|Theory of Physical Theories|
Metatheories in General
> s.a. correlations [classification of theories];
physical theories [frameworks, theories of everything].
* Semantic view: According to the semantic view of scientific theories, theories are classes of models.
* Change of level: When going from one physical theory to a deeper one, the singularities at the former level tend to be dissolved (see atomic stability from classical to quantum mechanics).
* Types of theories: Einstein [@ London Times 1919] distinguished between theories of principles, and theories of constructs (principle and constructive theories).
* Notions of equivalence of theories: Examples are categorical equivalence, definitional equivalence and generalized definitional (aka Morita) equivalence.
* Examples: The PPN formalism (> see modified newtonian gravity).
@ General references: Giere PhSc(94)jun [cognitive structure]; Smith BJPS(98) [approximate truth]; Halvorson SHPMP(04)qp/03 [insert, state space and information theory]; D'Agostini phy/04-conf [probabilistic reasoning]; 't Hooft IJMPA(08)-a0707 [grand view]; Matravers CP(07); Allen a1101 [statistical counting and stochastic fluctuations]; French & Vickers BJPS(11) [ontological status]; Halvorson PhSc(12) [against the semantic view of theories]; Jaroszkiewicz a1501 [generalized propositions and a classification scheme for theories].
@ Equivalence of theories: Weatherall a1411 [and Newtonian gravity vs geometrized Newtonian gravity]; Barrett & Halvorson a1506 [definitional, Morita and categorical equivalence]; Weatherall a1810 [types of equivalence, and dualities]; & de Haro; Weatherall a1812 [categorical]; Weatherall a1906-conf, De Haro a1906 [and electromagnetic duality]; > s.a. Einstein Algebras.
@ Relationships, types: Baumann PhSc(05)jan [re "better theories"]; Page a0712-proc [Bayesian meta-theories, "sensible quantum mechanics", and quantum cosmology]; Van Camp SHPMP(11) [types of theories, explanation, and quantum mechanics]; Bény & Osborne NJP(15)-a1403 [renormalization and effectively indistinguishable microscopic theories]; Oriti a1705-in [principle of proliferation of theories, and non-empirical theory assessment].
> Related topics: see category theory and physics; Deformations.
Space of Theories > s.a. Theory.
@ References: Cordova et al a1905, a1905 [4D gauge theories, anomalies in the space of coupling constants]; Barth a1910-MS [comparing classical field theories].
> Related topics: see types of distances; types of quantum theories; symplectic structures in physics [on the space of quantum field theories].
Structure of Theories
> s.a. computation; Explanations;
history of physics; Interpretation
of a Theory; logic; Physical Laws.
* Idea: A physical theory consists of a mathematical formalism and an interpretation (definition of symbols, measurement assignments, concepts and principles, ontology).
* Method: Knowledge in physics comes from interplay of theory and experiment; In the theory, one simplifies systems and considers simple, closed ones, supposes that observers are not important, identifies the simplest measurements, e.g., m, l, t, and sets up the mathematical description of the models; Later, one tries to get rid of ideal elements by making them dynamical, or giving a natural choice (Leibniz's principle of sufficient reason).
* Ideal elements: Formal element which are contingent (a different choice is possible) and play a role in the evolution of the physical degrees of freedom but are non-dynamical, absolute; Examples: Correspondence observables-operators, time, inner product; Number of spacetime dimensions, topology in general relativity; Preferred class of inertial observers in pre-general-relativity physics; > s.a. general relativity; inertia.
* Structure: A theory has a lattice of propositions (including assumptions), structural equations and equations of other origin, about some structure which constitutes a model (or metaphor) for the systems under consideration [P Duhem considered the metaphor itself as an educational tool, not a part of science, while J Bernstein and J Ziman view them as an integral part of science, @ pw(00)nov]; As with any metaphor, a key issue is to establish how far each theory can go; Theories can be regarded as organized into hierarchies in many cases, with higher levels sometimes called 'paradigms' and lower-level models encoding more specific or concrete hypotheses.
* Evolution: In the hierarchical point of view, higher-level theory change may be driven by the impact of evidence on lower levels.
@ Books: Holton & Roller 58; Ripley 64 [simple]; Cooper 68; Tonti 76; Shive & Weber 82 [II]; Sklar 85; Pavšič 01-gq/06 [overview]; Helland 09.
