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arXiv:2007.08431 · Quantum

An experiment to test the discreteness of time

Pierre Martin-Dussaud, Andrea Di Biagio, Marios Christodoulou

Published Oct 6, 2022• 8 citations
arXivHTMLPDF

Abstract

Abstract Time at the Planck scale (∼10−44s) is an unexplored physical regime. It is widely believed that probing Planck time will remain for long an impossible task. Yet, we propose an experiment to test the discreteness of time at the Planck scale and show that it is not far removed from current technological capabilities.
DOI
10.22331/q-2022-10-06-826

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By proposing a paradox between the impossibility of superluminal signal transfer and the normalization condition of wavefunctions, we predict that when a change happens to the conditions that determining the status of a quantum system, the system will show no response to this change at all, until after a certain time interval. Otherwise either special relativity or quantum mechanics will be violated. As a consequence, no physical process can actually happen within Planck time. Therefore time is discrete, with Planck time being the smallest unit. More intriguingly, systems with a larger size and a slower speed will have a larger unit of time. Unlike many other interpretations of the discreteness of time, our proof can be tested, at less partly, by experiments. Our result also sets a limit on the speed of computers, and gives instruction to the search of quantum gravity theories.
If the structure of spacetime is discrete, then Lorentz symmetry should only be an approximation, valid at long length scales. At finite lattice spacings there will be small corrections to the Dirac evolution. In particular, the lattice structure will be reflected in a modification of the free-particle dispersion relation. We show that these can produce a surprisingly large phase shift between the two arms of a nonparallel interferometer. This method could be employed to test any model that predicts a direction-dependent dispersion relation. Here, we calculate the size of this phase shift for a particular model, the three-dimensional quantum walk on the body-centered cubic lattice, which has been shown to give rise to the Dirac equation in the continuum limit. Though the details of this model will affect the size of the shift, its magnitude is set largely by dimensional analysis, so there is reason to believe that other models would yield similar results. We find that, with current technology, a modest-sized neutron interferometer could detect lattice spacings as small as ${10}^{\ensuremath{-}31}\text{ }\text{ }\mathrm{m}$, 13 orders of magnitude smaller than the scale probed by the LHC. A suitably scaled-up experiment could possibly detect lattice spacings even at the Planck scale.
FINDING: Tabletop quantum-gravity tests probe Planck-scale discreteness via matter-wave interferometry and optomechanical superposition, not yet yielding a confirmed equation but constraining collapse models and graviton signatures. | MATH: Planck length lP=ℏG/c3≈1.616×10−35 ml_P = \sqrt{\hbar G/c^3} \approx 1.616\times10^{-35}\,\text{m}lP​=ℏG/c3​≈1.616×10−35m; Planck mass mP=ℏc/G≈2.176×10−8 kgm_P = \sqrt{\hbar c/G} \approx 2.176\times10^{-8}\,\text{kg}mP​=ℏc/G​≈2.176×10−8kg; decoherence rate for gravitationally-induced collapse (Penrose–Diosi): Γ∼ΔEG/ℏ\Gamma \sim \Delta E_G/\hbarΓ∼ΔEG​/ℏ, where ΔEG=G2∫ ⁣ ⁣∫[ρ1(r)−ρ2(r)][ρ1(r′)−ρ2(r′)]∣r−r′∣d3r d3r′\Delta E_G = \frac{G}{2}\int\!\!\int \frac{[\rho_1(\mathbf{r})-\rho_2(\mathbf{r})][\rho_1(\mathbf{r}')-\rho_2(\mathbf{r}')]}{|\mathbf{r}-\mathbf{r}'|}d^3r\,d^3r'ΔEG​=2G​∫∫∣r−r′∣[ρ1​(r)−ρ2​(r)][ρ1​(r′)−ρ2​(r′)]​d3rd3r′; Folman T³ experiment: cubic scaling of phase shift Δϕ∝T3\Delta\phi \propto T^3Δϕ∝T3 (where TTT is free-fall time), testing equivalence principle at quantum level. | CONNECTION: The ratio lP2/λC2l_P^2/\lambda_C^2lP2​/λC2​ (Planck length squared over Compton wavelength squared) appears in gravitationally-induced entanglement rates — nume Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Abstract We develop and apply the Yugen wavefunction framework, a phase-geometric reformulation of quantum theory in which the vacuum is treated as an active medium with intrinsic stiffness set by the Planck scale. In this approach, physical fields and particles emerge from internal phase geometry rather than from fundamental point-like interactions. By identifying the amplitude of the Yugen wavefunction with the Planck energy, the Planck scale becomes a physical parameter governing vacuum rigidity and nonlinear phase response. We present explicit numerical predictions across atomic, particle, and mesoscopic regimes. In the atomic sector, the framework predicts small but systematic nonlinear deviations in isotope-shift spectroscopy, arising from coherent vacuum phase effects and consistent with recent high-precision datasets. In the neutrino sector, neutrino masses emerge naturally from localized topological phase interference, yielding the observed mass scale without introducing additional heavy fields. We further address the quantum–classical transition by deriving a nonlinear phase-induced decoherence mechanism for macroscopic objects. The resulting mass- and size-dependent decoherence times place mesoscopic systems near the picogram scale at the threshold of sustained quantum superpositions, a regime accessible to current optomechanical experiments. These results suggest that precision spectroscopy, neutrino phenomenology, and mesoscopic quantum tests probe a common underlying phase structure of the vacuum. The Yugen wavefunction thus provides a unified and experimentally falsifiable framework linking quantum fields, particle properties, and the emergence of classicality.