Table Of ContentS
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Idealizations are ubiquitous in physics. They are distortions or e
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falsities that enter into theories, laws, models, and scientific h
representations. Various questions suggest themselves: What
are idealizations? Why do we appeal to idealizations and how
do we justify them? Are idealizations essential to physics and, if
so, in what sense and for which purpose? How can idealizations Philosophy of Physics
provide genuine understanding? If our motivation for believing
in the existence of unobservable entities like electrons and
quarks is that they are indispensable to our best theories,
should we also believe in the existence of indispensable
idealizations? This Element will tackle such questions and offer
an opinionated and selective introduction to philosophical
Id Idealizations
issues concerning idealizations in physics. Topics to be e
a
covered include the concept of and reasons for introducing liz
a
idealization, abstraction, and approximation, possible taxonomy tio
n in Physics
and justification, and application to issues of mathematical s in
Platonism, scientific realism, and scientific understanding. P
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About the Series Series editor
This Cambridge Elements series provides James Owen
concise and structured introductions to Weatherall
all the central topics in the philosophy University of Elay Shech
of physics. The Elements in the series California, Irvine
are written by distinguished senior
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relevant expertise, producing balanced, tisre
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perspectives in the philosophy of physics. e
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Cover image: Newton’s Cradle (George Diebold / Getty .io
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ElementsinthePhilosophyofPhysics
editedby
JamesOwenWeatherall
UniversityofCalifornia,Irvine
IDEALIZATIONS
IN PHYSICS
Elay Shech
Auburn University
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Idealizations in Physics
ElementsinthePhilosophyofPhysics
DOI:10.1017/9781108946742
Firstpublishedonline:January2023
ElayShech
AuburnUniversity
Authorforcorrespondence:ElayShech,[email protected]
Abstract:Idealizationsareubiquitousinphysics.Theyaredistortions
orfalsitiesthatenterintotheories,laws,models,andscientific
representations.Variousquestionssuggestthemselves:Whatare
idealizations?Whydoweappealtoidealizationsandhowdowejustify
them?Areidealizationsessentialtophysicsand,ifso,inwhatsenseand
forwhichpurpose?Howcanidealizationsprovidegenuine
understanding?Ifourmotivationforbelievingintheexistenceof
unobservableentitieslikeelectronsandquarksisthattheyare
indispensabletoourbesttheories,shouldwealsobelieveinthe
existenceofindispensableidealizations?ThisElementwilltacklesuch
questionsandofferanopinionatedandselectiveintroductionto
philosophicalissuesconcerningidealizationsinphysics.Topicstobe
coveredincludetheconceptofandreasonsforintroducing
idealization,abstraction,andapproximation,possibletaxonomyand
justification,andapplicationtoissuesofmathematicalPlatonism,
scientificrealism,andscientificunderstanding.
ThisElementalsohasavideoabstract:www.cambridge.org/Philosophyof
sserP Physics_ElayShech_abstract
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tisre Keywords:idealization,abstraction,approximation,scientificmodels,
vin scientificrepresentation
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aC ISBNs:9781108925044(PB),9781108946742(OC)
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b e ISSNs:2632-413X(online),2632-4121(print)
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Contents
1 Introduction 1
2 Idealization,Abstraction,andApproximation 9
3 Taxonomy 22
4 Justification 32
5 Platonism 46
6 Realism 54
7 Understanding 65
8 Epilogue 73
References 74
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IdealizationsinPhysics 1
1Introduction
Milk production at a dairy farm was so low that the farmer wrote to the local
university,askingforhelpfrom[scientists].Amultidisciplinaryteamofprofessors
wasassembled,headedbyatheoreticalphysicist,andtwoweeksofintensiveon-site
investigation took place. The scholars then returned to the university, notebooks
crammedwithdata,wherethetaskofwritingthereportwaslefttotheteamleader.
Shortlythereafter[thephysicistreturnedtothefarminordertoexplainthereportto
thefarmer.Heaskedforablackboardandthendrewacircle.Hebegan:]“Assume
thecowisasphere....”
(Harte1988,xiii)
Idealizationsarewidespreadandpervasiveinphysics.Theyaredistortionsor
falsities that enter into theories, laws, models, or, more generally, scientific
descriptions and representations. Examples include the frictionless plane, the
simplependulum,pointandtestparticles,nonviscousfluidflow,infinitelythin
wiresandinfinitelylongcylindersorplanes,aperfectvacuum,theidealgaslaw,
the Bohr model of the atom, the Ising and Hubbard models, and, of course,
perfectlysphericalcows.
Various questions suggest themselves: What are idealizations? Why do
we appeal to idealizations and how do we justify them? Are idealizations
essential to physics and, if so, in what sense and for which purpose? How
can idealizations that are false and inaccurate afford true explanations,
accurate descriptions, and genuine understanding? If our motivation for
believing in the existence of unobservable entities like electrons and quarks is
that they are indispensable to our best theories, should we also believe in the
existence of indispensable idealizations? Would this mean that idealizations
sserP are abstract objects akin to Platonic forms, or fictions like literary characters?
