Alexander I. Poltorak

First Fruits and the Wave-Particle Duality

…Thou shalt take of the first of all the fruit of the ground, which thou shalt bring in from thy land that the Lord thy God giveth thee; and thou shalt put it in a basket and shalt go unto the place which the Lord thy God shall choose to cause His name to dwell there. And thou shalt come unto the priest that shall be in those days, and say unto him: ‘I profess this day unto the Lord thy God, that I am come unto the land which the Lord swore unto our fathers to give us.’ And the priest shall take the basket out of thy hand, and set it down before the altar of the Lord thy God. (Deut. 26:2-4)

And the priest shall take the basket out of thy hand: in order to wave it. (Rashi)

The debate about the nature of matter goes back to antiquity. A pre-Socratic Greek philosophers Leucippus (Fl. 5th c. BCE), and his student, Democritus (c. 460 –c. 370 BC) are considered to be the fathers of the atomic theory of nature. They held that everything consists of indivisible atoms. Their successors Epicurus (341–270 BCE) further developed this idea. Roman philosopher Lucretius (99 BCE – c. 55 BCE) presented a very lucid argument from decay in support of atomism in his poem De Rerum Natura (On the Nature of Things).

At the beginning of the 11th century, the Arabic scientist Alhazen developed the first comprehensive theory of optics based on the notion that the rays of light were composed of particles of light. In 1670, Isaac Newton formulated the corpuscular theory of light (corpusculum in Latin means a smal body or a particle). In the 19 c., a number of scientists including Antoine Lavoisier,  Joseph Louis Proust,  John Dalton, Amedeo Avogadro,  Dimitri Mendeleev contributed to the development of the atomic theory and its applications to physics and chemistry. In his famous 1905 paper on the Brownian motion, Einstein finally proved the existence of atoms.

Using atomic theory of black body (an ideal body that absorbs 100% of light without reflecting any of it back), in 1900, Max Planck proposed that the energy light emitted by the black body is proportionate to the frequency of the oscillator that emitted it: 

E = ,

where E is the energy, v is the frequency, and h is the Planck constant. In another landmark 1905 paper, Einstein explained photoelectric effect by postulating that energy is emitted and absorbed in discrete quantities—quanta. Einstein related the energy E with the frequency of the light f as

E = h f

Quantum revolution was born. In 1921, Einstein was awarded a Nobel Prize for the theory of photoelectric effect.

Parallel with the corpuscular theory of light, a competing wave theory was being developed. In 1630, René Descartes proposed a wave theory of light. He conceived of light as wave-like disturbances in a universal medium (“plenum” later replaced by aether). Newton’s contemporaries Robert Hooke and Christiaan Huygens (and later Augustin-Jean Fresnel) further developed wave theory of light. Thomas Young’s 1803 double-slit experiment producing interference seemed to have confirmed the wave theory of light.

Thomas Young’s sketch of two-slit diffraction of waves, 1803

At the end of the 19th century, James Clerk Maxwell applied his theory of electromagnetism to explain light waves. He demonstrated that visible light, ultraviolet light, and infrared light were all electromagnetic waves of differing frequency. So what is light – particles or waves?

In 1924, French physicist, Louis-Victor de Broglie, hypothesized that not just light but all matter has a wave-like nature:

λ = h / p

Louis-Victor de Broglie

where λ is wavelength, p is momentum and h is Planck constant. This formula is a simple generalization of the Einstein’s formula used to explain the photoelectric effect. The wave nature of electrons was confirmed three years later in experiments showing diffraction of electrons. De Broglie was awarded a Nobel Prize for his discovery of wave nature of particles in 1929. Later, the wave behavior of other particles, such as protons and neutrons, and even atoms and molecules was also observed.

So, is matter made up of particles (as ancient Greek atomists thought) or waves? Niels Bohr thought that “particle” and “wave” were classical concepts, which did not fully describe reality on a microscopic level. He proposed his principle of complementarity postulating that these two competing views of reality complement each other. A quantum-mechanical object is neither particle nor wave. Sometimes, when it has high energy and, therefore, short de Broglie wavelength, it behaves more like a particle. In other cases, when the energy is low, and de Broglie wavelength is substantial, it behaves more like a wave.

The debate about wave-particle dualism of nature rages to this day. Nobel Laureate Richard Feynman, who significantly contributed to the development of quantum field theory, conceived of fields as clouds of virtual particles exchanging energy between particles of matter. In this view, the electromagnetic field is a collection of virtual photons carrying energy between electrons. Another Nobel Laureate, Julian Schwinger who contributed greatly to the development of quantum electrodynamics, perceived particles as wave pockets. The pilot wave theory developed by de Broglie and Bohm maintains wave-particle dualism – a quantum particle is guided by a pilot wave (see my earlier post The Pilot Wave).

Perhaps this Torah portion, Ki Tavo, hints at the wave-particle dualism. Bikurim—the first fruits offered as a sacrifice—represent the particle view of the world. Fruits are separate and countable. However, they are placed together in a basket and waved (as Rashi explains) in front of the altar hinting at the wave view. Particles or waves, we elevate and unify both views by offering Bikurim at the alter emphasizing their common source:

I have brought the first of the fruit of the land, which Thou, O Lord, hast given me (Deut. 26:10)


Offering of the First Fruits — Bikkurim

Illustration from a Bible card published between 1896 and 1913 by the Providence

About the Author
Dr. Alexander Poltorak is Chairman and CEO of General Patent Corporation. He is also an Adjunct Professor of Physics at The City College of New York. In the past, he served as Assistant Professor of Physics at Touro College, Assistant Professor of Biomathematics at Cornell University Medical College, and Adjunct Professor of Law at the Globe Institute for Technology. He holds a Ph.D. in theoretical physics.
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