, the interaction between modes with frequencies of opposite sign can lead to negative-mass-like instabilities in the system.... invariably correlates with a superluminal regime,...Our study offers practical insights into how to efficiently extract gain from time-variant systems, with potential applications in photonic circuits.
Contradictions can then arise if we continue to view a photon’s energy as ℏω. There are, for instance, negative frequency components in the free space electromagnetic field, yet each photon only ever contributes a positive energy to the total. This positivity of the energy can be traced back to the definition of the photon creation and annihilation operators,....the importance of waves that make transitions across the positive or negative frequency divide to the emission of radiation. We shall show that such emission is essentially a quantum process associated with the creation of photon pairs (“qubits”),...The off diagonal elements represent transitions between different wave frequencies
https://pubs.aip.org/aip/apq/article/1/2/020901/3282301
neither energy nor frequency is conserved, but conservation violation comes in different forms for each. Although a positive frequency mode entering the time dependent region may emerge as a negative frequency one, this does not indicate that the final photon state has a negative energy. As discussed above, in free space, all photons have a positive energy and the quantum of energy will always be given by ℏω. Instead, as we shall see, a change in the sign of the frequency indicates a transformation of a creation operator into an annihilation operator, which, in turn, affects how we count photons. Therefore, although negative frequencies do not here imply negative energies, they are, nevertheless, central to understanding quantum processes occurring within space–time varying media.
....................
In a rotationally symmetric system that conserves spin, direct transitions of photons from positive to negative frequency are forbidden because reversing frequency reverses spin. Access to negative frequencies is facilitated by the creation of photon pairs (“qubits”), comprising both a positive and a negative frequency, thus satisfying spin conservation but by a process that has no classical counterpart and is responsible for the radiation produced by these systems operating on the ground state.
https://www.mdpi.com/2073-8994/17/3/360
4.3. What Do We Learn from the Review of the Models of Williamson and Dos Santos?
In
the model of Williamson, the factor 2 that appears in Dirac theory in
the spin, magnetic moment, and Zitterbewegung frequency comes from the
fact that we have a double loop (
).
The spin is not an intrinsic property of the electron; it emerges as a
tangible, physical phenomenon arising from the underlying
electromagnetic dynamics at the Compton scale.
Moreover
in both models, the charge is understood as the divergent signature of a
given self-oscillating electromagnetic field. This reinterpretation of
charge, as a field signature, aligns with the model of the electron as a
self-interacting electromagnetic field, potentially resolving the
paradoxes associated with point-like and/or extended charge
distributions. The correct value of the Lorentz force in Dos Santos’s
model further justifies this “closed orbit” assumption. This perspective
suggests that charge and charge density might be emergent properties of
field dynamics at the Compton scale rather than intrinsic properties.
Finally,
in this model, and following the lead of D. Hestenes, we identify the
electron’s rest mass with its electromagnetic field energy. This concept
aligns with Einstein’s equivalence principle (
, with c being speed of light), positing that mass is purely a form of energy.
Those
facts suggest that the fundamental properties of the electron,
including spin, charge, and mass, may be emergent phenomena arising from
the dynamics of electromagnetic fields rather than “intrinsic”
properties.
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