A theory of everything (TOE or TOE/ToE), final theory, ultimate theory, unified field theory or master theory is a hypothetical, singular, all-encompassing, coherent theoretical framework of physics that fully explains and links together all aspects of the

universe The universe is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy. The Big Bang theory is the prevailing cosmological description of the development of the universe. A ...

. Finding a theory of everything is one of the major unsolved problems in physics. String theory and

M-theory M-theory is a theory in physics that unifies all consistent versions of superstring theory. Edward Witten first conjectured the existence of such a theory at a string theory conference at the University of Southern California in 1995. Witte ...

have been proposed as theories of everything. Over the past few centuries, two theoretical frameworks have been developed that, together, most closely resemble a theory of everything. These two theories upon which all modern physics rests are

general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. ...

and

quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, q ...

. General relativity is a theoretical framework that only focuses on

gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the str ...

for understanding the universe in regions of both large scale and high mass:

planets A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a young ...

, stars, galaxies, clusters of galaxies etc. On the other hand, quantum mechanics is a theoretical framework that only focuses on the three non-gravitational forces for understanding the universe in regions of both very small scale and low mass: subatomic particles,

atoms Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas ...

molecules A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioc ...

, etc. Quantum mechanics successfully implemented the

Standard Model The Standard Model of particle physics is the theory describing three of the four known fundamental forces ( electromagnetic, weak and strong interactions - excluding gravity) in the universe and classifying all known elementary particles. I ...

that describes the three non-gravitational forces: strong nuclear, weak nuclear, and

electromagnetic In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...

force – as well as all observed elementary particles. General relativity and quantum mechanics have been repeatedly validated in their separate fields of relevance. Since the usual domains of applicability of general relativity and quantum mechanics are so different, most situations require that only one of the two theories be used. The two theories are considered incompatible in regions of extremely small scale – the Planck scale – such as those that exist within a black hole or during the beginning stages of the universe (i.e., the moment immediately following the

Big Bang The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from t ...

). To resolve the incompatibility, a theoretical framework revealing a deeper underlying reality, unifying gravity with the other three interactions, must be discovered to harmoniously integrate the realms of general relativity and quantum mechanics into a seamless whole: a theory of everything may be defined as a comprehensive theory that, in principle, would be capable of describing all physical phenomena in this universe. In pursuit of this goal,

quantum gravity Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics; it deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the v ...

has become one area of active research. One example is string theory, which evolved into a candidate for the theory of everything, but not without drawbacks (most notably, its apparent lack of currently

testable Testability is a primary aspect of Science and the Scientific Method and is a property applying to an empirical hypothesis, involves two components: #Falsifiability or defeasibility, which means that counterexamples to the hypothesis are logica ...

prediction A prediction (Latin ''præ-'', "before," and ''dicere'', "to say"), or forecast, is a statement about a future event or data. They are often, but not always, based upon experience or knowledge. There is no universal agreement about the exac ...

s) and controversy. String theory posits that at the

beginning of the universe Cosmogony is any model concerning the origin of the cosmos or the universe. Overview Scientific theories In astronomy, cosmogony refers to the study of the origin of particular astrophysical objects or systems, and is most commonly use ...

(up to 10⁻⁴³ seconds after the Big Bang), the four fundamental forces were once a single fundamental force. According to string theory, every particle in the universe, at its most ultramicroscopic level ( Planck length), consists of varying combinations of vibrating strings (or strands) with preferred patterns of vibration. String theory further claims that it is through these specific oscillatory patterns of strings that a particle of unique mass and force charge is created (that is to say, the

electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary partic ...

is a type of string that vibrates one way, while the

up quark The up quark or u quark (symbol: u) is the lightest of all quarks, a type of elementary particle, and a significant constituent of matter. It, along with the down quark, forms the neutrons (one up quark, two down quarks) and protons (two up qua ...

is a type of string vibrating another way, and so forth). String theory/M-theory proposes six or seven

dimensions In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coord ...

of hyperspace in addition to the four common dimensions for a ten- or eleven-dimensional

spacetime In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why diffe ...

