An arguable misnomer in physics: the term “quantum mechanics”

Analog or digital,  uninterrupted or pixilated, continuity or discontinuity, field or particle? These pairs of opposing adjectives and nouns often occur in texts and discussions about physical reality and theoretical modeling. The periodic table of discrete chemical elements with their characteristic numbers and spectra directs scientists towards a quantum view of matter. As an example: the solution of Schrödinger's equation for the hydrogen atom provides us with quantum numbers (n, l, and m), which are integers [1]. Important: these integers are coming forth from solving an equation formulated with continuous variables for physical quantities that encode electron movement and potential. Thus, quantum mechanics models reality on the basis of continuity. Discrete values result from the approach in which the theoretical model is treated and solved; but may not be nature-inherent.

Intrigued by cosmological challenges and debates over the fundamental laws of the physical world, David Tong—a theoretical physicist at the University of Cambridge—is giving the continuity-discontinuity interrelation a closer look. He writes that the term “quantum mechanics” could said to be a misnomer for a theory that formulates its equations in terms of continuous quantities [2].  He cites Leopold Kronecker's proclamation “God made the integers, all else is the work of man.” and counters with “God did not make the integers. He made continuous numbers, and the rest is the work of the Schrödinger equation.” [3].  Tong explains the latter in detail:

Integers are not inputs of the [quantum] theory, as Bohr thought [Danish physicist Niels Bohr “implemented” discreteness at the atomic scale]. They are outputs. The integers are an example of what physicists call an emergent quantity.  In this view, the term “quantum mechanics” is a misnomer. Deep down, the theory is not quantum. In systems such as the hydrogen atom, the processes described by the theory mold discreteness from underlying continuity. 

Quantum phenomena are these days demonstrated and animated in educational as well as entertaining videos. The Zeitgeist-driven perception: What I simulate and animate, is what I see and believe in. Yet, living in a digital age does not automatically imply living in a digital universe.

Keywords: physics, philosophy, quantum theory, physical world, pointillist universe, emergent integers.

References and more to explore
[1] Quantum Mechanics: Solving Schrödinger's equation [users.aber.ac.uk/ruw/teach/237/hatom.php].
[2] David Tong: The Unquantum Quantum. Scientific American, December 2012, 307 (6), pp. 46-49 [www.nature.com/scientificamerican/journal/v307/n6/full/scientificamerican1212-46.html].
[3] Quoted at axeleratio.tumblr.com: axeleratio.tumblr.com/post/36680758289/god-did-not-make-the-integers-he-made-continuous.

A lead-free borosilicate glass, G 702 EJ, named Py-Right, Pie Rite and eventually Pyrex

PYREX^® is  is a transparent, lead-free borosilicate glass with a low thermal expansion coefficient—an example of  a material with good heat shock resistance. The excellent thermal properties of Pyrex facilitate its use at high operating temperatures [1].

Pyrex-branded borosilicate glass products were invented and produced at Corning Glass Works in the upstate New York city of Corning, nicknamed Crystal City for its legacy of glass factories and glass cutting shops. In the early 20th century, a hot flame tolerant borosilicate glass, named “fire glass”or  Nonex, was successfully manufactured by the Corning specialty glassmaker and integrated as components in electric lightbulbs and railway signal lamps [2-5]. A borosilicate glass is made by adding borax (sodium tetraborate decahydrate) to the typical glass composition of silica, sodium oxide and lime. By further employing other minor additives, glass properties can be fine-tuned for desired applications.

Pyrex was developed by Corning scientist William Churchill, based on Corning's Nonex know-how. While Nonex released lead when exposed to acids (for example from food), a lead-free borosilicate variation with code G 702 EJ, did not. The latter showed promising properties for being used as ovenware and laboratory glassware.

In 1915, Churchill and Corning made G 702 EJ public under the tradename Pyrex—rhyming with Nonex—after playing with names such as Py-Right and Pie Rite, referring to the first appetizingly prepared cakes and custards in Pyrex dishes. In 1916, these look-right-through dishes were marketed and advertized as ovenware that saves time, labor and fuel [5]: one of the earliest ads further states that Pyrex will not crack, chip nor craze, not be affected by the hottest oven and that “Pyrex is everlastingly sanitary, durable, easy to wash, a constant source of satisfaction in the well-appointed home.”

Keywords: history, materials science, glass research, glass engineering, borosilicates, labware, kitchenware, baking, cooking.

References and more to explore
[1] Pyrex^® Borosilicate Glass [www.pgo-online.com/intl/katalog/pyrex.html].
[2] Washington Glass School: Historical Glass Fun Facts: Invention of Pyrex & the Studio Glass Movement [washingtonglass.blogspot.com/2012/01/historical-glass-fun-facts-invention-of.html].
[3] History of Pyrex^® [www.classickitchensandmore.com/page_4.html].
[4] William S. Ellis: Glass. Avon Books, Inc., New York, 1998; pp. 49-50.
[5] Regina Lee Blaszczyk: Cooking with Glass. Chemical Heritage Fall 2012/Winter 2013, 30 (3), pp. 8-9 [www.chemheritage.org/discover/online-resources/thanks-to-chemistry/ttc-food-pyrex.aspx].

Crystal City—a pseudonym for Corning, New York

The upstate New York city of Corning is located on the Chemung River in Steuben County. Along the river, the buildings of Corning Glass Works—originally named Corning Flint Glass Works—can be found, where glass and ceramic products for industrial and scientific applications are manufactured.  The Corning Museum of Glass at 1 Museum Way (Corning, NY 14830) calls itself a wonderland of glass, in which master glass-workers demonstrate the making of spectacular glass objects. World-changing innovations in glass can be discovered there [1]. Corning's cornucopia of glass-making arts and technology led to the nickname Crystal City [2], as this picturesque and industrial city often was and still is dubbed in the media.

Physicists and chemists may think of this pseudonym as a misnomer, since glass is an amorphous, non-crystalline material. But its optical transparency and large content of silica (SiO₂) may justify the crystal association. Students and hobbyist of glass-working can try their skills by enrolling  in classes at the Corning Museum of Glass, experimenting with phases and facets of non-crystalline matter in the Crystal City [3].

Two articles in a recent Chemical Heritage edition review the collections of the Corning Museum of Glass and feature the history of glass-making in Corning, beginning with Nonex for signaling lamps, Pyrex for lab- and kitchenware and continuing on with fiber optics and touch-screen technology [4,5]. According to the Hot Stuff article by Kelly Tuttle [5], the museum  showcases a Dale Chihuly sculpture in its glass-walled entrance and “houses the largest collection of glass in the world, with over 45,000 objects spanning 3,500 years. In 1868 the Brooklyn Flint Glass Company moved to Corning and bacame the Corning Glass Works. By 1905 upward of 2,500 glass craftspeople had moved into the then industrialized area, which acquired the pseudonym Crystal City.” 

References and more to explore
[1] Corning Museum of Glass [www.cmog.org].
[2] Corning, New York: The Crystal City [lcweb2.loc.gov/diglib/legacies/NY/200003367.html].
[3] William S. Ellis: Glass. Avon Books, Inc., New York, 1998; page 204 (also see www.cmog.org/programs/classes#.UKwALGeAYYs).
[4] Regina Lee Blaszczyk: Cooking with Glass. Chemical Heritage Fall 2012/Winter 2013, 30 (3), pp. 8-9 [www.chemheritage.org/discover/online-resources/thanks-to-chemistry/ttc-food-pyrex.aspx].
[5] Kelly Tuttle: Hot Stuff. Chemical Heritage Fall 2012/Winter 2013, 30 (3), page 46.