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For the notion of <em>model</em> in <a class="existingWikiWord" href="/nlab/show/logic">logic</a> see at <em><a class="existingWikiWord" href="/nlab/show/model+%28logic%29">model (logic)</a></em>.</p> </blockquote> <hr /> <div class="rightHandSide"> <div class="toc clickDown" tabindex="0"> <h3 id="context">Context</h3> <h4 id="physics">Physics</h4> <div class="hide"><div> <p><strong><a class="existingWikiWord" href="/nlab/show/physics">physics</a></strong>, <a class="existingWikiWord" href="/nlab/show/mathematical+physics">mathematical physics</a>, <a class="existingWikiWord" href="/nlab/show/philosophy+of+physics">philosophy of physics</a></p> <h2 id="surveys_textbooks_and_lecture_notes">Surveys, textbooks and lecture notes</h2> <ul> <li> <p><em><a class="existingWikiWord" href="/nlab/show/higher+category+theory+and+physics">(higher) category theory and physics</a></em></p> </li> <li> <p><em><a class="existingWikiWord" href="/nlab/show/geometry+of+physics">geometry of physics</a></em></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/books+and+reviews+in+mathematical+physics">books and reviews</a>, <a class="existingWikiWord" href="/nlab/show/physics+resources">physics resources</a></p> </li> </ul> <hr /> <p><a class="existingWikiWord" href="/nlab/show/theory+%28physics%29">theory (physics)</a>, <a class="existingWikiWord" href="/nlab/show/model+%28physics%29">model (physics)</a></p> <p><a class="existingWikiWord" href="/nlab/show/experiment">experiment</a>, <a class="existingWikiWord" href="/nlab/show/measurement">measurement</a>, <a class="existingWikiWord" href="/nlab/show/computable+physics">computable physics</a></p> <ul> <li> <p><strong><a class="existingWikiWord" href="/nlab/show/mechanics">mechanics</a></strong></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/mass">mass</a>, <a class="existingWikiWord" href="/nlab/show/charge">charge</a>, <a class="existingWikiWord" href="/nlab/show/momentum">momentum</a>, <a class="existingWikiWord" href="/nlab/show/angular+momentum">angular momentum</a>, <a class="existingWikiWord" href="/nlab/show/moment+of+inertia">moment of inertia</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/dynamics+on+Lie+groups">dynamics on Lie groups</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/rigid+body+dynamics">rigid body dynamics</a></li> </ul> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/field+%28physics%29">field (physics)</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Lagrangian+mechanics">Lagrangian mechanics</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/configuration+space">configuration space</a>, <a class="existingWikiWord" href="/nlab/show/state">state</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/action+functional">action functional</a>, <a class="existingWikiWord" href="/nlab/show/Lagrangian">Lagrangian</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/covariant+phase+space">covariant phase space</a>, <a class="existingWikiWord" href="/nlab/show/Euler-Lagrange+equations">Euler-Lagrange equations</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Hamiltonian+mechanics">Hamiltonian mechanics</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/phase+space">phase space</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/symplectic+geometry">symplectic geometry</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Poisson+manifold">Poisson manifold</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/symplectic+manifold">symplectic manifold</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/symplectic+groupoid">symplectic groupoid</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/multisymplectic+geometry">multisymplectic geometry</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/n-symplectic+manifold">n-symplectic manifold</a></li> </ul> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/spacetime">spacetime</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/smooth+Lorentzian+manifold">smooth Lorentzian manifold</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/special+relativity">special relativity</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/general+relativity">general relativity</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/gravity">gravity</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/supergravity">supergravity</a>, <a class="existingWikiWord" href="/nlab/show/dilaton+gravity">dilaton gravity</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/black+hole">black hole</a></p> </li> </ul> </li> </ul> </li> </ul> </li> <li> <p><strong><a class="existingWikiWord" href="/nlab/show/classical+field+theory">Classical field theory</a></strong></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/classical+physics">classical