Qubits and oriented matroids in four time and four space dimensions
arXiv:1210.0928 · doi:10.1016/j.physletb.2012.12.034
Abstract
We establish a connection between 4-rebits (real qubits) and the Nambu-Goto action with target `spacetime' of four time and four space dimensions ((4+4)-dimensions)). We motivate the subject with three observations. The first one is that a 4-rebit contains exactly the same number of degree of freedom as a complex 3-qubit and therefore 4-rebits are special in the sense of division algebras. Secondly, the (4+4)-dimensions can be splitted as (4+4)=(3+1)+(1+3) and therefore they are connected with an ordinary (1+3)-spacetime and with changed signature (3+1)-spacetime. Finally, we show how geometric aspects of 4-rebits can be related to the chirotope concept of oriented matroid theory.
15 pages, Latex, improved version
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- Some Mathematical and Physical Remarks on Surreal Numbers
- Towards an Alternative Gravitational Theory
- Nanbu-Goto action and qubit theory in any signature and higher dimensions
- Towards a unified Lagrangian formalism for Cosmology and Black Holes