Technically True but Deeply Misleading: The Wheeler-DeWitt Equation Really Has No Time Variable — but Not for the Reason You Think
“The Wheeler-DeWitt equation, first proposed in 1967, contained no time variable”
The argument in brief
The claim that the Wheeler-DeWitt equation contains no time variable is technically accurate but misleading in how it frames that fact. The absence of time is not an omission or quirk — it is a profound, intentional consequence of applying quantum mechanics to Einstein's general relativity, a puzzle so significant it has its own name: the 'problem of time.' Bryce DeWitt's 1967 paper confirms this, as do decades of follow-up scholarship.
Why it spread
The timeless nature of the Wheeler-DeWitt equation is legitimately counterintuitive and philosophically striking — it genuinely sounds like it shouldn't be true. When science communicators share it without context, the 'why' disappears and audiences are left with the impression of a bizarre accident rather than one of the deepest unsolved problems in physics. Surprising-sounding facts travel fast; careful explanations travel slowly.
The claim is half-right, and that's exactly what makes it slippery. Yes, the Wheeler-DeWitt equation — first published by physicist Bryce DeWitt in a landmark 1967 paper in Physical Review — does lack an explicit external time variable. But saying it simply 'contained no time variable' implies someone forgot to include it, or made an error. Neither is true.
The absence of time is built into the foundations of the equation itself. General relativity, Einstein's theory of gravity, has a mathematical feature called the Hamiltonian constraint, which essentially sets the total energy of a closed gravitational system to zero. When DeWitt applied quantum mechanics to this constraint, the result was the equation H|Ψ⟩ = 0 — and time dropped out automatically. As DeWitt's original paper makes clear, this was not an oversight but a direct consequence of the theory's structure.
Physicist John Wheeler, whose conceptual work inspired the equation, later explored this in his 1968 'Superspace' paper, framing the timelessness as a deep feature of quantum gravity rather than a bug. Physicist Chris Isham's comprehensive 1993 review confirmed the same: the missing time is a structural property of any theory that respects the symmetries of general relativity, a class of theories called diffeomorphism-invariant. Claus Kiefer's textbook Quantum Gravity and the Stanford Encyclopedia of Philosophy both reinforce this reading.
This matters because the 'problem of time' — how to recover our everyday experience of time from a fundamentally timeless equation — is one of the central unsolved puzzles in theoretical physics. Stripping that context away turns a profound open question into a trivia oddity.
This kind of misinformation spreads because the true story is genuinely strange and fascinating. 'Physics equation with no time' sounds like a shocking mistake or a mind-bending discovery, and in popular science writing, the nuanced 'why' often gets cut for brevity. What's left is a fact that is technically correct but points in entirely the wrong direction.
Sources
- DeWitt, B.S. (1967). 'Quantum Theory of Gravity. I. The Canonical Theory.' Physical Review, 160(5), 1113–1148.
DeWitt's original 1967 paper does present the canonical quantum gravity equation (later called the Wheeler-DeWitt equation) in a form that lacks an explicit external time parameter, but this is a consequence of the timeless nature of general relativistic constraints, not an omission. The equation is a constraint equation (H|Ψ⟩ = 0) derived from the Hamiltonian constraint of general relativity.
- Wheeler, J.A. (1968). 'Superspace and the Nature of Quantum Geometrodynamics.' Batelle Rencontres.
Wheeler's contributions framed the equation within superspace, reinforcing that the absence of an external time variable is a deep feature of quantum gravity — the 'problem of time' — not a simple oversight. Time is not absent by accident but because the Hamiltonian constraint eliminates it.
- Isham, C.J. (1993). 'Canonical Quantum Gravity and the Problem of Time.' NATO ASI Series, arXiv:gr-qc/9210011.
Isham's comprehensive review confirms that the Wheeler-DeWitt equation contains no explicit time variable, but clarifies this is a structural feature of diffeomorphism-invariant theories, known as the 'problem of time,' rather than a flaw or arbitrary choice in the 1967 formulation.
- Kiefer, C. (2007). 'Quantum Gravity.' Oxford University Press, 2nd edition.
Kiefer explains that the Wheeler-DeWitt equation is timeless because it emerges from the Hamiltonian constraint H=0 of general relativity. The year 1967 for DeWitt's paper is correct, and the absence of time is accurate, but framing it as simply 'containing no time variable' understates the profound theoretical reasons behind this feature.
- Stanford Encyclopedia of Philosophy: Quantum Gravity
Confirms the 1967 date for DeWitt's paper and the timeless character of the Wheeler-DeWitt equation, while noting that the problem of time is one of the central conceptual challenges in quantum gravity, meaning the absence of time is a deep issue, not merely a technical detail.