robert spekkens department of applied mathematics and theoretical physics university of cambridge...
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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? YESTRANSCRIPT
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Robert SpekkensDepartment of Applied Mathematics and Theoretical
Physics University of Cambridge
Quantum Mechanics over the real field
July 24, 2007 FQXi
Funding by:The Royal Society
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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?
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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
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QM with a superselection rule
Standard view: some conserved quantities are axiomatically superselected, others not
No SSR SSR
Linear momentumAngular momentumPhoton number
ChargeAtom numberunivalence
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no RF
QM with SSR is appropriate if one lacks a reference frame
2SO(3) Unknown!
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QM with SSR can describe *any* experiment
External RF paradigmStatesMeasurements
Internal RF paradigmStatesMeasurements
and group invariant
One can find a mapping such that
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Define
with
where
and
See: Kitaev, Mayers and Preskill, Phys. Rev. 69, 052326 (2004) Bartlett, Rudolph and Spekkens, Rev. Mod. Phys. 79, 555 (2007)
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QM with SSR can always be used if one wishes
External RF paradigmStatesMeasurements
Internal RF paradigmStatesMeasurements
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).
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Real Quantum Mechanics
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Without resource
Can Real QM emerge by lacking some resource?
Some resource
Relative arrow of time unknown?
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Can Real QM describe *any* experiment?
External resource paradigmStatesMeasurements
Internal resource paradigmStatesMeasurements
and real
Can one find a mapping such that
Some resource
Some resource
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Define
where
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External resource paradigmStatesMeasurements
Internal resource paradigmStatesMeasurements
and real
Some resource
Some resource
If so, then whether external or internal paradigm is used is a conventional choice of the physicisti.e. no matter of fact about nature of field!
Can Real QM describe *any* experiment?