Theory of everything

Theory of everything

Overview
A theory of everything (TOE) is a putative theory
Theory
The English word theory was derived from a technical term in Ancient Greek philosophy. The word theoria, , meant "a looking at, viewing, beholding", and referring to contemplation or speculation, as opposed to action...

 of theoretical physics
Theoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...

 that fully explains and links together all known physical phenomena, and predicts the outcome of any experiment that could be carried out in principle.

The theory of everything is also called the final theory. Many candidate theories of everything have been proposed by theoretical physicists during the twentieth century, but none have been confirmed experimentally.
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Encyclopedia
A theory of everything (TOE) is a putative theory
Theory
The English word theory was derived from a technical term in Ancient Greek philosophy. The word theoria, , meant "a looking at, viewing, beholding", and referring to contemplation or speculation, as opposed to action...

 of theoretical physics
Theoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...

 that fully explains and links together all known physical phenomena, and predicts the outcome of any experiment that could be carried out in principle.

The theory of everything is also called the final theory. Many candidate theories of everything have been proposed by theoretical physicists during the twentieth century, but none have been confirmed experimentally. The primary problem in producing a TOE is that general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

 and quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

 are hard to unify. This is one of the unsolved problems in physics
Unsolved problems in physics
This is a list of some of the major unsolved problems in physics. Some of these problems are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result...

.

Initially, the term 'theory of everything' was used with an ironic connotation to refer to various overgeneralized theories. For example, a great-grandfather of Ijon Tichy
Ijon Tichy
Ijon Tichy is a fictional character who appears in several works of Stanisław Lem, including The Futurological Congress, Peace on Earth, Observation on the Spot, The Star Diaries and Memoirs of a Space Traveller .-Character:Tichy is a space explorer whose interplanetary...

—a character from a cycle of Stanisław Lem's science fiction
Science fiction
Science fiction is a genre of fiction dealing with imaginary but more or less plausible content such as future settings, futuristic science and technology, space travel, aliens, and paranormal abilities...

 stories of the 1960s—was known to work on the "General Theory of Everything". Physicist John Ellis
John Ellis (physicist)
Jonathan Richard Ellis FRS is a British theoretical physicist who is currently Clerk Maxwell Professor of Theoretical Physics at King's College London. After completing his secondary education at Highgate School, he attended Cambridge University, earning his Ph.D. in theoretical particle physics...

 claims to have introduced the term into the technical literature in an article in Nature in 1986. Over time, the term stuck in popularizations of quantum physics to describe a theory that would unify or explain through a single model the theories of all fundamental interaction
Fundamental interaction
In particle physics, fundamental interactions are the ways that elementary particles interact with one another...

s and of all particles of nature: general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

 for gravitation, and the standard model
Standard Model
The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...

 of elementary particle physics — which includes quantum mechanics — for electromagnetism, the two nuclear interactions, and the known elementary particles.

Current candidates for a theory of everything include string theory
String theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...

, M theory, and loop quantum gravity
Loop quantum gravity
Loop quantum gravity , also known as loop gravity and quantum geometry, is a proposed quantum theory of spacetime which attempts to reconcile the theories of quantum mechanics and general relativity...

.

From ancient Greece to Einstein


Archimedes
Archimedes
Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an...

 was possibly the first scientist to describe nature with axioms (or principles) and then to deduce new results from them. He thus tried to describe "everything" starting from a few axioms. Also the putative theory of everything is expected to be based on axioms and to deduce all observable phenomena from them.

Also the concept of 'atom', introduced by Democritus
Democritus
Democritus was an Ancient Greek philosopher born in Abdera, Thrace, Greece. He was an influential pre-Socratic philosopher and pupil of Leucippus, who formulated an atomic theory for the cosmos....

, realized an aspect of unification: the concept unified all phenomena observed in nature as the motion of atoms. As part of the atomistic model of nature, already in ancient Greek
Ancient Greek
Ancient Greek is the stage of the Greek language in the periods spanning the times c. 9th–6th centuries BC, , c. 5th–4th centuries BC , and the c. 3rd century BC – 6th century AD of ancient Greece and the ancient world; being predated in the 2nd millennium BC by Mycenaean Greek...

 times philosophers
Pre-Socratic philosophy
Pre-Socratic philosophy is Greek philosophy before Socrates . In Classical antiquity, the Presocratic philosophers were called physiologoi...

 speculated that the apparent diversity of observed phenomena was due to a single type of interaction, namely the collisions of atoms. Following atomism
Atomism
Atomism is a natural philosophy that developed in several ancient traditions. The atomists theorized that the natural world consists of two fundamental parts: indivisible atoms and empty void.According to Aristotle, atoms are indestructible and immutable and there are an infinite variety of shapes...

