Making the quantum of relevance

Antonopoulos, C

dc.contributor.author	Antonopoulos, C	en
dc.date.accessioned	2014-03-01T01:22:40Z
dc.date.available	2014-03-01T01:22:40Z
dc.date.issued	2005	en
dc.identifier.issn	09254560	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16627
dc.subject	Factual incompatibility	en
dc.subject	Fourier	en
dc.subject	Logical incompatibility	en
dc.subject	Quantum of action	en
dc.subject	Self-sufficient incompatibility	en
dc.subject	Symmetry	en
dc.subject	Uncertainties	en
dc.subject	Unique wave-period	en
dc.title	Making the quantum of relevance	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s10838-006-5716-y	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s10838-006-5716-y	en
heal.publicationDate	2005	en
heal.abstract	The two Heisenberg Uncertainties (UR) 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 a matter of logic, the latter fact dependent, and thus a matter 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. Δ E Δ t ≥ h is known to derive from the quantum relation E = hν plus the Fourier relation Δ ν Δ t ≥ 1. And the Fourier relation assigns a logical incompatibility between Δ ν = 0, Δ t = 0. (Defining a repetitive phenomenon at an instant t → 0 is a self contradictory notion.) An incompatibility, therefore, which is fact independent and unconditional. How can one reconcile this with the fact that Δ EΔ t exists if and only if h > 0, which latter supposition is a factual truth, entailing that a Δ E = 0, Δ t = 0 incompatibility should itself be fact dependent? Are we to say that E and t are unconditionally incompatible (via Δ ν Δ t ≥ 1) on condition that E = hν is at all true? Hence, as presently standing, the UR express a self-contradicting type of incompatibility. To circumvent this undesirable result, I reinterpret E = hν as relating the energy with a period. Though only one such period. And not with frequency literally. (It is false that E = ν . It is true that E = ν times the quantum.) In this way, the literal concept of frequency does not enter as before, rendering Δ ν Δ t ≥ 1 inapplicable. So the above noted contradiction disappears. Nevertheless, the Uncertainties are derived. If energy is only to be defined over a period, momentum only over a distance (formerly a wavelength) resulting during such period, thus yielding quantized action of dimensions Et = pq, then energies will become indefinite at instants, momenta indefinite at points, leading, as demanded, to (symmetric!) Δ E Δ t = Δ p Δ q ≥ h's. © Springer Science+Business Media, Inc. 2006.	en
heal.journalName	Journal for General Philosophy of Science	en
dc.identifier.doi	10.1007/s10838-006-5716-y	en
dc.identifier.volume	36	en
dc.identifier.issue	2	en
dc.identifier.spage	223	en
dc.identifier.epage	241	en