by Joy Christian » Thu Sep 17, 2015 2:19 am
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Fred Diether asked me a question about the precise relationship between my model and quantum mechanics. In his words, what he wanted to know was how does my model "complete quantum mechanics." To understand this fully one has to go back to the original paper by EPR and understand their argument within the context of my model, as I have done in
this paper. However, it is also possible to understand this more simply through the following
Born correspondence. A useful reference is
my very first paper where I proposed the Clifford-algebraic model, but here is the precise mathematical correspondence between my model and quantum mechanics:
where
and
***
Fred Diether asked me a question about the precise relationship between my model and quantum mechanics. In his words, what he wanted to know was how does my model "complete quantum mechanics." To understand this fully one has to go back to the original paper by EPR and understand their argument within the context of my model, as I have done in [url=http://arxiv.org/pdf/0904.4259.pdf]this paper[/url]. However, it is also possible to understand this more simply through the following [color=#FF0000]Born correspondence[/color]. A useful reference is [url=http://arxiv.org/pdf/quant-ph/0703179.pdf]my very first paper[/url] where I proposed the Clifford-algebraic model, but here is the precise mathematical correspondence between my model and quantum mechanics:
[tex]\boxed{\,\left<\,{\bf n},\,\lambda\,\left|\,\sigma\cdot{\bf n}\,\right|\,{\bf n},\,\lambda\,\right> \,=\,\lambda\,=\,-\left({\rm I}\cdot{\bf n}\right)\left(\mu\cdot{\bf n}\right),}[/tex]
where
[tex]{\bf n} \,=\,\text{an ordinary vector},[/tex]
[tex]\sigma\,=\,\text{a vector made out of Pauli matrices},[/tex]
[tex]\lambda\,=\,\pm 1,[/tex]
[tex]{\rm I}\,=\,{\bf e}_x \wedge {\bf e}_y \wedge {\bf e}_z\,=\,\text{a trivector},[/tex]
[tex]\mu\,=\,\lambda\,{\rm I}\,=\,\text{a pair of trivectors},[/tex]
[tex]\mu\cdot{\bf n}\,=\,\text{a pair of spin bivectors},[/tex]
[tex]\rm{I}\cdot{\bf n}\,=\,\text{the detector bivector},[/tex]
and
[tex]\left|\,{\bf n},\,\lambda\,\right> \,=\, \text{the usual eigen vector of}\;\sigma\cdot{\bf n}\;\text{with the eigen value}\;\lambda.[/tex] :)