Critical phenomena and breaking drops: Infinite idealizations in physics

Batterman, Robert W.

doi:10.1016/j.shpsb.2004.05.004

Cited by 106 publications

(84 citation statements)

References 13 publications

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“…8 What is interesting about the anyon case study is that it appeals to a kind of infinitesimal idealization-a two--dimensional model of quantum mechanics-that in turn seems to play an essential role in the scientific account of anyons. This is similar to other infinite idealizations, such as thermodynamic--type limits for phase transitions and spontaneous symmetry breaking (Batterman 2002(Batterman , 2005Ruetsche 2011;Shech 2013), and infinitesimal idealizations, such as in the context of the quantum--classical limit (Batterman 2002, Bokulich 2008, which purportedly play an indispensible explanatory role. 9 Thus, in fleshing out the consequences of fractional quantum statistics for Leng's approach to easy road nominalism, I am attempting to fill a lacuna in the easy road nominalism debate.…”

Section: Introductionsupporting

confidence: 73%

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Infinitesimal idealization, easy road nominalism, and fractional quantum statistics

Shech

2018

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Section: Introductionsupporting

confidence: 73%

“…For more on the philosophical debate revolving around phase transitions see Batterman (2005), mathematically represented by a non--analytic partition function pertaining to the system. 32 However, for any system with finite many particles (degrees of freedom) the partition function is analytic.…”

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confidence: 99%

Infinitesimal idealization, easy road nominalism, and fractional quantum statistics

Shech

2018

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“…(Removing the cutoffs by taking infinite limits would turn the cutoff variant into the infinitely renormalized variant, which would mean adopting a different set of theoretical principles and introducing the attendant set of problems.) 33 The significance of idealization in quantum statistical mechanics (QSM) has recently been the subject of debate (see Callendar (2001), Batterman (2005) and Ruetsche (2003)). Since there are many similarities between QFT and QSM, one might expect this debate about idealization to map onto QFT; however, idealization plays opposing roles in the two cases.…”

Section: Resultsmentioning

confidence: 99%

Quantum Field Theory: Underdetermination, Inconsistency, and Idealization

Fraser

2009

Philos. of Sci.

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Quantum field theory (QFT) presents a genuine example of the underdetermination of theory by empirical evidence. There are variants of QFT which are empirically indistinguishable yet support different interpretations. This case is of particular interest to philosophers of physics because, before the philosophical work of interpreting QFT can proceed, the question of which variant should be subject to interpretation must be settled. At one end of the spectrum of variants of QFT is the version which is found in introductory textbooks and employed by most working physicists; this is the variant of QFT which introduces renormalization procedures to facilitate the calculation of scattering matrix elements. At the other end of the spectrum are axiomatic presentations of QFT, which are rigorous but remote from practical applications. New arguments are offered for basing the interpretation of QFT on a rigorous axiomatic variant of the theory. The pivotal considerations are the roles that consistency and idealization play in this case.

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“…These global properties can display features of the infinite system that no finite system could possibly have. As discussed in Batterman (2002, 2005, 2009), Callender (2001, and Butterfield (2011a,b), the thermodynamic quantities of a finite system always vary continuously while the thermodynamic quantities of an infinite system can display discontinuities. It is this feature that leads some to label certain statistical systems as involving "singular limits".…”

Section: Reduction Deduction and Definabilitymentioning

confidence: 99%

Deduction and definability in infinite statistical systems

Feintzeig

2017

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Classical accounts of intertheoretic reduction involve two pieces: first, the new terms of the higher-level theory must be definable from the terms of the lower-level theory, and second, the claims of the higher-level theory must be deducible from the lower-level theory along with these definitions. The status of each of these pieces becomes controversial when the alleged reduction involves an infinite limit, as in statistical mechanics. Can one define features of or deduce the behavior of an infinite idealized system from a theory describing only finite systems? In this paper, I change the subject in order to consider the motivations behind the definability and deducibility requirements. The classical accounts of intertheoretic reduction are appealing because when the definability and deducibility requirements are satisfied there is a sense in which the reduced theory is forced upon us by the reducing theory and the reduced theory contains no more information or structure than the reducing theory. I will show that, likewise, there is a precise sense in which in statistical mechanics the properties of infinite limiting systems are forced upon us by the properties of finite systems, and the properties of infinite systems contain no information beyond the properties of finite systems.

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Critical phenomena and breaking drops: Infinite idealizations in physics

Cited by 106 publications

References 13 publications

Infinitesimal idealization, easy road nominalism, and fractional quantum statistics

Infinitesimal idealization, easy road nominalism, and fractional quantum statistics

Quantum Field Theory: Underdetermination, Inconsistency, and Idealization

Deduction and definability in infinite statistical systems

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