View source for Theoretical physics

{{Short description|Branch of physics}}

[[File:LorentzianWormhole.jpg|thumb|Visual representation of a [[Wormhole#Schwarzschild_wormholes|Schwarzschild wormhole]]. Wormholes have never been observed, but they are predicted to exist through [[mathematical model]]s and [[scientific theory]].]]

'''Theoretical physics''' is a branch of [[physics]] that employs [[mathematical model]]s and [[abstraction]]s of physical objects and systems to rationalize, explain, and predict [[List of natural phenomena|natural phenomena]]. This is in contrast to [[experimental physics]], which uses experimental tools to probe these phenomena.

The advancement of [[science]] generally depends on the interplay between [[experiment]]al studies and [[theory]]. In some cases, theoretical physics adheres to standards of [[mathematical rigour]] while giving little weight to experiments and observations.<ref group="lower-alpha">There is some debate as to whether or not theoretical physics uses mathematics to build intuition and illustrativeness to extract physical insight (especially when normal [[experience]] fails), rather than as a tool in formalizing theories. This links to the question of it using mathematics in a less formally rigorous, and more intuitive or [[heuristic]] way than, say, [[mathematical physics]].</ref> For example, while developing [[special relativity]], [[Albert Einstein]] was concerned with the [[Lorentz transformation]] which left [[Maxwell's equations]] invariant, but was apparently uninterested in the [[Michelson–Morley experiment]] on [[Earth]]'s drift through a [[luminiferous aether]].<ref>{{cite journal |last=van Dongen |first=Jeroen |title=On the role of the Michelson-Morley experiment: Einstein in Chicago |journal=Archive for History of Exact Sciences |volume=63 |year=2009 |issue=6 |pages=655–663 |arxiv=0908.1545 |doi=10.1007/s00407-009-0050-5 |doi-access=free}}</ref> Conversely, Einstein was awarded the [[Nobel Prize]] for explaining the [[photoelectric effect]], previously an experimental result lacking a theoretical formulation.<ref name="Ref_s">{{cite web|title = The Nobel Prize in Physics 1921|publisher =The [[Nobel Foundation]]|url = http://nobelprize.org/nobel_prizes/physics/laureates/1921/index.html|access-date=2008-10-09}}</ref>

==Overview==
A '''physical theory''' is a model of physical events. It is judged by the extent to which its predictions agree with empirical observations. The quality of a physical theory is also judged on its ability to make new predictions which can be verified by new observations. A physical theory differs from a [[theorem|mathematical theorem]] in that while both are based on some form of [[axiom]]s, judgment of mathematical applicability is not based on agreement with any experimental results.<ref name=Nelson>[http://www.esotericka.org/cmc/tth.html Theorems and Theories] {{Webarchive|url=https://web.archive.org/web/20140819090102/http://www.esotericka.org/cmc/tth.html |date=2014-08-19 }}, Sam Nelson.</ref><ref name=Chu>Mark C. Chu-Carroll, March 13, 2007:[http://www.goodmath.org/blog/2007/03/13/theories-theorems-lemmas-and-corollaries/ Theories, Theorems, Lemmas, and Corollaries.] Good Math, Bad Math blog.</ref> A physical theory similarly differs from a [[mathematical theory]], in the sense that the word "theory" has a different meaning in mathematical terms.<ref group="lower-alpha">Sometimes the word "theory" can be used ambiguously in this sense, not to describe scientific theories, but research (sub)fields and programmes.  Examples: relativity theory, quantum field theory, string theory.</ref>
{{Rquote|right|
<math>\mathrm{Ric} = kg</math>

''The equations for an [[Einstein manifold]], used in [[general relativity]] to describe the curvature of [[spacetime]]''
}}

