Reciprocal System Research Society

I recall an ISUS Journal issue suggesting that time-adjacent coupling might provide an alternative explanation for quantum entanglement. That got me wondering: could this idea actually be tested in the lab?

I’m not a quantum optics specialist, but I’ve drafted a short paper describing how such a test might be carried out with fairly standard tools — an SPDC source, a variable optical delay line, and coincidence counting. The key idea is to look for a finite “Frame Width of Coupling” (FWC) in the coincidence histogram, which would show up as sharp correlation boundaries, rather than assuming the correlations are strictly unbounded.

To my knowledge, no published experiments have explicitly searched for such a finite coupling width beyond detector resolution effects — but if I’ve overlooked one, I’d be glad to know. I’d also greatly appreciate feedback from those with experience in experimental quantum optics, particularly on feasibility, possible refinements, or related prior work.

For those familiar with the Reciprocal System of theory (RST), this proposal can be interpreted as a direct test of whether “entanglement” is simply the observational signature of time-adjacent motion. In RST, photons are scalar units of motion with vibration in one sector (space or time) and rotation in the reciprocal sector. Normally, correlations between photons are understood spatially, but RST extends this to the temporal domain: two photons may be “adjacent” in three-dimensional time, even while spatially separated. Such adjacency in time imposes a coupling condition, because their scalar motions share a contiguous orientation at the temporal zero point. When projected into our spatial reference system, this coupling manifests as entanglement-like correlations.

The key point is that time adjacency is not “clock time” but the structural ordering of unit scalar motions in the temporal sector. This adjacency has a finite width, arising from the quantized nature of scalar displacements. Thus, while quantum mechanics assumes that entanglement correlations are unbounded, RST predicts that correlations should fall within a measurable “Frame Width of Coupling” (FWC). This FWC reflects the interval over which coupled temporal displacements remain contiguous, after which correlations degrade. In practice, the experiment would not attempt to alter this coupling — which is a fixed property of scalar motion — but would measure its projection into spatial coincidence timing. A finite boundary in the coincidence histogram would therefore be evidence of time-adjacent coupling as the underlying mechanism, providing a physically constructive explanation for entanglement that avoids the invocation of nonlocal causation.

Link: Experimental Proposal: Testing Frame Width of Coupling in Entangled Photon Correlations (This work is shared anonymously to allow community replication and evaluation without reputational or institutional bias. It introduces no new physical postulates and relies solely on established quantum-optical formalism.)

If the initial Hong–Ou–Mandel experiment confirms the presence of a finite temporal coupling window, the next question is what determines its magnitude. The first priority is to establish whether the observed width is intrinsic to the entangled state or depends on the geometry of the photon source. To make this distinction, a geometry-invariance study can be performed at a fixed wavelength using the same HOM protocol. The source parameters—pump bandwidth and chirp, crystal length and phase-matching conditions, filter bandwidth, and type-I/II configuration—are varied while keeping detection and analysis identical. An intrinsic coupling width should remain invariant under these changes, even as the Gaussian envelope set by the JSA or JTA broadens or narrows.

Once invariance is established, the next question is what governs the magnitude of the coupling width itself. If the initial experiment confirms the presence of a finite temporal window, it becomes important to determine whether this limit represents a universal constant or scales with photon energy. The most direct test is to measure the Frame Width of Coupling (FWC) across a range of photon frequencies.

The follow-up experiment would again use a Hong–Ou–Mandel interferometer but with tunable photon-pair sources, generating biphotons at several wavelengths spanning the infrared to the ultraviolet. For each wavelength, experimental conditions should remain comparable—similar pump bandwidths, matched spectral filtering, and equivalent dispersion compensation. The delay is scanned with femtosecond precision, and coincidence data are analyzed using the same finite-support model proposed for the first study. Plotting τFWC against the photons’ central frequency (ν) will indicate whether the coupling width follows a systematic scaling law.

If τFWC scales inversely with frequency (τFWC ∝ 1/ν), the correlation window likely corresponds to a fixed number of underlying temporal units, consistent with finite adjacency in a quantized temporal structure. A constant width across frequencies would suggest a universal temporal constant, while variation tied to filtering or dispersion would point to an optical origin.

The overall goal of this sequence is to establish both the invariance and the scaling behavior of the coupling width, providing direct empirical insight into what determines the extent of the temporal correlation window.

I'm no expert by any means but with a basic knowledge of both the Reciprocal System and quantum entanglement, which few people have, I think this is an excellent idea and would love to see what RS answers we could provide if doing the experiment ourselves. Great work!

If I am picking up the gist of your paper correctly, would this experiment (if successful) possibly show the boundary between speed zones? In other words (or layman terms for me), this could show the blending of the temporal and spacial at the boundary, a "thin place" from folklore, so to speak, where 3D space and 3D time meet? Essentially, the framework/structure of the temporal region is bleeding through to the spacial at the boundary and both are visible from our scientific observer perspective?

