While studying physics this past year, I noticed tension between theoretical and experimental physicists, especially between younger quantum field theoreticians and veteran particle physicists — regarding deep reality and the various formulations of quantum mechanics (addressed in another post).

Revisiting some archived debates, this philosophical question (“Is reality digital or analog?”) was posed in an essay contest by The Foundational Questions Institute (FQXi) in 2010-2011.^{1}

This tension is evident in David Tong’s 2011 essay “Physics and the Integers” (as well as a 2012 follow-on version in Scientific American) and Victor Stenger‘s response. That professional interaction will be discussed more below.

**Case 1**

First, however, here’s an excerpt from an Electronics World blog post on the question “Is reality digital or analog?” With the discovery of the Higgs boson/field at CERN, the article cautions that the Standard Model’s grounding in physical reality might be undermined via overreach by field theorists — in particular by statements like Tong’s that “discreteness in the world is simply the Fourier transform of compactness.” ^{2}

David Tong … has been fascinated by the historical debate concerning the Integers and the Continuum, and also in relation to Einstein’s insistence that both have to be grounded in Physical Reality and Unification.

In the December 2012 edition of Scientific American appears a short article entitled “The Unquantum Quantum” [“Is Quantum Reality Analog after All?”]. Therein Tong explores the boundaries of the Analogue and Digital universe in response to The Foundational Questions Institute’s open question competition to physicists and philosophers: ”Is Reality Digital or Analog?”

Essentially Tong is arguing that (Platonists can leave now) that Atoms and Molecules don’t really exist. [See this video of a lecture by Tong as to such a characterization.]

… Tong appears not to understand the limitations of the Complex Number System [CNS] itself, with its intrinsic fault-lines such as the j^4=j^8=j^12 problem [huh?] or the phase problem(s) associated with the Fourier Transform [huh?]. That I did not find surprising. What I did find surprising is that Tong clearly forgets how the CNS emerged itself as a framework for mathematicians to solve integer coefficient cubic equations, and the historical arguments that still persist. Schrödinger, can be left to Schrödinger and Einstein.

**Case 2**

There also are some comments on the 2011 paper on the FQXi forum.

Here’s Stenger’s response — “Particles Are for Real” — to that other version of Tong’s essay “Is Quantum Reality Analog after All?” ^{3} (Highlights and text in square brackets are mine.)

… No one has ever observed a quantum field.

Quantum fields are purely mathematical constructswithin quantum field theory.But note that what Tong calls “a lie” is the notion that the building blocks of nature are discrete particles while it is fields that are the building blocks of our theories. That is,

he is equating nature to theory.Tong is revealing his acceptance of a common conception that exists among today’s theoretical physicists (Paul Dirac and Richard Feynman, among other twentieth-century greats, were not part of that school). That is, the symbols that appear in their mathematical equations represent “true reality”

while our observations, which always look like localized particles, are just the way in which that reality manifests itself.As someone who 40 years as an experimental elementary particle physicist, I carry a different perspective. I started in the 1960s analyzing

bubble chamberpictures where one sat at a scanning table and traced the beautiful tracks of bubbles photographed during the time the superheated liquid in the chamber was exposed to a pulsed beam from an accelerator [a stream of confined particles].^{4}

It never occurred to my collaborators and me to describe what we observed as some kind of field in an abstract multidimensional space.(Quantum fields do not live in familiar space-time, despite Tong’s assertion). … From the rate at which the particle slowed down as it lost energy to ionization we could also determine its speed and, from these two measurements, determine the particle’s energy [i.e., the statistical properties of the stream].And, the workers at the LHC do not talk about colliding the quantum fields of two protons together to measure the wavelengths of some abstract wave oscillating in some imaginary aether. They speak of

banging particles togetherand measuring the particles they see coming out.The point is, while our mathematical theories are expressed in terms of abstract fields, what we always measure is best described as particles. [Which likely is not disputed — the common description of what is measured.]

Stenger then talks about the famous **double slit experiment** (for which some alternative views persist). He cites the photoelectric effect and concludes:

The fringe pattern does not appear until you have accumulated the statistical distribution of a large number of photons.

The so-called “wave nature” of light is thus not a characteristic of a single photon; it is a characteristic of the behavior of an ensemble of many photons.Now, other philosophical schools exist besides Platonism. Most experimentalists, if dragged kicking and screaming into having to think about a philosophical question, would probably say that the objects they observe, which they call particles, are “real.” But then, they have no better means to prove that assertion than their theoretical colleagues have to insist that only fields are real.

No one doubts the moon is real, and it’s just a particle when viewed from far enough away. How is it any different from a photon registered in a photodetector? So, even if I can’t prove it, it seems reasonable that photons, electrons, quarks, neutrinos, and Higgs bosons are for real.

Curiously, in the first case Tong is criticized as an anti-Platonist (numbers are derivative) and in the second case as a Platonist (objects are derivative)! Quite an accomplishment, eh.

My grappling with quantum field theory (QFT) has pros and cons, aside from the general mind boggling character of the 10^-n landscape. QFT provides a unifying framework for the dynamics of energy and time. For example, particle interactions and transformations. On the other hand, QFT leaves me puzzled as why particles are so stable (for example, electron mean lifetime is > 6.6×10^28 years). That is, how “particles” — as particular (wave packet) excitations or compact Fourier transforms — survive intact in the complex energy spectrum of a “fluid-like substance.” On the other hand, particles — as the fundamental building blocks of nature — provide that stable assurance.

