A response to Pikovski et al. (Phys. Rev. Lett., 2026), who predict that a trapped ion in a motional superposition will exhibit measurable clock-transition blurring, interpreted as evidence that time itself exists in quantum superposition. We show that the identical observable arises in a framework where the tick rate is set by the local amplitude of a decaying background field (Zuhars, The Self-Interacting Universe, 2026). The ion's motional wavepacket samples different background amplitudes at different spatial positions, producing the same phase spread without requiring time to be a quantum observable. The two interpretations make a distinguishable experimental prediction: varying the trap frequency while holding the quantum state fixed produces different scaling in the two frameworks. We identify the specific signature and propose the test.
A response to Pikovski et al. (Phys. Rev. Lett., 2026), who predict that a trapped ion in a motional superposition will exhibit measurable clock-transition blurring, interpreted as evidence that time itself exists in quantum superposition. We show that the identical observable arises in a framework where the tick rate is set by the local amplitude of a decaying background field (Zuhars, The Self-Interacting Universe, 2026). The ion's motional wavepacket samples different background amplitudes at different spatial positions, producing the same phase spread without requiring time to be a quantum observable. The two interpretations make a distinguishable experimental prediction: varying the trap frequency while holding the quantum state fixed produces different scaling in the two frameworks. We identify the specific signature and propose the test.
On 20 April 2026, Sorci, Foo, Leibfried, Sanner, and Pikovski (Phys. Rev. Lett.) proposed that next-generation optical ion clocks with squeezed-state preparation can probe whether proper time exists in quantum superposition — a single clock ticking faster and slower at once. Their work establishes the protocol; the laboratory measurement is forthcoming. That prospective window permits a genuine pre-registered prediction. Fibonacci Causal Loop Theory (FCLT) holds that any stable system governed by depth-2 necessity recursion, S(n)=S(n−1)+S(n−2), is driven to the golden ratio φ=(1+√5)/2 — the unique algebraically forced attractor of its characteristic equation x²−x−1=0. We advance the hypothesis that proper-time superposition is such a system, the two temporal branches playing the role of the two prior states, so that the ratio of fast- to slow-ticking amplitudes approaches φ upon decoherence. From this we obtain one parameter-free, falsifiable prediction — t₊/t₋ → φ ≈ 1.61803, with δ = |R−φ|/φ and falsification at δ > 0.10 — logged under Protocol V3.1 prior to experimental resolution. We claim no confirmation: the prediction is offered as not-yet-tested, to be adjudicated by the Stevens/NIST program. A second, independent signature (φ-structured fringe spacing in the squeezed regime) provides an internal consistency check.
Optical clocks based on atoms and ions probe relativistic effects with unprecedented sensitivity. They resolve time dilation due to atom motion or different positions in the gravitational potential through frequency shifts. However, all measurements of time dilation so far can be explained effectively as the result of dynamics with respect to a classical proper time parameter. Here we show that atomic clocks can probe effects where a classical description of the proper time dynamics is insufficient as superpositions of proper time emerge. We apply a Hamiltonian formalism to derive time dilation effects in harmonically trapped clock atoms and show how second-order Doppler shifts due to the vacuum energy, squeezing, and quantum corrections to the dynamics arise. We also demonstrate that time-dilation-induced entanglement between motion and clock evolution can become observable in state-of-the-art clocks when the motion of the atoms is strongly squeezed, realizing proper time interferometry. Our results show that experiments with trapped ion clocks are within reach of probing relativistic evolution of clocks for which a quantum description of proper time becomes necessary.