Name

Initially, the term ''theory of everything'' was used with an ironic reference to various overgeneralized theories. For example, a grandfather of Ijon Tichy – a character from a cycle of

Stanisław Lem Stanisław Herman Lem (; 12 September 1921 – 27 March 2006) was a Polish writer of science fiction and essays on various subjects, including philosophy, futurology, and literary criticism. Many of his science fiction stories are of satirica ...

science fiction Science fiction (sometimes shortened to Sci-Fi or SF) is a genre of speculative fiction which typically deals with imagination, imaginative and futuristic concepts such as advanced science and technology, space exploration, time travel, Paral ...

stories of the 1960s – was known to work on the " General Theory of Everything". Physicist Harald Fritzsch used the term in his 1977 lectures in Varenna. Physicist

John Ellis John Ellis may refer to: Academics *John Ellis (scrivener) (1698–1791), English political writer *John Ellis (naturalist) (1710–1776), English botanical illustrator *John Ellis (physicist, born 1946), British theoretical physicist at CERN * Jo ...

claims to have introduced the acronym "TOE" into the technical literature in an article in ''

Nature Nature, in the broadest sense, is the physical world or universe. "Nature" can refer to the phenomena of the physical world, and also to life in general. The study of nature is a large, if not the only, part of science. Although humans ar ...

'' in 1986. Over time, the term stuck in popularizations of

theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experi ...

research.

Historical antecedents

Antiquity to 19th century

Many ancient cultures such as

Babylonian astronomers Babylonian astronomy was the study or recording of celestial objects during the early history of Mesopotamia. Babylonian astronomy seemed to have focused on a select group of stars and constellations known as Ziqpu stars. These constellations ...

Indian astronomy Astronomy has long history in Indian subcontinent stretching from pre-historic to modern times. Some of the earliest roots of Indian astronomy can be dated to the period of Indus Valley civilisation or earlier. Astronomy later developed as a di ...

studied the pattern of the ''Seven Sacred Luminaires''/ Classical Planets against the background of stars, with their interest being to relate celestial movement to human events (

astrology Astrology is a range of divinatory practices, recognized as pseudoscientific since the 18th century, that claim to discern information about human affairs and terrestrial events by studying the apparent positions of celestial objects. Di ...

), and the goal being to predict events by recording events against a time measure and then look for recurrent patterns. The debate between the universe having either

a beginning "Don't Pass Me By" is a song by the English rock band the Beatles from their 1968 double album ''The Beatles'' (also known as the "White Album"). A country rock song, it was the first solo composition written by drummer Ringo Starr. The song ...

or eternal cycles can be traced back to ancient

Babylonia Babylonia (; Akkadian: , ''māt Akkadī'') was an ancient Akkadian-speaking state and cultural area based in the city of Babylon in central-southern Mesopotamia (present-day Iraq and parts of Syria). It emerged as an Amorite-ruled state ...

. Hindu cosmology posits that time is infinite with a ''cyclic universe'', where the current universe was preceded and will be followed by an infinite number of universes. Time scales mentioned in Hindu cosmology correspond to those of modern scientific cosmology. Its cycles run from our ordinary day and night to a day and night of Brahma, 8.64 billion years long. The

natural philosophy Natural philosophy or philosophy of nature (from Latin ''philosophia naturalis'') is the philosophical study of physics, that is, nature and the physical universe. It was dominant before the development of modern science. From the ancient wor ...

atomism Atomism (from Greek , ''atomon'', i.e. "uncuttable, indivisible") is a natural philosophy proposing that the physical universe is composed of fundamental indivisible components known as atoms. References to the concept of atomism and its atoms ...

appeared in several ancient traditions. In ancient

Greek philosophy Ancient Greek philosophy arose in the 6th century BC, marking the end of the Greek Dark Ages. Greek philosophy continued throughout the Hellenistic period and the period in which Greece and most Greek-inhabited lands were part of the Roman Empi ...

, the pre-Socratic philosophers speculated that the apparent diversity of observed phenomena was due to a single type of interaction, namely the motions and collisions of atoms. The concept of 'atom' proposed by

Democritus Democritus (; el, Δημόκριτος, ''Dēmókritos'', meaning "chosen of the people"; – ) was an Ancient Greek pre-Socratic philosopher from Abdera, primarily remembered today for his formulation of an atomic theory of the universe. ...

was an early philosophical attempt to unify phenomena observed in nature. The concept of 'atom' also appeared in the

Nyaya (Sanskrit: न्याय, ''nyā-yá''), literally meaning "justice", "rules", "method" or "judgment",Vaisheshika school of ancient

Indian philosophy Indian philosophy refers to philosophical traditions of the Indian subcontinent. A traditional Hindu classification divides āstika and nāstika schools of philosophy, depending on one of three alternate criteria: whether it believes the Veda ...