A physical theory involves one or more relationships between various measurable quantities. [[Archimedes]] realized that a ship floats by displacing its mass of water, [[Pythagoras]] understood the relation between the length of a [[oscillation|vibrating]] string and the musical tone it produces.<ref>{{cite book|title=Vibration of Continuous Systems |author= Singiresu S. Rao|edition= illustrated
|publisher= [[John Wiley & Sons]]|at=5,12|isbn=978-0471771715|year= 2007}} {{isbn|9780471771715}}</ref><ref>{{cite book|title= The Pythagorean Theorem: A 4,000-year History|url= https://archive.org/details/pythagoreantheor00maor_711|url-access= limited|author= Eli Maor |edition= illustrated |publisher= [[Princeton University Press]]|pages=[https://archive.org/details/pythagoreantheor00maor_711/page/n36 18]–20|year= 2007|isbn= 978-0691125268}} {{isbn|9780691125268}}</ref> Other examples include [[entropy]] as a measure of the uncertainty regarding the positions and [[motion (physics)|motions]] of unseen [[molecule|particles]] and the [[quantum mechanics|quantum mechanical]] idea that ([[action (physics)|action]] and) [[energy]] are not continuously variable.

Theoretical physics consists of several different approaches. In this regard, [[theoretical particle physics]] forms a good example. For instance: "[[Phenomenology (physics)|phenomenologists]]" might employ ([[semi-empirical|semi-]]) [[empirical]] formulas and [[heuristic]]s to agree with experimental results, often [[heuristic argument|without deep physical understanding]].<ref group="lower-alpha">The work of [[Johann Balmer]] and [[Johannes Rydberg]] in spectroscopy, and the [[semi-empirical mass formula]] of nuclear physics are good candidates for examples of this approach.</ref> "Modelers" (also called "model-builders") often appear much like phenomenologists, but try to model speculative theories that have certain desirable features (rather than on experimental data), or apply the techniques of [[mathematical modeling]]  to physics problems.<ref group="lower-alpha">The [[Ptolemaic model|Ptolemaic]] and [[Heliocentrism|Copernican]] models of the Solar system, the Bohr model of hydrogen atoms and [[nuclear shell model]] are good candidates for examples of this approach.</ref>  Some attempt to create approximate theories, called ''[[Effective field theories|effective theories]]'', because fully developed theories may be regarded as unsolvable or [[complexity|too complicated]]. Other theorists may try to [[unified field theories|unify]], formalise, reinterpret or generalise extant theories, or create completely new ones altogether.<ref group="lower-alpha">Arguably these are the most celebrated theories in physics: Newton's theory of gravitation, Einstein's theory of relativity and Maxwell's theory of electromagnetism share some of these attributes.</ref> Sometimes the vision provided by pure mathematical systems can provide clues to how a physical system might be modeled;<ref group="lower-alpha">This approach is often favoured by (pure) mathematicians and mathematical physicists.</ref> e.g., the notion, due to [[Bernhard Riemann|Riemann]] and others, that [[space]] itself might be curved. Theoretical problems that need computational investigation are often the concern of [[computational physics]].

Theoretical advances may consist in setting aside old, incorrect [[paradigm]]s (e.g., [[Luminiferous aether|aether theory]] of light propagation, [[caloric theory]] of heat, burning consisting of evolving [[phlogiston]], or astronomical bodies [[geocentrism|revolving around the Earth]]) or may be an alternative model that provides answers that are more accurate or that can be more widely applied. In the latter case, a [[correspondence principle]] will be required to recover the [[classical limit|previously known result]].<ref>Bokulich, Alisa, "[http://plato.stanford.edu/archives/spr2014/entries/bohr-correspondence/ Bohr's Correspondence Principle]", The [[Stanford Encyclopedia of Philosophy]] (Spring 2014 Edition), Edward N. Zalta (ed.)</ref><ref>Enc. Britannica (1994), pg 844.</ref>  Sometimes though, advances may proceed along different paths. For example, an essentially correct theory may need some conceptual or factual revisions; [[atomic theory]], first postulated millennia ago (by [[atomism|several thinkers in Greece and India]]) and the [[fluid theory of electricity|two-fluid theory]] of electricity<ref>Enc. Britannica (1994), pg 834.</ref>  are two cases in this point. However, an exception to all the above is the [[wave–particle duality]],  a theory combining aspects of different, opposing models via the [[Bohr complementarity principle]].