physics</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/classical+mechanics">classical mechanics</a></li> <li><a class="existingWikiWord" href="/nlab/show/waves">waves</a> and <a class="existingWikiWord" href="/nlab/show/optics">optics</a></li> <li><a class="existingWikiWord" href="/nlab/show/thermodynamics">thermodynamics</a></li> </ul> </li> </ul> </li> <li> <p><strong><a class="existingWikiWord" href="/nlab/show/quantum+mechanics">Quantum Mechanics</a></strong></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+mechanics+in+terms+of+dagger-compact+categories">in terms of ∞-compact categories</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+information">quantum information</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Hamiltonian+operator">Hamiltonian operator</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/density+matrix">density matrix</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Kochen-Specker+theorem">Kochen-Specker theorem</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Bell%27s+theorem">Bell's theorem</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Gleason%27s+theorem">Gleason's theorem</a></p> </li> </ul> </li> <li> <p><strong><a class="existingWikiWord" href="/nlab/show/quantization">Quantization</a></strong></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/geometric+quantization">geometric quantization</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/deformation+quantization">deformation quantization</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/path+integral">path integral quantization</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/semiclassical+approximation">semiclassical approximation</a></p> </li> </ul> </li> <li> <p><strong><a class="existingWikiWord" href="/nlab/show/quantum+field+theory">Quantum Field Theory</a></strong></p> <ul> <li> <p>Axiomatizations</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/AQFT">algebraic QFT</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/Wightman+axioms">Wightman axioms</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Haag-Kastler+axioms">Haag-Kastler axioms</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/operator+algebra">operator algebra</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/local+net">local net</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/conformal+net">conformal net</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Reeh-Schlieder+theorem">Reeh-Schlieder theorem</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Osterwalder-Schrader+theorem">Osterwalder-Schrader theorem</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/PCT+theorem">PCT theorem</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Bisognano-Wichmann+theorem">Bisognano-Wichmann theorem</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/modular+theory">modular theory</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/spin-statistics+theorem">spin-statistics theorem</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/boson">boson</a>, <a class="existingWikiWord" href="/nlab/show/fermion">fermion</a></li> </ul> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/FQFT">functorial QFT</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/cobordism">cobordism</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/%28%E2%88%9E%2Cn%29-category+of+cobordisms">(∞,n)-category of cobordisms</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/cobordism+hypothesis">cobordism hypothesis</a>-theorem</p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/extended+topological+quantum+field+theory">extended topological quantum field theory</a></p> </li> </ul> </li> </ul> </li> <li> <p>Tools</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/perturbative+quantum+field+theory">perturbative quantum field theory</a>, <a class="existingWikiWord" href="/nlab/show/vacuum">vacuum</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/effective+quantum+field+theory">effective quantum field theory</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/renormalization">renormalization</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/BV-BRST+formalism">BV-BRST formalism</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/geometric+%E2%88%9E-function+theory">geometric ∞-function theory</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/particle+physics">particle physics</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/phenomenology">phenomenology</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/model+%28in+particle+phyiscs%29">models</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/standard+model+of+particle+physics">standard model of particle physics</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/fields+and+quanta+-+table">fields and quanta</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/GUT">Grand Unified