Archimedes Archimedes of Syracuse (;; ) was a Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily. Although few details of his life are known, he is regarded as one of the leading scienti ...

was possibly the first philosopher to have described nature with axioms (or principles) and then deduce new results from them. Any "theory of everything" is similarly expected to be based on axioms and to deduce all observable phenomena from them. Following earlier atomistic thought, the

mechanical philosophy The mechanical philosophy is a form of natural philosophy which compares the universe to a large-scale mechanism (i.e. a machine). The mechanical philosophy is associated with the scientific revolution of early modern Europe. One of the first expo ...

of the 17th century posited that all forces could be ultimately reduced to contact forces between the atoms, then imagined as tiny solid particles. In the late 17th century,

Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a " natural philosopher"), widely recognised as one of the g ...

's description of the long-distance force of gravity implied that not all forces in nature result from things coming into contact. Newton's work in his '' Mathematical Principles of Natural Philosophy'' dealt with this in a further example of unification, in this case unifying Galileo's work on terrestrial gravity, Kepler's laws of planetary motion and the phenomenon of

tide Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon (and to a much lesser extent, the Sun) and are also caused by the Earth and Moon orbiting one another. Tide tables can ...

s by explaining these apparent actions at a distance under one single law: the law of

universal gravitation Newton's law of universal gravitation is usually stated as that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distanc ...

. In 1814, building on these results, Laplace famously suggested that a sufficiently powerful intellect could, if it knew the position and velocity of every particle at a given time, along with the laws of nature, calculate the position of any particle at any other time: Laplace thus envisaged a combination of gravitation and mechanics as a theory of everything. Modern

implies that uncertainty is inescapable, and thus that Laplace's vision has to be amended: a theory of everything must include gravitation and quantum mechanics. Even ignoring quantum mechanics, chaos theory is sufficient to guarantee that the future of any sufficiently complex mechanical or astronomical system is unpredictable. In 1820,

Hans Christian Ørsted Hans Christian Ørsted ( , ; often rendered Oersted in English; 14 August 17779 March 1851) was a Danish physicist and chemist who discovered that electric currents create magnetic fields, which was the first connection found between electricity ...

discovered a connection between electricity and magnetism, triggering decades of work that culminated in 1865, in

James Clerk Maxwell James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and scientist responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism and ligh ...

's theory of

electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions o ...

. During the 19th and early 20th centuries, it gradually became apparent that many common examples of forces – contact forces, elasticity,

viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...

friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding (motion), sliding against each other. There are several types of friction: *Dry friction is a force that opposes the relative la ...

, and

pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country a ...

– result from electrical interactions between the smallest particles of matter. In his experiments of 1849–50,

Michael Faraday Michael Faraday (; 22 September 1791 – 25 August 1867) was an English scientist who contributed to the study of electromagnetism and electrochemistry. His main discoveries include the principles underlying electromagnetic inductio ...

was the first to search for a unification of

with electricity and magnetism. However, he found no connection. In 1900, David Hilbert published a famous list of mathematical problems. In

Hilbert's sixth problem Hilbert's sixth problem is to axiomatize those branches of physics in which mathematics is prevalent. It occurs on the widely cited list of Hilbert's problems in mathematics that he presented in the year 1900. In its common English translation, ...

, he challenged researchers to find an axiomatic basis to all of physics. In this problem he thus asked for what today would be called a theory of everything.

Early 20th century

In the late 1920s, the new quantum mechanics showed that the

chemical bond A chemical bond is a lasting attraction between atoms or ions that enables the formation of molecules and crystals. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds, or through the sharing o ...

s between

atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas ...

s were examples of (quantum) electrical forces, justifying Dirac's boast that "the underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known". After 1915, when

Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theor ...

published the theory of gravity (

), the search for a

unified field theory In physics, a unified field theory (UFT) is a type of field theory that allows all that is usually thought of as fundamental forces and elementary particles to be written in terms of a pair of physical and virtual fields. According to the mode ...

combining gravity with electromagnetism began with a renewed interest. In Einstein's day, the strong and the weak forces had not yet been discovered, yet he found the potential existence of two other distinct forces, gravity and electromagnetism, far more alluring. This launched his 40-year voyage in search of the so-called ''"unified field theory"'' that he hoped would show that these two forces are really manifestations of one grand, underlying principle. During the last few decades of his life, this ambition alienated Einstein from the rest of mainstream of physics, as the mainstream was instead far more excited about the emerging framework of quantum mechanics. Einstein wrote to a friend in the early 1940s, "I have become a lonely old chap who is mainly known because he doesn't wear socks and who is exhibited as a curiosity on special occasions." Prominent contributors were Gunnar Nordström,

Hermann Weyl Hermann Klaus Hugo Weyl, (; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, he is ass ...

