the quantum mechanical principle that measuring an object can change its quantum nature.[6] Instead of a single measurement made at successive times, the experiment is based on two different measurements to produce a mass-independent probing of quantumness in an harmonic oscillator.[5]

The proposed experiment examines an harmonic oscillator at different times. A beam of light examines the object during one half of its area of oscillation to roughly determine its position as whether the object is in that half of its oscillation, or not. Another beam of light senses its position farther along in the harmonic cycle.[6] If the object is quantum, the first position measurement by the first light beam will collapse its wavefunction and change where it will be at the second measurement.[6] However, if the object is classical, the first observation will have no affect.[6] This experiment can be done with current technologies using a nanocrystal with trillions of atoms as the object.[6] The authors propose that the very massive (10 kilogram) mirrors at the Laser Interferometer Gravitational-Wave Observatory (LIGO), which vibrate together as a single object, could be used in such an experiment.[6]

Technicians inspect the coating on one of LIGO's four mirrors.

Technicians inspect the coating on one of LIGO's four mirrors. (LIGO Laboratory image, available here and here. Licensed under the Creative Commons CC BY License. Click for larger image.)


  1. Certs Two Mints in One, YouTube video by tvdays, January 21, 2022.
  2. WARNER LAMBERT COMPANY v. UNITED STATES, United States Court of Appeals,Federal Circuit, WARNER-LAMBERT COMPANY, Plaintiff-Appellant, v. UNITED STATES, Defendant-Appellee, No. 04-1489, Decided, May 11, 2005 (via findlaw.com).
  3. Louis Victor de Broglie, "Recherches sur sa Théorie Des Quanta (On the Theory of Quanta)," Ann. de Phys., Vol. 10, series III (January-February, 1925), A.F. Kracklauer, Trans., Foundation of Louis de Broglie, 2004.
  4. Louis de Broglie, "The Wave Nature of the Electron," Nobel Lecture, December 12, 1929.
  5. Debarshi Das, Dipankar Home, Hendrik Ulbricht, and Sougato Bose, "Mass-Independent Scheme to Test the Quantumness of a Massive Object," Phys. Rev. Lett., vol. 132, no. 3 (January 19, 2024), Article no. 030202, DOI:https://doi.org/10.1103/PhysRevLett.132.030202. This is an open source publication with a PDF file here.
  6. Experiment could test quantum nature of large masses for the first time, University College London Press Release, January 16, 2024.

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