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Quantum Mechanics over the real field

Quantum Mechanics over the real field. Robert Spekkens Department of Applied Mathematics and Theoretical Physics University of Cambridge. July 24, 2007 FQXi. Funding by: The Royal Society. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A A.

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Quantum Mechanics over the real field

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  1. Quantum Mechanics over the real field Robert Spekkens Department of Applied Mathematics and Theoretical Physics University of Cambridge July 24, 2007 FQXi Funding by: The Royal Society TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAA

  2. Questions about the utility of Real QM: Might there be experimental situations where the statistics are well described by Real QM? Might it be that *all* experimental statistics can be explained using Real QM, and that the use of Real vs. Complex is a conventional choice of the physicist?

  3. Questions about the utility of QM with a superselection rule: Might there be experimental situations where the statistics are well described by QM with a SSR? Might it be that *all* experimental statistics can be explained using QM with a SSR, and that the use of QM with vs. without SSR is a conventional choice of the physicist? YES YES

  4. QM with a superselection rule Standard view: some conserved quantities are axiomatically superselected, others not SSR No SSR Charge Atom number univalence Linear momentum Angular momentum Photon number

  5. QM with SSR is appropriate if one lacks a reference frame no RF W2SO(3) Unknown!

  6. QM with SSR can describe *any* experiment External RF paradigm States Measurements Internal RF paradigm States Measurements and group invariant One can find a mapping such that

  7. Define where with and See: Kitaev, Mayers and Preskill, Phys. Rev. 69, 052326 (2004) Bartlett, Rudolph and Spekkens, Rev. Mod. Phys. 79, 555 (2007)

  8. QM with SSR can always be used if one wishes External RF paradigm States Measurements Internal RF paradigm States Measurements and group invariant Whether internal RF paradigm or external RF paradigm is used is a conventional choice of the physicist See: Aharonov and Susskind, Phys. Rev. 155, 1428 (1967) Bartlett, Rudolph and Spekkens, Int. J. Quantum Inf. 4, 17 (2006).

  9. Real Quantum Mechanics

  10. Can Real QM emerge by lacking some resource? Some resource Without resource Relative arrow of time unknown?

  11. Can Real QM describe *any* experiment? External resource paradigm Some resource States Measurements Internal resource paradigm Some resource States Measurements and real Can one find a mapping such that

  12. Define where

  13. Can Real QM describe *any* experiment? External resource paradigm Some resource States Measurements Internal resource paradigm Some resource States Measurements and real If so, then whether external or internal paradigm is used is a conventional choice of the physicist i.e. no matter of fact about nature of field!

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