Geometric Origin of Photon Wave Properties

Junzheng Liu

Nicholas Chako

Y Q Cai, G. Papini, W. R. Wood +1 more

Berry's phase for photons is derived from Maxwell's theory and is shown to be classical. The approach is geometrically obvious and is shown to be equivalent to those of F.D.M. Haldane (1987) and J. Segert (1987). The phase remains the same for plane wave solutions in the Heisenberg-Euler nonlinear electrodynamics.

Longjian Wu

This paper, under the core framework of Boundary Interface Theory (BIT), takes the intrinsic property of electrons as standing waves on the spacetime membrane and the quantized orbital constraints induced by proton membrane pressure as the theoretical basis, to conduct an in-depth and systematic study on the physical mechanism and mathematical expression of electron transition, a core dynamic phenomenon of micro quantum systems. Different from traditional quantum mechanics theories that only describe electron transition from the perspective of quantum state superposition and fail to link it with the intrinsic spacetime geometric nature, this study defines electron transition as the modal reconstruction and dynamic evolution of discrete steady-state standing wave eigenmodes on the spacetime membrane, and completes the quantitative derivation and qualitative analysis of electron transition through the phase matching of standing wave superposition, the law of energy conservation and the constraints of geometric potential wells. It further reveals the geometric dynamic origins of the non-intermediate state characteristic and proton membrane-pressure orbital constraint of electron transition: the non-intermediate state is due to the fact that the spacetime geometric potential well formed by proton membrane pressure only supports discrete steady-state standing wave eigenmodes satisfying the phase matching condition, and non-eigenmode standing waves cannot stably exist due to rapid interference cancellation; the orbital constraint results from the fact that electron transition is only the coherent superposition of standing wave eigenmodes within the proton membrane-pressure orbit, and the superposed wave function always satisfies the geometric constraints and boundary conditions of proton membrane pressure with no mathematical possibility of out-of-orbital transition. In addition, the paper derives the quantitative expression of the electron transition energy difference composed of basic physical constants and the characteristic physical quantities of protons and electrons, without introducing any new adjustable parameters or experimental inputs. The derivation is highly self-consistent with the previous research conclusions of Boundary Interface Theory, and is consistent with the experimental observational facts of micro quantum mechanics such as the discreteness of atomic spectra and the shell transition rules of atoms. This research realizes the theoretical closed loop of Boundary Interface Theory from the "intrinsic static existence" of electrons to the "dynamic transition laws", reduces quantum transition phenomena to the geometric dynamic effects of the spacetime membrane, and provides a brand-new theoretical path for exploring the classical geometric origin of quantum phenomena. Finally, the paper prospects the future research directions of Boundary Interface Theory, including extending the research to multi-electron atomic systems, constructing an electron-photon interaction model based on spacetime membrane dynamics, exploring the electron transition characteristics of molecular systems, and studying the spacetime membrane origin of quantum entanglement, which points out the way for the further expansion of the theory and the in-depth integration of quantum mechanics and general relativity.

Lajos Jánossy

David Maker

Here we postulate a geometrical 2D closed path invariant ds=dst+dsΦ (geometrical interpretation) with the observer's own 2D ds=dst+dsΦ then giving a total direct sum 2⊕2=4 degrees of freedom for the resulting (observer translation) Dirac equation pde and its ψ. There are several, more or less technical, ways of stating the consequences of that new "observer interpretation" Dirac equation pde. Two such ways are "wave function collapse," and in a more common sense vein "Bertlmann's socks." Note that wavefunction collapse to ψ then (and experimental nonlocality implications) is the "observables translation" of that fundamental postulate and so not itself postulated. Also that geometrical postulate does not allow a Bohmian hidden variable interpretation because of its fundamental nature (i.e., we cannot go any deeper). For example that postulate states no x or p that we would be certain of in some hidden variable context. Thus we can ignore here the straw man arguments of J.S. Bell that are in response to Bohmian hidden variable theories only. Thus there cannot result Bell's kink at θ=0 in the correlation function between the polarization measurements on the two ends of an EPR experimental apparatus (Bell, 1987). Recall this kink required correlating in a hidden variable, classical statistical mechanical context, with resulting superluminal implications. Also note here the "observer interpretation" boundary condition conservation of angular momentum of the initial singlet state for our 4D Dirac pde results in this being a time independent solution to this pde. Thus wave function collapse to the measured value in no way implies superluminal communication. In laymen terms it is just the Bertlmann's socks common sense fact that we knew before hand about the original singlet state of the central emitter, no superluminal communication between the left and right ends of the Aspect apparatus was required to know about this. Thus our new observer representation Dirac equation pde (the below equation 3.7), and the geometrical postulate it originated from, solves the nonlocality problem which has been an enigma to physics ever since that original EPR paper of many decades ago. This is relevant to the origin of the photon since this wave function collapse is also a basic behavior of light and photons.