A Chronovibrational Interpretation of Entanglement

A Chronovibrational Interpretation of Entanglement Paolo Giordana Santo Stefano al Mare, July 23, 2025 Premise: the critical aspects of entanglement Quantum entanglement is one of the most fascinating and at the same time mysterious phenomena of modern physics. When two particles interact, they may find themselves in a joint state described by a global wave function ΨAB, such that the state of particle A cannot be described independently of the state of particle B. A typical example is a pair of photons in an entangled polarization state, which can be expressed as: ΨAB =1 √2(|H⟩A|V⟩B+|V⟩A|H⟩B), where |H⟩and |V⟩denote horizontal and vertical polarizations, respectively. A measurement of the polarization on Ainstantaneously determines the result of the measurement on B, regardless of the distance separating the two photons. This behavior, which Einstein called “spooky action at a distance”, has been experimentally verified through tests of Bell’s inequalities and a long series of experiments conducted since the 1980s (including those of Aspect, Zeilinger, and Gisin), which demonstrated that the observed correlations are incompatible with local hidden variable theories. Standard interpretations and their critical issues Quantum mechanics provides an extremely accurate mathematical description of entanglement phenomena, but its conceptual interpretation remains open. The main theoretical readings attempt to clarify the meaning of this nonlocal correlation: 1. Copenhagen Interpretation: The wave function Ψ does not represent a physical reality, but our knowledge of the system. The so-called collapse of the wave function occurs at the moment of measurement, projecting the state into one of the eigenstates of the observable: Ψ→ˆ PiΨ, where ˆ Piis the projection operator onto the eigenstate |i⟩. 1 2. Many-Worlds Theory (Everett): In this view, the wave function never collapses; all possible outcomes of a measurement coexist in parallel branches of the universe. The global state always evolves according to Schr¨odinger’s equation: iℏ∂Ψ ∂t =ˆ HΨ, with ˆ Hthe Hamiltonian of the total system. 3. Nonlocal Hidden Variable Theories (Bohm): Bohm’s interpretation postulates that particles have well-defined positions and momenta, determined by a quantum potential Qthat depends on the wave function: Q=−ℏ2 2m∇2R R, with R=|Ψ|the modulus of the wave function. Entanglement would then be a manifestation of this global potential. 4. Objective Collapse Theories (GRW): These theories propose spontaneous collapses of the wave function, independent of observation, through probabilistic mechanisms that modify Schr¨odinger’s equation. The Ghirardi-Rimini-Weber (GRW) dynamics, for example, introduces a stochastic collapse term with frequency λ≈ 10−16 s−1. 5. Gravitational Approaches (Penrose): According to some hypotheses, significant differences in the mass distribution between superposed states could induce the collapse of the wave function. In this context, the characteristic collapse time is estimated as: τ∼ℏ ∆E, where ∆Eis the gravitational energy difference between the two states. Limits and open issues The interpretations mentioned offer interesting conceptual scenarios, but none provides a definitive explanation of the simultaneity and nonlocality implicit in the collapse of the wave function. Entanglement experiments have shown that correlations between spatially separated systems cannot be described by signals traveling at finite speed within classical spacetime. Today we know how to create entangled states (for example through nonlinear optical processes or atomic decays), but we still lack a universally shared theory that explains why such a nonlocal correlation exists. 