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{{short description|Hypothetical physical concept}}
A '''theory of everything (TOE)''' is a theory of [[theoretical physics]] and mathematics that fully explains and links together all known physical phenomena (i.e. "everything"). Initially the term was used with an ironical connotation, to refer to various overgeneralized theories. For example, an uncle of [[Ijon Tichy]]— a character from a cycle of [[Stanislaw Lem]]'s [[science fiction]] stories of early 1970s — was known to work on "General Theory of Everything" ([[Polish language|Polish]]: "Ogólna Teoria Wszystkiego"). Over time, the term stuck in popularizations of [[quantum physics]] to describe a theory that would unify the theories of the four [[fundamental interaction]]s of nature, possibly due to the influence of ''[[The Theory of Everything]]'', a book with material written by [[Stephen Hawking]] but disowned by him.
{{about|the hypothetical physical concept}}
{{Beyond the Standard Model|expanded=Theories}}
 
A '''theory of everything''' ('''TOE''') or '''final theory''' is a hypothetical coherent [[theoretical physics|theoretical framework of physics]] containing all physical principles.<ref name="Weinberg2011">{{cite book |author=Weinberg |first=Steven |title=Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature |date=2011-04-20 |publisher=Knopf Doubleday Publishing Group |isbn=978-0-307-78786-6 |language=en-us}}</ref>{{rp|6}} The scope of the concept of a "theory of everything" varies. The original technical concept referred to [[Unification of theories in physics|unification]] of the four [[fundamental interactions]]: electromagnetism, strong and weak nuclear forces, and gravity.<ref name=Ellis-1986/>
There have been numerous theories of everything proposed by theoretical physicists over the last century, but as yet none has been able to stand up to experimental scrutiny or there is tremendous difficulty in getting the theories to produce even experimentally testable results. The primary problem in producing a theory of everything is that [[quantum mechanics]] and [[general relativity]] have radically different descriptions of the universe, and the obvious ways of combining the two lead quickly to the [[renormalization]] problem in which the theory does not give finite results for experimentally testable quantities.
Finding such a theory of everything is one of the major [[unsolved problems in physics]].<ref name="NYT-20201123" /><ref name="NYT-20230911">{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |date=11 September 2023 |title=Don't Expect a 'Theory of Everything' to Explain It All – Not even the most advanced physics can reveal everything we want to know about the history and future of the cosmos, or about ourselves. |work=[[The New York Times]] |url=https://www.nytimes.com/2023/09/11/science/space/astronomy-universe-simulations.html |url-status=live |access-date=11 September 2023 |archive-url=https://archive.today/20230911043212/https://www.nytimes.com/2023/09/11/science/space/astronomy-universe-simulations.html |archive-date=11 September 2023}}</ref> Numerous popular books apply the words "theory of everything" to more expansive concepts such as predicting everything in the universe from logic alone, complete with discussions on how this is not possible.<ref>{{Cite book |last=Barrow |first=John D. |title=New theories of everything: the quest for ultimate explanation |date=2008 |publisher=Oxford Univ. Press |isbn=978-0-19-954817-0 |___location=Oxford}}</ref>{{rp|1}}
 
Starting with [[Isaac Newton]]'s unification of [[Gravity on Earth|terrestrial gravity]], responsible for [[weight]], with celestial gravity, responsible for planetary [[orbit]]s, concepts in fundamental physics have been successively [[Unification of theories in physics|unified]]. The phenomena of [[electricity]] and [[magnetism]] were combined by [[James Clerk Maxwell]]'s theory of [[electromagnetism]] and [[Albert Einstein]]'s theory of [[special relativity|relativity]] explained how they are connected. By the 1930s, [[Paul Dirac]] combined relativity and [[quantum mechanics]] and, working with other physicists, developed [[quantum electrodynamics]] that combines quantum mechanics and electromagnetism.
== Mainstream physics ==
Work on [[nuclear physics|nuclear]] and [[particle physics|particle]] physics lead to the discovery of the [[strong force|strong nuclear]] and [[weak force|weak nuclear]] forces which were combined in the [[quantum field theory]] to implemented the [[Standard Model]] of physics, a unification of all forces except gravity. The lone fundamental force not built into the Standard Model is gravity. [[General relativity]] provides a theoretical framework for understanding [[gravity]] across scales from the laboratory to [[planets]] to the complete [[universe]], but it has not been successfully unified with quantum mechanics.<ref name="Hawking2006">{{cite book |author=Hawking |first=Stephen W. |title=The Theory of Everything: The Origin and Fate of the Universe |date=28 February 2006 |publisher=Phoenix Books; Special Anniversary |isbn=978-1-59777-508-3}}</ref>{{rp|122}}
 
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.<ref>{{cite journal |last1=SMOLIN |first1=L. |title=An Invitation to Loop Quantum Gravity |date=2004 |journal=Quantum Theory and Symmetries |volume=[] |pages=655–682 | doi=10.1142/9789812702340_0078|arxiv=hep-th/0408048 |bibcode=2004qts..conf..655S |isbn=978-981-256-068-1 |s2cid=16195175}}</ref><ref name="Carlip">{{cite journal |last=Carlip |first=Steven |title=Quantum Gravity: a Progress Report |journal=Reports on Progress in Physics |volume=64 |issue=8 |pages=885–942 |date=2001 |doi=10.1088/0034-4885/64/8/301 |arxiv=gr-qc/0108040 |bibcode=2001RPPh...64..885C |s2cid=118923209 }}</ref><ref name="Priest2010">{{cite book |author=Priest |first=Susanna Hornig |title=Encyclopedia of Science and Technology Communication |date=14 July 2010 |publisher=SAGE Publications |isbn=978-1-4522-6578-0}}</ref>{{rp|842–844}} 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]]). 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 the universe.
[[Albert Einstein]] was the first serious scientist who spent most of his life trying to find a TOE; he believed that the only task was to unify [[general relativity]] and [[electromagnetism]].
 
