A First Bound on the Moffat Energy and Thorium--229 Clock as a Probe of the Nonlocal Time-Energy Structure

arXiv:2607.18333v1 Announce Type: new Abstract: The new Thorium--229 nuclear clocks give us a new laboratory system in which to test if modification of the Time-Energy uncertainty principle is correct. In this paper we derive the nonlocal Time-Energy uncertainty principle and then apply the published $^{229}$Th nuclear clock data as a first probe of the nonlocality scale $E_M$. We note that since these experiments were not designed to test nonlocal quantum field theory the constraints are interpreted as motivating bounds and not definitive exclusions. By using the direct clock-energy channel, we find conservative lower bounds on $E_M$ at the tens of MeV scale, with optimistic present-data estimates reaching the hundred MeV scale. Including the known nuclear sensitivity enhancement of the $^{229}$Th transition gives us stronger model dependent bounds in the GeV range, while nuclear-scale reference-energy scenarios can reach the TeV range. The conclusion we draw from this is that nuclear clocks already provide an experimental route from nonlocal time--energy uncertainty to measurable laboratory bounds on non-Planckian nonlocality.

Abstract:The new Thorium--229 nuclear clocks give us a new laboratory system in which to test if modification of the Time-Energy uncertainty principle is correct. In this paper we derive the nonlocal Time-Energy uncertainty principle and then apply the published $^{229}$Th nuclear clock data as a first probe of the nonlocality scale $E_M$. We note that since these experiments were not designed to test nonlocal quantum field theory the constraints are interpreted as motivating bounds and not definitive exclusions. By using the direct clock-energy channel, we find conservative lower bounds on $E_M$ at the tens of MeV scale, with optimistic present-data estimates reaching the hundred MeV scale. Including the known nuclear sensitivity enhancement of the $^{229}$Th transition gives us stronger model dependent bounds in the GeV range, while nuclear-scale reference-energy scenarios can reach the TeV range. The conclusion we draw from this is that nuclear clocks already provide an experimental route from nonlocal time--energy uncertainty to measurable laboratory bounds on non-Planckian nonlocality.

arXiv:2607.18333 [quant-ph]

(or arXiv:2607.18333v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.18333 arXiv-issued DOI via DataCite (pending registration)

From: John W. Moffat [view email] [v1] Sun, 19 Jul 2026 15:28:34 UTC (29 KB)

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A First Bound on the Moffat Energy and Thorium--229 Clock as a Probe of the Nonlocal Time-Energy Structure

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