[Paper Review] Nonlocality - The party may be over

Trevor W. Marshall|ArXiv.org|Mar 9, 2002

Quantum Mechanics and Applications4 references3 citations

TL;DR

This paper proposes that Spontaneous Parametric Down Conversion (SPDC) is actually an amplification of zero-point field modes in a nonlinear crystal, and introduces the theoretically predicted but unobserved phenomenon of Spontaneous Parametric Up Conversion (SPUC). By showing SPUC is phase-matching symmetric to SPDC, the authors argue that optical entanglement can be consistently explained via a local, realist zero-point field theory, challenging the nonlocal photon-based interpretation of quantum optics.

ABSTRACT

We demonstrate that the phenomenon known as Spontaneous Parametric Down Conversion is really an amplification, in a nonlinear crystal pumped by a laser, of certain pairs of modes of the electromagnetic zeropoint field. The demonstration is achieved by showing the existence of a related phenomenon, Spontaneous Parametric Up Conversion. This phenomenon, once observed, will cast doubt on the quantum-optical theory, which treats photons as the elementary objects of the light field. It will also lend greater credibility to the zeropoint-field description of optical entanglement phenomena. That description is based on the unquantized light field and is consistently local, in contrast with the nonlocal description of Quantum Optics.

Motivation & Objective

• To challenge the nonlocal, photon-based interpretation of quantum optics by proposing a local, realist alternative based on the electromagnetic zero-point field (ZPF).
• To demonstrate that SPDC is not a creation of photons but an amplification of pre-existing ZPF modes in nonlinear crystals.
• To predict and justify the existence of Spontaneous Parametric Up Conversion (SPUC), a symmetric counterpart to SPDC, as a key testable prediction.
• To show that the standard quantum-optical detection model violates the Principle of Local Action (PLA), and propose a local detection theory based on field amplitudes.

Proposed method

• Formulates SPUC as the time-reversed process of SPDC, where an infrared laser and vacuum ultraviolet modes generate a visible signal, using identical phase-matching conditions.
• Applies linearized mode coupling equations for the amplitudes $A_1$, $A_2$, and $A_3$ of the pump, vacuum, and signal waves, respectively, under the assumption of constant pump amplitude.
• Uses the sinc-squared dependence on the phase mismatch $\Delta'$ to calculate intensity growth in the signal mode over crystal length $l$, with $\Delta' = \sqrt{\Delta^2 + \beta_1 I_2 \beta_3}$.
• Derives intensity transfer relations for SPUC via coupled differential equations: $dA_1/dz = i\beta_1 A_2 e^{i\Delta z} A_3$ and $dA_3/dz = i\beta_3 A_2^* e^{-i\Delta z} A_1$, assuming perfect transverse phase matching.
• Calculates SPUC intensity distributions across azimuthal angles and wavelengths using the sinc-squared envelope, showing off-centered rainbows due to birefringence in BBO crystals.
• Compares SPUC and SPDC intensities using identical pump intensities, finding SPUC intensity reaches ~50% of SPDC intensity across much of the visible spectrum.

Experimental results

Research questions

• RQ1 Can the phenomenon of Spontaneous Parametric Down Conversion (SPDC) be explained without invoking the creation of photons, instead as amplification of zero-point field modes?
• RQ2 Is there a symmetric counterpart to SPDC—Spontaneous Parametric Up Conversion (SPUC)—that would be experimentally indistinguishable in phase-matching but differ in its physical interpretation?
• RQ3 Does the existence of SPUC undermine the standard quantum-optical treatment of detection, which relies on nonlocal collapse and normal-ordering algorithms?
• RQ4 Can a local, realist detection theory be constructed that avoids the nonlocality inherent in the photon picture and still reproduce observed SPDC and SPUC intensities?
• RQ5 Does the violation of the no-enhancement hypothesis in Bell tests stem from an incorrect assumption about detector response, rather than from nonlocality?

Key findings

• SPUC is predicted to produce a visible, off-centered rainbow of light in a BBO crystal when a 845 nm infrared laser is normally incident, with the most intense emission near 180° azimuthal angle.
• The SPUC intensity is calculated to be approximately 50% of the SPDC intensity when both processes are pumped with lasers of equal intensity.
• The SPUC rainbow is not centered on the pump beam due to birefringence in the BBO crystal, which causes the ultraviolet mode to have an angle-dependent refractive index.
• The phase-matching conditions for SPUC are identical to those for SPDC, implying that if SPDC is a real process, SPUC must also be real, despite its lack of observation.
• The intensity transfer equations for SPUC show that the signal mode grows via a resonant coupling mechanism dependent on the pump intensity and crystal length, with a sinc-squared dependence on phase mismatch.
• The model demonstrates that the standard quantum-optical detection mechanism violates the Principle of Local Action, and that a local, realist theory based on field amplitudes can consistently explain both SPDC and SPUC.