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Beyond the Standard Model
Simulated Large Hadron Collider CMS particle detector data depicting a Higgs boson produced by colliding protons decaying into hadron jets and electrons
Standard Model
Evidence Hierarchy problem Dark matter Dark energy Quintessence Phantom energy Dark radiation Dark photon Cosmological constant problem Strong CP problem Neutrino oscillation
Theories Brans–Dicke theory Cosmic censorship hypothesis Fifth force F-theory Theory of everything Unified field theory Grand Unified Theory Technicolor Kaluza–Klein theory 6D (2,0) superconformal field theory Noncommutative quantum field theory Quantum cosmology Brane cosmology String theory Superstring theory M-theory Mathematical universe hypothesis Mirror matter Randall–Sundrum model N = 4 supersymmetric Yang–Mills theory Twistor string theory Dark fluid Doubly special relativity de Sitter invariant special relativity Causal fermion systems Black hole thermodynamics Unparticle physics Graviphoton Graviscalar Graviton Gravitino Massive gravity Gauge gravitation theory Gauge theory gravity CPT symmetry
Supersymmetry MSSM NMSSM Superstring theory M-theory Supergravity Supersymmetry breaking Extra dimensions Large extra dimensions
Quantum gravity False vacuum String theory Spin foam Quantum foam Quantum geometry Loop quantum gravity Quantum cosmology Loop quantum cosmology Causal dynamical triangulation Causal fermion systems Causal sets Canonical quantum gravity Semiclassical gravity Superfluid vacuum theory
Experiments ANNIE Gran Sasso INO LHC SNO Super-K Tevatron NOvA
v t e

A theory of everything (TOE

From the earliest days of Greek science until well into the 1900s, it seems to have often been believed that an ultimate model of the universe was not far away.

— Wolfram, Stephen (2002). A New Kind of Science. p. 1024.

Ancient

Archimedes was possibly the first philosopher to have described nature with axioms (or principles) and then deduce new results from them. Any "theory of everything" is similarly expected to be based on axioms and to deduce all observable phenomena from them.^[11]: 340

Following earlier atomistic thought, the

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. During the 19th and early 20th centuries, it gradually became apparent that many common examples of forces – contact forces, elasticity, viscosity, friction, and pressure – result from electrical interactions between the smallest particles of matter.

In his experiments of 1849–50, Michael Faraday was the first to search for a unification of gravity with electricity and magnetism.^[16] However, he found no connection.

In 1900, David Hilbert published a famous list of mathematical problems. In Hilbert's sixth problem, 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.^[17]

Early 20th century

In the late 1920s, the new quantum mechanics showed that the chemical bonds between atoms were examples of (quantum) electrical forces, justifying Dirac's boast that "the underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known".^[18]

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 thirty-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,^[19] 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^{[20]: ch 17} (see Einstein–Maxwell–Dirac equations).

Late 20th century and the nuclear interactions

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

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 twentieth century, focused on understanding the three forces described by quantum mechanics: electromagnetism and the weak and strong forces. The first two were combined in 1967–68 by Sheldon Glashow, Steven Weinberg, and Abdus Salam into the electroweak force.^[21] Electroweak unification is a

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 remains unsuccessful: neither a unification of the strong and electroweak forces – which Laplace would have called 'contact forces' – nor a unification of these forces with gravitation has been achieved.

Modern physics

Conventional sequence of theories

A Theory of Everything would unify all the

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

Several Grand Unified Theories (GUTs) have been proposed to unify electromagnetism and the weak and strong forces. Grand unification would imply the existence of an electronuclear force; it is expected to set in at energies of the order of 10¹⁶ GeV, far greater than could be reached by any currently feasible particle accelerator. Although the simplest GUTs 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 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 which require the problematic technique of renormalization to yield sensible answers. This is usually regarded as a sign that these are only effective field theories, omitting crucial phenomena relevant only at very high energies.^[5]

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. 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 may also explain the status of at least two candidate forces suggested by modern cosmology: an 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.