, Arthur Eddington, David Hilbert, Theodor Kaluza,

Oskar Klein Oskar Benjamin Klein (; 15 September 1894 – 5 February 1977) was a Swedish theoretical physicist. Biography Klein was born in Danderyd outside Stockholm, son of the chief rabbi of Stockholm, Gottlieb Klein from Humenné in Kingdom of Hungary ...

(see Kaluza–Klein theory), and most notably, Albert Einstein and his collaborators. Einstein searched in earnest for, but ultimately failed to find, a unifying theory (see Einstein–Maxwell–Dirac equations).

Late 20th century and the nuclear interactions

In the 20th century, the search for a unifying theory was interrupted by the discovery of the

strong Strong may refer to: Education * The Strong, an educational institution in Rochester, New York, United States * Strong Hall (Lawrence, Kansas), an administrative hall of the University of Kansas * Strong School, New Haven, Connecticut, United Sta ...

and

weak Weak may refer to: Songs * "Weak" (AJR song), 2016 * "Weak" (Melanie C song), 2011 * "Weak" (SWV song), 1993 * "Weak" (Skunk Anansie song), 1995 * "Weak", a song by Seether from '' Seether: 2002-2013'' Television episodes * "Weak" (''Fear t ...

nuclear forces, which differ both from gravity and from electromagnetism. A further hurdle was the acceptance that in a theory of everything, quantum mechanics had to be incorporated from the outset, rather than emerging as a consequence of a deterministic unified theory, as Einstein had hoped. Gravity and electromagnetism are able to coexist as entries in a list of classical forces, but for many years it seemed that gravity could not be incorporated into the quantum framework, let alone unified with the other fundamental forces. For this reason, work on unification, for much of the 20th century, focused on understanding the three forces described by quantum mechanics: electromagnetism and the weak and strong forces. The first two were

combined Combined may refer to: * Alpine combined (skiing), the combination of slalom and downhill skiing as a single event ** Super combined (skiing) * Nordic combined (skiing), the combination of cross country skiing and ski jumping as a single event * T ...

in 1967–68 by Sheldon Glashow, Steven Weinberg, and Abdus Salam into the electroweak force. Electroweak unification is a broken symmetry: the electromagnetic and weak forces appear distinct at low energies because the particles carrying the weak force, the W and Z bosons, have non-zero masses ( and , respectively), whereas the

photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are Massless particle, massless ...

, which carries the electromagnetic force, is massless. At higher energies W bosons and Z bosons can be created easily and the unified nature of the force becomes apparent. While the strong and electroweak forces coexist under the

of particle physics, they remain distinct. Thus, the pursuit of a theory of everything remained unsuccessful: neither a unification of the strong and electroweak forces – which Laplace would have called 'contact forces' – nor a unification of these forces with gravitation had been achieved.

Modern physics

Conventional sequence of theories

A theory of everything would unify all the

fundamental interaction In physics, the fundamental interactions, also known as fundamental forces, are the interactions that do not appear to be reducible to more basic interactions. There are four fundamental interactions known to exist: the gravitational and electr ...

s of nature: gravitation, the

strong interaction The strong interaction or strong force is a fundamental interaction that confines quarks into proton, neutron, and other hadron particles. The strong interaction also binds neutrons and protons to create atomic nuclei, where it is called th ...

, the

weak interaction In nuclear physics and particle physics, the weak interaction, which is also often called the weak force or weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interact ...

, and

. Because the weak interaction can transform

elementary particles In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include electrons, the fundamental fermions (quarks, leptons, an ...

from one kind into another, the theory of everything should also predict all the various different kinds of particles possible. The usual assumed path of theories is given in the following graph, where each unification step leads one level up on the graph. In this graph, electroweak unification occurs at around 100 GeV, grand unification is predicted to occur at 10¹⁶ GeV, and unification of the GUT force with gravity is expected at the Planck energy, roughly 10¹⁹ GeV. Several Grand Unified Theories (GUTs) have been proposed to unify electromagnetism and the weak and strong forces. Grand unification would imply the existence of an electronuclear force; it is expected to set in at energies of the order of 10¹⁶ GeV, far greater than could be reached by any currently feasible

particle accelerator A particle accelerator is a machine that uses electromagnetic fields to propel electric charge, charged particles to very high speeds and energies, and to contain them in well-defined particle beam, beams. Large accelerators are used for fun ...

