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Orthomodularity and the incompatibility of relativity and quantum mechanics

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We show that orthomodularity in general and non-existence of isotropic vectors in particular decisively yield the geometry of quantum mechanics and that a fundamental reason why quantum mechanics and relativity cannot be unified is because of the non-existence of isotropic vectors.

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  1. Non-zero vectors with zero norm.

  2. Let E be a precompact subset (in the norm topology) of an infinite dimensional, separable Hilbert space. Then there exists \((e_{n}) \) such that \(\sum \nolimits _{n=1}^{\infty }\left\langle x,e_{n}\right\rangle <\infty \) for all \(x\in E\).

  3. Not to be confused with a split space in theory of Quadratic Forms, a completely opposite concept.


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Correspondence to Abdullah Naeem Malik.

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Malik, A.N., Kamran, T. Orthomodularity and the incompatibility of relativity and quantum mechanics. Quantum Stud.: Math. Found. 4, 171–179 (2017).

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