Discerning fermions

Abstract
We demonstrate that the quantum-mechanical description of composite physical systems of an arbitrary number of similar fermions in all their admissible states, mixed or pure, for all finite-dimensional Hilbert spaces, is not in conflict with Leibniz's Principle of the Identity of Indiscernibles (PII). We discern the fermions by means of physically meaningful, permutation-invariant categorical relations, i.e. relations independent of the quantum-mechanical probabilities. If, indeed, probabilistic relations are permitted as well, we argue that similar bosons can also be discerned in all their admissible states; but their categorical discernibility turns out to be a state-dependent matter. In all demonstrated cases of discernibility, the fermions and the bosons are discerned (i) with only minimal assumptions on the interpretation of quantum mechanics; (ii) without appealing to metaphysical notions, such as Scotusian haecceitas, Lockean substrata, Postian transcendental individuality or Adamsian primitive thisness; and (iii) without revising the general framework of classical elementary predicate logic and standard set theory, thus without revising standard mathematics. This confutes: (a) the currently dominant view that, provided (i) and (ii), the quantum-mechanical description of such composite physical systems always conflicts with PII; and (b) that if PII can be saved at all, the only way to do it is by adopting one or other of the thick metaphysical notions mentioned above. Among the most general and influential arguments for the currently dominant view are those due to Schrödinger, Margenau, Cortes, Dalla Chiara, Di Francia, Redhead, French, Teller, Butterfield, Giuntini, Mittelstaedt, Castellani, Krause and Huggett. We review them succinctly and critically as well as related arguments by van Fraassen and Massimi. Introduction: The Currently Dominant View 1.1 Weyl on Leibniz's principle 1.2 Intermezzo: Terminology and Leibnizian principles 1.3 The rise of the currently dominant view 1.4 Overview Elements of Quantum Mechanics 2.1 Physical states and physical magnitudes 2.2 Composite physical systems of similar particles 2.3 Fermions and bosons 2.4 Physical properties 2.5 Varieties of quantum mechanics Analysis of Arguments 3.1 Analysis of the Standard Argument 3.2 Van Fraassen's analysis 3.3 Massimi's analysis The Logic of Identity and Discernibility 4.1 The language of quantum mechanics 4.2 Identity of physical systems 4.3 Indiscernibility of physical systems 4.4 Some kinds of discernibility Discerning Elementary Particles 5.1 Preamble 5.2 Fermions 5.3 Bosons Concluding Discussion CiteULike    Connotea    Del.icio.us    What's this?
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 9,357
External links
  •   Try with proxy.
  • Through your library Configure
    References found in this work BETA
    Jeremy Butterfield (1993). Interpretation and Identity in Quantum Theory. Studies in History and Philosophy of Science 24 (3):443--76.

    View all 16 references

    Citations of this work BETA

    View all 10 citations

    Similar books and articles
    Analytics

    Monthly downloads

    Added to index

    2009-01-28

    Total downloads

    25 ( #58,686 of 1,088,753 )

    Recent downloads (6 months)

    2 ( #42,750 of 1,088,753 )

    How can I increase my downloads?

    My notes
    Sign in to use this feature


    Discussion
    Start a new thread
    Order:
    There  are no threads in this forum
    Nothing in this forum yet.