In pursuit of this goal, [[quantum gravity]] has become one area of active research.<ref name="NYT-20221010">{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |date=10 October 2022 |title=Black Holes May Hide a Mind-Bending Secret About Our Universe – Take gravity, add quantum mechanics, stir. What do you get? Just maybe, a holographic cosmos. |work=[[The New York Times]] |url=https://www.nytimes.com/2022/10/10/science/black-holes-cosmology-hologram.html |url-status=live |access-date=22 October 2022 |archive-url=https://web.archive.org/web/20221116151210/https://www.nytimes.com/2022/10/10/science/black-holes-cosmology-hologram.html |archive-date=16 November 2022}}</ref><ref name="SA-20221116">{{cite news |last=Starr |first=Michelle |title=Scientists Created a Black Hole in The Lab, And Then It Started to Glow |url=https://www.sciencealert.com/scientists-created-a-black-hole-in-the-lab-and-then-it-started-to-glow |date=16 November 2022 |work=[[ScienceAlert]] |access-date=16 November 2022 |archive-date=15 November 2022 |archive-url=https://web.archive.org/web/20221115234327/https://www.sciencealert.com/scientists-created-a-black-hole-in-the-lab-and-then-it-started-to-glow |url-status=live }}</ref> 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]] [[prediction]]s) and controversy. String theory posits that at the [[Planck epoch|beginning of the universe]] (up to 10<sup>−43</sup> 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]] is a type of string that vibrates one way, while the [[up quark]] is a type of string vibrating another way, and so forth). String theory/[[M-theory]] proposes six or seven [[dimensions]] of [[spacetime]] in addition to the four common dimensions for a ten- or eleven-dimensional spacetime.
Current mainstream physics concepts require that a TOE unify the four [[fundamental interaction]]s of nature: [[gravity]], the [[strong nuclear force]], the [[weak nuclear force]], and the [[electromagnetism|electromagnetic force]]; it should also explain the spectrum of [[elementary particle]]s. There has been progress toward a TOE in unifying electromagnetism and the weak nuclear force in an electroweak [[unified field theory]] and in unifying all of the forces except for gravity (which in the present theory of [[general relativity]] is not a force) in the [[grand unified theory]]. One missing piece in a theory of everything involves combining [[quantum mechanics]] and general relativity into a theory of [[quantum gravity]].
 
== Name ==
The only serious candidate for a theory of everything at the moment is [[superstring theory]] / [[M-theory]]; current research on [[loop quantum gravity]] may eventually play a fundamental role in a TOE, but that is not its primary aim. These theories attempt to deal with the renormalization problem by setting up some lower bound on the length scales possible. Also, early [[21st century]] theories of everything tend to 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 adding one dimension to [[general relativity]] would produce the [[electromagnetic]] [[Maxwell's equations]]. This has led to efforts to work with theories with large number of dimensions in the hopes that this would produce equations which 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.
The scientific use of the term ''theory of everything'' occurred in the title of an article by physicist [[John Ellis (physicist, born 1946)|John Ellis]] in 1986<ref name=Ellis-1986>
{{cite journal
|first=John |last=Ellis
|date=1986
|journal=Nature
|title=The Superstring: Theory of Everything, or of Nothing?
|volume=323 |issue=6089 |pages=595–598
|doi=10.1038/323595a0
|bibcode=1986Natur.323..595E
|s2cid=4344940
}}</ref><ref>
{{cite journal
|first=John |last=Ellis
|date=2002
|title=Physics gets physical (correspondence)
|journal=[[Nature (journal)|Nature]]
|volume=415 |issue=6875
|page=957
|doi=10.1038/415957b |doi-access=free
|bibcode=2002Natur.415..957E
|pmid=11875539
}}</ref> but it was mentioned by [[John Henry Schwarz]] in a conference proceedings<ref>{{Cite book |last=Schwarz |first=John H. |chapter-url=http://link.springer.com/10.1007/978-1-4899-2254-0_11 |title=Quarks, Leptons, and Beyond |date=1985 |publisher=Springer US |isbn=978-1-4899-2256-4 |editor-last=Fritzsch |editor-first=H. |volume=122 |___location=Boston, MA |pages=441–446 |chapter=Superstrings |series=NATO ASI Series |doi=10.1007/978-1-4899-2254-0_11 |quote=of these lectures have concerned simple N = 1 SUSY. Many people believe that the final theory of everything will have extended SUSY, and may be the largest N = 8 supergravity. |editor-last2=Peccei |editor-first2=R. D. |editor-last3=Saller |editor-first3=H. |editor-last4=Wagner |editor-first4=F.}}</ref> in 1985.<ref>{{Cite book |last=Kragh |first=Helge |title=Higher Speculations: Grand Theories and Failed Revolutions in Physics and Cosmology |date=2011 |publisher=Oxford University Press, Incorporated |isbn=978-0-19-100334-9 |___location=Oxford}}</ref>{{rp|269}}
 
== Historical antecedents ==
In the late 1990s, it was noted that one problem with several of the candidates for theories of everything 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]]s. One bit of speculation is that there may indeed be 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]] rather than a consequence of the theory of everything.
 
=== Antiquity to 19th century ===
{{unsolved|physics|Is [[string theory]], [[superstring theory]], or [[M-theory]], or some other variant on this theme, a step on the road to a "[[theory of everything]]," or just a blind alley?}}
[[Archimedes]] was possibly the first philosopher to have described nature with axioms (or principles) and then deduce new results from them. Once [[Isaac Newton]] proposed his universal law of [[gravitation]], mathematician [[Pierre-Simon Laplace]] suggested that such laws could in principle allow deterministic prediction of the future state of the universe. Any "theory of everything" is similarly expected to be based on axioms and to deduce all observable phenomena from them.<ref name="Impey2012" />{{rp|340}}
 
In the late 17th century, [[Isaac Newton]]'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 ''[[Philosophiæ Naturalis Principia Mathematica|Mathematical Principles of Natural Philosophy]]'' dealt with this in a further example of [[Unification (physics)|unification]], in this case unifying [[Galileo]]'s work on terrestrial gravity, [[Kepler]]'s laws of planetary motion and the phenomenon of [[tide]]s by explaining these apparent actions at a distance under one single law: the law of [[universal gravitation]].<ref>{{cite book |page=255 |url=https://books.google.com/books?id=6EqxPav3vIsC&pg=PA255 |title=The Mathematical Principles of Natural Philosophy |volume=II |last1=Newton |first1=Sir Isaac |date=1729}}</ref> Newton achieved the [[Unification of theories in physics#Unification of gravity and astronomy|first great unification in physics]], and he further is credited with laying the foundations of future endeavors for a grand unified theory.
There is also a philosophical debate within the physics community as to whether or not a "theory of everything" should be seen as the fundamental law of the universe. One view is the hard [[reductionist]] view that the TOE is the fundamental law of the universe and that all other theories of the universe are a consequence of the TOE. Another view is that there are laws which [[Steven Weinberg]] calls '''free floating laws''' which govern the behavior of [[complex system]]s, and while these laws are related to the theory of everything, they cannot be seen as less fundamental than the TOE. Some argue that this explanation would violate [[Occam's Razor]] if a completely valid TOE were formulated.
 