String theory and M-theory

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 perturbative superstring theories, and in another by the maximally-supersymmetric 11-dimensional supergravity, is the theory of everything. However, there is no widespread consensus on this issue.

One remarkable property of

Current research on loop quantum gravity may eventually play a fundamental role in a TOE, but that is not its primary aim.^[35] 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. So far only the first generation of fermions (leptons and quarks) with correct parity properties have been modelled by Sundance Bilson-Thompson using preons constituted of braids of spacetime as the building blocks.^[36] However, there is no derivation of the 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. Utilization of quantum computing concepts made it possible to demonstrate that the particles are able to survive quantum fluctuations.^[37]

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.^[38]

Other attempts

Among other attempts to develop a theory of everything is the theory of

Outside the previously mentioned attempts there is Garrett Lisi's E8 proposal. This theory attempts to construct general relativity and the standard model within the Lie group E8. The theory doesn't provide a novel quantization procedure and the author suggests its quantization might follow the Loop Quantum Gravity approach above mentioned.^[40]

Causal dynamical triangulation does not assume any pre-existing arena (dimensional space), but rather attempts to show how the spacetime fabric itself evolves.

Christoph Schiller's Strand Model attempts to account for the

Stanley Jaki, in his 1966 book The Relevance of Physics, pointed out that, because any "theory of everything" will certainly be a consistent non-trivial mathematical theory, it must be incomplete. He claims that this dooms searches for a deterministic theory of everything.^[44]

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."^[45]

Stephen Hawking was originally a believer in the Theory of Everything, but after considering Gödel's Theorem, he concluded that one was not obtainable. "Some people will be very disappointed if there is not an ultimate theory that can be formulated as a finite number of principles. I used to belong to that camp, but I have changed my mind."^[46]

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 numbers into a physical question.^[51] 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.^[52] 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

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, 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 almost 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. Even in classical mechanics there are still unsolved problems, such as turbulence, although the equations have been known for centuries. 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,^[

) 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.

The theories generally do not account for the apparent phenomena of consciousness or free will, which are instead often the subject of philosophy and religion.

Infinite number of onion layers

Frank Close regularly argues that the layers of nature may be like the layers of an onion, and that the number of layers might be infinite.^[55] This would imply an infinite sequence of physical theories.

Impossibility of calculation

Weinberg^[56] 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 TOE 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.

See also

• Absolute (philosophy)
• A New Kind of Science
• Argument from beauty
• Attractor
• Beyond black holes
• Beyond the standard model
• Big Bang
• cGh physics
• Chronology of the universe
• Electroweak interaction
• ER=EPR
• Holographic principle
• Mathematical beauty
• Mathematical universe hypothesis
• Multiverse
• Penrose interpretation
• Scale relativity
• Standard Model (mathematical formulation)
• Superfluid vacuum theory (SVT)
• The Theory of Everything (2014 film)
• Timeline of the Big Bang
• Unified Field Theory
• Zero-energy universe

References

^[57]