, the mechanical philosophy of the 17th century posited that all forces could be ultimately reduced to contact force
Contact force
In physics, a contact force is a force that acts at the point of contact between two objects, in contrast to body forces. Contact forces are described by Newton's laws of motion, as with all other forces in dynamics....

s between the atoms, then imagined as tiny solid particles.

In the late 17th century, Isaac Newton's
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

 description of the long-distance force of gravity implied that the idea of exclusively contact forces in nature had to be amended. Nevertheless, Newton's work in his Principia
Philosophiae Naturalis Principia Mathematica
Philosophiæ Naturalis Principia Mathematica, Latin for "Mathematical Principles of Natural Philosophy", often referred to as simply the Principia, is a work in three books by Sir Isaac Newton, first published 5 July 1687. Newton also published two further editions, in 1713 and 1726...

provided an example of unification on its own: the work unified Galileo's work on terrestrial gravity, Kepler's laws of planetary motion and the phenomenon of tide
Tide
Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the moon and the sun and the rotation of the Earth....

s by explaining them with one single law: the law of universal gravitation.

In 1814, building on these results, Laplace famously suggested that a sufficiently powerful intellect
Laplace's demon
In the history of science, Laplace's demon was the first published articulation of causal or scientific determinism by Pierre-Simon Laplace in 1814...

 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 quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

 implies that uncertainty is inescapable, and thus that Laplace's vision needs to be amended: a theory of everything must include gravitation and quantum mechanics.

In 1820, Hans Christian Ørsted
Hans Christian Ørsted
Hans Christian Ørsted was a Danish physicist and chemist who discovered that electric currents create magnetic fields, an important aspect of electromagnetism...

 discovered a connection between electricity and magnetism, triggering decades of work that culminated in 1865, in James Clerk Maxwell
James Clerk Maxwell
James Clerk Maxwell of Glenlair was a Scottish physicist and mathematician. His most prominent achievement was formulating classical electromagnetic theory. This united all previously unrelated observations, experiments and equations of electricity, magnetism and optics into a consistent theory...

's theory of electromagnetism
Electromagnetism
Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...

. During the 19th and early 20th centuries, it gradually became apparent that many common examples of forces — contact forces, elasticity
Elasticity (physics)
In physics, elasticity is the physical property of a material that returns to its original shape after the stress that made it deform or distort is removed. The relative amount of deformation is called the strain....

, viscosity
Viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

, friction
Friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and/or material elements sliding against each other. There are several types of friction:...

, and pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

 — result from electrical interactions between the smallest particles of matter.

In his experiments of 1849–50, Michael Faraday
Michael Faraday
Michael Faraday, FRS was an English chemist and physicist who contributed to the fields of electromagnetism and electrochemistry....

 was the first to search for a unification of gravity with electricity and magnetism. However, he found no connection.

In 1900, David Hilbert
David Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...

 published a famous list of mathematical problems. In Hilbert's sixth problem
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...

, 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.

In the late 1920s, the new quantum mechanics showed that the chemical bond
Chemical bond
A chemical bond is an attraction between atoms that allows the formation of chemical substances that contain two or more atoms. The bond is caused by the electromagnetic force attraction between opposite charges, either between electrons and nuclei, or as the result of a dipole attraction...

s between atom
Atom
The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...

s were examples of (quantum) electrical forces, justifying Dirac
Paul Dirac
Paul Adrien Maurice Dirac, OM, FRS was an English theoretical physicist who made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics...

'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
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

 published the theory of gravity (general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

), the search for a unified field theory
Unified field theory
In physics, a unified field theory, occasionally referred to as a uniform field theory, 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 single field. There is no accepted unified field theory, and thus...

 combining gravity with electromagnetism started again with renewed intensity. At the time, it seemed plausible that no other fundamental forces exist. Prominent contributors were Gunnar Nordström
Gunnar Nordström
Gunnar Nordström was a Finnish theoretical physicist best remembered for his theory of gravitation, which was an early competitor of general relativity...

, Hermann Weyl
Hermann Weyl
Hermann Klaus Hugo Weyl was a German mathematician and theoretical physicist. Although much of his working life was spent in Zürich, Switzerland and then Princeton, he is associated with the University of Göttingen tradition of mathematics, represented by David Hilbert and Hermann Minkowski.His...

, Arthur Eddington, Theodor Kaluza
Theodor Kaluza
Theodor Franz Eduard Kaluza was a German mathematician and physicist known for the Kaluza-Klein theory involving field equations in five-dimensional space...

