On the Interpretation of Quantum Physics: Energy Transfer Between Field and Matter According to the “Pairwise Interference Model” and a Quantum-Physical Measurement Problem
In classical electrodynamic wave theory, the intensity of light is proportional to the square of the amplitude of the electric field; in quantum theory, according to the conventional interpretation, the probability of detecting a light particle (and hence, ultimately, the photon density) is given by the square of the probability amplitude (as prescribed by the Born rule, which itself lacks a deeper theoretical justification). A mathematical formulation equivalent to the path integral provides, within the framework of the Pairwise Interference Model (PIMOQ), an alternative interpretation that is mutually exclusive with the conventional one. According to this interpretation, quantum physics, within the scope considered here, describes the local (at the detector), intrinsically bidirectional, quantised energy transfer between field and matter (apart from quantisation this is in direct analogy with classical physics). In the case of constructive interference, this transfer is unidirectional, occurring exclusively from matter to the field, whereas in the case of destructive interference the two opposing energy fluxes are equal in magnitude. However, it appears that in the macroscopic world only the net balance of these two antagonistic and complementary fluxes is experimentally observable, whereas the individual contributions cannot be measured independently. This limitation is referred to here as a quantum-physical measurement problem. From this perspective, quantum physics constitutes a subdiscipline of thermodynamics with a correspondingly limited domain of applicability. Although the principle discussed is as fundamental as, for example, the principle of conservation of energy, this does not imply that the underlying physical processes must necessarily be identical in every situation in which the principle applies. This interpretation is further elaborated through a discussion of interference experiments employing coherent and incoherent light sources, as well as the generation of coherent light in the laser.
In classical electrodynamic wave theory, the intensity of light is proportional to the square of the amplitude of the electric field; in quantum theory, according to the conventional interpretation, the probability of detecting a light particle (and hence, ultimately, the photon density) is given by the square of the probability amplitude (as prescribed by the Born rule, which itself lacks a deeper theoretical justification). A mathematical formulation equivalent to the path integral provides, within the framework of the Pairwise Interference Model (PIMOQ), an alternative interpretation that is mutually exclusive with the conventional one. According to this interpretation, quantum physics, within the scope considered here, describes the local (at the detector), intrinsically bidirectional, quantised energy transfer between field and matter (apart from quantisation this is in direct analogy with classical physics). In the case of constructive interference, this transfer is unidirectional, occurring exclusively from matter to the field, whereas in the case of destructive interference the two opposing energy fluxes are equal in magnitude. However, it appears that in the macroscopic world only the net balance of these two antagonistic and complementary fluxes is experimentally observable, whereas the individual contributions cannot be measured independently. This limitation is referred to here as a quantum-physical measurement problem. From this perspective, quantum physics constitutes a subdiscipline of thermodynamics with a correspondingly limited domain of applicability. Although the principle discussed is as fundamental as, for example, the principle of conservation of energy, this does not imply that the underlying physical processes must necessarily be identical in every situation in which the principle applies. This interpretation is further elaborated through a discussion of interference experiments employing coherent and incoherent light sources, as well as the generation of coherent light in the laser.