{{quote|An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.|''Essai philosophique sur les probabilités'', Introduction. 1814}}
Other possibilities which may frustrate the explanatory capacity of a TOE may include sensitivity to the [[boundary condition]]s of the universe, or the existence of [[mathematical chaos]] in its solutions, making its predictions precise, but useless.
 
Modern [[quantum mechanics]] implies that [[Heisenberg uncertainty|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.
== Where the Standard Model comes up short ==
 
In 1820, [[Hans Christian Ørsted]] discovered a connection between electricity and magnetism, triggering decades of work that culminated in 1865, in [[James Clerk Maxwell]]'s theory of [[electromagnetism]], which achieved the [[Unification of theories in physics#Unification of magnetism, electricity, light and related radiation|second great unification in physics]]. During the 19th and early 20th centuries, it gradually became apparent that many common examples of forces – contact forces, [[elasticity (physics)|elasticity]], [[viscosity]], [[friction]], and [[pressure]] – result from electrical interactions between the smallest particles of matter.
The Standard Model of physics is among the most successful theories in history, but it fails to explain everything. It doesn't explain the origins of the universe before the [[big bang]]. There are 18 arbitrary constants and several dozen [[elementary particles]] in the Standard Model. Why are there so many? The Standard Model also fails to explain over 90% of the apparent mass-energy of the universe. The existence of [[dark matter]] and [[dark energy]], although never observed directly, is all but guaranteed if current theory is correct.
 
In his experiments of 1849–1850, [[Michael Faraday]] was the first to search for a unification of [[gravity]] with electricity and magnetism.<ref>
Why is so much of the universe invisible? What is the state of matter within a black hole? Is space-time curved, or is it flat? How many dimensions of space and time are there? What is the origin of matter and energy? What is the reason for them at all? Is there a most fundamental particle? What happens beyond Planck scales? Why is momentum quantized? Is the speed of light the fastest speed in the universe? These are among the many questions left unanswered by the most modern theories in physics. A successful Theory of Everything would explain each of these questions and provide solutions to every situation which could exist in the universe.
{{cite journal
|first=M.|last=Faraday
|date=1850
|title=Experimental Researches in Electricity. Twenty-Fourth Series. On the Possible Relation of Gravity to Electricity
|journal=Abstracts of the Papers Communicated to the Royal Society of London
|volume=5 |pages=994–995
|doi=10.1098/rspl.1843.0267 |doi-access=free
}}</ref> However, he found no connection.
 
=== SpeculativeEarly ideas20th century ===
In the late 1920s, the then new quantum mechanics showed that the [[chemical bond]]s between [[atom]]s were examples of (quantum) electrical forces, justifying [[Paul Dirac|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".<ref>
{{cite journal
|last=Dirac |first=P.A.M.
|date=1929
|title=Quantum mechanics of many-electron systems
|journal=[[Proceedings of the Royal Society of London A]]
|volume=123 |pages=714–733
|doi=10.1098/rspa.1929.0094 |doi-access=free
|bibcode=1929RSPSA.123..714D
|issue=792
}}</ref>
 
After 1915, when [[Albert Einstein]] published the theory of gravity ([[general relativity]]), the search for a [[unified field theory]] 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]], [[Arthur Eddington]], [[David Hilbert]],<ref>{{cite book |arxiv=physics/0405110 |doi=10.1007/0-8176-4454-7_14 |isbn=978-0-8176-4454-3 | title=Hilbert's "World Equations" and His Vision of a Unified Science |series=Einstein Studies |volume=11 |pages=259–276 |year=2005 |last1=Majer |first1=U. |last2=Sauer |first2=T. |bibcode=2005ugr..book..259M |journal=<!-- Citation bot--> |s2cid=985751 }}</ref> [[Theodor Kaluza]], [[Oskar Klein]] (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<ref name="Pais1982">{{cite book |author=Abraham Pais |title=Subtle is the Lord: The Science and the Life of Albert Einstein: The Science and the Life of Albert Einstein |url=https://archive.org/details/subtleislordscie00pais |url-access=registration |date=23 September 1982 |publisher=Oxford University Press |isbn=978-0-19-152402-8|author-link=Abraham Pais }}</ref>{{rp|ch 17}} (see Einstein–Maxwell–Dirac equations).
Attempts to create theories of everything are common among people outside the professional physics community. Some are created by amateurs, and their theories are often criticised on the basis of inability to make quantifiable and/or falsifiable predictions (for instance, [[Expansion theory]]). For example, a theory of everything would provide some insight into the relative strength of forces, and predictions of particle lifetimes and cross sections. It would need to be shown to explain all known universal phenomena. Unlike professional physicists, who are generally aware that their proposed theory is incomplete, untested, and likely to be wrong and who are aware of the huge difficulties and challenges involved in creating a TOE, amateurs who create TOE's tend to be unaware of what work has already been done, the [[scientific method|mechanisms]] for testing scientific theories and the fact that most proposed theories are wrong.
 
=== Late 20th century and the nuclear interactions ===
=== Evans Unified Theory ===
In the 20th century, the search for a unifying theory was interrupted by the discovery of the [[strong force|strong]] and [[weak force|weak]] 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 [[electroweak interaction|combined]] in 1967–1968 by [[Sheldon Glashow]], [[Steven Weinberg]], and [[Abdus Salam]] into the electroweak force.{{sfn|Weinberg|1993|loc=Ch 5}}
Dr. Mayron Evans has published the Evans Unified Theory which with mathematical rigour relates all forces in the known Universe ( see www.aias.us ). Electromagnetism is described as spinning spacetime while gravity is described as curved spacetime. A rigorous relationship between electromagnetism and gravity is presented allowing OU machines (over unity) and anti-gravity devices.
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 ({{val|80.4|u=GeV/c2}} and {{val|91.2|u=GeV/c2}}, respectively), whereas the [[photon]], which carries the electromagnetic force, is massless. At higher energies W bosons and Z bosons can be [[matter creation|created]] easily and the unified nature of the force becomes apparent.
 
