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Kind of report: Research.
Last version: 2010 Jun 28. Scheduled publication (may change): 2010 Oct 01.
Scientific knowledge is accumulative. Theoretical and fundamental scientists require a single comprehensive theory applying to all physical phenomena
. Quantum mechanics is used for a broad range of microscopic phenomena. This implies that any quantum theory, to be taken seriously, would reduce to quantum mechanics in some limit.
This Research report studies the quantum mechanical limit of three theories, presenting the difficulties and inconsistencies found when rigorously revised. The theories considered are: relativistic quantum electrodynamics —both field
and spacetime
formulations—; relativistic quantum dynamics; and action-at-a-distance quantum theory.
This Research report extend, to the quantum domain, the classical results obtained before (PRE 1997, 53, 5373; PRE 1998, 57, 3683; CSR:20093) and shows that (i) the assertions that relativistic quantum electrodynamics reduces to quantum mechanics as well as (ii) the assertion that the static-field-low-velocity relativistic equations are identical to the equation of motion do not hold up on close inspection. For instance, the Coulombian quantum potential operator ϕ = ϕ\(R\(t\)\) cannot be reproduced by the field potential operators (\ab v)ϕ = (\ab v)ϕ\((\ab v) x‚(\ab v) t\) of relativistic quantum electrodynamics in any limit. It is also explained that some observational difficulties of relativistic quantum theories —such as the localization of elementary particles— are related to their lack of compatibility with quantum mechanics. Among the theories revised, only that proposed by reduces to quantum mechanics.
One of the main findings of this Research report is that the theories revised belong to one of two incompatible classes, extending and generalizing the incompatibility between relativistic quantum electrodynamics and quantum mechanics first denounced by . The main pros and cons for each kind are presented.
Finally, this Research report introduces the new post-relativistic quantum theory and discusses its possibilities and advantages over current theories.
Manuscript in preparation.
Manuscript in preparation.
Manuscript in preparation.