. Although the simplest grand unified theories have been experimentally ruled out, the idea of a grand unified theory, especially when linked with

supersymmetry In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theories e ...

, remains a favorite candidate in the theoretical physics community. Supersymmetric grand unified theories seem plausible not only for their theoretical "beauty", but because they naturally produce large quantities of dark matter, and because the inflationary force may be related to grand unified theory physics (although it does not seem to form an inevitable part of the theory). Yet grand unified theories are clearly not the final answer; both the current standard model and all proposed GUTs are quantum field theories which require the problematic technique of renormalization to yield sensible answers. This is usually regarded as a sign that these are only

effective field theories In physics, an effective field theory is a type of approximation, or effective theory, for an underlying physical theory, such as a quantum field theory or a statistical mechanics model. An effective field theory includes the appropriate degrees ...

, omitting crucial phenomena relevant only at very high energies. The final step in the graph requires resolving the separation between quantum mechanics and gravitation, often equated with general relativity. Numerous researchers concentrate their efforts on this specific step; nevertheless, no accepted theory of

, and thus no accepted theory of everything, has emerged with observational evidence. It is usually assumed that the theory of everything will also solve the remaining problems of grand unified theories. In addition to explaining the forces listed in the graph, a theory of everything may also explain the status of at least two candidate forces suggested by modern

cosmology Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', and in 1731 taken up in Latin by German philosophe ...

: an inflationary force and dark energy. Furthermore, cosmological experiments also suggest the existence of

dark matter Dark matter is a hypothetical form of matter thought to account for approximately 85% of the matter in the universe. Dark matter is called "dark" because it does not appear to interact with the electromagnetic field, which means it does not ab ...

, supposedly composed of fundamental particles outside the scheme of the standard model. However, the existence of these forces and particles has not been proven.

String theory and M-theory

Since the 1990s, some physicists such as

Edward Witten Edward Witten (born August 26, 1951) is an American mathematical and theoretical physicist. He is a Professor Emeritus in the School of Natural Sciences at the Institute for Advanced Study in Princeton. Witten is a researcher in string theory, ...

believe that 11-dimensional

, which is described in some limits by one of the five

perturbative In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for wh ...

superstring theories Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modeling them as vibrations of tiny supersymmetric strings. 'Superstring theory' is a shorthand for supersymmetric string theor ...

, and in another by the maximally-

supersymmetric In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theorie ...

11-dimensional

supergravity In theoretical physics, supergravity (supergravity theory; SUGRA for short) is a modern field theory that combines the principles of supersymmetry and general relativity; this is in contrast to non-gravitational supersymmetric theories such as ...

, is the theory of everything. There is no widespread consensus on this issue. One remarkable property of

string String or strings may refer to: *String (structure), a long flexible structure made from threads twisted together, which is used to tie, bind, or hang other objects Arts, entertainment, and media Films * ''Strings'' (1991 film), a Canadian anim ...

is that seven extra dimensions are required for the theory's consistency, on top of the four dimensions in our universe. In this regard, string theory can be seen as building on the insights of the Kaluza–Klein theory, in which it was realized that applying general relativity to a 5-dimensional universe, with one space dimension small and curled up, looks from the 4-dimensional perspective like the usual general relativity together with Maxwell's electrodynamics. This lent credence to the idea of unifying gauge and

interactions, and to extra dimensions, but did not address the detailed experimental requirements. Another important property of string theory is its

, which together with extra dimensions are the two main proposals for resolving the

hierarchy problem In theoretical physics, the hierarchy problem is the problem concerning the large discrepancy between aspects of the weak force and gravity. There is no scientific consensus on why, for example, the weak force is 1024 times stronger than gra ...

of the

standard model The Standard Model of particle physics is the theory describing three of the four known fundamental forces ( electromagnetic, weak and strong interactions - excluding gravity) in the universe and classifying all known elementary particles. I ...

, which is (roughly) the question of why gravity is so much weaker than any other force. The extra-dimensional solution involves allowing gravity to propagate into the other dimensions while keeping other forces confined to a 4-dimensional spacetime, an idea that has been realized with explicit stringy mechanisms. Research into string theory has been encouraged by a variety of theoretical and experimental factors. On the experimental side, the particle content of the standard model supplemented with neutrino masses fits into a spinor representation of SO(10), a subgroup of E8 that routinely emerges in string theory, such as in

heterotic string theory In string theory, a heterotic string is a closed string (or loop) which is a hybrid ('heterotic') of a superstring and a bosonic string. There are two kinds of heterotic string, the heterotic SO(32) and the heterotic E8 × E8, abbreviate ...

or (sometimes equivalently) in F-theory. String theory has mechanisms that may explain why fermions come in three hierarchical generations, and explain the mixing rates between quark generations. On the theoretical side, it has begun to address some of the key questions in

, such as resolving the black hole information paradox, counting the correct entropy of black holes and allowing for

topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ho ...