While the strong and electroweak forces coexist under the [[Standard Model]] 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&nbsp;– which Laplace would have called 'contact forces'&nbsp;– nor a unification of these forces with gravitation had been achieved.
=== Time Cube ===
 
== Modern physics ==
[[Gene Ray]]'s [[Time Cube]] concept is an example of an amateur TOE that is quite well-known, although some argue that this is primarily due to its entertainment value rather than its scientific merit. Mr. Ray claims to explain all known universal phenomena through the postulate that "Time is cubic, not linear". See [[list of alternative, speculative and disputed theories]]. Like many similar theories, it is regarded by some as [[pseudoscience]]. Academians tend to oppose Mr. Ray's ideas and consider them lunacy, but some acknowledge that there may be a kernel of truth in the mathematical idea of cubic, or three dimensional, time. More research into the nature of time's passage will be necessary to rule out the possibility.
{{multiple image
|image1 =cube_of_theoretical_physics.svg
|caption1=A depiction of the [[cGh physics|''cGh'' cube]]
|image2 =Venn_diagram_of_theoretical_physics.svg
|caption2=Depicted as a Venn diagram
}}
 
=== Conventional sequence of theories ===
=== Burkhard Heim and quantised general relativity ===
A theory of everything would unify all the [[fundamental interaction]]s of nature: [[gravitation]], the [[strong interaction]], the [[weak interaction]], and [[electromagnetism]]. Because the weak interaction can transform [[elementary particles]] from one kind into another, the theory of everything should also predict all the 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.
 
{{tree chart/start}}
[[Burkhard Heim]]'s theory of quantised general relativity purports to be a TOE but this theory, begun in the 1950s and still under development, had until recently sunk into obscurity. A sign that it is undergoing a renewal of interest is that a paper by Droescher and Haeuser on aerospace applications of [[Heim Theory]] was published by the [[AIAA]] in 2005 and will be awarded the prize for best paper of the year by the Nuclear and Future Flight Propulsion Technical Committee. Supporters claim that Heim's six dimensional theory can predict the masses of some fundamental particles with considerable accuracy, which no established theory has yet been able to do.
{{tree chart| | | | |TOE| | TOE=Theory of everything }}
{{tree chart| | | | | |!| | }}
{{tree chart| | | | |QG| | QG=[[Quantum gravity]] }}
{{tree chart| | | | | |!| | }}
{{tree chart| |REL|-|^|-|GUT| | REL=[[General Relativity|Space Curvature]] | GUT=Electronuclear force ([[Grand Unified Theory]]) }}
{{tree chart| | |!| | | | | |!| | }}
{{tree chart| |SMC| | | |SMP| SMC=[[Lambda-CDM model|Standard model of cosmology]] | SMP=[[Standard Model of particle physics]]}}
{{tree chart| | | | | | | | |!| | }}
{{tree chart| | | | |QCD|-|^|-|-|EWT| | QCD=[[Strong interaction]]<br />[[Special unitary group|SU(3)]] | EWT=[[Electroweak interaction]]<br />[[Special unitary group|SU(2)]] x [[Unitary group|U(1)]]<sub>[[hypercharge|Y]]</sub> }}
{{tree chart| | | | | | | | | | | | |!| | }}
{{tree chart| | | | | | | | |WNF|-|^|-|EMF||WNF=[[Weak interaction]]<br />[[Special unitary group|SU(2)]]|EMF=[[Electromagnetism]]<br />[[Unitary group|U(1)]]<sub>EM</sub>}}
{{tree chart| | | | | | | | | | | | | | | |!| | | | | | }}
{{tree chart| | | | | | | | | | | |EF|-|^|-|MF| |EF=[[Electricity]]|MF=[[Magnetism]] }}
{{tree chart/end}}
 
In this graph, electroweak unification occurs at around 100 GeV, grand unification is predicted to occur at 10<sup>16</sup> GeV, and unification of the GUT force with gravity is expected at the [[Planck energy]], roughly 10<sup>19</sup> GeV.
=== Eino Kaila ===
 
Several [[Grand Unified Theory|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 10<sup>16</sup> GeV, far greater than could be reached by any currently feasible [[particle accelerator]]. Although the simplest grand unified theories have been experimentally ruled out, the idea of a grand unified theory, especially when linked with [[supersymmetry]], 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 theory|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 theory|effective field theories]], omitting crucial phenomena relevant only at very high energies.<ref name="Carlip" />
The prolific [[Finland|Finnish]] [[philosopher]] [[Eino Kaila]] attempted to construct a theory of everything based on the philosophical implications of [[quantum mechanics]] in the 1950s. His attempt did not get much attention outside Finland, and he only managed to write the first part of what he planned on making an extensive study on the subject. "''TERMINALKAUSALITÄT ALS DIE GRUNDLAGE EINES UNITARISCHEN NATURBEGRIFFS''" ("terminal causality as the foundation of a unitarian notion of nature"), published in [[1956]], formulated a new type of [[causality]] and was meant to be followed by similar works on [[psychology]] and [[biology]].
 
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 [[quantum gravity]], 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.
== TOE and Religion ==
 
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 [[physical cosmology|cosmology]]: an [[inflation (cosmology)|inflationary force]] and [[dark energy]]. Furthermore, cosmological experiments also suggest the existence of [[dark matter]], supposedly composed of fundamental particles outside the scheme of the Standard Model. However, the existence of these forces and particles has not been proven.
Some people believe that the finding of the TOE could disprove the existence of a God. Many theistic people hold the nihilist belief that we will never find the TOE. Other theists believe that a Theory of Everything would ultimately prove the power of God's intellect to design such an elegant universe.
 
=== String theory and M-theory ===
== Pythonism ==
{{unsolved|physics|Is [[string theory]], [[superstring theory]], or [[M-theory]], or some other variant on this theme, a step on the road to a "theory of everything", or just a blind alley?}}
 
Since the 1990s, some physicists such as [[Edward Witten]] believe that 11-dimensional [[M-theory]], which is described in some limits by one of the five [[perturbation theory|perturbative]] [[superstring theory|superstring theories]], and in another by the maximally-[[supersymmetry|supersymmetric]] [[eleven-dimensional supergravity]], is the theory of everything. There is no widespread consensus on this issue.
Others contend that the true meaning of life, the universe, and everything is, actually, very simple: 42. ''(See: [[Life, the Universe and Everything]], [[science fiction]].)''
 
