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- W1625156783 abstract "We shall show how elementary logic calculus can be represented within the Clifford algebras Cℓ1,1, Cℓ3,1 ≃ Cℓ2,2 and Cℓm,m , in general. Thus, we shall also understand why logic is connected with the standard model of physics and the quantum structure of spacetime, respectively. “It is not the substance which is in space,” as Alfred North Whitehead had pointed out, “but the attributes”. Accordingly, as we consider the Dirac algebra Mat(4, C), annihilation and time reversal turn out to be logic operations acting on Dirac spinors. This is remarkable as three generations of physicists have calculated time reverted wave functions. In a complete Clifford algebraic image of the Dirac equation, those wave functions do not exist because time reversal, when carried out in the whole algebra, annihilates any Dirac spinor. It is then, essentially in the quantum chromodynamics context of the Majorana algebra, that classical logic becomes incomplete with regard to definite truth. That is, color rotations cannot be represented as products of logic operations. It also follows that once we connect spinor spaces with probability distributions, classical logic naturally turns into quantum logic. Future developments may show how logic derivative procedures can be represented synchronically as elements in neutral signature and, further, how logic quantum computations can be generated practically by reflections of waves in subnuclear arrays." @default.
- W1625156783 created "2016-06-24" @default.
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- W1625156783 date "2000-01-01" @default.
- W1625156783 modified "2023-09-24" @default.
- W1625156783 title "Clifford Algebra of Quantum Logic" @default.
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- W1625156783 doi "https://doi.org/10.1007/978-1-4612-1368-0_12" @default.
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