Basic Concepts for a Quantum Mechanical Theory of Events
Abstract
A physical theory is proposed that obeys both the principles of special relativity and of quantum mechanics. As a key feature, the laws are formulated in terms of quantum events rather than of particle states. Temporal and spatial coordinates of a quantum event are treated on equal footing, namely as self-adjoint operators on a Hilbert space. The theory is not based upon Lagrangian or Hamiltonian mechanics, and breaks with the concept of a continuously flowing time. The physical object under consideration is a spinless particle exposed to an external potential. The theory also accounts for particle-antiparticle pair creation and annihilation, and is therefore not a single-particle theory in the usual sense. The Maxwell equations are derived as a straightforward consequence of certain fundamental commutation relations. In the non-relativistic limit and in the limit of vanishing time uncertainty, the Schrödinger equation of a spinless particle exposed to an external electromagnetic field is obtained.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2004
- DOI:
- arXiv:
- arXiv:quant-ph/0411175
- Bibcode:
- 2004quant.ph.11175B
- Keywords:
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- Quantum Physics
- E-Print:
- 48 pages, 4 figures, revised introduction, minor corrections