[[File:Mathematical Physics and other sciences.png|Relationship between mathematics and physics|left|thumb]]
Physical theories become accepted if they are able to make correct predictions and no (or few) incorrect ones. The theory should have, at least as a secondary objective, a certain economy and elegance (compare to [[mathematical beauty]]), a notion sometimes called "[[Occam's razor]]" after the 13th-century English philosopher [[William of Ockham|William of Occam]] (or Ockham), in which the simpler of two theories that describe the same matter just as adequately is preferred (but conceptual simplicity may mean mathematical complexity).<ref>[http://www.iep.utm.edu/simplici/ Simplicity in the Philosophy of Science] (retrieved 19 Aug 2014), [[Internet Encyclopedia of Philosophy]].</ref> They are also more likely to be accepted if they connect a wide range of phenomena. Testing the consequences of a theory is part of the [[scientific method]].

Physical theories can be grouped into three categories: ''[[theoretical physics#Mainstream theories|mainstream theories]]'', ''[[theoretical physics#Proposed theories|proposed theories]]'' and ''[[theoretical physics#Fringe theories|fringe theories]]''.

==History==
{{details|History of physics}}

Theoretical physics began at least 2,300 years ago, under the [[Pre-Socratic philosophy|Pre-socratic philosophy]], and continued by [[Plato]] and [[Aristotle]], whose views held sway for a millennium. During the rise of [[medieval universities]], the only [[Medieval university#Characteristics|acknowledged intellectual disciplines]] were the seven [[liberal arts]] of the ''[[Trivium]]'' like [[grammar]], [[logic]], and [[rhetoric]] and of the ''[[Quadrivium]]'' like [[arithmetic]], [[geometry]], [[music]] and [[astronomy]]. During the [[Middle Ages]] and [[Renaissance]], the concept of [[experiment]]al science, the [[counterpoint]] to theory, began with scholars such as [[Ibn al-Haytham]] and [[Francis Bacon]]. As the [[Scientific Revolution]] gathered pace, the concepts of [[matter]], energy, space, time and [[causality]] slowly began to acquire the form we know today, and other sciences spun off from the rubric of [[natural philosophy]]. Thus began the modern era of theory with the [[Nicolaus Copernicus|Copernican]] paradigm shift in astronomy, soon followed by [[Johannes Kepler]]'s expressions for planetary orbits, which summarized the meticulous observations of [[Tycho Brahe]]; the works of these men (alongside Galileo's) can perhaps be considered to constitute the Scientific Revolution.

The great push toward the modern concept of explanation started with [[Galileo Galilei|Galileo]], one of the few [[physicist]]s who was both a consummate theoretician and a great [[experimentalist]]. The [[analytic geometry]] and mechanics of [[René Descartes|Descartes]] were incorporated into the [[calculus]] and [[classical mechanics|mechanics]] of [[Isaac Newton]], another theoretician/experimentalist of the highest order, writing [[Philosophiæ Naturalis Principia Mathematica|''Principia Mathematica'']].<ref name="hooke1679nov24">See 'Correspondence of Isaac Newton, vol.2, 1676–1687' ed. H W Turnbull, Cambridge University Press 1960; at page 297, document #235, letter from Hooke to Newton dated 24 November 1679.</ref> In it contained a grand synthesis of the work of Copernicus, Galileo and Kepler; as well as Newton's theories of mechanics and gravitation, which held sway as worldviews until the early 20th century. Simultaneously, progress was also made in optics (in particular colour theory and the ancient science of [[geometrical optics]]), courtesy of Newton, Descartes and the Dutchmen Snell and Huygens. In the 18th and 19th centuries [[Joseph-Louis Lagrange]], [[Leonhard Euler]] and [[William Rowan Hamilton]] would extend the theory of classical mechanics considerably.<ref>{{cite book|author=Penrose, R|title= The Road to Reality| page= [https://archive.org/details/roadtoreality00penr_678/page/n499 471]|publisher= Jonathan Cape|year= 2004|title-link= The Road to Reality}}</ref> They picked up the interactive intertwining of [[mathematics]] and [[physics]] begun two millennia earlier by Pythagoras.

