A new relativistic quantum mechanics

John G. Williamson (University of Glasgow)

14-Jan-2023, 15:00-18:00 (14 months ago)

Abstract: Dirac's theory has been the "gold standard" of relativistic quantum mechanics (RQM) for more than ninety years. During that time the quantum mechanics used in the imagining and engineering of quantum devices has been in the realm of, almost exclusively, the non-relativistic Schroëdinger theory using complex wave-functions.

The merely complex is, however, too simple to properly represent covariant, relativistic wave-functions. Furthermore, the merely complex cannot properly represent intrinsic relativistic quantum properties such as the intrinsic spin. If one does not have the proper theory, the internal behaviour of the elementary particles, their mutual inter-actions, and the very quantum properties of collective quantum systems, such as high-temperature superconductors, cannot be properly thought about at all.

The new theory presented here aims to rectify those deficiencies: it treats the elementary particle masses in a fundamentally different way to Dirac, incorporating them as a pair of elements within a hypercomplex algebra including both the complex algebra, and the quaternion algebra as sub-algebras. This allows a simpler, and even more beautiful equation than the Dirac or Maxwell equations to be written down, which yet contains them both. This equation may be written simply as dG=C, where "d" is a relativistic space-time derivative, "G" is a sixteen component multi-vector, and "C" is a sixteen component array of real constants, most of which are zero.

The new theory opens up new vistas, new thinking, and new connections. It provides an underlying basis to the theory of Quantum ElectroDynamics, encompasses the Newton, Maxwell and Einstein, and removes all of the outstanding problems in RQM.

The talk will focus on answering the list of questions posed by the group (repeated below), as well as a set of further fundamental questions, including the origin of the g-2 term in the theory. This will include the nature of the "generations" of particles in the standard model. It is argued that the addition of this new element to the "standard model" will allow one to promote to a "standard theory" fit for progressing the new challenges of the 21st century.

Questions to be answered include, but are not limited to:

Why electric charge is quantized. Where the Coulomb interaction comes from How one can prevent infinites e.g. of electric field of a point charge Origins of the induced magnetic dipole and the intrinsic angular momentum Origin of the zitterbewegung/clock of the electron Why we have 3 generations of leptons Why the proton is lighter than neutron What holds nuclei together against the Coulomb force What holds charged elementary particles together against the enormous Coulomb repulsion How to get gravity from relativistic quantum mechanics and Q.E.D.

The talk will focus on answering the list of questions posed by the group, including the nature and origin of charge, the reason for and the nature of the "generations" of particles in the standard model. It is argued that the addition of this new element to the "standard model" will allow one to promote to a "standard theory" fit for progressing the new challenges of the 21st century.

mathematical physicsgeneral physicsquantum physics

Audience: researchers in the topic

( paper )


QM Foundations & Nature of Time seminar

Series comments: Description: Physics foundations discussion seminar

Current access link in th.if.uj.edu.pl/~dudaj/QMFNoT

Organizer: Jarek Duda*
*contact for this listing

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