1. What is entanglement from the point of view of the τ-field Entanglement is the synchronization of the τ field of two (or more) particles, in which their chronal quanta become a single whole. χ₁ = φ₁·τ₁ = χ₂ = φ₂·τ₂ When two particles are entangled, their individual τ-pulses and phases are no longer independent. They form a single chronal system connected by a common phase. 2. Why a change in one particle instantly affects another The chronal wave propagates at a speed v_chron = 2π·c ≈ 6.28c.But this is in space. And in phase space (the space χ = φ·τ), synchronization does not require any time at all, because it is not a transfer of energy, but a transfer of state. When we measure one entangled particle, we record its χ. The second particle, bound to the first by a single χ, instantly assumes a consistent state. This is not "faster-than-light information transfer." This is a manifestation of the fact that χ is conserved in the system, and the division in space does not break this connection.
What is entanglement from the point of view of the τ-field Entanglement is the synchronization of the τ field of two (or more) particles, in which their chronal quanta become a single whole. χ₁ = φ₁·τ₁ = χ₂ = φ₂·τ₂ When two particles are entangled, their individual τ-pulses and phases are no longer independent. They form a single chronal system connected by a common phase. 2. Why a change in one particle instantly affects another The chronal wave propagates at a speed v_chron = 2π·c ≈ 6.28c.But this is in space. And in phase space (the space χ = φ·τ), synchronization does not require any time at all, because it is not a transfer of energy, but a transfer of state. When we measure one entangled particle, we record its χ. The second particle, bound to the first by a single χ, instantly assumes a consistent state. This is not "faster-than-light information transfer." This is a manifestation of the fact that χ is conserved in the system, and the division in space does not break this connection.
Entanglement in the S-Field 1. Ontic basis of entanglement In the S-framework, each particle is a two-mode S-oscillator: Φ = (Φ_sb , Φ_bs). Entanglement occurs when two or more S-oscillators share a common S-phase structure. This is not information transmission between particles in B-space — it is a single, joint S-configuration projected into multiple B-locations. Thus entanglement is a multi-projection of one S-state, not a correlation between two separ ate B-states. 2. Shared S-Phase Condition (the core definition) Let particles A and B have states: Φ_A = (A_sb exp(i φ_A_sb), A_bs exp(i φ_A_bs)) Φ_B = (B_sb exp(i φ_B_sb), B_bs exp(i φ_B_bs)). They are entangled if and only if: Δφ_A = Δφ_B, and the bs-components satisfy a joint coherence: Φ_A_bs = λ Φ_B_bs, where λ is a complex ratio with |λ| fixed during the entangled interval. This means: The S-components form a single connected oscillatory object. Mathematically, define the Joint S-State: Ψ_S = Φ_A_bs ⊗ Φ_B_bs. Entanglement corresponds to: rank(Ψ_S) = 1. This is the most compact mathematical expression of entanglement in this theory. 3. Why entanglement is instantaneous Inside the S-domain: • there is no spatial metric • there is no propagation • there is only phase structure. Thus a change in Φ_A_sb or Φ_A_bs that forces a new Δφ_A immediately alters Δφ_B because both projections originate from the same Ψ_S. This explains experimental observations: • zero-time correlations • infinite effective signaling speed • independence from spatial separation • no energy or momentum transfer. All of them follow automatically from: S has no distance and no finite propagation speed. 4. Collapse as B-projection selection Measurement is interpreted as: P_B Φ_A → specific eigen-projection. Because A and B share the same Ψ_S, selecting one B-projection forces the entire Ψ_S to project consistently. Thus: Measurement collapse is not a physical signal. It is selection of one branch of a shared S-object. No superluminal influence is needed. 5. Conservation laws Because both particles share the same S-state: • Spin correlations • Momentum conservation • Polarization complements appear automatically from the structure of Ψ_S: Ψ_S = Φ_A_bs ⊗ Φ_B_bs. Constraints on Φ_A_bs impose the complementary constraints on Φ_B_bs. Thus conservation laws are not maintained through 3D interaction, but through S-symmetry of the joint state. 6. Entanglement swapping and teleportation Teleportation in the S-framework is simple: 1. Two particles share Ψ_S₁. 2. One particle from Ψ_S₁ interacts with a particle from Ψ_S₂. 3. Their S-phases align (Δφ matching). 4. This merges Ψ_S₁ and Ψ_S₂ into a new unified Ψ_S. The B-space interpretation is “entanglement swapping,” but the S-interpretation is: merging or re-partitioning of phase-coherent S-objects. Teleportation = transfer of B-state through S-resonance alignment, not physical movement. 7. Unified S-Equation of Entanglement The full formal criterion for entanglement is: P_S (Φ_A ⊗ Φ_B) ≠ (P_S Φ_A) ⊗ (P_S Φ_B). This inequality means: “The S-projection of the joint system cannot be expressed as a product of the S-projections of its parts.” Or verbally: Entanglement is non-factorability of the S-projection. This matches all known experimental results but gives a far clearer ontology. Summary in one sentence Entanglement is the multi-location projection of a single S-phase coherent structure into baryonic space, explaining the instantaneous correlations and nonlocal behavior naturally.