-changing processes. It has also led to many insights in

pure mathematics Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications ...

and in ordinary, strongly-coupled

gauge theory In physics, a gauge theory is a type of field theory in which the Lagrangian (and hence the dynamics of the system itself) does not change (is invariant) under local transformations according to certain smooth families of operations (Lie groups ...

due to the Gauge/String duality. In the late 1990s, it was noted that one major hurdle in this endeavor is that the number of possible 4-dimensional universes is incredibly large. The small, "curled up" extra dimensions can be compactified in an enormous number of different ways (one estimate is 10⁵⁰⁰ ) each of which leads to different properties for the low-energy particles and forces. This array of models is known as the string theory landscape. One proposed solution is that many or all of these possibilities are realized in one or another of a huge number of universes, but that only a small number of them are habitable. Hence what we normally conceive as the

fundamental constants In physics, a dimensionless physical constant is a physical constant that is dimensionless, i.e. a pure number having no units attached and having a numerical value that is independent of whatever system of units may be used. For example, if one co ...

of the universe are ultimately the result of the anthropic principle rather than dictated by theory. This has led to criticism of string theory, arguing that it cannot make useful (i.e., original, falsifiable, and verifiable) predictions and regarding it as a

pseudoscience Pseudoscience consists of statements, beliefs, or practices that claim to be both scientific and factual but are incompatible with the scientific method. Pseudoscience is often characterized by contradictory, exaggerated or unfalsifiable claim ...

/ philosophy. Others disagree, and string theory remains an active topic of investigation in

Loop quantum gravity

Current research on

loop quantum gravity Loop quantum gravity (LQG) is a theory of quantum gravity, which aims to merge quantum mechanics and general relativity, incorporating matter of the Standard Model into the framework established for the pure quantum gravity case. It is an attem ...

may eventually play a fundamental role in a theory of everything, but that is not its primary aim. Loop quantum gravity also introduces a lower bound on the possible length scales. There have been recent claims that loop quantum gravity may be able to reproduce features resembling the

. So far only the first generation of

fermion In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks and ...

s (

lepton In particle physics, a lepton is an elementary particle of half-integer spin (spin (physics), spin ) that does not undergo strong interactions. Two main classes of leptons exist: electric charge, charged leptons (also known as the electron-li ...

s and

quark A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. All common ...

s) with correct parity properties have been modelled by Sundance Bilson-Thompson using preons constituted of braids of spacetime as the building blocks. However, there is no derivation of the

Lagrangian Lagrangian may refer to: Mathematics * Lagrangian function, used to solve constrained minimization problems in optimization theory; see Lagrange multiplier ** Lagrangian relaxation, the method of approximating a difficult constrained problem with ...

that would describe the interactions of such particles, nor is it possible to show that such particles are fermions, nor that the gauge groups or interactions of the Standard Model are realised. Utilization of

quantum computing Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Thou ...

concepts made it possible to demonstrate that the particles are able to survive quantum fluctuations. This model leads to an interpretation of electric and color charge as topological quantities (electric as number and chirality of twists carried on the individual ribbons and colour as variants of such twisting for fixed electric charge). Bilson-Thompson's original paper suggested that the higher-generation fermions could be represented by more complicated braidings, although explicit constructions of these structures were not given. The electric charge, color, and parity properties of such fermions would arise in the same way as for the first generation. The model was expressly generalized for an infinite number of generations and for the weak force bosons (but not for photons or gluons) in a 2008 paper by Bilson-Thompson, Hackett, Kauffman and Smolin.

Other attempts

Among other attempts to develop a theory of everything is the theory of causal fermion systems, giving the two current physical theories (

and

quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles a ...

) as limiting cases. Another theory is called Causal Sets. As some of the approaches mentioned above, its direct goal isn't necessarily to achieve a theory of everything but primarily a working theory of quantum gravity, which might eventually include the standard model and become a candidate for a theory of everything. Its founding principle is that spacetime is fundamentally discrete and that the spacetime events are related by a

partial order In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a binary ...