2 1 Chronovibration and the Critical Function The theory of chronovibration1proposes that time is not a simple geometric coordinate, but emerges from a global quantum harmonic field ψ(t)2, common to all matter and energy, and subject to damping phenomena. This field describes the fundamental oscillation of the temporal metric, whose coherence is regulated by two main functions: a harmonization function Γharm(t) and a critical function fcrit(t). Harmonic field and temporal metric Physical time is described by a global wave function: ψ(t) = ⟨ˆ ψ(t)⟩, where ˆ ψ(t) is the quantum operator associated with the temporal field and ψ(t) its mean value, responsible for the observable metric properties. The harmonic deformation of the temporal metric is expressed by the normalized factor: Γharm(t) = exp"β τ∗Zt t0 f2 crit(τ)dτ#, where: •τ∗is the characteristic temporal scale (cosmic, coherence, or burst scale), •βis a dimensionless coupling constant regulating the strength of harmonization. This normalized definition ensures that the exponential argument remains dimensionless, and that Γharm can be consistently compared across different processes. The critical function The critical function fcrit(t) quantifies the intensity of the internal instabilities of the temporal metric: fcrit(t) = e−Λtcos(Ωt+ϕ) √1−e−2Λt, where: •Λ is the damping coefficient [s−1], •Ω is the angular oscillation frequency [rad s−1], •ϕis the initial phase, 1See https://zenodo.org/records/15240876 for a detailed treatment of the chronovibration theory. 2See https://zenodo.org/records/15306364 for further details on the quantum structure of this QCTT field. 3 •the denominator accounts for the gradual build-up of metric coherence as tincreases. For the entanglement context, Ω refers to the characteristic oscillation frequency associated with the optical or atomic transition defining the entangled pair (e.g. Ω = 2πc/λ for photons of wavelength λ), while Λ encodes the effective damping of the temporal field coherence. These parameters are setup-dependent, not universal constants, and their values must be distinguished from the cosmological or gravitational scales used in other chronovibrational applications. 2 Carrier wave and creation of a common critical function In the standard description of quantum mechanics, entanglement is represented as a superposition of states of the joint wave function ΨAB of two particles Aand B. For example, for a pair of photons with crossed polarization, the entangled state is expressed as: ΨAB =1 √2|H⟩A|V⟩B+|V⟩A|H⟩B, where the properties of Aand Bcan no longer be treated separately. However, quantum theory does not provide an explicit physical mechanism to explain how this instantaneous correlation arises. Within the framework of chronovibration, it is hypothesized that entanglement is the consequence of a simultaneous perturbation of the critical function fcrit(t), associated with the global temporal field ψ(t), which is common to all matter and energy. In this perspective, a physical process (for example, a pump photon or an energy source) acts as a carrier wave, imposing an identical modulation of fcrit(t) on both particles. Entanglement would therefore represent a condition of phase resonance within the universal temporal metric. In this context, the carrier wave does not propagate as a physical signal between particles, but operates as a synchronization mechanism that adjusts the temporal phases within the shared chronovibrational field. It aligns the oscillatory components of fcrit for both subsystems without requiring any exchange of energy or information in spacetime. Phase resonance in the critical function Each particle i=A, B is associated with a local critical function: f(i) crit(t) = Aie−Λtcos(Ωt+ϕi), where ϕiis the harmonic phase with respect to the global field ψ(t). Under normal conditions, fA crit(t) and fB crit(t) evolve with uncorrelated phases (ϕA=ϕB). 