Among the great conceptual achievements of the 19th and 20th centuries were the consolidation of the idea of [[energy]] (as well as its global conservation) by the inclusion of [[heat]], [[electricity and magnetism]], and then [[light]]. The [[laws of thermodynamics]], and most importantly the introduction of the singular concept of [[entropy]] began to provide a macroscopic explanation for the properties of matter. [[Statistical mechanics]] (followed by [[statistical physics]] and [[Quantum statistical mechanics]]) emerged as an offshoot of thermodynamics late in the 19th century. Another important event in the 19th century was the discovery of [[electromagnetic theory]], unifying the previously separate phenomena of electricity, magnetism and light.

The pillars of [[modern physics]], and perhaps the most revolutionary theories in the history of physics, have been [[theory of relativity|relativity theory]] and [[quantum mechanics]]. Newtonian mechanics was subsumed under special relativity and Newton's [[gravity]] was given a [[kinematic]] explanation by [[general relativity]]. Quantum mechanics led to an understanding of [[black body|blackbody]] [[electromagnetic radiation|radiation]] (which indeed, was an original motivation for the theory) and of anomalies in the [[specific heat capacity|specific heats]] of [[solid]]s — and finally to an understanding of the internal structures of [[atom]]s and [[molecule]]s. Quantum mechanics soon gave way to the formulation of [[quantum field theory]] (QFT), begun in the late 1920s. In the aftermath of World War 2, more progress brought much renewed interest in QFT, which had since the early efforts, stagnated. The same period also saw fresh attacks on the problems of superconductivity and phase transitions, as well as the first applications of QFT in the area of theoretical condensed matter. The 1960s and 70s saw the formulation of the [[Standard model of particle physics]] using QFT and progress in condensed matter physics (theoretical [[BCS theory|foundations of superconductivity]] and [[critical phenomena]], [[Landau-Ginzburg theory|among others]]), in parallel to the applications of relativity to [[golden age of general relativity|problems in astronomy]] and [[golden age of cosmology|cosmology respectively]].

All of these achievements depended on the theoretical physics as a moving force both to suggest experiments and to consolidate results — often by ingenious application of existing mathematics, or, as in the case of Descartes and Newton (with [[Gottfried Leibniz|Leibniz]]), by inventing new mathematics. [[Joseph Fourier|Fourier's]] studies of heat conduction led to a new branch of mathematics: [[Fourier series|infinite, orthogonal series]].<ref>{{cite book|author=Penrose, R|title= The Road to Reality| chapter= 9: Fourier decompositions and hyperfunctions|publisher= Jonathan Cape|year= 2004|title-link= The Road to Reality}}</ref>

Modern theoretical physics attempts to unify theories and explain phenomena in further attempts to understand the [[Universe]], from the [[physical cosmology|cosmological]] to the [[elementary particle]] scale. Where experimentation cannot be done, theoretical physics still tries to advance through the use of mathematical models.

==Mainstream theories==
'''Mainstream theories''' (sometimes referred to as ''central theories'') are the body of knowledge of both factual and scientific views and possess a usual scientific quality of the tests of repeatability, consistency with existing well-established science and experimentation. There do exist mainstream theories that are generally accepted theories based solely upon their effects explaining a wide variety of data, although the detection, explanation, and possible composition are subjects of debate.

===Examples===
{{colbegin|colwidth=18em}}
<!-- Please keep these in alphabetical order. -->
* [[Big Bang]]
* [[Chaos theory]]
* [[Classical mechanics]]
* [[Classical field theory]]
* [[Dynamo theory]]
* [[Field theory (physics)|Field theory]]
* [[Ginzburg–Landau theory]]
* [[Kinetic theory of gases]]
* [[Classical electromagnetism]]
* [[Perturbation theory (quantum mechanics)]]
* [[Physical cosmology]]
* [[Quantum chromodynamics]]
* [[Quantum complexity theory]]
* [[Quantum electrodynamics]]
* [[Quantum field theory]]
* [[Quantum field theory in curved spacetime]]
* [[Quantum information theory]]
* [[Quantum mechanics]]
* [[Quantum thermodynamics]]
* [[Relativistic quantum mechanics]]
* [[Scattering theory]]
* [[Standard Model]]
* [[Statistical physics]]
* [[Theory of relativity]]
* [[Wave–particle duality]]
{{colend}}