Theories</a>, <a class="existingWikiWord" href="/nlab/show/MSSM">MSSM</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/scattering+amplitude">scattering amplitude</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/on-shell+recursion">on-shell recursion</a>, <a class="existingWikiWord" href="/nlab/show/KLT+relations">KLT relations</a></li> </ul> </li> </ul> </li> <li> <p>Structural phenomena</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/universality+class">universality class</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/quantum+anomaly">quantum anomaly</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Green-Schwarz+mechanism">Green-Schwarz mechanism</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/instanton">instanton</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/spontaneously+broken+symmetry">spontaneously broken symmetry</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Kaluza-Klein+mechanism">Kaluza-Klein mechanism</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/integrable+systems">integrable systems</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/holonomic+quantum+fields">holonomic quantum fields</a></p> </li> </ul> </li> <li> <p>Types of quantum field thories</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/TQFT">TQFT</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/2d+TQFT">2d TQFT</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Dijkgraaf-Witten+theory">Dijkgraaf-Witten theory</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Chern-Simons+theory">Chern-Simons theory</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/TCFT">TCFT</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/A-model">A-model</a>, <a class="existingWikiWord" href="/nlab/show/B-model">B-model</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/homological+mirror+symmetry">homological mirror symmetry</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/QFT+with+defects">QFT with defects</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/conformal+field+theory">conformal field theory</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/%281%2C1%29-dimensional+Euclidean+field+theories+and+K-theory">(1,1)-dimensional Euclidean field theories and K-theory</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/%282%2C1%29-dimensional+Euclidean+field+theory">(2,1)-dimensional Euclidean field theory and elliptic cohomology</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/CFT">CFT</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/WZW+model">WZW model</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/6d+%282%2C0%29-supersymmetric+QFT">6d (2,0)-supersymmetric QFT</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/gauge+theory">gauge theory</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/field+strength">field strength</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/gauge+group">gauge group</a>, <a class="existingWikiWord" href="/nlab/show/gauge+transformation">gauge transformation</a>, <a class="existingWikiWord" href="/nlab/show/gauge+fixing">gauge fixing</a></p> </li> <li> <p>examples</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/electromagnetic+field">electromagnetic field</a>, <a class="existingWikiWord" href="/nlab/show/QED">QED</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/electric+charge">electric charge</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/magnetic+charge">magnetic charge</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Yang-Mills+field">Yang-Mills field</a>, <a class="existingWikiWord" href="/nlab/show/QCD">QCD</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Yang-Mills+theory">Yang-Mills theory</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/spinors+in+Yang-Mills+theory">spinors in Yang-Mills theory</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/topological+Yang-Mills+theory">topological Yang-Mills theory</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Kalb-Ramond+field">Kalb-Ramond field</a></li> <li><a class="existingWikiWord" href="/nlab/show/supergravity+C-field">supergravity C-field</a></li> <li><a class="existingWikiWord" href="/nlab/show/RR+field">RR field</a></li> <li><a class="existingWikiWord" href="/nlab/show/first-order+formulation+of+gravity">first-order formulation of gravity</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/general+covariance">general covariance</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/supergravity">supergravity</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/D%27Auria-Fre+formulation+of+supergravity">D'Auria-Fre formulation of supergravity</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/gravity+as+a+BF-theory">gravity as a BF-theory</a></p> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/sigma-model">sigma-model</a></p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/particle">particle</a>, <a