Theoretical physics

Visual representation of aSchwarzschild wormhole.Wormholes have never been observed, but they are predicted to exist throughmathematical modelsandscientific theory.

Theoretical physicsis a branch ofphysicsthat employsmathematical modelsandabstractionsof physical objects and systems to rationalize, explain, and predictnatural phenomena.This is in contrast toexperimental physics,which uses experimental tools to probe these phenomena.

The advancement ofsciencegenerally depends on the interplay betweenexperimentalstudies andtheory.In some cases, theoretical physics adheres to standards ofmathematical rigourwhile giving little weight to experiments and observations.For example, while developingspecial relativity,Albert Einsteinwas concerned with theLorentz transformationwhich leftMaxwell's equationsinvariant, but was apparently uninterested in theMichelson–Morley experimentonEarth's drift through aluminiferous aether.Conversely, Einstein was awarded theNobel Prizefor explaining thephotoelectric effect,previously an experimental result lacking a theoretical formulation.

Overview

Aphysical theoryis 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 amathematical theoremin that while both are based on some form ofaxioms,judgment of mathematical applicability is not based on agreement with any experimental results.A physical theory similarly differs from amathematical theory,in the sense that the word "theory" has a different meaning in mathematical terms.

$\mathrm {Ric} =kg$ The equations for anEinstein manifold,used ingeneral relativityto describe the curvature ofspacetime

A physical theory involves one or more relationships between various measurable quantities.Archimedesrealized that a ship floats by displacing its mass of water,Pythagorasunderstood the relation between the length of avibratingstring and the musical tone it produces.Other examples includeentropyas a measure of the uncertainty regarding the positions andmotionsof unseenparticlesand thequantum mechanicalidea that (actionand)energyare not continuously variable.

Theoretical physics consists of several different approaches. In this regard,theoretical particle physicsforms a good example. For instance: "phenomenologists"might employ (semi-)empiricalformulas andheuristicsto agree with experimental results, oftenwithout deep physical understanding."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 ofmathematical modelingto physics problems.Some attempt to create approximate theories, calledeffective theories,because fully developed theories may be regarded as unsolvable ortoo complicated.Other theorists may try tounify,formalise, reinterpret or generalise extant theories, or create completely new ones altogether.Sometimes the vision provided by pure mathematical systems can provide clues to how a physical system might be modeled;e.g., the notion, due toRiemannand others, thatspaceitself might be curved. Theoretical problems that need computational investigation are often the concern ofcomputational physics.

Theoretical advances may consist in setting aside old, incorrectparadigms(e.g.,aether theoryof light propagation,caloric theoryof heat, burning consisting of evolvingphlogiston,or astronomical bodiesrevolving 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, acorrespondence principlewill be required to recover thepreviously known result.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 (byseveral thinkers in Greece and India) and thetwo-fluid theoryof electricityare two cases in this point. However, an exception to all the above is thewave–particle duality,a theory combining aspects of different, opposing models via theBohr complementarity principle.

Relationship between mathematics and physics

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 tomathematical beauty), a notion sometimes called "Occam's razor"after the 13th-century English philosopherWilliam 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).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 thescientific method.

Physical theories can be grouped into three categories:mainstream theories,proposed theoriesandfringe theories.

History

Further information:History of physics

Theoretical physics began at least 2,300 years ago, under thePre-socratic philosophy,and continued byPlatoandAristotle,whose views held sway for a millennium. During the rise ofmedieval universities,the onlyacknowledged intellectual disciplineswere the sevenliberal artsof theTriviumlikegrammar,logic,andrhetoricand of theQuadriviumlikearithmetic,geometry,musicandastronomy.During theMiddle AgesandRenaissance,the concept ofexperimentalscience, thecounterpointto theory, began with scholars such asIbn al-HaythamandFrancis Bacon.As theScientific Revolutiongathered pace, the concepts ofmatter,energy, space, time andcausalityslowly began to acquire the form we know today, and other sciences spun off from the rubric ofnatural philosophy.Thus began the modern era of theory with theCopernicanparadigm shift in astronomy, soon followed byJohannes Kepler's expressions for planetary orbits, which summarized the meticulous observations ofTycho 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 withGalileo,one of the fewphysicistswho was both a consummate theoretician and a greatexperimentalist.Theanalytic geometryand mechanics ofDescarteswere incorporated into thecalculusandmechanicsofIsaac Newton,another theoretician/experimentalist of the highest order, writingPrincipia Mathematica.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 ofgeometrical optics), courtesy of Newton, Descartes and the Dutchmen Snell and Huygens. In the 18th and 19th centuriesJoseph-Louis Lagrange,Leonhard EulerandWilliam Rowan Hamiltonwould extend the theory of classical mechanics considerably.They picked up the interactive intertwining ofmathematicsandphysicsbegun two millennia earlier by Pythagoras.