One remarkable property of [[string theory|string]]/[[M-theory]] 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 equations|Maxwell's electrodynamics]]. This lent credence to the idea of unifying [[gauge theory|gauge]] and [[gravity]] interactions, and to extra dimensions, but did not address the detailed experimental requirements. Another important property of string theory is its [[supersymmetry]], which together with extra dimensions are the two main proposals for resolving the [[hierarchy problem]] of the [[Standard Model]], 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.<ref>{{cite journal |pmid=16196251 |date=2005 |title=The Beauty of Branes |journal=Scientific American |pages=38–40 |doi=10.1038/scientificamerican1005-38 |url=http://randall.physics.harvard.edu/RandallCV/ScientificAm10-05.pdf |access-date=August 13, 2012 |last1=Holloway |first1=M |volume=293 |issue=4 |bibcode=2005SciAm.293d..38H |archive-date=November 22, 2014 |archive-url=https://web.archive.org/web/20141122023615/http://randall.physics.harvard.edu/RandallCV/ScientificAm10-05.pdf }}</ref>
 
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 [[Seesaw mechanism|neutrino masses]] fits into a [[spinor]] representation of [[SO(10)]], a subgroup of [[E8 (mathematics)|E<sub>8</sub>]] that routinely emerges in string theory, such as in [[heterotic string theory]]<ref>{{cite journal |arxiv=0806.3905 |doi=10.1140/epjc/s10052-008-0740-1 |title=From strings to the MSSM |year=2009 |last1=Nilles |first1=Hans Peter |last2=Ramos-Sánchez |first2=Saúl |last3=Ratz |first3=Michael |last4=Vaudrevange |first4=Patrick K. S. |journal=The European Physical Journal C |volume=59 |issue=2 |pages=249–267 |bibcode=2009EPJC...59..249N |s2cid=17452924 }}</ref> or (sometimes equivalently) in [[F-theory]].<ref>{{cite journal |doi=10.1088/1126-6708/2009/01/058 |arxiv=0802.3391 |title=GUTs and exceptional branes in F-theory — I |date=2009 |last1=Beasley |first1=Chris |last2=Heckman |first2=Jonathan J |last3=Vafa |first3=Cumrun |journal=Journal of High Energy Physics |volume=2009 |issue=1 |page=058 |bibcode=2009JHEP...01..058B |s2cid=119309173 }}</ref><ref>{{cite arXiv |eprint=0802.2969v3 |last1=Donagi |first1=Ron |title=Model Building with F-Theory |last2=Wijnholt |first2=Martijn |class=hep-th |year=2008}}</ref> String theory has mechanisms that may explain why fermions come in three hierarchical generations, and explain the [[CKM matrix|mixing rates]] between quark generations.<ref>{{Cite journal |arxiv=0811.2417 |last1=Heckman |first1=Jonathan J. |title=Flavor Hierarchy from F-theory |journal=Nuclear Physics B |volume=837 |issue=1 |pages=137–151 |last2=Vafa |first2=Cumrun |year=2010 |doi=10.1016/j.nuclphysb.2010.05.009 |bibcode=2010NuPhB.837..137H |s2cid=119244083 }}</ref> On the theoretical side, it has begun to address some of the key questions in [[quantum gravity]], such as resolving the [[black hole information paradox]], counting the correct [[black hole thermodynamics|entropy of black holes]]<ref>{{cite journal |doi=10.1016/0370-2693(96)00345-0 |arxiv=hep-th/9601029 |title=Microscopic origin of the Bekenstein-Hawking entropy |date=1996 |last1=Strominger |first1=Andrew |last2=Vafa |first2=Cumrun |journal=Physics Letters B |volume=379 |issue=1–4 |pages=99–104 |bibcode=1996PhLB..379...99S |s2cid=1041890 }}</ref><ref>{{cite arXiv<!--Citation bot deny, the arxiv metadata is wrong-->|arxiv=gr-qc/9604051 |last1=Horowitz |first1=Gary |title=The Origin of Black Hole Entropy in String Theory}}</ref> and allowing for [[topology]]-changing processes.<ref>{{cite journal |doi=10.1016/0550-3213(95)00371-X |arxiv=hep-th/9504145 |title=Black hole condensation and the unification of string vacua |date=1995 |last1=Greene |first1=Brian R. |last2=Morrison |first2=David R. |last3=Strominger |first3=Andrew |journal=Nuclear Physics B |volume=451 |issue=1–2 |pages=109–120 |bibcode=1995NuPhB.451..109G |s2cid=11145691 }}</ref><ref>{{cite journal |doi=10.1016/0550-3213(94)90321-2 |arxiv=hep-th/9309097 |title=Calabi-Yau moduli space, mirror manifolds and spacetime topology change in string theory |date=1994 |last1=Aspinwall |first1=Paul S. |last2=Greene |first2=Brian R. |last3=Morrison |first3=David R. |journal=Nuclear Physics B |volume=416 |issue=2 |page=414 |bibcode=1994NuPhB.416..414A |s2cid=10927539 }}</ref><ref>{{cite journal |doi=10.1088/1126-6708/2005/10/033 |arxiv=hep-th/0502021 |title=Things fall apart: Topology change from winding tachyons |date=2005|author-link1=Allan Adams |last1=Adams |first1=Allan |last2=Liu |first2=Xiao |last3=McGreevy |first3=John |last4=Saltman |first4=Alex |last5=Silverstein |first5=Eva |journal=Journal of High Energy Physics |volume=2005 |issue=10 |page=033 |bibcode=2005JHEP...10..033A |s2cid=14320855 }}</ref> It has also led to many insights in [[pure mathematics]] and in ordinary, strongly-coupled [[gauge theory]] due to the [[AdS/CFT|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 [[compact dimension|compactified]] in an enormous number of different ways (one estimate is 10<sup>500</sup>) 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]].<ref name="Impey2012" />{{rp|347}}
 