Footnotes

1. arXiv:gr-qc/9910036
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2. ISBN 978-0-307-78786-6
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3. ^ ^{a b} Overbye, Dennis (23 November 2020). "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". The New York Times. Retrieved 23 November 2020.
4. ISBN 978-1-59777-508-3
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5. ^
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7. ^ Fritzsch, Harald (1977). "THE WORLD OF FLAVOUR AND COLOUR". CERN Report. Ref.TH.2359-CERN. (download at http://cds.cern.ch/record/875256/files/CM-P00061728.pdf )
8. ^ Ellis, John (2002). "Physics gets physical (correspondence)".
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9. ^ Ellis, John (1986). "The Superstring: Theory of Everything, or of Nothing?". Nature. 323 (6089): 595–598.
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13. ^ Shapin, Steven (1996). The Scientific Revolution.
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14. ^ Newton, Sir Isaac (1729). The Mathematical Principles of Natural Philosophy. Vol. II. p. 255.
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16. ^ Faraday, M. (1850). "Experimental Researches in Electricity. Twenty-Fourth Series. On the Possible Relation of Gravity to Electricity". Abstracts of the Papers Communicated to the Royal Society of London. 5: 994–995.
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17. doi:10.1090/S0273-0979-2013-01439-3
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18. ^ Dirac, P.A.M. (1929). "Quantum mechanics of many-electron systems".
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19. ISBN 978-0-8176-4454-3
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20. ISBN 978-0-19-152402-8
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21. ^ Weinberg (1993), Ch. 5
22. PMID 16196251
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28. arXiv:gr-qc/9604051
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34. ^ Chui, Glennda (May 1, 2007). "The Great String Debate". Symmetry Magazine. Retrieved 2018-10-17.
35. ^ Potter, Franklin (15 February 2005). "Leptons And Quarks In A Discrete Spacetime" (PDF). Frank Potter's Science Gems. Retrieved 2009-12-01.
36. doi:10.1088/0264-9381/24/16/002
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37. ^ Castelvecchi, Davide; Valerie Jamieson (August 12, 2006). "You are made of space-time". New Scientist (2564).
38. arXiv:0804.0037 [hep-th
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40. arXiv:0711.0770 [hep-th
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42. ^ Staff (2016). "This New Equation Could Unite The Two Biggest Theories in Physics". futurism.com. Retrieved May 19, 2017.
43. PMID 26581274
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44. ^ Jaki, S.L. (1966). The Relevance of Physics. Chicago Press. pp. 127–130.
45. ^ Freeman Dyson, NYRB, May 13, 2004
46. ^ Stephen Hawking, Gödel and the end of physics, July 20, 2002
47. ^ Schmidhuber, Jürgen (1997). A Computer Scientist's View of Life, the Universe, and Everything. Lecture Notes in Computer Science. Lecture Notes in Computer Science. Vol. 1337.
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48. ^ Schmidhuber, Jürgen (2002). "Hierarchies of generalized Kolmogorov complexities and nonenumerable universal measures computable in the limit". International Journal of Foundations of Computer Science. 13 (4): 587–612.
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49. ^ Feferman, Solomon (17 November 2006). "The nature and significance of Gödel's incompleteness theorems" (PDF). Institute for Advanced Study. Retrieved 2009-01-12.
50. ^ Robertson, Douglas S. (2007). "Goedel's Theorem, the Theory of Everything, and the Future of Science and Mathematics".
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51. ^ Hawking, Stephen (20 July 2002). "Gödel and the end of physics". Retrieved 2009-12-01.
52. ^ Einstein, letter to Felix Klein, 1917. (On determinism and approximations.) Quoted in Pais (1982), Ch. 17.
53. ^ Weinberg (1993), Ch 2.
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55. ISBN 978-1584887980
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57. ^ https://www.theguardian.com/news/2015/nov/04/relativity-quantum-mechanics-universe-physicists

Bibliography

• ISBN 0-19-853907-X
• ISBN 0-09-177395-4

External links

Wikimedia Commons has media related to Theory of everything.

Wikiquote has quotations related to Theory of everything.

• The Elegant Universe,
  Nova
  episode about the search for the theory of everything and string theory.
• Theory of Everything, freeview video by the Vega Science Trust, BBC and Open University.
• The Theory of Everything: Are we getting closer, or is a final theory of matter and the universe impossible? Debate between John Ellis (physicist), Frank Close and Nicholas Maxwell.
• Why The World Exists, a discussion between physicist
  George Francis Rayner Ellis
  and philosopher David Wallace about dark matter, parallel universes and explaining why these and the present Universe exist.
• Theories of Everything, BBC Radio 4 discussion with Brian Greene, John Barrow & Val Gibson (In Our Time, Mar. 25, 2004)
• A new kind of science, A book which discusses an arising fundamental theory of everything from simple computational programs.