Local Scale Invariance in Quantum Theory: Experimental Predictions

• URL: http://arxiv.org/abs/2601.07883v1
• Date: Mon, 12 Jan 2026 00:23:49 GMT
• Title: Local Scale Invariance in Quantum Theory: Experimental Predictions
• Authors: Indrajit Sen, Matthew Leifer,
• Abstract summary: We explore the experimental predictions of the local scale invariant, non-Hermitian pilot-wave (de Broglie-Bohm) formulation of quantum theory introduced in arXiv:2601.03567.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We explore the experimental predictions of the local scale invariant, non-Hermitian pilot-wave (de Broglie-Bohm) formulation of quantum theory introduced in arXiv:2601.03567. We use Weyl's definition of gravitational radius of charge to obtain the fine-structure constant for non-integrable scale effects $α_S$. The minuteness of $α_S$ relative to $α$ ($α_S/α\sim 10^{-21}$) effectively hides the effects in usual quantum experiments. In an Aharonov-Bohm double-slit experiment, the theory predicts that the position probability density depends on which slit the particle trajectory crosses, due to a non-integrable scale induced by the magnetic flux. This experimental prediction can be realistically tested for an electrically neutral, heavy molecule with mass $m \sim 10^{-19} \text{g}$ at a $\sim 10^6 \text{ esu}$ flux regime. We analyse the Weyl-Einstein debate on the second-clock effect using the theory and show that spectral frequencies are history-independent. We thereby resolve Einstein's key objection against local scale invariance, and obtain two further experimental predictions. First, spectral intensities turn out to be history-dependent. Second, energy eigenvalues are modified by tiny imaginary corrections that modify spectral linewidths. We argue that the trajectory dependence of the probabilities renders our theory empirically distinguishable from other quantum formulations that do not use pilot-wave trajectories, or their mathematical equivalents, to derive experimental predictions.

Related papers

• Local Scale Invariance in Quantum Theory: A Non-Hermitian Pilot-Wave Formulation [0.0]
  We show that Weyl's abandoned idea of local scale invariance has a natural realization at the quantum level in pilot-wave theory.<n>We implement it for the Schrdinger, Pauli, and Dirac equations coupled to an external electromagnetic field.
  arXiv  Detail & Related papers  (2026-01-07T04:27:59Z)
• Experiment to test the incompleteness of quantum mechanics [45.88028371034407]
  We propose an experiment to test the incompleteness of the standard quantum formalism.<n>We show with simulations that the transmission densities in the standard interpretation and in the double solution interpretation give very different results.
  arXiv  Detail & Related papers  (2025-09-05T08:02:14Z)
• Solitons, chaos, and quantum phenomena: a deterministic approach to the Schrödinger equation [0.0]
  We show that the Schr"odinger equation describes the ensemble mean dynamics of solitons in a Galilean invariant field theory.<n>We conclude by a discussion of how our theory does not present statistical independence between measurement and experiment outcome.
  arXiv  Detail & Related papers  (2025-07-30T17:43:06Z)
• Real-Time Scattering in Ising Field Theory using Matrix Product States [0.17476232824732776]
  We study scattering in Ising Field Theory using matrix product states and the time-dependent variational principle. We find that the high energy behavior of the two-to-two particle scattering probability in IFT is consistent with a conjecture of Zamolodchikov.
  arXiv  Detail & Related papers  (2024-11-20T19:00:01Z)
• Testing trajectory-based determinism via time probability distributions [41.99844472131922]
  We introduce a prescription for constructing an arrival-time probability distribution within generic trajectory-equipped theories.<n>We derive a conditional probability distribution that is unreachable by quantum mechanics.<n>Our results can be tested experimentally, thereby assessing the validity of trajectory-based determinism.
  arXiv  Detail & Related papers  (2024-04-15T11:36:38Z)
• Ultracold Neutrons in the Low Curvature Limit: Remarks on the post-Newtonian effects [49.1574468325115]
  We apply a perturbative scheme to derive the non-relativistic Schr"odinger equation in curved spacetime. We calculate the next-to-leading order corrections to the neutron's energy spectrum. While the current precision for observations of ultracold neutrons may not yet enable to probe them, they could still be relevant in the future or in alternative circumstances.
  arXiv  Detail & Related papers  (2023-12-30T16:45:56Z)
• Real-time dynamics of false vacuum decay [49.1574468325115]
  We investigate false vacuum decay of a relativistic scalar field in the metastable minimum of an asymmetric double-well potential. We employ the non-perturbative framework of the two-particle irreducible (2PI) quantum effective action at next-to-leading order in a large-N expansion.
  arXiv  Detail & Related papers  (2023-10-06T12:44:48Z)
• Dispersive readout of molecular spin qudits [68.8204255655161]
  We study the physics of a magnetic molecule described by a "giant" spin with multiple $d > 2$ spin states. We derive an expression for the output modes in the dispersive regime of operation. We find that the measurement of the cavity transmission allows to uniquely determine the spin state of the qudits.
  arXiv  Detail & Related papers  (2021-09-29T18:00:09Z)
• Effective Theory for the Measurement-Induced Phase Transition of Dirac Fermions [0.0]
  A wave function exposed to measurements undergoes pure state dynamics. For many-particle systems, the competition of these different elements of dynamics can give rise to a scenario similar to quantum phase transitions. A key finding is that this field theory decouples into one set of degrees of freedom that heats up indefinitely.
  arXiv  Detail & Related papers  (2021-02-16T19:00:00Z)
• Probing eigenstate thermalization in quantum simulators via fluctuation-dissipation relations [77.34726150561087]
  The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems. Here, we propose a theory-independent route to probe the full ETH in quantum simulators by observing the emergence of fluctuation-dissipation relations. Our work presents a theory-independent way to characterize thermalization in quantum simulators and paves the way to quantum simulate condensed matter pump-probe experiments.
  arXiv  Detail & Related papers  (2020-07-20T18:00:02Z)
• Probing the Universality of Topological Defect Formation in a Quantum Annealer: Kibble-Zurek Mechanism and Beyond [46.39654665163597]
  We report on experimental tests of topological defect formation via the one-dimensional transverse-field Ising model. We find that the quantum simulator results can indeed be explained by the KZM for open-system quantum dynamics with phase-flip errors. This implies that the theoretical predictions of the generalized KZM theory, which assumes isolation from the environment, applies beyond its original scope to an open system.
  arXiv  Detail & Related papers  (2020-01-31T02:55:35Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.