Wave Particle Unity and a Physically Realist Interpretation of Light
| Scientific Paper | |
|---|---|
| Title | Wave Particle Unity and a Physically Realist Interpretation of Light |
| Read in full | Link to paper |
| Author(s) | Robert E French |
| Keywords | Wave Particle Unity, Bell States, Entanglement, Advanced Wave |
| Published | 2009 |
| Journal | Physics Essays |
| Volume | 21 |
| Number | 3 |
| No. of pages | 15 |
| Pages | 196-199 |
Read the full paper here
Abstract
This paper sketches a program towards giving a physically realist model of the photon in terms of properties of the electromagnetic field. It is both shown how to rework traditional wave and particle concepts so as to have a unified concept and how parallel electromagnetic fields can be associated with each charged particle. An account of both light propagation and of interactions with matter is sketched. A suggestion is made as to how the account may be able to explain EPR correlations in the case of polarization entanglement. A possible empirical test is also discussed.
Overview
Robert French sets out to give a realist model of the photon — one in which light really is something definite in the world between emission and detection, rather than a probability amplitude with no referent. His method is to abolish the wave/particle distinction by identifying the two: a photon simply is an oscillating electromagnetic field, and he calls the resulting object a "wave-particle." The obstacles to this identification are the familiar ones — particles are localised, waves are spread out; particles are impenetrable and indivisible, waves pass through one another and break into wavelets — and French's strategy is to remove them by changing the geometry of the field rather than the physics.
The change is this. Conventionally the electric field at a point is a single field, obtained by summing the contributions of every charge. French instead assigns each charged source particle its own three-dimensional subspace, these subspaces lying parallel within an overall four-dimensional space that is purely spatial — "not Minkowski spacetime since all of the dimensions are just spatial." The observable force at a point is then the vector sum of the effects of the separate fields at that point. He is explicit that "mathematically, the two approaches are the same though, it is just that the summations occur at different locations." The gain is interpretive: wave-particles in different subspaces can "glide by" each other without interacting, which restores something like particle impenetrability, while absorbers are taken to be finitely-sized four-dimensional objects that intersect every subspace at once. This is a realist and, as he says, an emission account of light, and its most heterodox commitment is a superluminal but not retrocausal signal used to explain entanglement.
The argument
Wave-particles and their rotational waves
French holds that photon emission creates a photon number state (Fock state) in the field associated with the emitting particle, propagating at c. He anticipates the objection from quantum electrodynamics that the electric field vanishes for number states, replying that this is only the average value — fluctuations about it remain, and the average intensity, being the square of the field strength, stays positive.
Light is then modelled as spherical waves oscillating perpendicular to the line of propagation, with the E and B waves in adjacent subspaces on orthogonal axes. He assigns them effective angular velocities
- Ω1 = (c/r)a cos(ωt), Ω2 = (c/r)b sin(ωt),
with r the radius from the source, ω the angular frequency, and a, b orthogonal radial unit vectors aligned with the rotation axes of the E and B fields. The waves have radial propagation c and a transverse rotational oscillation whose maximum speed is also c; the polarisation angle is fixed by the rotation axis of the E wave. He postulates that these fields carry both a vector (force) and a scalar (energy) aspect, related for a plane wave by the energy density in E2 and B2, and that they are modulated at an inverse-square rate.
Probability amplitudes read as field properties
The realist step is to interpret the Feynman path-integral amplitude Φ = eiS/h = cos(S/h) + i sin(S/h) as a description of these rotational waves. French writes the real and imaginary parts as
- Φ1 = A(ω1/2/c1/2r)cos(ωt), Φ2 = A(ω1/2/c1/2r)sin(ωt),
with A = (c/4πωΔr)1/2 a normalisation for a wave packet of width Δr emitted between two times, and interprets Φ1 and Φ2 physically as the E and B force fields. The absorption probability density is then P = Φ12 + Φ22, which falls as 1/r2 even though the amplitudes fall as 1/r — matching the energy density of the field. He notes, following Feynman, that only paths near the classical path contribute, "the crazy ones cancel out."
For many paths the kernel splits into K1 and K2, the summed cosine and sine amplitudes, giving P = K12 + K22 = (ΣΦ1)2 + (ΣΦ2)2. Interference is thus a real superposition of rotational effects occurring where the subspaces meet a potential absorber, and French observes that Feynman showed the resulting differential equation to be the Schrödinger equation.
Partial photons, splitting and absorption
Because he identifies the particle with the wave, French must accept that a beamsplitter splits the particle, not merely a probability wave. He therefore introduces partial photons: in elastic scattering only a partial collapse of the wave packet occurs, the photon being "literally divided into distinct portions" that propagate in different subspaces as spherical rotational waves of the same frequency centred on the scattering location. Unscattered light is "pushed aside" — the Renninger effect — creating a shadow and raising the absorption density elsewhere. He does not derive the cross-sections for the two processes. Correspondingly, he does not claim that the numerically identical photon is emitted and absorbed; a discrete quantum E = hν is drawn from a pool to which many sources contribute, in ratios matching the partial-photon densities at the absorber.