, Oskar Klein
Oskar Klein
Oskar Benjamin Klein was a Swedish theoretical physicist.Klein was born in Danderyd outside Stockholm, son of the chief rabbi of Stockholm, Dr. Gottlieb Klein from Homonna in Hungary and Antonie Levy...

, and most notably, Albert Einstein and his collaborators. Einstein intensely searched for such a unifying theory during the last decades of his life. However, none of these attempts were successful.

Twentieth century and the nuclear interactions


In the twentieth century, the search for a unifying theory was interrupted by the discovery of the strong and weak nuclear forces (or interactions), which differ both from gravity and from electromagnetism. A further hurdle was the acceptance that in a TOE, quantum mechanics had to be incorporated from the start, rather than emerging as a consequence of a deterministic unified theory, as Einstein had hoped.

Gravity and electromagnetism could always peacefully coexist as entries in a list of classical forces, but for many years it seemed that gravity could not even be incorporated into the quantum framework, let alone unified with the other fundamental forces. For this reason, work on unification, for much of the twentieth century, focused on understanding the three "quantum" forces: electromagnetism and the weak and strong forces. The first two were combined
Electroweak interaction
In particle physics, the electroweak interaction is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very different at everyday low energies, the theory models them as two different...

 in 1967–68 by Sheldon Glashow, Steven Weinberg
Steven Weinberg
Steven Weinberg is 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 interaction between elementary particles....

, and Abdus Salam
Abdus Salam
Mohammad Abdus Salam, NI, SPk Mohammad Abdus Salam, NI, SPk Mohammad Abdus Salam, NI, SPk (Urdu: محمد عبد السلام, pronounced , (January 29, 1926– November 21, 1996) was a Pakistani theoretical physicist and Nobel laureate in Physics for his work on the electroweak unification of the...

 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
W and Z bosons
The W and Z bosons are the elementary particles that mediate the weak interaction; their symbols are , and . The W bosons have a positive and negative electric charge of 1 elementary charge respectively and are each other's antiparticle. The Z boson is electrically neutral and its own...

, have non-zero masses of and , whereas the photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

, which carries the electromagnetic force, is massless. At higher energies Ws and Zs can be created
Matter creation
Matter creation is the process inverse to particle annihilation. It is the conversion of massless particles into one or more massive particles. This process is the time reversal of annihilation. Since all known massless particles are bosons and the most familiar massive particles are fermions,...

 easily and the unified nature of the force becomes apparent.

While the strong and electroweak forces peacefully coexist in the Standard Model
Standard Model
The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...

 of particle physics, they remain distinct. So far, the quest for a theory of everything is thus unsuccessful on two points: neither a unification of the strong and electroweak forces – which Laplace would have called `contact forces' – has been achieved, nor a unification of these forces with gravitation has been achieved.

Conventional sequence of theories


A Theory of Everything would unify all the fundamental interaction
Fundamental interaction
In particle physics, fundamental interactions are the ways that elementary particles interact with one another...

s of nature: gravitation
Gravitation
Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...

, strong interaction
Strong interaction
In particle physics, the strong interaction is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a non-contact force...

, weak interaction
Weak interaction
Weak interaction , is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars...

, and electromagnetism
Electromagnetism
Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...

. Because the weak interaction can transform elementary particles from one kind into another, the TOE should also yield a deep understanding of the various different kinds of possible particles. The usual assumed path of theories is given in the following graph, where each unification step leads one level up:
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
Grand unification theory
The term Grand Unified Theory, often abbreviated as GUT, refers to any of several similar candidate models in particle physics in which at high-energy, the three gauge interactions of the Standard Model which define the electromagnetic, weak, and strong interactions, are merged into one single...

 (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 possible Earth-based particle accelerator
Particle accelerator
A particle accelerator is a device that uses electromagnetic fields to propel charged particles to high speeds and to contain them in well-defined beams. An ordinary CRT television set is a simple form of accelerator. There are two basic types: electrostatic and oscillating field accelerators.In...

. Although the simplest GUTs have been experimentally ruled out, the general idea, especially when linked with supersymmetry
Supersymmetry
In particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...

, remains a favorite candidate in the theoretical physics community. Supersymmetric GUTs 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 GUT physics (although it does not seem to form an inevitable part of the theory). Yet GUTs are clearly not the final answer; both the current standard model and all proposed GUTs are quantum field theories
Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...

 which require the problematic technique of renormalization
Renormalization
In quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, renormalization is any of a collection of techniques used to treat infinities arising in calculated quantities....

 to yield sensible answers. This is usually regarded as a sign that these are only effective field theories
Effective field theory
In physics, an effective field theory is, as any effective theory, an approximate theory, that includes appropriate degrees of freedom to describe physical phenomena occurring at a chosen length scale, while ignoring substructure and degrees of freedom at shorter distances .-The renormalization...

