Particlewave duality: a dichotomy between symmetry and asymmetry
Abstract
Symmetry plays a central role in many areas of modern physics. Here we show that it also underpins the dual particle and wave nature of quantum systems. We begin by noting that a classical point particle breaks translational symmetry whereas a wave with uniform amplitude does not. This provides a basis for associating particle nature with asymmetry and wave nature with symmetry. We derive expressions for the maximum amount of classical information we can have about the symmetry and asymmetry of a quantum system with respect to an arbitrary group. We find that the sum of the information about the symmetry (wave nature) and the asymmetry (particle nature) is bounded by log(D) where D is the dimension of the Hilbert space. The combination of multiple systems is shown to exhibit greater symmetry and thus more wavelike character. In particular, a class of entangled systems is shown to be capable of exhibiting wavelike symmetry as a whole while exhibiting particlelike asymmetry internally. We also show that superdense coding can be viewed as being essentially an interference phenomenon involving wavelike symmetry with respect to the group of Pauli operators.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 April 2012
 DOI:
 10.1098/rspa.2011.0271
 arXiv:
 arXiv:1105.0083
 Bibcode:
 2012RSPSA.468.1065V
 Keywords:

 Quantum Physics
 EPrint:
 20 pages, 3 figures