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2 althoughlotsoftheliteratureonidealizationinphysicsconcernsissuessuchas
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64 explanation (Batterman 2002; Batterman and Rice 2014; Bokulich 2008;
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01 JanssonForthcoming),confirmation(Shaffer2012,ch.3),mathematicalrepre-
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9 sentationandapplicability(BuenoandFrench2018;Pincock2012),reduction
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01 andemergence(Batterman2002;Palacios2022;Shech2019a),andsoforth,I
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2 PhilosophyofPhysics
or models, which are false or nonveridical, can provide scientific explanation
will not be treated explicitly, for instance.1 My approach then is to cover a
limitednumberoftopicsbyinteractingcriticallywithasmallsubsetofrecent
contributions.2
What further complicates our study is that the notion of idealization is
entangled with other issues that necessitate a detailed treatment (Fletcher et
al. 2019a; Shech 2018a; Shech et al. 2022). For instance, some distinguish
between idealization and abstraction (Jones 2005), and idealization and
approximation (Norton 2012). Theories (French 2020), laws (Cartwright
1983; Liu 2004), models (Frigg and Hartmann 2020; Gelfert 2016; Jacquart
Forthcoming),simulations(Humphreys2004;Winsberg2010),andrepresenta-
tions(FriggandNguyen2020;Shech2015a,2016)tendtobetheobjectsthat
are idealized in some sense. Approximate truth (Oddie 2016) and analogy
(Bartha2019)arecandidaterelationsthatholdbetweenwhatIcallthe“vehicle”
of idealization and its “target” (Shech 2015a). Thought experiments (Stuart
2018)ofteninvolveaplethoraofidealizations.Thelistgoeson.Nevertheless,
idealizationsareinterestingintheirownright.Accordingly,insofaraspossible,
I concentrate specifically on idealizations in physics. For other reviews see
Hüttemann (2002) for idealizations in physics, Elliott-Graves and Weisberg
(2014) for idealizations more generally, and Shech and colleagues (2022) for
connectionswithrepresentationandexplanation.Forissuesconcerninginfinite
andinfinitesimalidealizationsseeShech(2018a)andtheessaysinFletcherand
colleagues(2019b).
ThestructureoftherestoftheElementisasfollows.Section2willdiscuss
sse the concept of idealization and identify reasons requiring the introduction of
rP y idealization. I will distinguish between idealization broadly and narrowly
tisre construedandgivetwoexamplesofthelatternotionviaadistinctionbetween
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dirb considerawell-receivedtaxonomyofidealizationsandSection4willdiscuss
ma justificatoryissues.Sections5,6,and7willconnectbetweenidealizationsand
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silbu variousidealizations.
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4 Brownianmotionconcernsthejigglingseenunderamicroscopeofparticles
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9 likepollensuspendedinaliquid.Takingadilutesolutionofsugar(thesolute)in
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IdealizationsinPhysics 3
water (the solvent) as his target system of interest and modeling said target
as solid spheres suspended in a fluid solvent allowed Albert Einstein to
infer the size of said molecules and Avogadro’s constant( Einstein 1926/
1956). While the phenomenon of Brownian motion is an actual effect
found in the real world, the model of the water-sugar solution is highly
idealized since it represents the sugar molecules as solid spheres and the
water molecules as a fluid solvent in which the sugar molecules are
suspended. Einstein also appealed to other idealizations such as abstracting
away the inertia of the translation and rotational motions of the sugar
molecules, assuming that any molecule’s motion is unaffected by the
motion of other molecules and that motion is only due to the stress at
the surface, ignoring external forces such as gravity, and so on (Cheng
2013, 5). Additionally, he assumed that the equations of classical hydro-
dynamics that pertain to fluids will be applicable to the molecular system,
thereby idealizing away the complexities involved in the consideration of
molecular structure (Einstein 1926/1956, 36–37). All such assumptions in the
construction and application of the rigid-sphere model of the water-sugar
solution are examples of idealizations, abstractions, and approximations
(which I will discuss further in the following section).
TheprimaryexampleIwillrefertothroughouttheElementistheAharonov–
Bohm(AB)effect.Duetoitssomewhattechnicalnature,Iwillfirstpresentthe
case study qualitatively and only then add some technical details. To begin,
recallthat,whenoneshinesabeamofhomogenouslightonascreenwithtwo
slits,aninterferencepatternwithdarkandlightfringesemergesonadetector
sse screen. It is possible to also produce interference patterns with particles like
rP y electrons (Figure 1, left), which arise from the buildup of single electrons
tisre (Figure1,right).
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dirb of a magnetic field, say, by adding a cylindrical solenoid and turning it “on.”
ma Duetothepresenceofchargedparticlesmovingthroughamagneticfield,the
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silbu pattern emergingon thedetector screen(however, thepresence ofa wavelike
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4 PhilosophyofPhysics
Figure1(Left)Anexampleofaninterferencepatternfromadouble-slit
experiment(fromMöllenstedtandBayh1962,304).(Right)Single-electron
buildupof(biprism)interferencepattern(fromTonomura1999,15).(a)8
electrons,(b)270electrons,(c)2,000electrons,and(d)60,000electrons.
sse Figure2Anillustrationofthe(magnetic)ABeffect
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