Optical ion clocks now approach a regime in which relativistic time dilation is no longer exhausted by a classical proper-time parameter read by a quantum sensor. Recent work by Sorci, Foo, Leibfried, Sanner, and Pikovski shows that harmonically trapped optical clock atoms can exhibit vacuum-induced, squeezing-induced, and intrinsically quantum corrections to the second-order Doppler shift, with time-dilation-induced entanglement between motional and internal clock degrees of freedom becoming observable in strongly squeezed trapped-ion motion. This paper develops the significance of that result within CPT-Coherence Theory. The central principle of CPT-Coherence is Onto-Physical Entanglement: what a system is cannot be separated from how it is allowed to remain coherent under admissible transformation. In the clock setting, this principle appears in branch-visible form. The internal clock transition is not merely an isolated label transported through spacetime; its phase identity is dynamically bound to the motional state through the relativistic proper-time operator. Proper-time interferometry therefore supplies a laboratory instance of a more general structural rule: physical identity is stabilized only through the admissible evolution channels by which it can be read out. The paper distinguishes the relativistic proper time of the ion-clock experiment from the coherence-depth coordinate of CPT-Coherence. The former is a branch-visible observable associated with worldline evolution; the latter is a structural coordinate organizing parent-boundary admissibility, trace access, Schur response, and stable observable descent. Their relation is not identity but projection: quantum proper-time readout provides an experimentally precise interface through which branch observers can test how internal identity, motion, coherence, and record formation remain coupled. We formulate a CPT-Coherence clock-readout sector in which a quantum clock is represented by a triple consisting of an internal identity generator, an external motion algebra, and a proper-time readout operator. The Sorci-Foo-Leibfried-Sanner-Pikovski protocol is then interpreted as a high-precision realization of an OPE readout channel: classical time dilation corresponds to scalar proper-time averaging; vacuum and squeezing shifts correspond to state-dependent branch corrections; and visibility loss corresponds to trace-visible entanglement between identity and admissible motion. This establishes optical ion clocks as a natural experimental grammar for CPT-Coherence, while CPT-Coherence supplies a unifying interpretation of why such experiments probe not simply clock rates, but the inseparability of physical being and physical evolution. Scope note: the quantitative predictions below coincide with those of standard relativistic quantum clock theory; CPT-Coherence contributes an interpretation and vocabulary, together with an explicit falsification target for that interpretation.
We show how a single trapped ion may be used to test a variety of important physical models realized as time-dependent harmonic oscillators. The ion itself functions as its own motional detector through laser-induced electronic transitions. Alsing et al., [Phys. Rev. Lett. 94, 220401 (2005)] proposed that an exponentially decaying trap frequency could be used to simulate (thermal) Gibbons-Hawking radiation in an expanding universe, but the Hamiltonian used was incorrect. We apply our general solution to this experimental proposal, correcting the result for a single ion and showing that while the actual spectrum is different from the Gibbons-Hawking case, it nevertheless shares an important experimental signature with this result.
Quantum mechanics requires the time evolution of the wave function to be linear. While this feature has been associated with the preservation of causality, a consistent causal nonlinear theory was recently developed. Interestingly, this theory is unavoidably sensitive to the full physical spread of the wave function, rendering existing experimental tests for nonlinearities inapplicable. Here, using well-controlled motional superpositions of a trapped ion, we set a stringent limit of 5.4×10^{-12} on the magnitude of the unitless scaling factor ε[over ˜]_{γ} for the predicted causal nonlinear perturbation.
Measurements of internal energy states of atomic ions confined in traps can be used to illustrate fundamental properties of quantum systems, because long relaxation times and observation times are available. In the experiments described here, a single ion or a few identical ions were prepared in well-defined superpositions of two internal energy eigenstates. The populations of the energy levels were then measured. For an individual ion, the outcome of the measurement is uncertain, unless the amplitude for one of the two eigenstates is zero, and is completely uncertain when the magnitudes of the two amplitudes are equal. In one experiment, a single 199Hg+ ion, confined in a linear rf trap, was prepared in various superpositions of two hyperfine states. In another experiment, groups of 9Be+ ions, ranging in size from about 5 to about 400 ions, were confined in a Penning trap and prepared in various superposition states. The measured population fluctuations were greater when the state amplitudes were equal than when one of the amplitudes was nearly zero, in agreement with the predictions of quantum mechanics. These fluctuations, which we call quantum projection noise, are the fundamental source of noise for population measurements with a fixed number of atoms. These fluctuations are of practical importance, since they contribute to the errors of atomic frequency standards.