Quantum mechanics without the quantum

Antonopoulos, C; Papadimitropoulos, T

dc.contributor.author	Antonopoulos, C	en
dc.contributor.author	Papadimitropoulos, T	en
dc.date.accessioned	2014-03-01T01:55:27Z
dc.date.available	2014-03-01T01:55:27Z
dc.date.issued	2006	en
dc.identifier.issn	01824295	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/27739
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-49249134135&partnerID=40&md5=2bcb84a9a250552af8c29e6138c17bee	en
dc.title	Quantum mechanics without the quantum	en
heal.type	journalArticle	en
heal.publicationDate	2006	en
heal.abstract	The two Heisenberg Uncertainties entail an incompatibility between the two pairs of conjugated variables E, t and p, q. But incompatibility comes in two kinds, exclusive of one another. There is incompatibility defineable as: (p → ¬q) ∧ (q → ¬p) or defineable as [(P → ¬q) ∧ (q → ¬p)] ⇔ r. The former kind is unconditional, the latter conditional. The former, in accordance, is fact independent, and thus ascertainable by virtue of logic, the latter fact dependent, and thus ascertainable by virtue of fact. The two types are therefore diametrically opposed. In spite of this, however, the existing derivations of the Uncertainties are shown here to entail both types of incompatibility simultaneously. ΔEΔt ≥ h, for example, is known to derive from the quantum relation E = hv plus the Fourier relation ΔvΔt ≃ 1. And the Fourier relation assignes a logical incompatibility between a Δv = 0, Δt = 0. (No frequency defineable at an instant.) Which is therefore fact independent and unconditional. How can one reconcile this with the fact that ΔEΔt if and only if h > 0, which latter supposition is a factual truth, entailing that a ΔE = 0, Δt = 0 incompatibility should itself be fact dependent? To then say that the incompatibility at hand is only logical, i.e. that resulting from ΔvΔt ≥ 1, is to treat ΔE = 0, Δt = 0 as unconditionally incompatible, since this is what their equivalents, Δv = 0, Δt = 0 are, and therefore as incompatible independently of the quantum. And to say that it is only factual, amounts to disputing E = hv itself, whose presence alone is what necessitates application of the -logical-relation ΔvΔt ≥ 1. Since either option sacrifices an equally essential requirement, it can only follow that this Uncertainty expresses both a conditional and an unconditional form of incompatibility. We continue by tracing the exact same phenomenon right within the heart of the noncommutative formalism of QM. The fact dependent p,q noncommutativity, expressed in pq ≠ qp as derived from the relation pq- qp =iℏI, has given its place to the abstract Hilbertian, fact independent noncommutativity, expressed in AB ≠ BA, without explicit or implicit reference to ℏ. Hence, to identify the two would lead to a contradiction comparable to the previous.	en
heal.journalName	Annales de la Fondation Louis de Broglie	en
dc.identifier.volume	31	en
dc.identifier.issue	4	en
dc.identifier.spage	421	en
dc.identifier.epage	439	en