Abstract
Assuming the Dirac wavefunction describes the state of a single particle. We propose that the relation derived by Schrödinger, which contains the Zitterbewegung term, is a position equation for an amplitude modulated wave. Namely, the elementary constituents are amplitude modulated waves. Indeed, we surmise that a second wave is associated with the particle, which corresponds to a signal. At the same time, we interpret that Broglie’s wave corresponds to a carrier. Furthermore, the quantum object is a recording medium and, like in a hologram, information encoded on its surface. We suggest a description and the cause of the Zitterbewegung heretofore never considered regarding the previous assertions. Hereunder, we shall also apply the quantum amplitude modulation interpretation to the single-photon wave function by Bialynicki-Birula. The predictions are testable, thence providing evidence for the proposed hypothesis.
Highlights
Per the analysis by Schrödinger of the position operator regarding Dirac’s relativistic formalism [1], the free particle, along with its translational motion, ought to exhibit an oscillatory activity that he called the Zitterbewegung [2]
We propose that the relation derived by Schrödinger, which contains the Zitterbewegung term, is a position equation for an amplitude modulated wave
As we shall see, the photon has a particular “trembling motion” and conveys a binary unit of information. We reach this conclusion by interpreting the consequences of applying the amplitude modulation hypothesis to the single-photon wave function Bialynicki-Birula and other researchers proposed
Summary
Per the analysis by Schrödinger of the position operator regarding Dirac’s relativistic formalism [1], the free particle, along with its translational motion, ought to exhibit an oscillatory activity that he called the Zitterbewegung [2]. The positive and negative plane waves are interpreted or replaced by a particle-antiparticle annihilating pair, and when the function describing the electron is separated, the Zitterbewegung disappears. With a fundamental relation between sine and exponential functions, manipulating the Zitterbewegung term in the position equation resembles the mathematical representation of amplitude-modulated waves. Suggesting quantum objects described by Dirac’s relativistic formalism are amplitude modulated waves and, the Dirac wave function represents a single entity. Regarding the formalism of the Dirac equation, it is our impression that it describes the encoding and transfer of information through a communication channel. This channel is the vacuum or any other medium. We suggest testable predictions about the photon, illustrating the photon’s Zitterbewegung and introducing the correct matrices that encode Maxwell’s equations in a Dirac-Schrödinger type equation
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