Absorption itself involves a node — a four-dimensional particle providing a link between three-dimensional subspaces. Energy is drawn backwards along past trajectories to the node, then forward along other trajectories to wherever the partial photon already has a "presence," meaning a potential to be absorbed there. Since this must all happen within the absorption time, both legs travel faster than c. French compares this to Klyshko's advanced waves and to Cramer's transactional interpretation, but insists on the difference: his waves act instantly in the present and do not travel backwards in time, which he "find[s] to be quite implausible."
Polarisation entanglement and the Bell states
The application is to polarisation entanglement. A polariser at angle Θ changes the force-field strengths at cosΘ and sinΘ rates, so the energy fields — being squares — are cut according to Malus's law I ∝ cos2Θ. French stresses that on his account the polariser does not filter or attenuate the original field: "new fields (driven by the old ones) are being created by the polarizer," with the new basis given by the polariser's Jones operator. This is what he means by defending an emission theory.
Singles counts are then constant in angle, since sin2Θ + cos2Θ = 1. Coincidences are the subtle case. He proposes that advanced waves from the energy fields at one detector are cut by the polariser at the opposite detection system, leaving sin2Θ1cos2Θ2 and cos2Θ1sin2Θ2 energy fields at each. Applying sinΘ1cosΘ2 = ½[sin(Θ1 + Θ2) + sin(Θ1 − Θ2)] and expanding produces the cross term 2 sinΘ1cosΘ2sinΘ2cosΘ1 shared by all four Bell states, and the sum and difference terms are shared at each detector, yielding the coincidence functions sin2(Θ1 ± Θ2) for the Ψ± states and cos2(Θ1 ± Θ2) for the Φ± states, the latter after a 45° basis change by a quarter-wave plate. He invokes Young's inequality to show the cross term never exceeds the squared terms, so no negative energy arises.
The joint absorption is treated as correlated two-photon absorption over the extended region containing both detectors, and French notes, citing Maudlin, that a preferred reference frame — for instance the source's — is required. He accepts Aspect's switched-polariser experiments as ruling out a common-cause explanation, since the absorption events are spacelike separated. Finally he proposes a test: if the correlations are produced by the backward-then-forward wave, blocking the backward wave with a fast optical chopper after detection should destroy them. Kilometre-scale fibre delays, he notes, are well within reach given that down-converted light had been sent over 100 km.
Assessment
The paper's real merit is that it takes the interpretive problem seriously in a specific rather than a rhetorical way, and that it is unusually honest about its own status — French calls it a sketch of a programme, and it is. Three things in it are genuinely interesting. First, the observation that his parallel-subspace reformulation is mathematically identical to the usual field summation, differing only in where the sums are taken, is stated up front rather than hidden; he is claiming an interpretive gain, not a new prediction, and says so. Second, the reading of the Euler decomposition of the path amplitude onto the E and B rotational waves is an ingenious attempt to give the complex phase a physical referent, and the fact that amplitudes fall as 1/r while the probability falls as 1/r2 is exactly the right consistency check to make. Third, and most creditably, the paper ends with a concrete falsifiable proposal: chop the backward wave and see whether the correlations survive. Very few interpretive papers of this kind offer anything that could fail.
The difficulties are correspondingly specific. Most of the machinery is postulated rather than derived. The fields are simply "postulated to possess both vector (force) and scalar (energy) aspects," the modulation rate is postulated, the node is defined into existence as a four-dimensional particle without any account of what such a thing is or how it is constrained, and the cross-sections for elastic scattering versus the Renninger effect — which would be needed for any quantitative prediction — are explicitly not derived. The reply to the QED objection is too quick: for a Fock state the mean field vanishes and the variance is nonzero, but a nonzero variance is not an oscillating classical field with a definite phase, and it is the definite phase that French's rotational waves require. Nothing in the paper bridges that gap.
The entanglement account has a sharper problem. French's derivation of the Bell-state coincidence functions proceeds by writing down products of polariser transmission factors and manipulating them with trigonometric identities until expressions in (Θ1 ± Θ2) appear. But the correct quantum prediction for the singlet is a coincidence rate in cos2(Θ1 − Θ2) — a function of the difference alone — and it is precisely this that violates the CHSH bound. Producing terms containing (Θ1 ± Θ2) is not the same as deriving the correct rate with the correct normalisation, and the paper never actually computes a CHSH combination to check that its model reproduces the measured value of 2√2 rather than something at or below 2. Given that the Aspect experiments he cites, and the far more stringent loophole-free Bell tests since, are exactly the measurements at issue, this omission is the central weakness. Relatedly, French accepts a preferred frame and superluminal influence, which is a coherent position — Bohmian mechanics does the same — but he does not address the resulting tension with Lorentz invariance, nor explain why the superluminal link cannot be used to signal.
The "partial photon" is also in trouble against a measurement French himself cites. Grangier, Roger and Aspect's beamsplitter anticorrelation experiment is invoked in support, but its actual result is that a single photon at a beamsplitter is detected at one output or the other and essentially never both — the measured anticorrelation parameter falls far below the classical bound. A model in which the particle is literally divided at the beamsplitter has to explain why the two halves are never jointly detected, and the appeal to energy being redrawn through a node at the beamsplitter does this only by making the node do whatever the data require. Finally, the paper is a sketch in the strict sense: it contains no numbers, no computed curve, and no comparison of any calculated quantity with any experiment. Its proposed chopper test is its best feature, and remains, so far as this paper goes, unperformed.