This paper focuses on the reason behind the entanglement phenomena, which is still an unknown fundamental question. It argues that while two entangled particles are separated in the 3D space the flow of information between them is instantaneous through the 4D space. The fourth dimension of space has the unit of measurement of length like the other three space dimensions. We shall call it Q, from the word quatre (four) in French. Its magnitude is equal to the invariant proper time τ times the speed of light c. Q = cτ. Each point in the 4D space corresponds to an event. Distances between events in the four-dimensional space can be computed using the Pythagoras theorem. It is argued that time t as measured by clock in our 3D space times the speed of light gives the length of the position vector of an event in the 4D space. At time t, when an observation is made at one of the entangled particles, the length of the position vectors of both entangled particles, sharing the same wave function, in 4D space are equal to t times the speed of light, i.e., ct. The time t is also the same for all the points on the line connecting the two events in the 3D space. Consequently, the length of the position vectors of all the points on the line connecting the two events in the 3D space is equal to ct in the 4D space. The corresponding points in the 4D space make an arc of equidistance to the origin. It is conjectured that the flow of information between the two entangled particles through this arc in the 4D space is not carried by energy or mass particles. It is, therefore, not bound by the time nor the speed of light constraint in 4D space and is instantaneous.
Quantum entanglement is traditionally framed as spatial non-locality: two particles at arbitrary separation maintain correlated states, with measurement of one instantaneously affecting the other. We propose a reformulation: entanglement is fundamentally a temporal phenomenon — a synchronization of quantum phases via universal harmonic oscillations. Spatial entanglement is recovered as the special case where both particles are created at the same time and location. Three independent experiments support this framework: (1) Megidish et al. (2013) demonstrated entanglement between photons that never coexisted; (2) temporal qubit encoding (|𝜓⟩ = 𝛼|early⟩ + 𝛽|late⟩) achieves full quantum information capacity; (3) Jiang et al. (2024) measured entanglement formation taking 232 attoseconds — the time for a wave to establish phase coherence. In the Fractal Mechanics framework, all particles oscillate at Fibonacci-harmonic frequencies 𝜔_𝑛 = 𝜔_𝑃×(𝜑^−𝑛), and entanglement is their synchronization to common harmonics. This formulation predicts that entanglement fidelity is maximized for time separations Δ𝑡_𝑛 = 𝑇₀/𝜑^𝑛 (Fibonacci timing), testable with current attosecond technology.
Quantum entanglement is widely regarded as the most puzzling phenomenon in quantum mechanics---two particles, no matter how far apart, appear to instantly determine each other's state upon measurement. For a century, this has been interpreted as "nonlocal correlation" or "spooky action at a distance", yet none of these interpretations have answered a fundamental question: What is the physical carrier of the correlation? This paper offers a simple answer using Time Field Theory (TFT): Entanglement is not the transmission of information, but the inevitable geometric consequence of conservation laws. In TFT, spacetime is governed by strict conservation laws---local intrinsic total velocity conservation and spacetime flux conservation together form the underlying logic of the theory. An entangled photon pair emerges from the ground state of the background time field, and their total phase is locked by the conservation law: the two photons combined must return to the original ground state, because the default setting of the universe allows nothing to be created or lost without constraint. Measurement merely "reads out" this pre-written result. No information transfer is needed, because a conservation law is not a signal---it is the default constraint of the cosmic background. This interpretation requires no wave-function collapse, no postulate of nonlocality, no hidden variables, and no "observer trigger". It is simply an inevitable corollary of the strict conservation laws that permeate TFT. The mystery of entanglement is not a riddle of nature, but a consequence of asking the wrong question---we have always thought something was being transmitted, when in fact nothing is. This is the 12th paper in the Time Field Theory (TFT) series.
Abstract Entanglement is a random phenomenon that is instantly synchronized, regardless of the space that mediates between entangled particles. However, the instantaneous transmission of information using entanglement is impossible. This is because the instantaneity in the synchronization of non-local outcomes as a consequence of quantum measurement (after the distribution of the entangled pairs) cannot be used for an entanglement-based communication system to transmit information instantaneously. This impossibility stems from the following two reasons: a) the difficulty of controlling non-local outcomes through local actions without the intervention of an auxiliary channel (classical), and b) regardless of the previous point, no communication system based on entanglement can be instantaneous due to the distribution of an entangled pair at relativistic speeds, necessary to generate the quantum channel, each time a qubit must be transmitted. Three simple experiments help to clarify this controversial point. In fact, this study establishes what is truly responsible for the impossibility to transmit information instantaneously of any communication system based on entanglement. In this respect, functional models of the internal behavior of quantum measurement, and entanglement were developed, which allow analyzing the instantaneity post-distribution of entangled particles, before and after a quantum measurement, as well as the randomness in the results obtained from a quantum measurement of the entanglement. In this sense, this study establishes a debate about three possible responsible for the aforementioned randomness: the quantum measurement itself, entanglement, and the human intervention. Finally, homology between the entanglement and the double-slit experiment is presented.