, 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
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

. Numerous researchers concentrate their efforts on this specific step; nevertheless, no accepted theory of quantum gravity
Quantum gravity
Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...

 – and thus no accepted theory of everything – has emerged yet. It is usually assumed that the TOE will also solve the remaining problems of GUTs.

In addition to explaining the forces listed in the graph, a TOE must also explain the status of at least two candidate forces suggested by modern cosmology
Cosmology
Cosmology is the discipline that deals with the nature of the Universe as a whole. Cosmologists seek to understand the origin, evolution, structure, and ultimate fate of the Universe at large, as well as the natural laws that keep it in order...

: an inflationary force and dark energy
Dark energy
In physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...

. Furthermore, cosmological experiments also suggest the existence of dark matter
Dark matter
In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...

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

String theory and M-theory


Since the 1990s, many physicists believe that 11-dimensional M-theory
M-theory
In theoretical physics, M-theory is an extension of string theory in which 11 dimensions are identified. Because the dimensionality exceeds that of superstring theories in 10 dimensions, proponents believe that the 11-dimensional theory unites all five string theories...

, which is described in many sectors by matrix string theory
Matrix string theory
In physics, Matrix string theory is a set of equations that describe superstring theory in a non-perturbative framework. Type IIA string theory can be shown to be equivalent to a maximally supersymmetric two-dimensional gauge theory, the gauge group of which is U for a large value of N...

, in many other sectors by perturbative string theory
Dual resonance model
In theoretical physics, a dual resonance model arose the early investigation of string theory as an S-matrix theory of the strong interaction....

, is the theory of everything. However, there is no widespread consensus on this issue, because M-theory and superstring theory
Superstring theory
Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modelling them as vibrations of tiny supersymmetric strings...

 is not a completed theory but rather an approach for producing one. All these theories attempt to deal with the renormalization problem by setting up some lower bound on the length scales possible.

String theories and supergravity
Supergravity
In theoretical physics, supergravity is a field theory that combines the principles of supersymmetry and general relativity. Together, these imply that, in supergravity, the supersymmetry is a local symmetry...

 (both believed to be limiting cases of the yet-to-be-defined M-theory) suppose that the universe actually has more dimensions than the easily observed three of space and one of time. The motivation behind this approach began with the Kaluza-Klein theory in which it was noted that applying general relativity to a five dimensional universe (with the usual four dimensions plus one small curled-up dimension) yields the equivalent of the usual general relativity in four dimensions together with Maxwell's equations
Maxwell's equations
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...

 (electromagnetism, also in four dimensions). This has led to efforts to work with theories with large number of dimensions in the hopes that this would produce equations that are similar to known laws of physics. The notion of extra dimensions also helps to resolve the hierarchy problem, which is the question of why gravity is so much weaker than any other force. The common answer involves gravity leaking into the extra dimensions in ways that the other forces do not.

In the late 1990s, it was noted that one problem with several of the candidates for theories of everything (but particularly string theory) was that they did not constrain the characteristics of the predicted universe. For example, many theories of quantum gravity can create universes with arbitrary numbers of dimensions or with arbitrary cosmological constant
Cosmological constant
In physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...

s. Even the "standard" ten-dimensional string theory allows the "curled up" dimensions to be compactified
Compact dimension
In string theory, a model used in theoretical physics, a compact dimension is curled up in itself and very small . Anything moving along this dimension's direction would return to its starting point almost instantaneously, and the fact that the dimension is smaller than the smallest particle means...

 in an enormous number of different ways (one estimate is 10500 ) each of which corresponds to a different collection of fundamental particles and low-energy forces. This array of theories is known as the string theory landscape
String theory landscape
The string theory landscape or anthropic landscape refers to the large number of possible false vacua in string theory. The "landscape" includes so many possible configurations that some physicists think that the known laws of physics, the standard model and general relativity with a positive...

.

A speculative solution is that many or all of these possibilities are realised in one or another of a huge number of universes, but that only a small number of them are habitable, and hence the fundamental constants of the universe are ultimately the result of the anthropic principle
Anthropic principle
In astrophysics and cosmology, the anthropic principle is the philosophical argument that observations of the physical Universe must be compatible with the conscious life that observes it. Some proponents of the argument reason that it explains why the Universe has the age and the fundamental...

 rather than a consequence of the theory of everything. This anthropic approach is often criticised in that, because the theory is flexible enough to encompass almost any observation, it cannot make useful (i.e., original, falsifiable, and verifiable) predictions. In this view, string theory would be considered a pseudoscience
Pseudoscience
Pseudoscience is a claim, belief, or practice which is presented as scientific, but which does not adhere to a valid scientific method, lacks supporting evidence or plausibility, cannot be reliably tested, or otherwise lacks scientific status...