4 The carrier wave – for example generated by a parametric down-conversion process in photons – acts as a synchronization field that forces the alignment of phases: ∆ϕ(t) = |ϕA(t)−ϕB(t)| −→ 0, until a shared critical function is reached: fA crit(t)≃fB crit(t)≡fcrit(t). The convergence ∆ϕ→0 indicates that both particles evolve under the same temporal modulation, not that they exchange any real signal. This distinction preserves the nosignaling condition of quantum mechanics. Entanglement condition We define a chronovibrational condition of entanglement as: CAB(t) = DfA crit(t)fB crit(t)E q⟨fA crit(t)2⟩⟨fB crit(t)2⟩≈1, which represents the maximum degree of correlation between the two systems. The normalization ensures that CAB remains dimensionless and bounded in the range [−1,1], similar to a cosine similarity or normalized correlation coefficient. When this condition is satisfied, the collapse of fcrit(t) simultaneously affects both particles: fcrit(tc)→0⇒ΨAB(tc) fixed as a joint state. This collapse is understood as a transition of the temporal metric to a stationary configuration, not as an exchange of information. Independence from space Since the temporal field ψ(t) is global and identical for all matter, entanglement does not require the exchange of information in space, but only a common phase perturbation in time. The simultaneity of the collapse does not depend on the spatial distance between the particles, but on the fact that they share the same temporal state: ψA(t) = ψB(t) = ψ(t)eiϕ(t). In this sense, what appears as “instantaneous” correlation across space is simply a manifestation of a unified temporal background. 5 Physical interpretation In this scenario, the carrier wave does not merely generate a superposition of states, but actively modulates the local temporal metric, imposing on the two particles the same dynamics of fcrit(t). Entanglement thus appears as a natural effect of the global temporal coherence, explaining why correlations manifest independently of spatial separation. This interpretation remains fully consistent with relativistic causality: no measurable signal can be transmitted through the synchronization of fcrit. In Section ??, we formalize this statement as a no-signaling lemma, showing that chronovibrational coupling can only modulate joint probabilities while leaving local marginals invariant. 3 Energy and variation of temporal coherence in entangled states In this section, we attempt to estimate—as a working hypothesis—the minimum variation ∆Λ of temporal coherence induced by the critical function that is required to prepare an entangled state, starting from the pump photon’s energy. An often overlooked aspect of entanglement is the energetic cost of preparing the initial state. While no net energy transfer occurs during spacelike-separated measurements, the creation of photon pairs via parametric down-conversion (PDC) requires the pump energy: Eγ=hc λ≈2.48 ×10−19 J (λ= 800 nm). 3.1 Latency energy and activation time The pump photon experimentally generates the entanglement of a pair of quanta and provides a known energy: Eγ=hc λ. Since this energy is distributed over two quanta, we model the minimum energy that must be available per quantum to “activate” the critical function of the temporal field as Ethreshold 1q=1 2Eγ≈1.24 ×10−19 J. In quantum mechanics, energy and time are related through the spectral identity E=ℏω, hence a characteristic period T= 2π/ω and a time scale τE=ℏ/E. We stress that τEis a characteristic scale (not a deterministic lower bound). Accordingly, we define the single-quantum latency scale as t(1) 0=ℏ Ethreshold 1q≈1.054 ×10−34 J s 1.24 ×10−19 J≈8.49 ×10−16 s, 6 and for a two-quantum preparation window we take t(2) 0= 2 t(1) 0≈1.70 ×10−15 s. 3.2 Connection with the critical function fcrit(t) In the chronovibrational theory, global temporal coherence is described by Γharm(t) = exp"β τ∗Zt t0 f2 crit(τ)dτ#, where τ∗is the characteristic time scale of the setup (e.g., coherence window) and βis a dimensionless coupling. When Γharm ≈1, the field is effectively inert. To relate a local perturbation of the critical function to an effective energy per quantum, we introduce a harmonic coupling efficiency 0< χ ≤1 that quantifies the fraction of the optical energy scale ℏΩ effectively channelled into the chronovibrational mode: E1q=χℏΩ1 ∆tZt0+∆t t0 f2 crit(t)dt. Here Ω = 2πc/λ (optical angular frequency of the process) and Λ denotes the background damping of the temporal field for this setup (not a universal value). We do not import gravitational/LIGO values for Λ in this optical context. We assume that surpassing the latency threshold corresponds to E1q=Ethreshold 1q. This determines the minimum local damping variation ∆Λ in the regularized critical function: fcrit(t) = e−(Λ+∆Λ)tcos(Ωt) √1−e−2(Λ+∆Λ)(t+t0), with Ω = 2πc λ, t0=t(2) 0,∆t= coherence window of the source. 