Ghost Frequency-Time Combs Without Ghosts A CPM Reinterpretation of Shih (2026): Rotating Dipole Phase Synchrony, Mode Beating and the Absence of Vacuum Agents
Shih (2026) reported the observation of ghost frequency-time combs (GFC, 50% contrast) from continuous-wave laser beams, and theoretically predicted quantum ghost frequency-time combs (QGFC, 100% contrast) from entangled coherent states, concluding that classical statistical theory cannot explain the phenomena and that quantum coherence theory — specifically non-local superposition of probability amplitudes — is required. This paper demonstrates that the GFC and QGFC are fully consistent with the Conjugate Photonic Model (CPM) without invoking either vacuum agents or non-local wave-function collapse. In the CPM, each photon is a rotating dipole with internal phase . The GFC emerges from the local beating between the internal phases of randomly paired dipoles across the two detectors — the same mechanism responsible for photonic trimers and mode-locking. The QGFC emerges from the phase synchrony imposed by the energy conservation condition — the macroscopic analogue of the Pi-Cosmic Generating Function . The Path provides fixed propagation conditions (, , ) with no internal structure to act as vacuum agent. The "non-locality" of GFC is resolved: the correlation is local in the phase of each dipole, propagated deterministically through the closed Energy–Path system to the two detectors.
Shih (2026) reported the observation of ghost frequency-time combs (GFC, 50% contrast) from continuous-wave laser beams, and theoretically predicted quantum ghost frequency-time combs (QGFC, 100% contrast) from entangled coherent states, concluding that classical statistical theory cannot explain the phenomena and that quantum coherence theory — specifically non-local superposition of probability amplitudes — is required. This paper demonstrates that the GFC and QGFC are fully consistent with the Conjugate Photonic Model (CPM) without invoking either vacuum agents or non-local wave-function collapse. In the CPM, each photon is a rotating dipole with internal phase . The GFC emerges from the local beating between the internal phases of randomly paired dipoles across the two detectors — the same mechanism responsible for photonic trimers and mode-locking. The QGFC emerges from the phase synchrony imposed by the energy conservation condition — the macroscopic analogue of the Pi-Cosmic Generating Function . The Path provides fixed propagation conditions (, , ) with no internal structure to act as vacuum agent. The "non-locality" of GFC is resolved: the correlation is local in the phase of each dipole, propagated deterministically through the closed Energy–Path system to the two detectors.
Introduction: Proceeding from the recently discovered ghost frequency-time comb (GFC) of 50% contrast found through intensity-intensity correlation measurements of multi-cavity-mode continues-wave (CW) laser beams, this report further extends this analysis to a novel type of entangled coherent state, or entangled laser beams, capable of producing GFC of 100% contrast, described as the “quantum ghost frequency-time comb” (QGFC). Despite being in continuous-wave operation, both classical and entangled laser beams produce sharp periodic comb-like correlation functions. Why is there a “nonlocal” and periodic correlation between the two distant locally and independently measured CW laser beams? Can the GFC and QGFC phenomena be interpreted as correlations between statistical intensity fluctuations? For the QGFC specifically, this question becomes particularly acute: How do “zero-coincidences” occur in the measurement of CW laser beams? Why do “zero-coincidences” occur periodically? This report address these questions. Although both GFC and QGFC are observed, or more precisely, calculated from locally measured intensity fluctuations, the 50% contrast GFC is caused by an incoherent superposition of quantum probability amplitudes of all possible randomly paired cavity modes, while the 100% contrast QGFC is caused by a coherent superposition of quantum probability amplitudes of all possible entangled pairs of cavity-modes, where these amplitudes contribute to a nonlocal joint photodetection event. Experimental observations of GFC and QGFC may finally resolve the long-standing debate between classical statistics and quantum coherence. Besides their fundamental significance, bright GFC and QGFC make important contributions to the fields of nonlocal positioning, time transfer and precision spectroscopy. High-brightness entangled laser beams may also open up new applications that might not be realizable by using entangled photon pairs at the single-photon level.
How macroscopic definite outcomes and nonlocal correlations emerge from entangled superpositions across spacelike-separated regions without superluminal action or {\it ad hoc} wavefunction collapse remains a defining open question in the foundations of quantum mechanics. Here, we resolve this century-long paradox within \textit{linear} relativistic quantum electrodynamics by developing an open-system and measurement-defined framework realized in dual, spacelike-separated nonlinear crystals driven synchronously by a multi-mode optical frequency comb and seeded by an ultra-narrow coherent laser. Expanding the transverse electromagnetic vector potential into discrete single-photon frequency-comb supermodes, we show that tracing out the unmeasured continuous-wave idler field yields an exact spatial dephasing Lindblad master equation whose decoherence rate is governed by the non-orthogonal state overlap of single-photon-added coherent states. Connecting this open-system map to free-vector-space quotient measurement theory, we demonstrate that single-particle interference arises from the geometric projection of the composite state onto detector-defined conditional cosets rather than remote collapse, establishing strict operational equivalence across pump, seed, and signal phase scans. The resulting wave-particle-entanglement triality equality P2+E2+V2=1 is saturated across the complete parameter space, while the atomic-clock-referenced comb structure anchors continuous-variable time-frequency displacement stabilizers directly at the hardware layer. Our work unifies induced coherence, Bohr's complementarity, and quotient measurement theory, providing a microscopic pathway toward fault-tolerant bosonic quantum information processing.