class="existingWikiWord" href="/nlab/show/relativistic+particle">relativistic particle</a>, <a class="existingWikiWord" href="/nlab/show/fundamental+particle">fundamental particle</a>, <a class="existingWikiWord" href="/nlab/show/spinning+particle">spinning particle</a>, <a class="existingWikiWord" href="/nlab/show/superparticle">superparticle</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/string">string</a>, <a class="existingWikiWord" href="/nlab/show/spinning+string">spinning string</a>, <a class="existingWikiWord" href="/nlab/show/superstring">superstring</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/membrane">membrane</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/AKSZ+theory">AKSZ theory</a></p> </li> </ul> </li> </ul> </li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/string+theory">String Theory</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/string+theory+results+applied+elsewhere">string theory results applied elsewhere</a></li> </ul> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/number+theory+and+physics">number theory and physics</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Riemann+hypothesis+and+physics">Riemann hypothesis and physics</a></li> </ul> </li> </ul> <div> <p> <a href="/nlab/edit/physicscontents">Edit this sidebar</a> </p> </div></div></div> </div> </div> <h1 id="contents">Contents</h1> <div class='maruku_toc'> <ul> <li><a href='#ideaa_framework_is_not_a_model_of_a_specific_system_but_a_way_of_formulating_and_studying_a_variety_of_systems_classical_mechanics_quantum_mechanics_and_statistical_mechanics_are_all_really_frameworks_in_and_of_themselves_none_of_these_makes_direct_predictions_that_can_be_tested_or_falsified_for_example_in_classical_mechanics_one_can_write_down_the_hamiltonian_of_a_hypothetical_system_and_study_the_solutions_of_this_problem_even_if_such_a_system_has_no_existence_in_nature_and_therefore_the_solutions_cannot_be_compared_to_any_experiment_within_a_framework_we_can_make_a_model_of_a_chosen_physical_system_and_try_to_experimentally_test_it_if_the_model_has_been_designed_with_suitable_hindsight_it_usually_works_up_to_some_level_of_accuracy_we_then_test_it_by_working_to_greater_accuracy_or_varying_the_experimental_parameters_what_if_the_predictions_of_a_model_disagree_with_an_experimental_observation_there_are_several_different_conclusions_that_may_be_drawn_i_the_model_is_incomplete_and_can_be_improved_by_tweaking_it_ii_the_model_is_inappropriate_to_the_problem_at_hand_or_iii_the_framework_within_which_the_model_was_formulated_is_actually_inadequate_example_in_category_i_would_be_a_model_of_fluid_dynamics_that_lacks_some_important_feature_of_the_fluid_under_study_this_may_be_redressable_by_putting_in_a_new_term_that_captures_the_missing_feature_in_category_ii_we_have_fermi_liquid_theory_mentioned_above_which_is_inappropriate_to_describe_certain_classes_of_materials_category_iii_is_exemplified_by_the_fact_that_the_hydrogen_atom_simply_cannot_be_described_by_any_hamiltonian_within_classical_mechanics'>Idea:A framework is not a model of a specific system, but a way of formulating and studying a variety of systems. Classical mechanics, quantum mechanics and statistical mechanics are all really frameworks. In and of themselves, none of these makes direct predictions that can be ‘tested’ or ‘falsified’. For example, in classical mechanics one can write down the Hamiltonian of a hypothetical system and study the solutions of this problem, even if such a system has no existence in nature and therefore, the solutions cannot be compared to any experiment. Within a framework we can make a model of a chosen physical system and try to experimentally test it. If the model has been designed with suitable hindsight, it usually works up to some level of accuracy. We then test it by working to greater accuracy or varying the experimental parameters. What if the predictions of a model disagree with an experimental observation? There are several different conclusions that may be drawn: (i) the model is incomplete and can be improved by tweaking it; (ii) the model is inappropriate to the problem at hand, or (iii) the framework within which the model was formulated is actually inadequate. Example in category (i) would be a model of fluid dynamics that lacks some important feature of the fluid under study; this may be redressable by putting in a new term that captures the missing feature. In category (ii) we have Fermi liquid theory, mentioned above, which is inappropriate to describe certain classes of materials. Category (iii) is exemplified by the fact that the hydrogen atom simply cannot be described by any Hamiltonian within classical mechanics</a></li> <ul> <li><a href='#in_particle_physics'>In particle