==Proposed theories==
The '''proposed theories''' of physics are usually relatively new theories which deal with the study of physics which include scientific approaches, means for determining the validity of models and new types of reasoning used to arrive at the theory. However, some proposed theories include theories that have been around for decades and have eluded methods of discovery and testing. Proposed theories can include fringe theories in the process of becoming established (and, sometimes, gaining wider acceptance). Proposed theories usually have not been tested. In addition to the theories like those listed below, there are also different [[interpretations of quantum mechanics]], which may or may not be considered different theories since it is debatable whether they yield different predictions for physical experiments, even in principle. For example, [[AdS/CFT correspondence]], [[Chern–Simons theory]], [[graviton]], [[magnetic monopole]], [[string theory]], [[theory of everything]].

<!--===Examples===
{{cols|colwidth=16em}}
* [[6D (2,0) superconformal field theory]]
* [[AdS/CFT correspondence]]
* [[Alternatives to general relativity]]
* [[Anthropic principle]]
* [[Black hole thermodynamics]]
* [[Brane cosmology]]
* [[Brans–Dicke theory]]
* [[Canonical quantum gravity]]
* [[Causal dynamical triangulation]]
* [[Causal fermion systems]]
* [[Causal sets]]
* [[Chern–Simons theory]]
* [[Closed timelike curve]]
* [[Conformal cyclic cosmology]]
* [[Conformal field theory]]
* [[Cosmic string]]
* [[Cyclic model]]
* [[Dark flow]]
* [[Dark fluid]]
* [[de Sitter invariant special relativity]]
* [[Dilaton]]
* [[Doubly special relativity]]
* [[Einstein–Rosen Bridge]] (Wormhole)
* [[Ekpyrotic universe]]
* [[ER = EPR]]
* [[Eternal inflation]]
* [[Extra dimensions]]
* [[False vacuum]]
* [[Fifth force]]
* [[F-theory]]
* [[Gauge gravitation theory]]
* [[Gauge theory gravity]]
* [[Geon (physics)|Geon]]
* [[Grand Unified Theory]]
* [[Gravastar]]
* [[Graviphoton]]
* [[Graviscalar]]
* [[Gravitino]]
* [[Graviton]]
* [[Hawking radiation]]
* [[Hartle–Hawking state]]
* [[Heterotic string theory]]
* [[Holographic principle]]
* [[Kaluza–Klein theory]]
* [[Large extra dimensions]]
* [[Loop quantum cosmology]]
* [[Loop quantum gravity]]
* [[Magnetic monopole]]
* [[Massive gravity]]
* [[Mirror matter]]
* [[M-theory]]
* [[Multiverse]]
* [[N = 4 supersymmetric Yang–Mills theory|''N'' = 4 supersymmetric Yang–Mills theory]]
* [[Noncommutative quantum field theory]]
* [[Nonsingular black hole models]]
* [[Proton decay]]
* [[Quantum cosmology]]
* [[Quantum foam]]
* [[Quantum geometry]]
* [[Quantum gravity]]
* [[Randall–Sundrum model]]
* [[Semiclassical gravity]]
* [[Sphaleron]]
* [[Spin foam]]
* [[String theory]]
* [[Superfluid vacuum theory]]
* [[Supergravity]]
* [[Superstring theory]]
* [[Supersymmetry]]
* [[Supersymmetry breaking]]
* [[Technicolor (physics)|Technicolor]]
* [[Theory of everything]]
* [[Toda field theory]]
* [[Unified field theory]]
* [[Universal extra dimensions]]
* [[Unparticle physics]]
* [[Weak gravity conjecture]]
{{colend}}-->
<!-- Please keep these in alphabetical order. -->

==Fringe theories==
'''Fringe theories''' include any new area of scientific endeavor in the process of becoming established and some proposed theories. It can include speculative sciences. This includes physics fields and physical theories presented in accordance with known evidence, and a body of associated predictions have been made according to that theory.