I've been lucky enough to witness a rotational *event* bleeding through from 3D time into our spacial reality and it was mind-blowing.

3D time and 3D space "meet" at unity, defined by RS as the unit speed boundary (the "speed" of light). The other boundary being the unit boundary (within a unit of space: matter, or a unit of time: anti-matter, really inverse matter) is not so much a boundary between 3D time and 3D space as a boundary between the macro (1D) and the micro (2D).

Of course, 3D space and 3D time are just both constructs of consciousness, really there's only motion (the ratio of space to time or time to space in 3 scalar dimensions). Motion in time are "forces", and so we can indirectly measure motion in time through the effect on locations in space.

The scientific experiments have been conducted. Time-adjacency IS the reason for quantum entanglement. They just don't know (or accept) that time and space are the same in ALL respects... it's simply a matter of perspective. And since we can only measure in 3D space (with clock time - not the same as 3D time), they miss the other "half": 3D time with clock space. Recall that motion in time is based on clock space, which is instantaneous from a temporal frame.

Good to see you on the boards again.

Measurement of the Frame Width of Coupling (FWC) in Entangled-Photon Interference

1) Objective
We measure the temporal extent of phase coherence between two entangled photons from a type-II SPDC source using a Hong–Ou–Mandel (HOM) interferometer.
Define the Frame Width of Coupling (FWC) as the range of relative delays τ for which the photons remain phase-coupled (interference present). Outside that range, coincidences return to the uncorrelated baseline.

<figure 1> Simplified Hong–Ou–Mandel interferometer showing SPDC source, variable delay, beamsplitter, and coincidence detectors.

2) Measurement principle
In a HOM setup, two indistinguishable photons arrive at a 50:50 beamsplitter from opposite inputs. When their arrival times match within the coherence window, both photons bunch into the same output and the coincidence rate drops (HOM dip).

Write the coincidence curve as a function of delay τ using the two-photon joint temporal amplitude A(t):

• R_c(τ) ∝ 1 − ∫ A(t) · A^*(t + τ) dt

Standard models assume A(t) is Gaussian/sinc-like ⇒ a smooth dip.
If the correlation has finite temporal support, model:

• A(t) = G_σc(t) · Π_Tfwc(t)

where G_σc is the usual coherence envelope with scale σ_c, and Π_Tfwc is a rectangular kernel of width T_FWC.
Prediction: a flat minimum with steep edges for |τ| < T_FWC/2, then rapid return to baseline.

<figure 2> Two-Photon Overlap in HOM (Standard View).
Space–time depiction of two temporal wave packets. When the packets overlap at the beamsplitter, coincidence counts drop (HOM dip); when separated, coincidences return to baseline.

3) Standard quantum-optics interpretation
Within conventional quantum mechanics and quantum optics, the Hong–Ou–Mandel (HOM) interferometer is interpreted entirely through the joint temporal amplitude A(t), which describes the combined two-photon wave packet in time.
The coincidence rate R_c(τ) is determined by the temporal overlap of these amplitudes as the relative delay τ is scanned.

• T_FWC corresponds to the interval of mutual indistinguishability of the photon wave packets—the range over which they interfere.
• A finite T_FWC does not conflict with quantum mechanics; it simply refines the source-specific form of A(t). The underlying formalism (superposition, Born rule) remains unchanged.
• A smooth Gaussian-like dip reflects continuously decaying overlap; a flat region with steep edges would indicate that the overlap function has finite support.

In nearly all prior HOM measurements, attention has centered on the visibility of the dip and on the delay at which minimum coincidence occurs, not on the detailed shape of the dip itself.
This is because the coincidence envelope is normally assumed to be Gaussian or sinc-like—an assumption that holds well in practice:

• The pump pulse is typically Gaussian or close to it.
• The phase-matching function of the nonlinear crystal, together with spectral filtering, further enforces a Gaussian-like form.
• Detector timing jitter and statistical averaging smooth out any residual non-Gaussian structure.

Consequently, the HOM dip has usually been treated as a calibration curve rather than as an independent observable.
No strong theoretical argument within standard quantum mechanics predicts a non-Gaussian shape, so there has been little motivation to measure it with femtosecond-level precision.

The present proposal departs from that convention by treating the dip shape itself as a physical observable—a potential indicator of the temporal structure of entanglement.
Modern piezo-driven delay lines and interferometric stabilization now make sub-10 fs resolution and <5 fs path stability feasible, enabling for the first time a systematic test of whether the two-photon interference envelope has finite temporal support or merely a smooth Gaussian tail.