[1] Also see The Scientific American announcement regarding winners by George Musser on June 14, 2011.

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, thestair-step energy levels of atomsreflect the fact that atoms are held together by a balance of forces.

[2] On the FQXi forum’s page this is Tong’s elaboration on that statement.

If you put a quantum particle in a compact box then its momentum and energy is necessarily discrete. If you put the same particle in an infinite line, then its momentum can be anything at all.

The same argument works in reverse. If the momentum of a particle is restricted in its range (i.e. a Brillouin zone) then the space it lives on is discrete (i.e. a lattice).

The maths that underlies this is simply the Fourier transform. Your cosine transform is just the real part of the Fourier transform.

[3] Published in Scientific American in December 2012. The same sentiment is found in his February 15, 2017 lecture “Quantum Fields: The Real Building Blocks of the Universe.” This excerpt from that lecture provides the context for Stenger’s response.

The spirit is exactly what Democritus said 2,500 years ago, that they’re like LEGO bricks from which everything in the world is constructed. These LEGO bricks are particles, and the particles are the electron and two quarks. It’s a very nice picture. It’s a very comforting picture. It’s the picture we teach kids at school. It’s the picture we even teach students in undergraduate university.

And there’s a problem with it. The problem is it’s a lie. It’s a white lie. It’s a white lie that we tell our children because we don’t want to expose them to the difficult and horrible truth too early on it. It makes it easier to learn if you believe that these particles are the fundamental building blocks of the universe. But it’s simply not true. The best theories that we have of physics do not have underlying them … the electron particle and the two quark particles.

In fact, the very best theories we have of physics don’t rely on particles at all. The best theories we have tell us that the fundamental building blocks of nature are not particles, but something much more nebulous and abstract.

The fundamental building blocks of nature are fluid-like substances which are spread throughout the entire universe and ripple in strange and interesting ways.That’s the fundamental reality in which we live. These fluid-like substances we have a name for. We call them fields.

[4] His experience with bubble chamber experiments reminds me of the dramatized story of Heisenberg in Gilder’s book **The Age of Entanglement**, in the chapter “Uncertainty Winter 1926–1927.”

Heisenberg almost ran out of the little attic room, down the stairs of the institute, the door slamming behind him as he emerged into the fresh cold air and emptiness of the park. He walked between the bare trees at the gate, his booted feet leaving dark footprints, melting the frost that fringed the grass. It is theory, it is theory, it is theory which first determines what can be observed.

“We have always said so glibly,” Heisenberg told his frustration, or the trees, or Bohr, or Einstein, “that the path of the electron in the

cloud chambercan be observed.” He turned to see his footprints among the frost, and he thought of the electron shooting through the cloud chamber, leaving its footprints of dew behind, small condensed clouds. “But perhaps,” he continued slowly, “what we really observed was something much less. Perhaps”—he was walking faster now, his breath, like the electron, leaving clouds behind him—“we merely saw a series of discrete and ill-defined spots through which the electron had passed. In fact, all we do see in the cloud chamber are individual water droplets which must certainly be much larger than an electron.” He stopped again. “The right question should therefore be: Can quantum mechanics represent the fact that an electron finds itself approximately in a given place and that it moves approximately with a given velocity, and can we make these approximations so close that they do not cause experimental difficulties?” — Gilder, Louisa (2008-11-11). The Age of Entanglement (Kindle Locations 1934-1944). Knopf Doubleday Publishing Group. Kindle Edition.

Note 1 of the post references George Musser’s overview of the essay contest and another essay by Ken Wharton who, like Tong, argues that reality is analog — built on a continuous foundation — and that “Discrete quantities appear only when a system is constrained in some way.”

While admitting that there’s no definitive answer due to a possibly even deeper, underlying reality, Wharton proposes a coherent framework for modern physics — reconciling the continuum of general relativity (GR) and blended aspects of quantum theory (QT). Whether one is partial to conforming QT to GR or to exploring a theory of quantum gravity, he suggests that the “measurement problem” needs to be resolved.

Wharton questions the natural assumption that measurement reveals underlying reality — that measured discreteness implies unobserved things are discrete as well. He suggests that measurement is analogous to “boundary-induced quantization” (BIQ) of unconstrained superpositions — continuous energy modes, within the following context:

BIQ is illustrated with standing waves of vibrating strings (strings fixed at both ends) and the width of peaks — variable discreteness — of resonant frequencies in laser cavities.

The more strongly a system is constrained, the more precise the emergent discreteness. From which follows the analogy that “stricter measurements produce stricter discreteness.” He addresses issues with this analogy — of measurement and a mirror (reflectivity of a laser cavity mirror) — by discussing the “block universe” and boundaries between regions in spacetime, correlations between those regions, and how correlations may be considered a measurement.

This new perspective is at odds with QT.

But he notes that the mathematical framework of action principles bridges the divide between GR and QT.

[Ken Wharton is an Associate Professor in the Department of Physics and Astronomy at San Jose State University. His research is focused on the foundations of quantum theory, with a particular interest in fully time-symmetric approaches.]