, where an unfalsifiable theory is constantly adapted to fit the experimental results.

Loop quantum gravity


Current research on loop quantum gravity
Loop quantum gravity
Loop quantum gravity , also known as loop gravity and quantum geometry, is a proposed quantum theory of spacetime which attempts to reconcile the theories of quantum mechanics and general relativity...

 may eventually play a fundamental role in a TOE, but that is not its primary aim. Also loop quantum gravity 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 Standard Model
Standard Model
The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...

. So far only the first generation of fermions (leptons and quarks) with correct parity properties have been modelled by Sundance Bilson-Thompson
Sundance Bilson-Thompson
Sundance Osland Bilson-Thompson is an Australian theoretical particle physicist. He has developed the idea that certain preon models may be represented topologically, rather than by treating preons as pointlike particles. His ideas have attracted interest in the field of loop quantum gravity, as...

 using preon
Preon
In particle physics, preons are postulated "point-like" particles, conceived to be subcomponents of quarks and leptons. The word was coined by Jogesh Pati and Abdus Salam in 1974...

s constituted of braids of spacetime as the building blocks. However, there is no derivation of the Lagrangian
Lagrangian
The Lagrangian, L, of a dynamical system is a function that summarizes the dynamics of the system. It is named after Joseph Louis Lagrange. The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics by Irish mathematician William Rowan Hamilton known as...

 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 concepts made it possible to demonstrate that the particles are able to survive quantum fluctuation
Quantum fluctuation
In quantum physics, a quantum fluctuation is the temporary change in the amount of energy in a point in space, arising from Werner Heisenberg's uncertainty principle.According to one formulation of the principle,energy and time can be related by the relation...

s.

This model leads to an interpretation of electric and colour 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, colour, 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.

Causal dynamical triangulation


Causal dynamical triangulation (abbreviated as "CDT") invented by Renate Loll
Renate Loll
Renate Loll is a physicist who works at the , The Netherlands. She received her Ph.D. from , London, in 1989. In 2001 she joined the permanent staff of the ITP, after spending several years at the Max Planck Institute for Gravitational Physics in Golm, Germany...

, Jan Ambjørn and Jerzy Jurkiewicz, and popularized by Fotini Markopoulou and Lee Smolin
Lee Smolin
Lee Smolin is an American theoretical physicist, a researcher at the Perimeter Institute for Theoretical Physics, and an adjunct professor of physics at the University of Waterloo. He is married to Dina Graser, a communications lawyer in Toronto. His brother is David M...

, is an approach to quantum gravity
Quantum gravity
Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...

 that like loop quantum gravity
Loop quantum gravity
Loop quantum gravity , also known as loop gravity and quantum geometry, is a proposed quantum theory of spacetime which attempts to reconcile the theories of quantum mechanics and general relativity...

 is background independent. This means that it does not assume any pre-existing arena (dimensional space), but rather attempts to show how the spacetime
Spacetime
In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

 fabric itself evolves. The Loops '05 conference, hosted by many loop quantum gravity theorists, included several presentations which discussed CDT in great depth, and revealed it to be a pivotal insight for theorists. It has sparked considerable interest as it appears to have a good semi-classical description. At large scales, it re-creates the familiar 4-dimensional spacetime, but it shows spacetime to be 2-d near the Planck scale
Planck scale
In particle physics and physical cosmology, the Planck scale is an energy scale around 1.22 × 1019 GeV at which quantum effects of gravity become strong...

, and reveals a fractal
Fractal
A fractal has been defined as "a rough or fragmented geometric shape that can be split into parts, each of which is a reduced-size copy of the whole," a property called self-similarity...

 structure on slices of constant time.

By far the greatest advantage of this theory is that it derives the observed nature and properties of spacetime from a minimal set of assumptions, and needs no adjusting factors. The idea of deriving what is observed from first principles is very attractive to physicists, as it often indicates a concept that is close to the truth, or offers powerful tools for investigating the nature of reality.

Other attempts


Any TOE must include general relativity and the standard model of particle physics. Outside the previously mentioned attempts, the best-known one is Garrett Lisi's E8 proposal
An Exceptionally Simple Theory of Everything
"An Exceptionally Simple Theory of Everything" is a preprint proposing a basis for a unified field theory, very often referred to as "E8 Theory," which attempts to describe all known fundamental interactions in physics and to stand as a possible theory of everything...

.