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]] of the universe are ultimately the result of the [[anthropic principle]] rather than dictated by theory. This has led to criticism of string theory,<ref>{{cite book |last=Smolin |first=Lee |title=The Trouble With Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next |date=2006 |publisher=Houghton Mifflin |isbn=978-0-618-55105-7|title-link=The Trouble With Physics }}</ref> arguing that it cannot make useful (i.e., original, [[falsifiable]], and verifiable) predictions and regarding it as a [[pseudoscience]]/[[philosophy]]. Others disagree,<ref>{{cite journal |author=Duff, M. J. |arxiv=1112.0788 |doi=10.1007/s10701-011-9618-4 |title=String and M-Theory: Answering the Critics |date=2011 |journal=Foundations of Physics |volume=43 |issue=1 |pages=182–200 |bibcode=2013FoPh...43..182D |s2cid=55066230 }}</ref> and string theory remains an active topic of investigation in [[theoretical physics]].<ref>{{Cite news|url=https://www.symmetrymagazine.org/article/may-2007/the-great-string-debate|title=The Great String Debate|last=Chui|first=Glennda|date=May 1, 2007|work=Symmetry Magazine|access-date=2018-10-17|language=en|archive-date=2018-10-17|archive-url=https://web.archive.org/web/20181017123651/https://www.symmetrymagazine.org/article/may-2007/the-great-string-debate|url-status=live}}</ref>
 
=== Loop quantum gravity ===
Current research on [[loop quantum gravity]] may eventually play a fundamental role in a theory of everything, but that is not its primary aim.<ref>{{cite web
|last=Potter
|first=Franklin
|date=15 February 2005
|url=http://www.sciencegems.com/discretespace.pdf
|title=Leptons And Quarks In A Discrete Spacetime
|work=Frank Potter's Science Gems
|access-date=2009-12-01
|archive-date=2021-03-09
|archive-url=https://web.archive.org/web/20210309121814/http://www.sciencegems.com/discretespace.pdf
|url-status=live
}}</ref> 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 [[Standard Model]]. So far only the first generation of [[fermion]]s ([[lepton]]s and [[quark]]s) with correct parity properties have been modelled by [[Sundance Bilson-Thompson]] using [[preon]]s constituted of braids of spacetime as the building blocks.<ref>{{cite journal |title=Quantum gravity and the standard model |last=Bilson-Thompson |first=Sundance O. |author2=Markopoulou, Fotini |author3=Smolin, Lee |doi=10.1088/0264-9381/24/16/002 |date=2007 |journal=Classical and Quantum Gravity |volume=24 |issue=16 |pages=3975–3994 |arxiv=hep-th/0603022 |bibcode=2007CQGra..24.3975B|s2cid=37406474 }}</ref> However, there is no derivation of the [[Lagrangian (field theory)|Lagrangian]] 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. Use of [[quantum computing]] concepts made it possible to demonstrate that the particles are able to survive [[quantum fluctuation]]s.<ref>{{cite journal |url=https://www.newscientist.com/channel/fundamentals/mg19125645.800 |journal=New Scientist |title=You are made of space-time |first=Davide |last=Castelvecchi |author2=Valerie Jamieson |issue=2564 |date=August 12, 2006 |access-date=September 16, 2017 |archive-date=February 9, 2008 |archive-url=https://web.archive.org/web/20080209025208/http://www.newscientist.com/channel/fundamentals/mg19125645.800 |url-status=live }}</ref>
 
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.<ref>{{cite arXiv |eprint=0804.0037 |class=hep-th |first1=Sundance |last1=Bilson-Thompson |first2=Jonathan |last2=Hackett |title=Particle Identifications from Symmetries of Braided Ribbon Network Invariants |date=2008 |author3=Kauffman, Lou |author4=Smolin, Lee}}</ref>
 
=== 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]].<ref name="NYT-20201123" /> Most particle physicists expect that the outcome of ongoing experiments – the search for new particles at the large [[particle accelerator]]s and for [[dark matter]] – are needed in order to provide further input for a theory of everything.
 
== Other proposals ==
The search for a Theory of Everything is hindered by fundamental incompatibility between the noncommutative and discrete operator algebra structures underlying quantum mechanics and the commutative continuous geometric nature of classical spacetime in general relativity. Reconciling the background-independent, diffeomorphism-invariant formulation of gravity with the fixed-background, time-ordered framework of quantum theory raises profound conceptual issues such as the problem of time and quantum measurement.{{cn|date=July 2025}} While a fully successful and experimentally confirmed unified field theory remains elusive, several recent proposals have been advanced, each employing distinct mathematical structures and physical assumptions.
 
[[Twistor theory]], developed by [[Roger Penrose]], reinterprets the structure of spacetime and fundamental particles through complex geometric objects called twistors. Instead of treating spacetime points as fundamental, twistor theory encodes physical fields and particles into complex projective spaces, aiming to unify quantum theory and general relativity in a geometric framework. Twistors provide potential descriptions of massless fields and scattering amplitudes and have influenced modern approaches in mathematical physics and quantum field theory, including advances in scattering amplitude calculations. Twistor theory has not yet yielded a complete unified field theory.<ref>{{cite journal |last=Penrose |first=Roger |title=Twistor Algebra |journal=Journal of Mathematical Physics |year=1967 |volume=8 |pages=345–366 |doi=10.1063/1.1705276}}</ref>{{Primary source inline|reason=A 1967 paper by Penrose is insufficient for all claims about the influence or significance of Penrose's work and for everything that has happened since 1967|date=July 2025}}
 
[[Alain Connes]] developed a geometric framework known as [[noncommutative geometry]] in which spacetime is extended via noncommutative operator algebras. When combined with [[spectral triple]]s, this approach can reproduce features of the Standard Model, including the Higgs field, from purely geometric data.<ref>{{cite book |last=Connes |first=Alain |title=Noncommutative Geometry |year=1994 |publisher=Academic Press}}</ref><ref>{{cite journal |last1=Chamseddine |first1=Ali H. |last2=Connes |first2=Alain |title=The Spectral Action Principle |journal=Communications in Mathematical Physics |year=1997 |volume=186 |issue=3 |pages=731–750 |doi=10.1007/s002200050126 |arxiv=hep-th/9606001 |bibcode=1997CMaPh.186..731C }}</ref>
 
