Abstract:Quantum mechanics represents states by exactly specified density operators, whereas experimentally available information is necessarily finite in precision. We develop \emph{Interval Quantum Mechanics (IQM)}, in which finite observational information is represented by a \emph{quantum parcel}, a convex open set of density operators. Experimental parcels are determined by finitely many expectation intervals and form a basis for the state-space topology. A single parcel represents the states compatible with the available information, while a double parcel $(O_1,O_2)$ consists of disjoint possible and excluded regions. Exact point states are recovered as ideal limits of successive parcel refinement.
Unitary dynamics lifts to a reversible evolution of parcels. Finite-resolution measurements are represented by fuzzy POVMs and Kraus updates; single parcels are preserved, while double-parcel updates are order-compatible whenever they remain double parcels. We give a useful sufficient condition for such preservation, together with examples showing it is not necessary. Under suitable conditions measurement contracts ambient Hilbert--Schmidt volume and strictly increases the associated geometric information. This contrasts with von Neumann entropy, which can remain unchanged under a selective measurement even though information has been gained.
In this formulation, several familiar foundational paradoxes no longer arise in standard form. Wave--particle duality becomes a continuous suppression of interference as which-path resolution increases. Schrödinger's cat is described by a finite parcel updated toward the observed outcome sector, rather than an exact superposition undergoing abrupt collapse. Entanglement remains genuinely nonclassical: CHSH violation persists throughout an open parcel around a Bell state.
From: Abbas Edalat [view email]
[v1]
Tue, 19 May 2026 11:43:32 UTC (233 KB)
[v2]
Wed, 27 May 2026 13:14:56 UTC (239 KB)
[v3]
Thu, 28 May 2026 14:02:03 UTC (241 KB)
[v4]
Sat, 30 May 2026 09:57:20 UTC (241 KB)
[v5]
Wed, 19 Aug 2026 12:27:21 UTC (234 KB)
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