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;
Models; Operationalism.

* __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;
paradigms; Simplicity.

* __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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send feedback and suggestions to bombelli at olemiss.edu – modified 14 sep 2020