@ General references: Caianello RNC(92); Foy qp/00 [logical basis]; Tarantola & Mosegaard mp/00 [use of inference]; Fellman et al a1001 [importance of discourse]; Henderson et al PhSc(10)apr [hierarchical Bayesian models]; Székely in(11)-a1101 [why-type questions]; Vignale 11; Fayer hp(12)jan [popular misunderstanding of the meaning of the word]; Weatherall a1206-ch ["puzzleball view", theories as networks of mutually interdependent principles and assumptions]; Wallace a1306 [inferential vs dynamical conceptions]; Coecke et al a1409 [mathematical theory of resources]; Curiel a1603 [kinematics and dynamics]; in Krizek a1707 [classification scheme].
@ Evolution of theories: Lederer a1510 [conflicting theories and scientific pluralism, example of high-temperature superconductivity].
Construction of Theories > s.a. Axioms for Physical Theories;
* Approaches: The main distinction is between operational and deductive ones; The danger with an operational approach is that one may get stuck with technical difficulties and make little progress; The danger with a deductive approach is that progress in the right direction is more likely to be impeded by idealizations.
* Remark: It is important to understand which are the right variables; Which questions we can ask and which make no sense (see Newton's laws, Einstein's relativity, Bohr-Heisenberg principle).
@ References: Corry 04 [Hilbert and the axiomatization of physics]; Emch SHPMP(07); Moldoveanu a1001-FQXi [complete axiomatization of physics as an achievable goal]; Nguyen et al BJPS-a1712, Bradley & Weatherall a1904 [the need for surplus structure].
> Specific theories: see cosmology; particle physics; etc.
Criteria for Physical Theories
> s.a. Consistency; Fine Tuning;
Naturalness; Occam's Razor;
* Traditional: Adequacy, i.e., verifiability / falsifiability, and good agreement with experiment.
* Stability under variations: Often assumed as a dogma and not discussed explicitly.
* Also: Accuracy, elegance and simplicity (XX century aesthetic judgment), scope, symmetries.
* Verifiability / Falsifiability: 2015, Some theorists have called for a relaxation of this requirement for a theory, in particular proponents of string theory and multiverse theory.
* Beauty: The sense of what's natural or elegant is subjective, as can be seen in people's opinions of various proposed explanations of the apparent cosmological acceleration; It can be evoked by a pattern or symmetry (as in gauge theories or cosmology), or by logical or formal simplicity.
* Examples: Ther issue of whether Copernicus' theory of the Solar System was more "harmonious" and simpler than Ptolemy's; The interpretation of the predicted positron in Dirac theory, which according to "truth" of knowledge at the time was the proton (Dirac), and according to "beauty" it was not (Weyl).
* On unobservable quantities: Around 1926, W Heisenberg advocated using only directly observable quantities in the theory; The point of view was picked up by G Chew in his S-matrix approach to quantum field theory; It appears that the use of some unobservable quantities is unavoidable.
@ General references: Einstein JFI(36); Mermin PT(00)mar [elegance]; Norton SHPMP(00) [Einstein and simplicity]; Falmagne FP(04) [meaningfulness + order-invariance]; Wells a1211 [consistency, and effective field theories]; Scorzato Syn(13)-a1402 [simplicity]; Hossenfelder 18 [overreliance on beauty].
@ Considerations on different types of theories: Nelson AS(85); Von Weizsäcker 85; Cushing 90; Tavakol BJPS(91) [fragility]; Elby et al FP(93); Barrett PhSc(03)dec [our best physical theories are false]; Streater 07 ["lost causes"].
@ Verifiability / Falsifiability: Scott et al a1504 [giving up Falsifiability :-)]; Nemenman a1505, PT(15)oct [quantifying]; Hossenfelder blog(14)jul, Woit blog (14)jul, Ellis & Silk Nat(14)dec, blog sa(15)dec [defense of falsifiability]; Rovelli a1609-conf, Dawid a1702-ch [on non-empirical confirmation]; Curiel a1804 [Newtonian abduction]; Alamino a1907 [weaker condition, ignoring isolated spacetime regions]; Patton SHPMP(20)-a2002 [confirmation vs testing; parametrized frameworks and gravity]; Weilenmann & Colbeck PRL(20)-a2003 [theory self-test, and quantum theory].
@ Stability: Bouligand ARB(35); Destouches ARB(35); Duhem 54; Thom 67; Vilela Mendes JPA(94).
@ Beauty: McAllister AS(98); Tsallis PhyA(04) [beauty, truth and new ideas]; Martens SHPSA(09) [beauty and simplicity as metaphors, Copernican theory]; Vignale 11; Spratt & Elgammal a1410; Wilczek 15; Deser a1706 [elegance/simplicity and supergravity].
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– other sites – acknowledgements
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