Electromagnetism as Quantum Physics
arXiv:1902.01930 · doi:10.1007/s10701-019-00253-3
Abstract
One can interpret the Dirac equation either as giving the dynamics for a classical field or a quantum wave function. Here I examine whether Maxwell's equations, which are standardly interpreted as giving the dynamics for the classical electromagnetic field, can alternatively be interpreted as giving the dynamics for the photon's quantum wave function. I explain why this quantum interpretation would only be viable if the electromagnetic field were sufficiently weak, then motivate a particular approach to introducing a wave function for the photon (following Good, 1957). This wave function ultimately turns out to be unsatisfactory because the probabilities derived from it do not always transform properly under Lorentz transformations. The fact that such a quantum interpretation of Maxwell's equations is unsatisfactory suggests that the electromagnetic field is more fundamental than the photon.
28 pages, 4 figures
References in corpus (6)
- Bohmian Mechanics and Quantum Field Theory
- The role of the Riemann-Silberstein vector in classical and quantum theories of electromagnetism
- Self-Locating Uncertainty and the Origin of Probability in Everettian Quantum Mechanics
- Pilot-wave approaches to quantum field theory
- Hydrodynamic construction of the electromagnetic field
- Forces on Fields
Cited by in corpus (13)
- The Fundamentality of Fields
- Maxwell quantum mechanics
- How Electrons Spin
- Can the double-slit experiment distinguish between quantum interpretations?
- Reflection and transmission of electromagnetic pulses at a planar dielectric interface -- theory and quantum lattice simulations
- On detection statistics in double-double-slit experiment
- Putting Positrons into Classical Dirac Field Theory
- QED based on eight-dimensional spinorial wave equation of the electromagnetic field and the emergence of quantum gravity
- Localizable Particles in the Classical Limit of Quantum Field Theory
- On the Majorana representation of the optical Dirac equation
- A new matrix representation of the Maxwell equations based on the Riemann-Silberstein-Weber vector for a linear inhomogeneous medium
- Non-Heisenbergian quantum mechanics
- Quantizing Galilean spacetime: a reconstruction of Maxwell's equations in empty space