Is anything truly continuous in the physical world?
Everything we have ever measured behaves like a continuum. Everything we know about information and gravity suggests that, at the bottom floor, it cannot be one. No one has yet designed the experiment that would settle it.
Shannon's sampling theorem: a band-limited continuous signal is captured perfectly by discrete samples. Nothing is lost. If spacetime had a natural bandwidth near the Planck scale, it would be continuous and discrete at once — and this chapter's question would be a false dichotomy.
The question holds up. The wording doesn't.
This isn't an idle or poorly framed question: it's one of the deepest open questions in fundamental physics. The Foundational Questions Institute devoted its 2011 world essay contest exactly to it —Is Reality Digital or Analog?— with leading physicists competing, and fifteen years later it's still unsettled.
It's also the natural question for a book called bitsapiens: it asks whether the universe is, at bottom, like us —made of bits— or whether bits are just our way of biting into a continuum.
"Analog" is an engineering term, not an ontological one: a signal is analogous to something else —the vinyl groove is analogous to the air-pressure wave—. Any physicist interviewed will object to the word within the first two minutes. The precise term is continuous versus discrete.
Three questions hiding inside one
- It confuses a relation with a property — "Analog" describes a correspondence between two things; "continuous" describes what a thing is like. The analog/digital distinction was analyzed by Nelson Goodman and by David Lewis in 1971, and it does not line up with continuous/discrete.
- It bundles three questions experts answer differently — Do physical quantities take values with infinitely many decimals? Is spacetime divisible without limit? How much information fits, at most, in a finite region? The third is the one that matters most to a bitsapiens.
- It confuses the map with the territory — Our theories are written with real numbers and continuous manifolds. That doesn't prove reality is.
Is the physical world continuous all the way down — or does every continuity we perceive emerge from something discrete and finite, like the pixels on a screen? And could we ever tell the difference experimentally?
The three sub-questions also work as the interview's structure: each expert enters through one of them.
Twenty-five centuries of the same tension
"Quantum" mechanics is, in its formalism, a rigorously continuous theory. The name has been misleading us for a century.
This is the point almost everyone gets backwards, and it's the chapter's best material. The wavefunction evolves smoothly, it lives in a continuous Hilbert space, its amplitudes are continuous complex numbers, and position and momentum have continuous spectra. What we observe as discrete —an atom's energy levels— emerges from boundary conditions imposed on something continuous.
The image is David Tong's, quoted as is: the atom is analogous to an organ pipe, which produces a discrete series of notes even though the air moves continuously. In quantum field theory the fundamental objects aren't particles but fields —continuous fluids filling space— and particles are their ripples. General relativity, in turn, models spacetime as a differentiable manifold, with no minimal grain.
Uncomfortable and correct conclusion: no experimentally confirmed physical theory posits a discrete space, time, or state. The pixelated universe is today a hypothesis, not a result.
Who argues what, and with what
- The Nielsen–Ninomiya theorem (1981) — We've spent forty-five years trying to put the full Standard Model on a lattice to simulate it, and there's a mathematical obstruction: chiral fermions can't be discretized. The Standard Model is chiral. If we can't even write our laws in discrete form in principle, maybe nature isn't discrete either. Nuance for the interview: overlap and domain-wall fermions partially dodge the theorem via Ginsparg–Wilson, and Tong's own argument is debated.
- Lorentz symmetry holds up to everything — A naive lattice would break special relativity and make light of different energies travel at different speeds. Gamma-ray burst data says the opposite, brutally.
- The fruitfulness argument — All of successful physics is written in the language of the continuum and works to twelve decimal places on the electron's magnetic moment. The continuum isn't baggage physics is trying to shed: it's its most productive tool.
- The Bekenstein bound and the holographic principle — A black hole's entropy scales with its surface, not its volume. 't Hooft and Susskind elevate this to a principle: the maximum information in a region is finite, about 10⁶⁹ bits per square meter. A genuine continuum demands infinite information.
- Loop quantum gravity — Rovelli and Smolin derive in 1995 that area and volume operators have discrete spectra. Important nuance: this is spectral discreteness, like an atom's energy levels, not a fixed lattice — which is why it coexists with relativity.