Present status


At present, no convincing candidate for a TOE is available. Most particle physicists state that the outcome of the ongoing experiments – the search for new particles at the large particle accelerator
Particle accelerator
A particle accelerator is a device that uses electromagnetic fields to propel charged particles to high speeds and to contain them in well-defined beams. An ordinary CRT television set is a simple form of accelerator. There are two basic types: electrostatic and oscillating field accelerators.In...

s and for dark matter
Dark matter
In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...

 – are needed in order to provide theoretical physicists with precise input for a TOE.

Theory of everything and philosophy


The philosophical implications of a physical TOE are frequently debated. For example, if philosophical physicalism
Physicalism
Physicalism is a philosophical position holding that everything which exists is no more extensive than its physical properties; that is, that there are no kinds of things other than physical things...

 is true, a physical TOE will coincide with a philosophical theory of everything.

The "system building" style of metaphysics
Metaphysics
Metaphysics is a branch of philosophy concerned with explaining the fundamental nature of being and the world, although the term is not easily defined. Traditionally, metaphysics attempts to answer two basic questions in the broadest possible terms:...

 attempts to answer all the important questions in a coherent way, providing a complete picture of the world. Plato
Plato
Plato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...

 and Aristotle
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...

 could be said to be early examples of comprehensive systems. In the early modern period (17th and 18th centuries), the system-building scope of philosophy is often linked to the rationalist method of philosophy, which is the technique of deducing the nature of the world by pure apriori reason. Examples from the early modern period include the Leibniz's Monadology
Monadology
The Monadology is one of Gottfried Leibniz’s best known works representing his later philosophy. It is a short text which sketches in some 90 paragraphs a metaphysics of simple substances, or monads.- Text :...

, Descarte's Dualism
Dualism
Dualism denotes a state of two parts. The term 'dualism' was originally coined to denote co-eternal binary opposition, a meaning that is preserved in metaphysical and philosophical duality discourse but has been diluted in general or common usages. Dualism can refer to moral dualism, Dualism (from...

, and Spinoza's Monism
Monism
Monism is any philosophical view which holds that there is unity in a given field of inquiry. Accordingly, some philosophers may hold that the universe is one rather than dualistic or pluralistic...

. Hegel's Absolute idealism
Absolute idealism
Absolute idealism is an ontologically monistic philosophy attributed to G. W. F. Hegel. It is Hegel's account of how being is ultimately comprehensible as an all-inclusive whole. Hegel asserted that in order for the thinking subject to be able to know its object at all, there must be in some...

 and Whitehead
Whitehead
-With common given names on further disambiguation pages:*Alan Whitehead *George Whitehead *Henry Whitehead *James Whitehead *John Whitehead...

's Process philosophy
Process philosophy
Process philosophy identifies metaphysical reality with change and dynamism. Since the time of Plato and Aristotle, philosophers have posited true reality as "timeless", based on permanent substances, whilst processes are denied or subordinated to timeless substances...

 were later systems.

Other philosophers do not believe its techniques can aim so high. Some scientists think a more mathematical approach than philosophy is needed for a TOE, for instance Stephen Hawking
Stephen Hawking
Stephen William Hawking, CH, CBE, FRS, FRSA is an English theoretical physicist and cosmologist, whose scientific books and public appearances have made him an academic celebrity...

 wrote in A Brief History of Time
A Brief History of Time
A Brief History of Time is a popular science book written by renown physicist Stephen Hawking and first published by the Bantam Dell Publishing Group in 1988. It became a best-seller and has sold more than 10 million copies...

that even if we had a TOE, it would necessarily be a set of equations. He wrote, “What is it that breathes fire into the equations and makes a universe for them to describe?”.

Arguments against a theory of everything


In parallel to the intense search for a theory of everything, various other scholars are debating the possibility of success.

Gödel's incompleteness theorem


A number of scholars claim that Gödel's incompleteness theorem proves that any attempt to construct a TOE is bound to fail. Gödel's theorem, informally stated, asserts that any formal theory expressive enough for elementary arithmetical facts to be expressed 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 about natural numbers that can't be derived in the formal theory.

Stanley Jaki
Stanley Jaki
Stanley L. Jaki, OSB was a Benedictine priest and Distinguished Professor of Physics at Seton Hall University, New Jersey since 1975...

, 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. In a later reflection, Jaki states that it is wrong to say that a final theory is impossible, but rather that "when it is on hand one cannot know rigorously that it is a final theory."

Freeman Dyson
Freeman Dyson
Freeman John Dyson FRS is a British-born American theoretical physicist and mathematician, famous for his work in quantum field theory, solid-state physics, astronomy and nuclear engineering. Dyson is a member of the Board of Sponsors of the Bulletin of the Atomic Scientists...

 has stated that

Stephen Hawking
Stephen Hawking
Stephen William Hawking, CH, CBE, FRS, FRSA is an English theoretical physicist and cosmologist, whose scientific books and public appearances have made him an academic celebrity...

 was originally a believer in the Theory of Everything but, after considering Gödel's Theorem, concluded that one was not obtainable.

