Correction: Gill, R.D. Does Geometric Algebra Provide a Loophole to Bell's Theorem? Entropy 2020, 22, 61.

Corrections are made to my paper "Gill, R.D. Does Geometric Algebra Provide a Loophole to Bell's Theorem? Entropy 2020, 22, 61" [...].

Corrections are made to my paper “Gill, R.D. Does Geometric Algebra Provide a Loophole to Bell’s Theorem? Entropy 2020, 22, 61”. Firstly, there was an obvious and easily corrected mathematical error at the end of Section 6 of the paper. In the Clifford algebra under consideration, the basis bivectors do not square to the identity, but to minus the identity. However, the trivector M does square to the identity and hence non-zero divisors of zero, and , can be found by the same argument as was given in the paper.

Secondly, in response to a complaint about ad hominem and ad verecundam arguments, a number of scientifically superfluous but insulting sentences have been deleted, and other disrespectful remarks have been rendered neutral by omission of derogatory adjectives. I would like to apologize to Dr. Joy Christian for unwarranted offence.

The end of Section 6 of Gill (2020) [1] discussed the even sub-algebra of , isomorphic to :

One can take as basis for the eight-dimensional real vector space the scalar 1, three anti-commuting vectors , three bivectors , and the pseudo-scalar . The algebra multiplication is associative and unitary (there exists a multiplicative unit, 1). The pseudo-scalar M squares to . Scalar and pseudo-scalar commute with everything. The three basis vectors , by definition, square to . The three basis bivectors square to . Take any unit bivector v. It satisfies hence . If the space could be given a norm such that the norm of a product is the product of the norms, we would have hence either or (or both), implying that either or (or both), implying that or , neither of which are true.

But the bivectors square to and the trivector M squares to . Still, it then follows that , and by the argument originally given, it follows that or , a contradiction.