3.3 Closed-form estimate for ∆Λ (high-Ω, short window) For optical Ω we can average cos2(Ωt)→1 2over the window, and for short windows ∆t≪Λ−1the exponential envelope varies slowly. Expanding the denominator for small arguments, 1−e−2(Λ+∆Λ)(t+t0)≈2(Λ+∆Λ)(t+t0), we obtain the approximate normalized integral 1 ∆tZt0+∆t t0 f2 crit(t)dt ≈1 4(Λ + ∆Λ) ∆tln1 + ∆t t0. Imposing E1q=Ethreshold 1qyields the analytic estimate ∆Λ ≈χℏΩ 4Ethreshold 1q∆tln1 + ∆t t0−Λ (high-Ω,∆t≪Λ−1). 7 This formula shows the correct scalings: ∆Λ grows with the coupling χ, with the spectral scale ℏΩ, and with the “logarithmic leverage” ln(1 + ∆t/t0), while it decreases for larger threshold energy Ethreshold 1qand longer windows ∆t. Numerical illustration (setup-scale, not universal). Take λ= 800 nm ⇒ℏΩ = Eγ≈2.48 ×10−19 J, Ethreshold 1q=1 2Eγ,t0≈1.70 ×10−15 s, ∆t= 10−12 s. Then ln1 + ∆t t0≈ln(1 + 589) ≈6.37, and the bracket reads ℏΩ 4Eth 1q∆tln1 + ∆t t0≈Eγ (2Eγ) ∆t×6.37 ≈6.37 2∆t≈3.2×1012 s−1. Hence ∆Λ ≈χ·3.2×1012 s−1−Λ. In optical PDC one expects only a tiny fraction of the optical scale to couple into the temporal metric channel, i.e. χ≪1. For instance, χ∼10−12 would yield ∆Λ ∼ O(1) s−1. This reconciles the small perturbation picture of entanglement with the large carrier frequency: a weak harmonic coupling χsuffices to trigger synchronization without macroscopic damping. 3.4 Interpretation The estimate above shows that entanglement can be activated by a very small modulation of temporal coherence provided that the harmonic coupling χis weak (optical energy couples inefficiently to the chronovibrational mode). Operationally: •the pump provides the spectral scale ℏΩ and the preparation window ∆t; •only a fraction χof that scale perturbs the temporal metric; •surpassing Ethreshold 1qis equivalent to reaching a logarithmic gain ln(1 + ∆t/t0) sufficient to lift Γharm >1. This keeps the mechanism compatible with the energetic fragility of entanglement and avoids importing non-optical parameters. No-signaling consistency (pointer) The above mechanism perturbs joint probabilities via Γharm while leaving local marginals invariant (hence no superluminal communication). We formalize this as a lemma in Sec. ??. 8 Appendix: Energy and Quantum Coherence The analysis of entanglement and ANITA events highlights two physically distinct regimes that can both be framed within chronovibration. In entanglement, the pump photon energy only activates a minimal variation of temporal coherence in the joint wavefunction ΨAB, with no net energy release at measurement. In contrast, in ANITA events, the detected burst is interpreted as a strong (up to complete) harmonic collapse of the temporal field ψ(t), with an effective release of measurable energy. Model revision For burst-like events (ANITA) we adopt the normalized single-quantum energy E1q=ℏΩharm 1 ∆tZt0+∆t t0 f2 crit(t)dt, where ∆tis the observational/coherence window of the burst and Ωharm is the internal harmonic scale of the temporal mode (not the carrier frequency of the radio pulse). This normalization ensures dimensional consistency and aligns the ANITA treatment with the entanglement case. Accordingly, the critical function is written with latency fcrit(t) = e−Λtcos(Ωharm t+ϕ) √1−e−2Λ(t+t0), with Λ the setup-dependent damping, t0a latency scale (regularization), and ϕa phase that averages out over typical burst windows. From single-quantum energy to observed fluence Given an observed burst fluence Eobs (energy per unit area at the detector), the corresponding number of effective quanta per unit area is N=Eobs E1q =Eobs ℏΩharm      ∆t Zt0+∆t t0 f2 crit(t)dt      . If the emission is isotropic from distance R, the total energy is Etot = 4πR2Eobs; for beamed emission on solid angle Ωs,Etot = ΩsR2Eobs. Once E1qis fixed by the model, Ntot =Etot/E1q. 9