Jürgen Schmidhuber
Jürgen Schmidhuber
Jürgen Schmidhuber is a computer scientist and artist known for his work on machine learning, universal Artificial Intelligence , artificial neural networks, digital physics, and low-complexity art. His contributions also include generalizations of Kolmogorov complexity and the Speed Prior...

 (1997) has argued against this view; he points out that Gödel's theorems are irrelevant for computable physics. In 2000, Schmidhuber explicitly constructed limit-computable, deterministic universes whose pseudo-randomness based on undecidable
Undecidable
Undecidable may refer to:In mathematics and logic* Undecidable problem - a decision problem which no algorithm can decide* "Undecidable" is sometimes used as a synonym of "independent", where a formula in mathematical logic is independent of a logical theory if neither that formula nor its negation...

, Gödel-like halting problem
Halting problem
In computability theory, the halting problem can be stated as follows: Given a description of a computer program, decide whether the program finishes running or continues to run forever...

s is extremely hard to detect but does not at all prevent formal TOEs describable by very few bits of information.

Related critique was offered by Solomon Feferman
Solomon Feferman
Solomon Feferman is an American philosopher and mathematician with major works in mathematical logic.He was born in New York City, New York, and received his Ph.D. in 1957 from the University of California, Berkeley under Alfred Tarski...

, among others. Douglas S. Robertson offers Conway's game of life
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....

 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 TOE 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
Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...

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. Following this view, we may reasonably hope for a theory of everything which self-consistently incorporates all currently known forces, but we should not expect it to be the final answer.

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 fundamental physical constants, the theories are becoming simpler. If this is the case, the process of simplification cannot continue indefinitely.

Lack 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 position that the TOE is the fundamental law and that all other theories that apply within the universe are a consequence of the TOE. Another view is that emergent
Emergence
In philosophy, systems theory, science, and art, emergence is the way complex systems and patterns arise out of a multiplicity of relatively simple interactions. Emergence is central to the theories of integrative levels and of complex systems....

 laws, which govern the behavior of complex system
Complex system
A complex system is a system composed of interconnected parts that as a whole exhibit one or more properties not obvious from the properties of the individual parts....

s, should be seen as equally fundamental. Examples of emergent laws are the second law of thermodynamics
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...

 and the theory of natural selection
Natural selection
Natural selection is the nonrandom process by which biologic traits become either more or less common in a population as a function of differential reproduction of their bearers. It is a key mechanism of evolution....

. 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 TOE.

It is not clear that there is any point at issue in these debates. A well-known one took place between Steven Weinberg and Philip Anderson
Philip Warren Anderson
Philip Warren Anderson is an American physicist and Nobel laureate. Anderson has made contributions to the theories of localization, antiferromagnetism and high-temperature superconductivity.- Biography :...

. Possibly the only issue at stake is the right to apply the high-status term "fundamental" to the respective subjects of research.

Impossibility of being "of everything"


Although the name "theory of everything" suggests the determinism of Laplace's quotation, this gives a very misleading impression. Determinism is frustrated by the probabilistic nature of quantum mechanical predictions, by the extreme sensitivity to initial conditions that leads to mathematical chaos
Chaos theory
Chaos theory is a field of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the...

, by the limitations due to event horizons, and by the extreme mathematical difficulty of applying the theory. Thus, although the current standard model of particle physics "in principle" predicts all known non-gravitational phenomena, in practice only a few quantitative results have been derived from the full theory (e.g., the masses of some of the simplest hadrons), and these results (especially the particle masses which are most relevant for low-energy physics) are less accurate than existing experimental measurements. The TOE would almost certainly be even harder to apply for the prediction of experimental results, and thus might be of limited use.

A motive for seeking a TOE, apart from the pure intellectual satisfaction of completing a centuries-long quest, is that all prior examples of unification have predicted new phenomena, some of which (e.g., electrical generator
Electrical generator
In electricity generation, an electric generator is a device that converts mechanical energy to electrical energy. A generator forces electric charge to flow through an external electrical circuit. It is analogous to a water pump, which causes water to flow...

s) have proved of great practical importance. And like in these prior examples of unification, the TOE would probably allow us to confidently define the domain of validity and residual error of low-energy approximations to the full theory.

Infinite number of onion layers


Lee Smolin
Lee Smolin
Lee Smolin is an American theoretical physicist, a researcher at the Perimeter Institute for Theoretical Physics, and an adjunct professor of physics at the University of Waterloo. He is married to Dina Graser, a communications lawyer in Toronto. His brother is David M...

 regularly argues that the layers of nature may be like the layers of an onion, and that the number of layers might be infinite. This would imply an infinite sequence of physical theories.