Within the framework of the ‘Pairwise Interference Model’ of light–matter interaction, it is postulated that light particles follow definite trajectories, and thus, for example, in the double-slit experiment, a particle can pass through only one of the two slits. On this premise, the interference of two photons is examined in greater detail. It is hypothesized that the interference of a photon pair requires the involvement of matter and, initially, that both molecular excitations and photons oscillate at the same frequency and that the continuity of the oscillation is not disrupted by absorption and emission. The molecular excitations in the light source are supposed to oscillate synchronously. Both photons arrive at the same point on the detector but may travel along different paths and therefore arrive at different times. Under these conditions, their phase difference, φ(2) – φ(1), is always zero. Consequently, no interference pattern can form on the detector screen and therefore the assumptions made are incorrect. Alternatively, one may assume that only the photon oscillates, whereas the excitation stores the phase, φ, possessed by the photon at the instant of absorption. In this case, φ(2) – φ(1) corresponds to the difference in travel times modulo the oscillation period, and an interference pattern can form. However, this assumption is problematic for some reasons: the nature of the matter-based memory remains unclear; according to the special theory of relativity, no time elapses for a particle travelling at the speed of light, meaning that it cannot oscillate; and the assumption contradicts Bohr’s correspondence principle. In a classical wave, the phase information propagates away from the source at the wave velocity without changing. This leads to the alternative possibility that the excitations oscillate, whereas the photons do not. Instead, the photons transport information about the phase of the excitation at the instant of emission. As can be shown, in this case, φ(2) – φ(1) likewise corresponds to the difference in travel times modulo the oscillation period. However, this hypothesis contradicts the de Broglie postulate, according to which all particles exhibit wave properties, and the relation ε = hν must therefore be interpreted differently. It also raises the question of how the dimensions of a laser, specifically the mirror separation, can influence the wavelength of the amplified light if a photon has no wavelength. Using replicator dynamics and the ‘Pairwise Interference Model’ of light–matter interaction, a simulation demonstrates that, in a simplified laser model, assuming that photons do not oscillate whereas excitations do, self-organisation gives rise to a phase pattern in the sequence of photons within the emitted light beam that corresponds to the pattern obtained by discretising a classical wave. Thus, coherent light can exhibit wave properties even if photons themselves do not. Finally, the possibility of how incoherent light acquires wave properties is briefly discussed.
## AbstractA deterministic interpretation of the double-slit experiment is proposed, in which the electron is treated as a localized particle at all times. The observed interference pattern is attributed to a real physical energy wave in the electromagnetic field, generated by the electron's accelerated motion through the field. This energy wave reaches the slit barrier, where the slit geometry creates coherent waves that merge to form a constructive interference wave. This wave redistributes energy in the field, creating an Electron-EMF coupled pathway that guides the particle to the detector. The apparent randomness of individual impacts arises from incomplete knowledge of the initial conditions, not from intrinsic indeterminism. The measurement effect is modelled as a disturbance of the coherent energy waves, either preventing the formation of the coupled pathway or destroying it after formation. The model is extended to the quantum eraser experiment, where the restoration of coherence via a polarizer naturally explains the reappearance of interference. A further extension to the delayed-choice quantum eraser is proposed, introducing the Entangled Constructive Interference Wave (ECIW) as a physical mechanism for entanglement within the model. The mechanism is shown to apply across geometries beyond the double slit. Predictions include a correlation between landing position and flight time, offering a testable distinction from standard quantum mechanical interpretations. A preliminary, illustrative mathematical framework is provided, situating the model within the pilot-wave tradition. **Keywords: ** Double-slit experiment, pilot wave, electromagnetic field, quantum interpretation, determinism, hidden variables, measurement problem, energy wave, coupled pathway, quantum eraser, delayed-choice quantum eraser, entanglement.
According to R. Feynman 1963-1965 [10], the interference pattern that appears on the observation screen in the double-slit experiment with light cannot be explained by classical physics. The detection probability is supposed to result from the superposition of all paths that the photon can take from the source to the detector, the light quantum is self-interfering. However, Jin et al. 2010 [11] showed that this is not necessarily the case. In their computer simulation, they assumed that the trajectory of a photon corresponds to that of a classical particle. Thus, the interference only occurs at the detector with the participation of several photons. Not every photon causes a detection.Tiefenbrunner 2024 [17] investigated the detector further and recognized that particle interference under this and some other conditions presupposes a monochromatic resonator (all permissible energy levels are integer (ℕ0) multiples of a basal energy unit ε, where ε is also referred to as the ‘colour’ of the resonator). A monochromatic two-state system, e.g. a molecule that can only exist in two energetic states (ground and excited) and can only absorb one quantum (with respect to one ‘colour’), is, however, not sufficient for this. This prompted an evaluation of the significance of the monochromatic resonator for the Boltzmann-factor and Planck's radiation law. It turns out that the Boltzmann-factor and thus also the radiation law require resonators and hence are incompatible with two-state systems. The radiation law is derived using a kinetic model for the interaction of light with matter and without a priori use of the Boltzmann-factor, whereby it is also assumed that photons follow classical trajectories.