physics</a></li> </ul> <li><a href='#examples'>Examples</a></li> <ul> <li><a href='#in_theoretical_physics'>In theoretical physics</a></li> <li><a href='#in_solid_state_physics'>In solid state physics</a></li> <li><a href='#in_particle_physics_2'>In particle physics</a></li> <li><a href='#in_cosmology'>In cosmology</a></li> </ul> <li><a href='#related_concepts'>Related concepts</a></li> </ul> </div> <h2 id="ideaa_framework_is_not_a_model_of_a_specific_system_but_a_way_of_formulating_and_studying_a_variety_of_systems_classical_mechanics_quantum_mechanics_and_statistical_mechanics_are_all_really_frameworks_in_and_of_themselves_none_of_these_makes_direct_predictions_that_can_be_tested_or_falsified_for_example_in_classical_mechanics_one_can_write_down_the_hamiltonian_of_a_hypothetical_system_and_study_the_solutions_of_this_problem_even_if_such_a_system_has_no_existence_in_nature_and_therefore_the_solutions_cannot_be_compared_to_any_experiment_within_a_framework_we_can_make_a_model_of_a_chosen_physical_system_and_try_to_experimentally_test_it_if_the_model_has_been_designed_with_suitable_hindsight_it_usually_works_up_to_some_level_of_accuracy_we_then_test_it_by_working_to_greater_accuracy_or_varying_the_experimental_parameters_what_if_the_predictions_of_a_model_disagree_with_an_experimental_observation_there_are_several_different_conclusions_that_may_be_drawn_i_the_model_is_incomplete_and_can_be_improved_by_tweaking_it_ii_the_model_is_inappropriate_to_the_problem_at_hand_or_iii_the_framework_within_which_the_model_was_formulated_is_actually_inadequate_example_in_category_i_would_be_a_model_of_fluid_dynamics_that_lacks_some_important_feature_of_the_fluid_under_study_this_may_be_redressable_by_putting_in_a_new_term_that_captures_the_missing_feature_in_category_ii_we_have_fermi_liquid_theory_mentioned_above_which_is_inappropriate_to_describe_certain_classes_of_materials_category_iii_is_exemplified_by_the_fact_that_the_hydrogen_atom_simply_cannot_be_described_by_any_hamiltonian_within_classical_mechanics">Idea:A framework is not a model of a specific system, but a way of formulating and studying a variety of systems. Classical mechanics, quantum mechanics and statistical mechanics are all really frameworks. In and of themselves, none of these makes direct predictions that can be ‘tested’ or ‘falsified’. For example, in classical mechanics one can write down the Hamiltonian of a hypothetical system and study the solutions of this problem, even if such a system has no existence in nature and therefore, the solutions cannot be compared to any experiment. Within a framework we can make a model of a chosen physical system and try to experimentally test it. If the model has been designed with suitable hindsight, it usually works up to some level of accuracy. We then test it by working to greater accuracy or varying the experimental parameters. What if the predictions of a model disagree with an experimental observation? There are several different conclusions that may be drawn: (i) the model is incomplete and can be improved by tweaking it; (ii) the model is inappropriate to the problem at hand, or (iii) the framework within which the model was formulated is actually inadequate. Example in category (i) would be a model of fluid dynamics that lacks some important feature of the fluid under study; this may be redressable by putting in a new term that captures the missing feature. In category (ii) we have Fermi liquid theory, mentioned above, which is inappropriate to describe certain classes of materials. Category (iii) is exemplified by the fact that the hydrogen atom simply cannot be described by any Hamiltonian within classical mechanics</h2> <h3 id="in_particle_physics">In particle physics</h3> <p>In <a class="existingWikiWord" href="/nlab/show/particle+physics">particle physics</a> <a class="existingWikiWord" href="/nlab/show/phenomenology">phenomenology</a> a <em>model</em> is the specification of a <a class="existingWikiWord" href="/nlab/show/physical+theory">physical theory</a>, fundamentally of a <a class="existingWikiWord" href="/nlab/show/quantum+field+theory">quantum field theory</a>, that reproduces aspects <a class="existingWikiWord" href="/nlab/show/phenomenology">phenomenology</a>, notably the fundamental physics observed in <span class="newWikiWord">particle accelerators<a href="/nlab/new/particle+accelerators">?</a></span>.</p> <p>The <em><a class="existingWikiWord" href="/nlab/show/standard+model+of+particle+physics">standard model of particle physics</a></em> is, by default, the currently best model available, given the available experimental data.