The argument is not universally accepted, because it is not obvious that infinity is a concept that applies to the foundations of nature. The results of quantum theory strongly suggest that nature is not infinite in its foundations.

Summary


No argument against the existence of a theory of everything has gained general acceptance. Most physicists expect that experiments and theory will allow to reach a deeper level of understanding and a higher degree of unification in the future. Whether the next, if any, level will be the actual theory of everything, however, is unknown.

See also


  • An Exceptionally Simple Theory of Everything
    An Exceptionally Simple Theory of Everything
    "An Exceptionally Simple Theory of Everything" is a preprint proposing a basis for a unified field theory, very often referred to as "E8 Theory," which attempts to describe all known fundamental interactions in physics and to stand as a possible theory of everything...

     based on the exceptional Lie group E8 proposed by Antony Garrett Lisi
    Antony Garrett Lisi
    Antony Garrett Lisi , who uses the name Garrett by preference, is an American theoretical physicist and adventure sports enthusiast. Lisi works as an independent researcher without an academic position...

  • Beyond the standard model
    Beyond the Standard Model
    Physics beyond the Standard Model refers to the theoretical developments needed to explain the deficiencies of the Standard Model, such as the origin of mass, the strong CP problem, neutrino oscillations, matter–antimatter asymmetry, and the nature of dark matter and dark energy...

  • Standard Model (mathematical formulation)
  • Electroweak interaction
    Electroweak interaction
    In particle physics, the electroweak interaction is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very different at everyday low energies, the theory models them as two different...

  • Holographic principle
    Holographic principle
    The holographic principle is a property of quantum gravity and string theories which states that the description of a volume of space can be thought of as encoded on a boundary to the region—preferably a light-like boundary like a gravitational horizon...

  • Multiverse
    Multiverse
    The multiverse is the hypothetical set of multiple possible universes that together comprise all of reality.Multiverse may also refer to:-In fiction:* Multiverse , the fictional multiverse used by DC Comics...

  • Omniverse
    Omniverse
    The Omniverse is the conceptual ensemble of all possible universes, with all possible laws of physics.In this physical cosmology context, the limitation of the definition of "universe" that it has only one set of "physical laws and constants that govern them," is expanded to include multiple sets...


Notations

  • John D. Barrow
    John D. Barrow
    -External links:****** The Forum-Publications available on the Internet:************...

    , Theories of Everything: The Quest for Ultimate Explanation (OUP, Oxford, 1990) ISBN 0-09-998380-X
  • Stephen Hawking
    Stephen Hawking
    Stephen William Hawking, CH, CBE, FRS, FRSA is an English theoretical physicist and cosmologist, whose scientific books and public appearances have made him an academic celebrity...

    , 'The Theory of Everything: The Origin and Fate of the Universe
    The Theory of Everything
    The Theory of Everything: The Origin and Fate of the Universe is an unauthorized 2002 book of some collected works by Stephen Hawking. It was assembled from seven lectures on audiotape by Hawking originally released in 1994 under the title, Stephen W. Hawking's Life Works: The Cambridge Lectures...

    '
    is an unauthorized 2002 book taken from recorded lectures (ISBN 1-893224-79-1)
  • Stanley Jaki
    Stanley Jaki
    Stanley L. Jaki, OSB was a Benedictine priest and Distinguished Professor of Physics at Seton Hall University, New Jersey since 1975...

     OSB, 2005. The Drama of Quantities. Real View Books (ISBN 1-892548-47-X)
  • Abraham Pais
    Abraham Pais
    Abraham Pais was a Dutch-born American physicist and science historian. Pais earned his Ph.D. from University of Utrecht just prior to a Nazi ban on Jewish participation in Dutch universities during World War II...

    , Subtle is the Lord...: The Science and the Life of Albert Einstein (OUP, Oxford, 1982). ISBN 0-19-853907-X
  • John Thompson
    John Thompson
    -Academics:* Sir John Eric Sidney Thompson , English archeologist and Mayan scholar* John G. Thompson , mathematician* John Thompson , professor at Cambridge...

    , Nature's Watchmaker: The Undiscovered Miracle of Time. (Blackhall Publishing Ltd. Ireland, 2009) ISBN 1-84218-174-2 http://natureswatchmaker.com
  • Steven Weinberg
    Steven Weinberg
    Steven Weinberg is 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 interaction between elementary particles....

    , Dreams of a Final Theory: The Search for the Fundamental Laws of Nature (Hutchinson Radius, London, 1993) ISBN 0-09-177395-4

External links