Some fringe theories go on to become a widely accepted part of physics. Other fringe theories end up being disproven. Some fringe theories are a form of [[protoscience]] and others are a form of [[pseudoscience]]. The falsification of the original theory sometimes leads to reformulation of the theory.

===Examples===
{{colbegin}}
<!-- Please keep these in alphabetical order. -->
* [[Aether (classical element)]]
**[[Luminiferous aether]]
* [[Digital physics]]
* [[Electrogravitics]]
* [[Stochastic electrodynamics]]
* [[Nikola Tesla#On experimental and theoretical physics|Tesla's dynamic theory of gravity]]
{{colend}}

==Thought experiments vs real experiments==
{{Main|Thought experiment}}

"Thought" experiments are situations created in one's mind, asking a question akin to "suppose you are in this situation, assuming such is true, what would follow?". They are usually created to investigate phenomena that are not readily experienced in every-day situations. Famous examples of such thought experiments are [[Schrödinger's cat]], the [[EPR paradox|EPR thought experiment]], [[Time dilation|simple illustrations of time dilation]], and so on. These usually lead to real experiments designed to verify that the conclusion (and therefore the assumptions) of the thought experiments are correct. The EPR thought experiment led to the [[Bell inequalities]], which were then [[Bell test experiments|tested to various degrees of rigor]], leading to the acceptance of the current formulation of [[quantum mechanics]] and [[Quantum indeterminacy|probabilism]] as a [[working hypothesis]].

==See also==
* [[List of theoretical physicists]]
* [[Philosophy of physics]]
* [[Symmetry in quantum mechanics]]
* [[Timeline of developments in theoretical physics]]
*[[Double field theory]]

==Notes==
{{reflist|group=lower-alpha}}

==References==
{{reflist|30em}}

==Further reading==
*{{cite book|edition=15th|title=Physical Sciences|series= [[Encyclopædia Britannica]] (Macropaedia)|year=1994|volume=25}}
*Duhem, Pierre. ''La théorie physique - Son objet, sa structure'', (in French). 2nd edition - 1914. English translation: ''The physical theory - its purpose, its structure''. Republished by [[:fr:Joseph Vrin|Joseph Vrin]] philosophical bookstore (1981), {{isbn|2711602214}}.
* Feynman, et al. [https://feynmanlectures.caltech.edu ''The Feynman Lectures on Physics''] (3 vol.). First edition: Addison–Wesley, (1964, 1966).
:Bestselling three-volume textbook covering the span of physics. Reference for both (under)graduate student and professional researcher alike.
* Landau et al. ''[[Course of Theoretical Physics]]''.
: Famous series of books dealing with theoretical concepts in physics covering 10 volumes, translated into many languages and reprinted over many editions. Often known simply as "Landau and Lifschits" or "Landau-Lifschits" in the literature.
* Longair, MS. ''Theoretical Concepts in Physics: An Alternative View of Theoretical Reasoning in Physics''. [[Cambridge University Press]]; 2d edition (4 Dec 2003). {{isbn|052152878X}}. {{isbn|978-0521528788}}
* Planck, Max (1909). [https://books.google.com/books?id=KisvtatMApwC ''Eight Lectures on theoretical physics'']. Library of Alexandria. {{isbn|1465521887}}, {{isbn|9781465521880}}.
: A set of lectures given in 1909 at [[Columbia University]].
* Sommerfeld, Arnold. ''Vorlesungen über theoretische Physik'' (''[[Lectures on Theoretical Physics]]''); German, 6 volumes.
:A series of lessons from a master educator of theoretical physicists.

==External links==
{{wikibooks|Introduction to Theoretical Physics}}
*[https://physics.mit.edu/research/labs-centers/center-for-theoretical-physics/ MIT Center for Theoretical Physics]
*[https://webspace.science.uu.nl/~gadda001/goodtheorist/ How to become a GOOD Theoretical Physicist], a website made by [[Gerard 't Hooft]]

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