Among the great conceptual achievements of the 19th and 20th centuries were the consolidation of the idea ofenergy(as well as its global conservation) by the inclusion ofheat,electricity and magnetism,and thenlight.Thelaws of thermodynamics,and most importantly the introduction of the singular concept ofentropybegan to provide a macroscopic explanation for the properties of matter.Statistical mechanics(followed bystatistical physicsandQuantum statistical mechanics) emerged as an offshoot of thermodynamics late in the 19th century. Another important event in the 19th century was the discovery ofelectromagnetic theory,unifying the previously separate phenomena of electricity, magnetism and light.

The pillars ofmodern physics,and perhaps the most revolutionary theories in the history of physics, have beenrelativity theoryandquantum mechanics.Newtonian mechanics was subsumed under special relativity and Newton'sgravitywas given akinematicexplanation bygeneral relativity.Quantum mechanics led to an understanding ofblackbodyradiation(which indeed, was an original motivation for the theory) and of anomalies in thespecific heatsofsolids— and finally to an understanding of the internal structures ofatomsandmolecules.Quantum mechanics soon gave way to the formulation ofquantum 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 theStandard model of particle physicsusing QFT and progress in condensed matter physics (theoreticalfoundations of superconductivityandcritical phenomena,among others), in parallel to the applications of relativity toproblems in astronomyandcosmology 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 (withLeibniz), by inventing new mathematics.Fourier'sstudies of heat conduction led to a new branch of mathematics:infinite, orthogonal series.

Modern theoretical physics attempts to unify theories and explain phenomena in further attempts to understand theUniverse,from thecosmologicalto theelementary particlescale. Where experimentation cannot be done, theoretical physics still tries to advance through the use of mathematical models.

Mainstream theories

Mainstream theories(sometimes referred to ascentral 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

• Big Bang
• Chaos theory
• Classical mechanics
• Classical field theory
• Dynamo theory
• 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

Proposed theories

Theproposed theoriesof 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 differentinterpretations 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.

Fringe theories

Fringe theoriesinclude 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 ofprotoscienceand others are a form ofpseudoscience.The falsification of the original theory sometimes leads to reformulation of the theory.

Examples

• Aether (classical element)
  • Luminiferous aether
• Digital physics
• Electrogravitics
• Stochastic electrodynamics
• Tesla's dynamic theory of gravity

Thought experiments vs real experiments

Main article: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 areSchrödinger's cat,theEPR thought experiment,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 theBell inequalities,which were thentested to various degrees of rigor,leading to the acceptance of the current formulation ofquantum mechanicsandprobabilismas aworking hypothesis.

See also

• List of theoretical physicists
• Philosophy of physics
• Symmetry in quantum mechanics
• Timeline of developments in theoretical physics
• Double field theory

Further reading

• Physical Sciences.Encyclopædia Britannica(Macropaedia). Vol. 25 (15th ed.). 1994.
• Duhem, Pierre.La théorie physique - Son objet, sa structure,(in French). 2nd edition - 1914. English translation:The physical theory - its purpose, its structure.Republished byJoseph Vrinphilosophical bookstore (1981),ISBN2711602214.
• Feynman, et al.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).ISBN052152878X.ISBN978-0521528788
• Planck, Max (1909).Eight Lectures on theoretical physics.Library of Alexandria.ISBN1465521887,ISBN9781465521880.

A set of lectures given in 1909 atColumbia 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

• MIT Center for Theoretical Physics
• How to become a GOOD Theoretical Physicist,a website made byGerard 't Hooft