We report an experimental demonstration of a time transfer and distant clock synchronization scheme based on what we have labeled as a ghost frequency comb, observed from the nonlocal correlation measurements of a laser beam. Unlike a conventional frequency comb, the laser beam used in this work does not consist of a pulse train but instead it is in a continuous-wave operation. The laser beam, consisting of half a million longitudinal cavity modes from a fiber ring laser, is split into two beams, each sent to a distant observer. In their local measurements, both observers observe constant intensity with no pulse structure present. Surprisingly, a pulse train of comb-like, ultra-narrow peaks is observed from their nonlocal correlation function measurement. This observation makes an important contribution to the field of precision spectroscopy, as we show in optical correlation-based nonlocal timing and positioning.
The recent experiment by Angulo, Steinberg et al. (2025) reported the observation of negative weak values for the time atoms spend in the excited state as a photon is transmitted through a cold rubidium gas. Within standard quantum mechanics, this result is interpreted as evidence that the photon must possess real longitudinal spatial extension — a "front" and a "tail" whose phase interference drives the atomic clock backwards. This paper demonstrates that the result admits a complete and causally transparent reinterpretation within the Conjugate Photonic Model (CPM). In the CPM, the photon is a compact rotating electromagnetic dipole — a photonic disc — with along the propagation axis. Atomic matter is itself composed of Hopf-soliton EM structures (electron hopfions) organised by nuclear field confinement. The passage of a photonic disc through a material medium is therefore not the interaction of a wave-packet with passive atoms, but the coupling of one rotating EM field structure with another. The measured "dwell time" is reinterpreted as the integral of the phase displacement of the electron hopfion induced by the passing disc — a displacement that can be negative when the disc arrives out of phase with the hopfion's natural resonance cycle, producing a sub-threshold oscillation that returns to equilibrium without absorption. No longitudinal photon extension is required, no causal paradox arises, and no ontologically negative time exists. The apparent paradox is an artefact of the standard model's assignment of spatial extension to the photon's wavelength — an assignment the CPM identifies as an unwarranted inference from the rotating path geometry of the photonic disc.
The two-photon temporal coincidence detection amplitude obeys a pair of equations identical to those of classical partially coherent plane-wave pulses propagating in linearly dispersive media. These equations are also the same as the paraxial Wolf equations, for both the two-photon spatial probability amplitude and the cross-spectral density function. Therefore, a fourfold analogy between space and time, as well as between quantum entanglement and partial coherence, arises. In accordance to this, we predict nonlocal interference structures in a fourth-order interferometric configuration with classical partially coherent pulses under the assumption of Gaussian statistics. As an example, we present the classical temporal counterpart of the ghost diffraction phenomenon. Our work suggests that some time-domain entanglement phenomena that hitherto were considered as uniquely quantum can be mimicked by conventional partially coherent light pulses.
Ghost imaging is a novel non-conventional technique allowing to generate high resolution images by correlating the intensity of two light beams, neither of which independently contains sufficient information about the spatial distribution and shape of the object. The first demonstration of ghost imaging used light in double photon state, obtained from spontaneous parametric down-conversion. Owing to the entanglement of the source photons, the proposed theory required quantum descriptions for both the optical source and its photo-detection statistics1. However, subsequent experimental and theoretical considerations2,3 demonstrated that ghost imaging can be performed also with thermalized light, utilizing either CCD detector arrays or photon-counting detectors, thus admitting to a semi-classical description, employing classical fields and shot-noise limited detectors. This has generated increasing interest4-6 in establishing a unifying theory that characterizes the fundamental physics of ghost imaging and defines the boundary between classical and quantum domains. In this view, we exploited recent progress obtained through the application of Fourier Transform Techniques to demonstrate ghost imaging in the frequency domain, in order to measure a continuous spectrum by using a highly brilliant and coherent monochromatic source. In particular, we demonstrate the application of this ghost imaging technique to broadband spectroscopic measurements by means of interaction free photon detection. The experimental apparatus and the collected data are described in a dedicated work7. In this paper, we consider the theoretical aspects underlying the proposed Spectroscopic technique. In particular, two alternative theoretical models are presented. In one case, a statistical approach (semi-classical) is applied, where the states of the sampling beam are considered, whereas in the other case a pure quantum treatment is carried on, by describing the interaction of vacuum states generated by photon conversion processes. Both theoretical models, though carried on by means of a complementary formalism, lead to equivalent results and offer a physical interpretation of the collected experimental data. The application of these results offer novel perspectives for remote sensing in low light conditions, or in spectral regions where sensitive detectors are lacking.