Is Reality Digital or Analog?
Look for answers in the winning essays of the third Foundational Questions Institute essay contest.
By George Musser

Last week, the Foundation Questions Institute announced the winners of its third essay contest, which Scientific American co-sponsored. (I helped to decide on the question, judge the essays and hand out the awards at the World Science Festival in New York City.) The essay question was, “Is Reality Digital or Analog?” Is nature, at root, continuous or discretized? You can make a powerful case for either option. Or both options. Or neither. A venerable tradition in essay-writing is to question the question.

In fact, whenever I tell people about the contest, many object to the word “reality.” What does it even mean? Will we humans ever be able to grasp it? The deeper that physicists dive, the more the concept of reality keeps swimming away from them. Leonard Susskind suggests in an interview in our August issue that reality is inherently slithery. Black holes, in particular, introduce an unavoidable ambiguity into our description of nature. That said, we have no choice but to keep swimming after it. I personally am optimistic that one day we’ll succeed. (I wrote a whole book on that premise.) The progress physics has made over the centuries makes a strong case that the amazing complexity of the natural world arises from the repeated application of a few simple rules that are within our power to apprehend.

Essay contests have a distinguished history in physics to gain traction on slippery problems, outside the strictures of the standard journal paper. They also broaden the pool of intellectual talent. A total of 161 people from 30 countries entered this contest, and 70 percent of them were not academic physicists or philosophers. The awards reflected a combination of public ratings and judge deliberations. I would say that all the essays that placed deserve reading. They don’t provide watertight arguments—I daresay I found something to object to in nearly all of them—but do get you thinking. Let me offer a sense of the range of ideas.

Living in the age of bits and bytes, we tend to think reality must be digital, so some of my favorite essays were ones that took the contrary point of view that the world is really analog.

David Tong of the University of Cambridge and Ken Wharton of San Jose State University did just that. Quantum theory is usually thought of as discrete; after all, that’s what the word “quantum” connotes. But its equations are actually formulated in terms of continuous quantities. Discrete quantities appear only when a system is constrained in some way, just as a guitar string produces certain tones because it is pinned down at both ends. For instance, the stair-step energy levels of atoms reflect the fact that atoms are held together by a balance of forces.

Partisans of the digital view argue that even the continuous quantities are, on closer inspection, discrete: they lie on a grid whose elements are spaced so tightly together that they give the illusion of a continuum, like the pixels on an iPhone 4 screen. But Tong observed that at least one feature of nature really does seem to require a true continuum: the fact that elementary particles of matter come in distinct left- and right-handed versions. And Wharton, by considering the varieties of constraints we can impose on continuous quantum systems, offered a provocative interpretation of one of the most important concepts in physics, the principle of least action.

That said, the digital view has strong appeal. The main evidence is that quantum mechanics, when applied to gravity, implies that distance and duration come in smallest possible units. Susskind’s work on black holes showed that quantities such as energy and entropy are discretized, too. True, space and time can’t be anything so straightforward as a grid of pixels, because such a grid would spoil the symmetries we observe in nature. Instead, discreteness suggests to many physicists that space and time are derivative concepts that emerge from some deeper level of reality. A number of essays reviewed the solutions proposed by mainstream schools of thought, including string theory (Moshe Rozali of the University of British Columbia and Philip Gibbs, who was trained as a physicist and now works as a software engineer) and loop quantum gravity (Daniele Oriti of the Max Planck Institute for Gravitational Physics), as well as dark-horse candidates for a deep theory of nature, such as Stephen Adler’s noncommutative matrix model (Tejinder Singh of the Tata Institute of Fundamental Research in Mumbai) and the proposition that the world is a big computer (Giacomo Mauro D’Ariano of the University of Pavia, among other entrants).

Finally, some of the best essays approached the discrete-vs.-analog dilemma in a fresh way. Jarmo Mäkelä of Vaasa University in Finland imagined a dialogue with Isaac Newton in which he described how to count the possible discrete internal states of a black hole—a quantity known as the partition function, which in turn defines the hole’s thermodynamic properties. Tobias Fritz of the Institute of Photonic Sciences in Barcelona proposed studying graphene as an analogue to quantum gravity. Dean Rickles of the University of Sydney and Thomas McFarlane, a mathematician-turned-patent-agent, suggested that our conceptual and experimental tools bias us toward discrete models of reality.

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