Beyond closing a long-standing experimental gap, the motivation for this test is conceptual:
if entanglement correlations exhibit a finite temporal extent, that width becomes a new measurable parameter of quantum coherence.
Determining whether the correlation envelope decays smoothly or instead terminates within a definite frame directly tests whether the appearance of “instantaneous” entanglement represents a genuinely unbounded coherence or merely an approximation to a bounded process.
The experiment therefore addresses one of the simplest yet experimentally untested questions in quantum optics: is two-photon coherence fundamentally continuous, or finitely delimited in time?

The femtosecond-scale resolution employed here is sufficient to resolve any physically meaningful deviation from a Gaussian profile while spanning the full coherence range of typical SPDC sources.

4) Reciprocal System of Theory (RST) interpretation
In RST, a photon is a unit of radiation: a simple harmonic unit motion with alternating scalar displacement between space and time. Radiation occupies both space–time (material sector) and time–space (reciprocal counterpart). Propagation at unit speed in space–time corresponds to a synchronized oscillation between these reciprocal aspects of motion.

Note that in RST, the term “time–space” does not denote clock time but the reciprocal coordinate domain of scalar motion. Correlations that appear instantaneous in the material (space–time) sector correspond to simultaneous adjacency relations in this reciprocal domain.

When two photons are generated together, their time–space displacements start with a common scalar phase; they are adjacent units in the reciprocal region. This adjacency establishes continuity of unit motion that underlies the observed coherence in space–time.

<figure 3> Time–Space Adjacency and Scalar-Phase Alignment (RST View).
Reciprocal-domain schematic: the photons remain adjacent in time–space (outer region), but only the inner sub-region of scalar-phase alignment produces interference. The measured Frame Width of Coupling (FWC) corresponds to this aligned interval projected into the space–time delay axis.

Key point: adjacency in time–space persists, but scalar-phase alignment need not be permanent. Small differences in effective scalar displacement rates (set by frequency/energy and local generation conditions) produce a phase differential. As that differential accumulates, the correspondence between their space–time projections diminishes—even though scalar adjacency remains.

Therefore, the HOM loss of interference marks the limit of active scalar-phase alignment between the two radiation units. The measured T_FWC is the temporal interval during which the time–space displacements remain sufficiently in phase to produce coherent coincidence suppression. Beyond T_FWC, adjacency persists but scalar-phase correlation does not; interference ceases.

Because all material-sector phenomena observed in extension space are projections of scalar motion with conjugate components in both space–time and time–space, correlations observed within the coupling frame appear instantaneous—not due to transmission through either region, but because they originate from the shared structure of motion itself. The finite width T_FWC identifies the range over which reciprocal scalar motion projects coherently into extension space — a limit of structural coupling, not a temporal delay or propagation phenomenon.

Note: In Larson’s framework, extension space is not a separate physical region but the three-dimensional spatial reference system through which scalar motion in space–time and time–space is represented. Observable phenomena in the material sector appear in extension space as projections of these reciprocal motions, giving rise to the measurable spatial relations of experiment.

5) What the experiment is sampling
Detectors do not resolve optical cycles; they register statistics that depend on whether the two-photon amplitudes remain phase-coherent. The HOM scan samples:

• Inside the coupling frame (|τ| < T_FWC/2): coherent interference ⇒ suppressed coincidences (flat minimum).
• Outside: no coherent overlap ⇒ coincidences at baseline.

Thus, the FWC is the directly measurable temporal interval over which coherent interference can be sampled.

6) Practical notes (resolution and statistics)

• Delay step: Δτ ≤ min(T_FWC/5, σ_c/10). For σ_c ~ 100 fs and plausible T_FWC = 30–80 fs, use 5–10 fs steps (densify near edges).
• Counts per point: ≥ 5×10³ at edges for robust discrimination between “bounded” and “smooth” models (Poisson likelihood or AIC/BIC).
• Scan range: at least ±2 ps to establish a clean baseline.
• Stabilization: path stability < 5 fs rms over the scan or interleaved symmetric sampling.

7) Outcomes and interpretation

• Smooth Gaussian-like dip: standard continuous coherence envelope; tighter constraints on σ_c.
• Flat-bottom with steep edges: evidence for a bounded component of the joint amplitude; within QM this is a refined A(t) with finite support. Within RST, this corresponds to the finite range of scalar-phase congruence between adjacent radiation units in the time–space region—the interval over which their reciprocal displacements remain harmonically aligned when projected into space–time.

To summarize
— The HOM interferometer measures coincidence rate vs. delay τ.
— The Frame Width of Coupling, T_FWC, is the delay interval where coherent interference is observable.
— QM view: T_FWC refines the functional form of the two-photon amplitude (bounded support).
— RST view: T_FWC quantifies the finite duration of scalar-phase alignment between adjacent radiation units in the time–space region.
— The formalism of QM is preserved; the experiment determines whether coherence is unbounded (smooth) or has a measurable finite extent (bounded).