. This partial order has the physical meaning of the causality relations between relative

past and future distinguishing In the study of Lorentzian manifold spacetimes there exists a hierarchy of causality conditions which are important in proving mathematical theorems about the global structure of such manifolds. These conditions were collected during the late 1970 ...

spacetime events. Causal dynamical triangulation does not assume any pre-existing arena (dimensional space), but rather attempts to show how the spacetime fabric itself evolves. Another attempt may be related to ER=EPR, a conjecture in physics stating that entangled particles are connected by a

wormhole A wormhole ( Einstein-Rosen bridge) is a hypothetical structure connecting disparate points in spacetime, and is based on a special solution of the Einstein field equations. A wormhole can be visualized as a tunnel with two ends at separate p ...

(or Einstein–Rosen bridge).

Present status

At present, there is no candidate theory of everything that includes the standard model of particle physics and general relativity and that, at the same time, is able to calculate the fine-structure constant or the mass of the electron. Most particle physicists expect that the outcome of ongoing experiments – the search for new particles at the large

s and for

– are needed in order to provide further input for a theory of everything.

Arguments against

In parallel to the intense search for a theory of everything, various scholars have seriously debated the possibility of its discovery.

Gödel's incompleteness theorem

A number of scholars claim that Gödel's incompleteness theorem suggests that any attempt to construct a theory of everything is bound to fail. Gödel's theorem, informally stated, asserts that any formal theory sufficient to express elementary arithmetical facts and strong enough for them to be proved is either inconsistent (both a statement and its denial can be derived from its axioms) or incomplete, in the sense that there is a true statement that can't be derived in the formal theory. Stanley Jaki, in his 1966 book ''The Relevance of Physics'', pointed out that, because any "theory of everything" will certainly be a consistent non-trivial mathematical theory, it must be incomplete. He claims that this dooms searches for a deterministic theory of everything.

Freeman Dyson Freeman John Dyson (15 December 1923 – 28 February 2020) was an English-American theoretical physicist and mathematician known for his works in quantum field theory, astrophysics, random matrices, mathematical formulation of quantum m ...

has stated that "Gödel's theorem implies that pure mathematics is inexhaustible. No matter how many problems we solve, there will always be other problems that cannot be solved within the existing rules. ��Because of Gödel's theorem, physics is inexhaustible too. The laws of physics are a finite set of rules, and include the rules for doing mathematics, so that Gödel's theorem applies to them." Stephen Hawking was originally a believer in the Theory of Everything, but after considering Gödel's Theorem, he concluded that one was not obtainable. "Some people will be very disappointed if there is not an ultimate theory that can be formulated as a finite number of principles. I used to belong to that camp, but I have changed my mind." Jürgen Schmidhuber (1997) has argued against this view; he asserts that Gödel's theorems are irrelevant for computable physics. In 2000, Schmidhuber explicitly constructed limit-computable, deterministic universes whose pseudo-randomness based on undecidable, Gödel-like

halting problem In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running, or continue to run forever. Alan Turing proved in 1936 that a ...

s is extremely hard to detect but does not at all prevent formal theories of everything describable by very few bits of information. Related critique was offered by Solomon Feferman and others. Douglas S. Robertson offers

Conway's game of life The Game of Life, also known simply as Life, is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is a zero-player game, meaning that its evolution is determined by its initial state, requiring no furt ...

as an example: The underlying rules are simple and complete, but there are formally undecidable questions about the game's behaviors. Analogously, it may (or may not) be possible to completely state the underlying rules of physics with a finite number of well-defined laws, but there is little doubt that there are questions about the behavior of physical systems which are formally undecidable on the basis of those underlying laws. Since most physicists would consider the statement of the underlying rules to suffice as the definition of a "theory of everything", most physicists argue that Gödel's Theorem does ''not'' mean that a theory of everything cannot exist. On the other hand, the scholars invoking Gödel's Theorem appear, at least in some cases, to be referring not to the underlying rules, but to the understandability of the behavior of all physical systems, as when Hawking mentions arranging blocks into rectangles, turning the computation of

prime number A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only way ...

s into a physical question. This definitional discrepancy may explain some of the disagreement among researchers.

Fundamental limits in accuracy

No physical theory to date is believed to be precisely accurate. Instead, physics has proceeded by a series of "successive approximations" allowing more and more accurate predictions over a wider and wider range of phenomena. Some physicists believe that it is therefore a mistake to confuse theoretical models with the true nature of reality, and hold that the series of approximations will never terminate in the "truth". Einstein himself expressed this view on occasions. On the other hand, it is often claimed that, despite the apparently ever-increasing complexity of the mathematics of each new theory, in a deep sense associated with their underlying gauge symmetry and the number of dimensionless physical constants, the theories are becoming simpler. If this is the case, the process of simplification cannot continue indefinitely.

