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Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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The Boat on the River: Two Barwise Situations, the Double Haloed Monad, and Why the Wheeler-Dewitt Equation Has No Solution

Authors: Lee Gerald Bloomquist; Claude 4.6 (AI);

The Boat on the River: Two Barwise Situations, the Double Haloed Monad, and Why the Wheeler-Dewitt Equation Has No Solution

Abstract

The Wheeler–DeWitt equation, the central equation of canonical quantum gravity, has never been solved in its general form, and its solutions cannot be normalized by the ordinary Born rule. We argue that this is not a temporary mathematical failure but a permanent structural signature: the equation's solution belongs to a situation, in the technical sense Jon Barwise gave that word, which does not support the kind of information a solution would have to be expressed in. We build this claim through the innerProperTime (iPT) framework — non-wellfounded set theory, a modification of Robinson's nonstandard analysis into a double halo of possibility and fact, Barwise situation theory, and a reading of the Born rule as a logical AND performed by the multiplication of a complex number and its conjugate. We apply the framework to a modified Bohmian mechanics of the two-slit experiment and to Dirac's discovery of antimatter, which we treat as precedent for a destruction operator that terminates a life's coinductive stream. We then state formally what we call the two Barwise situations, use a large language model as a working instance of the first, and show that Barontini et al.'s 2026 cold-atom experiment is the first quantitative evidence consistent with the resulting picture. We further show that the double-haloed monad is not, as a first pass through Barwise-Seligman channel theory suggests, a core token pairing two independent classifications; it is a single prior situation, bisected by orientation into nonStandardFuture and nonStandardPast, with the channel theory's genuine convergence occurring instead in the standard-part map that collapses the whole halo onto NOW. NOW_ofTheWorldLine is a stream of such monads, and its self-identity across time follows from Aczel's uniqueness theorem rather than from an appeal to memory or feeling. We close by extending Wheeler's own dictum — that philosophy is too important to leave to philosophers — to say that physics needs the poets too. Kabir and Parmenides, we suggest, were already reporting from the second situation, in the only language available for it.

Originally archived at Atopos: https://a-topos.org/papers/ATOPOS-2026-000009

Keywords

non-standard analysis. smooth infinitesimal analysis, Quantum gravity, set theory, Bohmian mechanics, proper time, physics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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