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    The mathematical framework physicists actually use presup... — Carmelics
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    Supports→The separable Hilbert space formulation of quantum mechanics is unsatisfactory.

    The mathematical framework physicists actually use presupposes structures (delta functions, plane waves) that only become rigorous in the larger rigged Hilbert space setting.

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    Reasons For

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    Reason for
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    • 1.Physicists routinely use delta functions and plane waves in calculations that yield experimentally verified predictions, suggesting these tools capture real structure.
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    • 2.Standard Hilbert space cannot accommodate eigenstates of continuous spectra; rigged Hilbert spaces mathematically justify what physicists do informally.
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    • 3.The gap between physics practice and standard mathematical rigor indicates the formalism used presupposes a deeper structure than conventional mathematics provides.
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    Reasons Against

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    • 1.Physicists' informal methods work without invoking rigged Hilbert spaces; their success doesn't prove these structures are actually presupposed rather than post-hoc justifications.
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    • 2.Distribution theory (Schwartz distributions) makes delta functions rigorous within standard mathematics without requiring the full apparatus of rigged Hilbert spaces.
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    • 3.The claim conflates pedagogical convenience with metaphysical necessity; physicists could adopt distribution theory straightforwardly without philosophical conclusions.
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    Related

    Distribution theory (Schwartz distributions) makes delta functions rigorous with...Physicists routinely use delta functions and plane waves in calculations that yi...Physicists' informal methods work without invoking rigged Hilbert spaces; their ...Standard Hilbert space cannot accommodate eigenstates of continuous spectra; rig...
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    The claim conflates pedagogical convenience with metaphysical necessity; physici...The gap between physics practice and standard mathematical rigor indicates the f...The separable Hilbert space formulation of quantum mechanics is unsatisfactory.

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    claim
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    2 (1 for, 1 against)
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