Definition of fundamental laws

There is a philosophical debate within the physics community as to whether a theory of everything deserves to be called ''the'' fundamental law of the universe. One view is the hard

reductionist Reductionism is any of several related philosophical ideas regarding the associations between phenomena which can be described in terms of other simpler or more fundamental phenomena. It is also described as an intellectual and philosophical pos ...

position that the theory of everything is the fundamental law and that all other theories that apply within the universe are a consequence of the theory of everything. Another view is that

emergent Emergent may refer to: * ''Emergent'' (album), a 2003 album by Gordian Knot * Emergent (software), Neural Simulation Software * Emergent BioSolutions, a multinational biopharmaceutical company headquartered in Gaithersburg, Maryland, USA * Emerg ...

laws, which govern the behavior of

complex system A complex system is a system composed of many components which may interact with each other. Examples of complex systems are Earth's global climate, organisms, the human brain, infrastructure such as power grid, transportation or communicatio ...

s, should be seen as equally fundamental. Examples of emergent laws are the

second law of thermodynamics The second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unles ...

and the theory of

natural selection Natural selection is the differential survival and reproduction of individuals due to differences in phenotype. It is a key mechanism of evolution, the change in the heritable traits characteristic of a population over generations. Cha ...

. The advocates of emergence argue that emergent laws, especially those describing complex or living systems are independent of the low-level, microscopic laws. In this view, emergent laws are as fundamental as a theory of everything. The debates do not make the point at issue clear. Possibly the only issue at stake is the right to apply the high-status term "fundamental" to the respective subjects of research. A well-known debate over this took place between Steven Weinberg and Philip Anderson.

Impossibility of calculation

WeinbergWeinberg (1993) p. 5 points out that calculating the precise motion of an actual projectile in the Earth's atmosphere is impossible. So how can we know we have an adequate theory for describing the motion of projectiles? Weinberg suggests that we know ''principles'' (Newton's laws of motion and gravitation) that work "well enough" for simple examples, like the motion of planets in empty space. These principles have worked so well on simple examples that we can be reasonably confident they will work for more complex examples. For example, although

includes equations that do not have exact solutions, it is widely accepted as a valid theory because all of its equations with exact solutions have been experimentally verified. Likewise, a theory of everything must work for a wide range of simple examples in such a way that we can be reasonably confident it will work for every situation in physics.

References

Bibliography

* Pais, Abraham (1982) '' Subtle is the Lord: The Science and the Life of Albert Einstein'' (Oxford University Press, Oxford, . Ch. 17, *

Weinberg, Steven Steven Weinberg (; May 3, 1933 – July 23, 2021) was an American theoretical physicist and Nobel laureate in physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic interactio ...

(1993) ''Dreams of a Final Theory: The Search for the Fundamental Laws of Nature'', Hutchinson Radius, London, *

Corey S. Powell Corey Stevenson Powell (born January 7, 1966) is an American science writer and journalist, particularly known for his writing for ''Discover'' magazine, of which he became Editor-in-Chief in 2012, and his longstanding collaboration with Bill Nye ...

''Relativity versus quantum mechanics: the battle for the universe'', The Guardian (2015) https://www.theguardian.com/news/2015/nov/04/relativity-quantum-mechanics-universe-physicists

External links

The Elegant Universe
'' Nova'' episode about the search for the theory of everything and string theory.
Theory of Everything
freeview video by the Vega Science Trust, BBC and

Open University The Open University (OU) is a British Public university, public research university and the largest university in the United Kingdom by List of universities in the United Kingdom by enrolment, number of students. The majority of the OU's underg ...

.
The Theory of Everything
Are we getting closer, or is a final theory of matter and the universe impossible? Debate between John Ellis (physicist), Frank Close and Nicholas Maxwell.
Why The World Exists
a discussion between physicist Laura Mersini-Houghton, cosmologist

George Francis Rayner Ellis George Francis Rayner Ellis, Fellow of the Royal Society, FRS, Hon. FRSSAf (born 11 August 1939), is the emeritus distinguished professor of complex systems in the Department of Mathematics and Applied Mathematics at the University of Cape Town ...

and philosopher David Wallace about dark matter, parallel universes and explaining why these and the present Universe exist.
Theories of Everything
BBC Radio 4 discussion with Brian Greene, John Barrow & Val Gibson (''In Our Time'', Mar. 25, 2004) {{Authority control Physics beyond the Standard Model Theoretical physics Theories of gravity