[[Asymptotic safety]], a concept developed by [[Steven Weinberg]] in 1976 and also known as Quantum Einstein Gravity and nonperturbative renormalizability, suggests that gravity could find a role in quantum theory if its behavior at very high energies becomes stabilized into a nontrivial ultraviolet (UV) fixed point.<ref>{{cite book |last=Weinberg |first=Steven |chapter=Critical Phenomena for Field Theorists |title=Understanding the Fundamental Constituents of Matter |publisher=Plenum Press |year=1977 |pages=1–52 |doi=10.1007/978-1-4684-0931-4_1 |isbn=978-1-4684-0931-4 |chapter-url=https://link.springer.com/chapter/10.1007/978-1-4684-0931-4_1 |access-date=2 September 2025}}</ref> This form has been studied through functional renormalization group methods<ref>{{cite journal |last=Reuter |first=Martin |title=Nonperturbative evolution equation for quantum gravity |journal=Physical Review D |volume=57 |issue=2 |pages=971–985 |year=1998 |doi=10.1103/PhysRevD.57.971 |arxiv=hep-th/9605030 |bibcode=1998PhRvD..57..971R |url=https://link.aps.org/doi/10.1103/PhysRevD.57.971 |access-date=2 September 2025}}</ref> and on the lattice<ref>{{cite journal |last=Litim |first=Daniel F. |title=Fixed Points of Quantum Gravity |journal=Physical Review Letters |volume=92 |article-number=201301 |year=2004 |issue=20 |doi=10.1103/PhysRevLett.92.201301 |pmid=15169333 |arxiv=hep-th/0312114 |bibcode=2004PhRvL..92t1301L |url=https://link.aps.org/doi/10.1103/PhysRevLett.92.201301 |access-date=2 September 2025}}</ref>, and applied in cosmology, particle physics, black hole physics, and quantum gravity.<ref>{{cite book |last=Percacci |first=Roberto |title=An Introduction to Covariant Quantum Gravity and Asymptotic Safety |publisher=World Scientific |year=2017 |doi=10.1142/10233 |isbn=978-981-314-251-0 |url=https://www.worldscientific.com/worldscibooks/10.1142/10233 |access-date=2 September 2025}}</ref> Whereas overwhelming numerical evidence does exist that such a fixed point does occur in lower-dimensional constructions and in the numerics,<ref>{{cite journal |last1=Falls |first1=Kevin |last2=Litim |first2=Daniel F. |last3=Nikolakopoulos |first3=Konstantinos |last4=Rahmede |first4=Christoph |title=A bootstrap towards asymptotic safety |journal=Physical Review D |volume=89 |issue=8 |article-number=084002 |year=2014 |doi=10.1103/PhysRevD.89.084002 |url=https://link.aps.org/doi/10.1103/PhysRevD.89.084002 |access-date=2 September 2025|arxiv=1212.1821 }}</ref> a rigorous proof even for four-dimensional spacetime remains to be found.<ref>{{cite book |last1=Reuter |first1=Martin |last2=Saueressig |first2=Frank |title=Quantum Gravity and the Functional Renormalization Group |publisher=Cambridge University Press |year=2019 |isbn=978-1-316-22759-6|url=https://www.cambridge.org/core/books/quantum-gravity-and-the-functional-renormalization-group/2D4FC0A7E2C40F6BFE0B1D7CC95A2A3A |access-date=2 September 2025}}</ref>
 
== Arguments against ==
In parallel to the intense search for a theory of everything, various scholars have debated the possibility of its discovery.
 
=== Gödel's incompleteness theorem ===
A number of scholars claim that [[Gödel's incompleteness theorem]] suggests that attempts to construct a theory of everything are 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.
 
The Benedictine priest and science writer [[Stanley Jaki]], in his 1966 book ''The Relevance of Physics'', suggested that Gödel's theorem casts doubt on the "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.<ref>
{{cite book
|last=Jaki |first=S.L.
|date=1966
|pages=127–130
|title=The Relevance of Physics
|publisher=Chicago Press
}}</ref>
 
[[Freeman Dyson]] 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."<ref>{{cite web |last=Dyson |first=Freeman |date=2004-05-13 |title=The World on a String |url=https://www.nybooks.com/articles/2004/05/13/the-world-on-a-string/ |access-date=2025-07-22 |website=The New York Review of Books |language=en}}</ref>
 
[[Stephen Hawking]] originally believed that a theory of everything could be found, 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."<ref>
{{cite web
|last=Hawking
|first=Stephen
|date=20 July 2002
|title=Gödel and the end of physics
|url=http://www.damtp.cam.ac.uk/strings02/dirac/hawking/
|access-date=2009-12-01
|archive-date=2011-05-21
|archive-url=https://web.archive.org/web/20110521123113/http://www.damtp.cam.ac.uk/strings02/dirac/hawking/ }}</ref>
 
[[Jürgen Schmidhuber]] (1997) has argued against this view; he asserts that Gödel's theorems are irrelevant for [[computable]] physics.<ref>{{cite book
|last=Schmidhuber
|first=Jürgen
|date=1997
|title=A Computer Scientist's View of Life, the Universe, and Everything. Lecture Notes in Computer Science
|volume=1337
|url=http://www.idsia.ch/~juergen/everything/
|pages=201–208
|publisher=[[Springer (publisher)|Springer]]
|isbn=978-3-540-63746-2
|doi=10.1007/BFb0052071
|citeseerx=10.1.1.580.1970
|s2cid=21317070
|access-date=2008-03-26
|archive-date=2014-02-27
|archive-url=https://web.archive.org/web/20140227162350/http://www.idsia.ch/~juergen/everything/
|url-status=live
}}</ref> In 2000, Schmidhuber explicitly constructed limit-computable, deterministic universes whose [[pseudo-randomness]] based on [[undecidable problem|undecidable]], Gödel-like [[halting problem]]s is extremely hard to detect but does not prevent formal theories of everything describable by very few bits of information.<ref>
{{cite journal
|author=Schmidhuber, Jürgen
|date=2002
|title=Hierarchies of generalized Kolmogorov complexities and nonenumerable universal measures computable in the limit
|journal=International Journal of Foundations of Computer Science
|volume=13
|issue=4
|pages=587–612
|arxiv=quant-ph/0011122
|bibcode=2000quant.ph.11122S
|doi=10.1142/s0129054102001291
}}</ref>
 
Related critique was offered by [[Solomon Feferman]]<ref>{{cite web
|last=Feferman
|first=Solomon
|url=http://math.stanford.edu/~feferman/papers/Godel-IAS.pdf
|title=The nature and significance of Gödel's incompleteness theorems
|publisher=[[Institute for Advanced Study]]
|date=17 November 2006
|access-date=2009-01-12
|archive-date=2008-12-17
|archive-url=https://web.archive.org/web/20081217035530/http://math.stanford.edu/~feferman/papers/Godel-IAS.pdf
|url-status=live
}}</ref> and others. Douglas S. Robertson offers [[Conway's game of life]] as an example:<ref>
{{cite journal
|last=Robertson |first=Douglas S.
|date=2007
|title=Goedel's Theorem, the Theory of Everything, and the Future of Science and Mathematics
|journal=[[Complexity (journal)|Complexity]]
|volume=5 |issue=5 |pages=22–27
|doi=10.1002/1099-0526(200005/06)5:5<22::AID-CPLX4>3.0.CO;2-0
|bibcode=2000Cmplx...5e..22R}}</ref> 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.
 