</p> <p>Despite the success of this model, it is conceptually unsatisfactory in many ways and it is clear that it can be a roughly accurate description of reality not high above the currently experimentally available <a class="existingWikiWord" href="/nlab/show/energy">energy</a>-scales. Therefore <a class="existingWikiWord" href="/nlab/show/phenomenology">phenomenologists</a> still “build” plenty of other models that refine the standard model in one way or other, being compatible with the present data, but making various other predictions for what should be observed at higher energies.</p> <p>It is generally understood that models are approximations to reality. The proverbial saying goes:</p> <blockquote> <p>Every model is wrong. But some models are useful.</p> </blockquote> <h2 id="examples">Examples</h2> <h3 id="in_theoretical_physics">In theoretical physics</h3> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/lattice+model">lattice model</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Ising+model">Ising model</a></li> </ul> </li> </ul> <h3 id="in_solid_state_physics">In solid state physics</h3> <p>In <a class="existingWikiWord" href="/nlab/show/solid+state+physics">solid state physics</a>:</p> <ul> <li><a class="existingWikiWord" href="/nlab/show/Haldane+model">Haldane model</a></li> </ul> <h3 id="in_particle_physics_2">In particle physics</h3> <p>In <a class="existingWikiWord" href="/nlab/show/particle+physics">particle physics</a>:</p> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/standard+model+of+particle+physics">standard model of particle physics</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Connes-Lott-Chamseddine+model">Connes-Lott-Chamseddine model</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/Grand+Unified+Theory">Grand Unified Theory</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/composite+Higgs+model">composite Higgs model</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/MSSM">MSSM</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/G%E2%82%82-MSSM">G₂-MSSM</a></li> </ul> </li> </ul> <h3 id="in_cosmology">In cosmology</h3> <p>In <a class="existingWikiWord" href="/nlab/show/cosmology">cosmology</a></p> <ul> <li><a class="existingWikiWord" href="/nlab/show/standard+model+of+cosmology">standard model of cosmology</a></li> </ul> <h2 id="related_concepts">Related concepts</h2> <ul> <li> <p><a class="existingWikiWord" href="/nlab/show/theory+%28physics%29">theory (physics)</a>, <a class="existingWikiWord" href="/nlab/show/experiment">experiment</a>, <a class="existingWikiWord" href="/nlab/show/coordination">coordination</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/bottom-up+and+top-down+model+building">bottom-up and top-down model building</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/intersecting+D-brane+model">intersecting D-brane model</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/computable+physics">computable physics</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/mathematical+physics">mathematical physics</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/naturalness">naturalness</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/landscape+of+string+theory+vacua">landscape of string theory vacua</a></p> </li> <li> <p><a class="existingWikiWord" href="/nlab/show/string+inspired+model">string inspired model</a></p> </li> <li> <p><a href="string+theory+FAQ#HowDoesStringTheoryMakePredictions">string theory FAQ – Does string theory make predictions?</a></p> </li> <li> <p><a href="http://ncatlab.org/nlab/show/string+theory+FAQ#WhatDoesItMeanToSayStringTheoryHasALandscapeOfSolutions">string theory FAQ – What does it mean to say that string theory has a “landscape of solutions”?</a></p> </li> </ul> </body></html> </div> <div class="revisedby"> <p> Last revised on January 8, 2025 at 16:02:54. See the <a href="/nlab/history/model+%28in+theoretical+physics%29" style="color: #005c19">history</a> of this page for a list of all contributions to it. </p> </div> <div class="navigation navfoot"> <a href="/nlab/edit/model+%28in+theoretical+physics%29" accesskey="E" class="navlink" id="edit" rel="nofollow">Edit</a><a href="https://nforum.ncatlab.org/discussions/?CategoryID=0">Discuss</a><span class="backintime"><a href="/nlab/revision/model+%28in+theoretical+physics%29/20" accesskey="B" class="navlinkbackintime" id="to_previous_revision" rel="nofollow">Previous revision</a></span><a href="/nlab/show/diff/model+%28in+theoretical+physics%29" accesskey="C" class="navlink" id="see_changes" rel="nofollow">Changes from previous revision</a><a href="/nlab/history/model+%28in+theoretical+physics%29" accesskey="S" class="navlink" id="history" rel="nofollow">History (20 revisions)</a> <a href="/nlab/show/model+%28in+theoretical+physics%29/cite" style="color: black">Cite</a> <a href="/nlab/print/model+%28in+theoretical+physics%29" accesskey="p" id="view_print" rel="nofollow">Print</a> <a href="/nlab/source/model+%28in+theoretical+physics%29" id="view_source" rel="nofollow">Source</a> </div> </div>  </div>  </body> </html>