The particle-interference-experiments, with the photons and electrons have clearly shown that they are always detected as localized ‘particles’; and the density of their detections exhibit a pattern similar to the interference of waves. This experimental-observation is alternatively interpreted here, different from the current, ‘probabilistic interpretation’. The ‘particle’ is first mathematically characterized as an ‘impulse function’ in space; and then Fourier-transformed into the wave-number-domain, as a wide band of constituent-waves as shown in the fig. 1&2. The ‘particle’ is an ‘event’ of constructive-superimposition of a wide band of ‘pre-quantum-waves’. This ‘event’ occurs in space at regular distances; and at regular instances in time. In the particle-interference-experiments, they are the wide band of ‘pre-quantum-waves which interfere physically. This physical interference of the pre-quantum-waves determines the position and time of emergence of the ‘impulse in space’ detectable as the ‘particle’. In the real-world-situation, the ‘pre-quantum-waves of a wide bandwidth arrive from all the directions, so the amplitude and phase of every constituent wave keep changing; so the place of constructive superimposition of all the spectral-components, keep varying unpredictably; and only the ‘probability’ of detection in a given volume is possible in practice. Thus, form the theoretical view-point, there are only the pre-quantum-waves; and ‘particle’ is a specific situation of constructive-superimposition of all the spectral-components of pre-quantum-waves; so there is no wave-particle-duality. The ‘probabilistic-interpretation’ is only a ‘practical-limitation’, detector being able to detect only the ‘particle’, and not the spectrum of constituent waves.
The nature of the problem The quantum world is inexplicable in classical terms. The predictions pertaining to the interaction of matter and light embodied in Newton's laws for the motion of particles and Maxwell's equations governing the propagation of electromagnetic fields are in flat contradiction with the experimental facts at the microscopic scale. A key feature of quantum effects is their apparent indeterminism, that individual atomic events are unpredictable, uncontrollable and literally seem to have no cause. Regularities emerge only when one considers a large ensemble of such events. This indeed is generally considered to constitute the heart of the conceptual problem posed by quantum phenomena, necessitating a fundamental revision of the deterministic classical world view. Some of the principal phenomena, among those discussed in this book, are as follows: ( a ) Self-interference: a beam of electrons sent one at a time through a barrier containing two apertures builds up through a series of localized detection events on a screen an interference pattern characteristic of waves (cf. the frontispiece and §5.1). ( b ) Tunnelling: an α-particle trapped in a nucleus can pass through a potential barrier in a manner forbidden to a classical particle (§5.3). ( c ) The stability of matter: atoms and molecules are found to exist only in certain discrete, or ‘stationary’, energy states. For this reason they do not ‘collapse’, the result predicted by classical electrodynamics. During transitions between stationary states (quantum jumps) an atom exchanges a discrete quantity of energy with the electromagnetic field (§§4.5, 7.6). […]
This paper proposes a discrete active-medium model in which Born-type probabilities arise as normalized intensities of coherent local transfer amplitudes. The model assumes that elementary cells of a discrete substrate carry directional complex states, and that transitions between neighboring cells are described by complex transfer amplitudes. The main result is a derivation of the probability rule from explicit assumptions of positivity, null transfer, global phase invariance, quadratic intensity scaling, and normalization over mutually exclusive channels. In this framework, the squared modulus is not introduced directly as a probability postulate, but appears as the physical intensity associated with a coherent transfer amplitude. The paper also discusses how interference arises from coherent addition of amplitudes, how the standard Born rule is recovered in a local channel basis, and how Schrödinger-type dynamics can appear as the long-wavelength limit of conservative local transfer. The proposed interpretation is presented as a limited and mathematically explicit contribution to the foundations of quantum mechanics, not as a complete solution to the measurement problem.