=== 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".<ref>{{cite book |title=The New Cosmic Onion: Quarks and the Nature of the Universe |first=search |last=results|date=17 December 2006 |publisher=CRC Press |isbn=978-1-58488-798-0 }}</ref> Einstein himself expressed this view on occasions.<ref>Einstein, letter to Felix Klein, 1917. (On determinism and approximations.) Quoted in {{harvtxt|Pais|1982|loc=Ch. 17}}.</ref>
 
=== 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.{{sfn|Weinberg|1993|loc=Ch 2}} One view is the hard [[reductionist]] 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 [[emergence|emergent]] laws, which govern the behavior of [[complex system]]s, should be seen as equally fundamental. Examples of emergent laws are the [[second law of thermodynamics]] and the theory of [[natural selection]]. 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.
 
A well-known debate over this took place between Steven Weinberg and [[Philip Warren Anderson|Philip Anderson]].<ref>{{cite book |title=Superstrings, P-branes and M-theory |author=Wikipedians |url=https://books.google.com/books?id=B_2R_jY2KiEC |page=7 |publisher=PediaPress }}</ref>
 
==== Impossibility of calculation ====
Weinberg{{sfn|Weinberg|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 [[general relativity]] 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. Difficulties in creating a theory of everything often begin to appear when combining [[quantum mechanics]] with the theory of [[general relativity]], as the equations of quantum mechanics begin to falter when the force of gravity is applied to them.
 
== See also ==
{{portal|Physics}}
{{div col|colwidth=30}}
* {{annotated link|Absolute (philosophy)}}
* {{annotated link|Argument from beauty}}
* {{annotated link|Attractor}}
* {{annotated link|Black hole thermodynamics#Beyond black holes|Beyond black holes}}
* {{annotated link|cGh physics}}
* {{annotated link|Chronology of the universe}}
* {{annotated link|ER{{=}}EPR}}
* {{annotated link|Grand Unified Theory}}
* {{annotated link|Holographic principle}}
* {{annotated link|List of unsolved problems in mathematics}}
* {{annotated link|List of unsolved problems in neuroscience}}
* {{annotated link|List of unsolved problems in physics}}
* {{annotated link|Mathematical beauty}}
* {{annotated link|Mathematical universe hypothesis}}
* {{annotated link|Multiverse}}
* {{annotated link|Penrose interpretation}}
* {{annotated link|Physics beyond the Standard Model}}
* {{annotated link|Standard Model (mathematical formulation)}}
* {{annotated link|Superfluid vacuum theory}}
* {{annotated link|The Theory of Everything (2014 film)|''The Theory of Everything''}}
* {{annotated link|Timeline of the Big Bang}}
* {{annotated link|Unification (physics)|Unification}}
* {{annotated link|Unity of science}}
* {{annotated link|Zero-energy universe}}
{{div col end}}
 
== References ==
{{reflist|35em|refs=
 
<ref name="Impey2012">{{cite book |author=Impey |first=Chris |url=https://archive.org/details/howitbegantimetr0000impe |title=How It Began: A Time-Traveler's Guide to the Universe |date=26 March 2012 |publisher=W. W. Norton |isbn=978-0-393-08002-5 |url-access=registration}}</ref>
 
<ref name="NYT-20201123">{{cite news |last=Overbye |first=Dennis |author-link=Dennis Overbye |date=23 November 2020 |title=Can a Computer Devise a Theory of Everything? - It might be possible, physicists say, but not anytime soon. And there's no guarantee that we humans will understand the result. |work=[[The New York Times]] |url=https://www.nytimes.com/2020/11/23/science/artificial-intelligence-ai-physics-theory.html |archive-url=https://web.archive.org/web/20201123100612/https://www.nytimes.com/2020/11/23/science/artificial-intelligence-ai-physics-theory.html |archive-date=23 November 2020 |url-status=live |access-date=23 November 2020}}</ref>
 
}}
 
=== Bibliography ===
* {{cite book |author1-link=Abraham Pais |last1=Pais |first1=Abraham |date=1982 |title=Subtle is the Lord: The Science and the Life of Albert Einstein |title-link=Subtle is the Lord: The Science and the Life of Albert Einstein |publisher=Oxford University Press |isbn=0-19-853907-X }}
* {{citation |author1-link=Steven Weinberg |last1=Weinberg |first1=Steven |date=1993 |title=Dreams of a Final Theory: The Search for the Fundamental Laws of Nature |publisher=Hutchinson Radius, London |isbn=0-09-177395-4 }}
* {{citation |author1-link=Corey S. Powell |last1=Powell |first1=Corey S. |title=Relativity versus quantum mechanics: the battle for the universe |magazine=The Guardian |date=2015 |url=https://www.theguardian.com/news/2015/nov/04/relativity-quantum-mechanics-universe-physicists }}
 
== External links ==
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* [https://www.pbs.org/wgbh/nova/elegant/program.html The Elegant Universe], ''[[Nova (American TV series)|Nova]]'' episode about the search for the theory of everything and string theory.
* [http://www.vega.org.uk/video/programme/7 Theory of Everything], freeview video by the [[Vega Science Trust]], BBC and [[Open University]].
* [http://iai.tv/video/the-theory-of-everything The Theory of Everything]: Are we getting closer, or is a final theory of matter and the universe impossible? Debate between [[John Ellis (physicist, born 1946)|John Ellis (physicist)]], [[Frank Close]] and [[Nicholas Maxwell]].
* [http://iai.tv/video/why-the-world-exists Why The World Exists], a discussion between physicist [[Laura Mersini-Houghton]], cosmologist [[George Francis Rayner Ellis]] and philosopher David Wallace about dark matter, parallel universes and explaining why these and the present Universe exist.
* [https://www.bbc.co.uk/programmes/p004y24b Theories of Everything], BBC Radio 4 discussion with Brian Greene, John Barrow & Val Gibson (''In Our Time'', March 25, 2004).
 
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* [http://www.pbs.org/wgbh/nova/elegant/program.html The Elegant Universe-Nova online]- a 3 hour PBS show about the search for the Theory of everything and string theory.
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[[Category:Physics beyond the Standard Model]]
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