- Causal sets — Bombelli, Lee, Meyer, and Sorkin (1987): spacetime would be a discrete set of causally ordered events, from which continuous geometry emerges statistically. It's the discrete proposal that best preserves Lorentz invariance.
- The reals as informational monsters — Gisin: a typical real number carries infinite information, and by Bekenstein's bound a finite volume can't store it. Classical determinism's "initial conditions with infinitely many decimals" would be mathematical fiction.
- Digital physics — Zuse (1969), Fredkin, Wolfram, Seth Lloyd —who calculated the observable universe has performed some 10¹²⁰ operations on 10⁹⁰ bits— and 't Hooft with his cellular-automaton interpretation. The speculative wing: suggestive, minority, unconfirmed.
The third way, and the most elegant one
Achim Kempf (New Journal of Physics, 2010): "spacetime could be simultaneously continuous and discrete, the same way information can be." The key is the Shannon–Nyquist sampling theorem, the same one that makes your Spotify work: a band-limited continuous signal is captured perfectly by discrete samples. Nothing is lost; continuous and discrete are two equivalent descriptions of the same thing.
If spacetime has a natural bandwidth —an ultraviolet cutoff at the Planck scale— then the chapter's dichotomy is false. That the possible answer comes from Shannon's information theory is, for a book titled bitsapiens, too good to pass up.
What they've looked for, what they've found
Every experimental search for spacetime "pixels" has come back negative. Honesty demands the nuance: these tests rule out the naive versions of discreteness —the ones that break Lorentz symmetry— but not causal sets, nor loop quantum gravity's spectral discreteness.
| Experimento | Buscaba | Resultado | Lectura |
|---|---|---|---|
| Fermi / GRB 0905102009 | Photons of different energy arriving out of sync after billions of light-years | No detectable dispersion | Continuous |
| Holometer, Fermilab2015 | "Holographic noise": spacetime fluctuations at the Planck scale | Null | Continuous |
| Quasar imaging2015 | Accumulated blurring from spacetime "foam" | Rules out stochastic Planck-scale dispersion | Continuous |
| LHAASO / GRB 221009A2023–24 | The same test, with the brightest burst ever recorded | Linear effects bounded above the Planck energy itself | Continuous |
| Black hole thermodynamicsTheoretical | Maximum information capacity of a finite region | Finite, and proportional to area | Discrete |
Yes and no, and honesty demands both halves
By everything we've measured: yes, the world is continuous.
Our confirmed theories are continuous top to bottom, the discreteness we observe is emergent, and every search for graininess has come back negative, with bounds that already exceed the Planck scale for the simplest effects.
By frontier theoretical arguments: probably not, underneath.
Black hole thermodynamics says the information in a finite region is finite, and a genuine continuum demands infinite information. Nearly all of quantum gravity expects the continuum to dissolve around 10⁻³⁵ meters. But that's an expectation, not a data point.
And maybe the dichotomy is the wrong one.
Continuous and discrete may be equivalent descriptions of the same reality, like a song and its lossless digital file.
That unresolved tension isn't a flaw in the chapter: it's its content.
No guests yet. Candidates for this question have already been identified and are being contacted.
Terms the chapter needs to define
Primary and verified
- FQXi 2011 essay contest, Is Reality Digital or Analog? — winners and essays
- D. Tong, The Unquantum Quantum, Scientific American (2012) — article
- N. Gisin, Indeterminism in Physics and Intuitionistic Mathematics, Synthese (2021) — arXiv:2011.02348
- A. Kempf, Spacetime could be simultaneously continuous and discrete…, New J. Phys. 12, 115001 (2010) — IOPscience · arXiv:1010.4354
- Lorentz-violation bounds from GRB 221009A (LHAASO) — arXiv:2402.06009 · JCAP 04 (2024) 060
- Bound on spacetime "diffusiveness" from quasar imaging — Nature Physics (2015)
- Profiles verified in August 2026 — Tong, DAMTP Cambridge · Gisin, Constructor · Kempf, Waterloo · Rovelli, CPT Marseille
- Background: J. A. Wheeler, Information, Physics, Quantum (1989) · G. 't Hooft, The Cellular Automaton Interpretation of Quantum Mechanics (2016) · C. Rovelli, Reality Is Not What It Seems (2016) · S. Wolfram, A New Kind of Science (2002)