Spontaneous symmetry breaking in quantum systems: Emergence or reduction?

Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 44 (4):379-394 (2013)
  Copy   BIBTEX

Abstract

Beginning with Anderson, spontaneous symmetry breaking in infinite quantum systems is often put forward as an example of emergence in physics, since in theory no finite system should display it. Even the correspondence between theory and reality is at stake here, since numerous real materials show ssb in their ground states, although they are finite. Thus against what is sometimes called ‘Earman's Principle’, a genuine physical effect seems theoretically recovered only in some idealisation, disappearing as soon as the idealisation is removed.We review the well-known arguments that no finite system can exhibit ssb, using the formalism of algebraic quantum theory in order to control the thermodynamic limit and unify the description of finite- and infinite-volume systems. Using the striking mathematical analogy between the thermodynamic limit and the classical limit, we show that a similar situation obtains in quantum mechanics versus classical mechanics.This discrepancy between formalism and reality is quite similar to the measurement problem, and hence we address it in the same way, adapting an argument of the Landsman and Reuvers that was originally intended to explain the collapse of the wave-function within conventional quantum mechanics. Namely, exponential sensitivity to perturbations of the dynamics as the system size increases causes symmetry breaking already in finite but very large quantum systems. This provides continuity between finite- and infinite-volume descriptions of quantum systems featuring ssb and hence restores Earman's Principle.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,931

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Curie’s Principle and spontaneous symmetry breaking.John Earman - 2004 - International Studies in the Philosophy of Science 18 (2 & 3):173 – 198.
How is spontaneous symmetry breaking possible? Understanding Wigner's theorem in light of unitary inequivalence.David John Baker & Hans Halvorson - 2013 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 44 (4):464-469.
Reduction and Emergence in Bose-Einstein Condensates.Richard Healey - 2011 - Foundations of Physics 41 (6):1007-1030.
A Reconstruction of Quantum Mechanics.Simon Kochen - 2015 - Foundations of Physics 45 (5):557-590.
How to solve the measurement problem of quantum mechanics.Jeffrey Bub - 1988 - Foundations of Physics 18 (7):701-722.

Analytics

Added to PP
2014-01-23

Downloads
148 (#130,326)

6 months
47 (#93,442)

Historical graph of downloads
How can I increase my downloads?

References found in this work

Emergent properties.Timothy O'Connor - 1994 - American Philosophical Quarterly 31 (2):91-104.
More is different.P. W. Anderson - 1994 - In H. Gutfreund & G. Toulouse (eds.), Biology and Computation: A Physicist's Choice. World Scientific. pp. 3--21.
Emergence, Singularities, and Symmetry Breaking.Robert W. Batterman - 2011 - Foundations of Physics 41 (6):1031-1050.

View all 19 references / Add more references