[ The idea was devised by John Wheeler in 1955.]
Background
With an incomplete theory of quantum gravity, it is impossible to be certain what spacetime looks like at small scales. However, there is no definitive reason that spacetime needs to be fundamentally smooth. It is possible that instead, in a quantum theory of gravity, spacetime would consist of many small, ever-changing regions in which space and time are not definite, but fluctuate in a foam-like manner.[ See Derek Leinweber's QCD animations of spacetime foam, as exhibited in Wilczek lecture.]
John Wheeler suggested that the uncertainty principle might imply that over sufficiently small distances and sufficiently brief intervals of time, the "very geometry of spacetime fluctuates".
Experimental results
The experimental proof of the Casimir effect, which is possibly caused by Virtual particle, is strong evidence for the existence of virtual particles. The g-2 experiment, which predicts the strength of Magnet formed by Muon and Electron, also supports their existence.[ Quantum Foam, Don Lincoln, Fermilab, 2014-10-24.]
In 2005, during observations of gamma ray arriving from the blazar Markarian 501, MAGIC (Major Atmospheric Gamma-ray Imaging Cherenkov) telescopes detected that some of the Photon at different Energy level arrived at different times, suggesting that some of the photons had moved more slowly and thus were in violation of special relativity's notion that the speed of light is constant, a discrepancy which could be explained by the irregularity of quantum foam.
Other experiments involving the polarization of light from distant Gamma-ray burst have also produced contradictory results.[ Integral challenges physics beyond Einstein / Space Science / Our Activities / ESA.] More Earth-based experiments are ongoing
Constraints on the size of quantum fluctuations
The fluctuations characteristic of a spacetime foam would be expected to occur on a length scale on the order of the Planck length (≈ 10−35 m),
Photons should be slowed by quantum foam, with the rate depending on the wavelength of the photons. This would violate Lorentz invariance. But observations of radiation from nearby by Floyd Stecker of NASA Goddard Space Flight Center failed to find evidence of violation of Lorentz invariance.
A foamy spacetime also sets limits on the accuracy with which distances can be measured because photons should diffuse randomly through a spacetime foam, similar to light diffusing by passing through fog. This should cause the image quality of very distant objects observed through telescopes to degrade. X-ray and gamma-ray observations of quasars using NASA's Chandra X-ray Observatory, the Fermi Gamma-ray Space Telescope and ground-based gamma-ray observations from the VERITAS (VERITAS) showed no detectable degradation at the farthest observed distances, implying that spacetime is smooth at least down to distances 1000 times smaller than the nucleus of a hydrogen atom,
Relation to other theories
The vacuum fluctuations provide vacuum with a non-zero energy known as vacuum energy.
Spin foam theory is a modern attempt to make Wheeler's idea quantitative.
An alternative to Spin foam is the self-consistent theoretical framework of Gaussian Quantum Foam, described separately below.
Gaussian Quantum Foam
The theoretical framework of Gaussian Quantum Foam
In this framework, the ADM formalism field in its Gaussian gauge is identified as the geometric remnant of the quantum imprint of vacuum fluctuations.
The model provides a formulation in which Quantum Foam as a self-gravitating entity — and hence a representation of the Geon — is defined as the distributional limit of a sequence of Homotopy, globally hyperbolic spacetimes, constructed from Gaussian functions converging in the sense of distributions.
An intrinsic feature of the Gaussian Quantum Foam framework is that it is singularity-free and formulated entirely within a non-linear distribution algebra. A distributional geometry, allowing a broad class of classical, globally hyperbolic spacetimes to emerge from quantum fluctuations without introducing an Inflaton or modifying Einstein’s equations.
The quantisation proceeds through a Gelfand triple structure, promoting the shift vector to an operator-valued distribution consistent with the Wightman axioms. In this formulation, and thus in a process driven by quantum displacement of the vacuum, the expectation values of geometric scalars in Coherent state coincide with their classical counterparts, thereby recovering classical spacetime in the correspondence limit in accordance with the correspondence principle.
The smooth and regular time function defining the Foliation—through its level surfaces of each spacetime element in the sequence—satisfies an Eikonal equation.
In the distributional geometry of Gaussian Quantum Foam, these Level set converge to ‘‘characteristic surfaces’’.
The associated ADM formalism, which arises naturally in the foliation of any globally hyperbolic spacetime and, in the quantum-gravitational context, within the ADM formalism of general relativity, not only determines the dynamical evolution of the hypersurfaces in quantum foam, but also guarantees distributional integrity while acting as an effective Refractive index in the eikonal equation for the global time function.
Within this framework, a non-linear Wave equation governs the dynamics of the shift vector field inside a Renormalization distributional algebra closed under addition, multiplication, and differentiation.
This partial differential equation in distributional geometry reveals sharply localised curvature impulses associated with vacuum displacement, interpreted as the origin of inflationary expansion.
Singularity Theorems in Quantum Foam
Two central singularity theorems further characterise the Gaussian Quantum Foam geometry:
Projected Curvature Structure and the Strong Energy Condition Theorem – The projected scalar Ricci curvature is non-negative at the singular support and converges to a well-defined, positive distribution involving both the Dirac delta function and its second derivative.
Locally, and for finite values of the sequence index, the curvature scalar projection changes sign across open subsets, signalling controlled local violations of the strong energy condition.
These are not pathologies but manifestations of the dipolar structure of vacuum fluctuations, which — under the non-linear dynamics of the shift vector — drive inflationary displacement and enable the emergence of classical spacetime at macroscopic scales.
Null Expansion Theorem – In the distributional limit, both the extrinsic-curvature terms and the mean curvature integrate to zero.
Consequently, the total expansion of null congruences vanishes at the singular support, rendering spacetime effectively frozen at that point.
However, for finite values of the sequence index — when spacetime evolves away from its frozen configuration and the shift vector is driven into oscillatory motion by the curvature impulse described by the wave equation — open regions appear in which both the ingoing and outgoing null expansions are strictly negative.
This implies the existence of transient Trapped surface during the inflationary phase, acting as thermodynamic compression zones during reheating and signalling the transition from a coherent quantum-foam phase to the emergence of classical spacetime geometry.
Together, these results indicate that the singular support is not a breakdown of predictability.
Instead, it marks the precise location of vacuum displacement — a sharply supported curvature impulse that initiates the emergence of time.
This reinterpretation honours the legacy of Roger Penrose and Stephen Hawking, whose classical singularity theorems demonstrated the inevitability of curvature accumulation under classical assumptions,
See also
Notes
