Theory of everything

A  (ToE), a major unsolved problem, would be a hypothetical single, all-encompassing, coherent theory of physics that explains and links all physical aspects of the universe. It is also known as the final, ultimate, or master theory. String theory has emerged as a current approach to a theory of everything.

Quotes

 * If all you have is a hammer, everything looks like a nail.
 * Anonymous


 * [T]he single equation of nature, aimed at by Lagrange and Hamilton, by Weber and Maxwell in their several ways, has... reached a more profound significance and now even holds dynamics, awkwardly it is true but none the less inexorably, in its grasp. That it is not complete, that it never can be complete, is admitted (for the absolute truth poured into the vessel of the human mind would probably dissolve it); but that it is immeasurably more complete to-day than it was yesterday is as incontrovertably true as it is inspiring.
 * , "The Mathematician in Modern Physics" (Nov. 20, 1914) Science Vol. 40, Jul-Dec 1914, p. 727.


 * Concerning such [ dimensionless constants] I would like to state a theorem which at present cannot be based upon anything more than upon faith in the simplicity, i.e., intelligibility, of nature: there are no arbitrary constants of this kind; that is to say, nature is so constituted that it is possible logically to lay down such strongly determined laws that within these laws only rationally completely determined constants occur (not constants, therefore, whose numerical value could be changed without destroying the theory).
 * Albert Einstein, "Autobiographical Notes" (1949)


 * All science has one aim, namely, to find a theory of nature. We have theories of races and of functions, but scarcely yet a remote approach to an idea of creation. We are now so far from the road to truth, that religious teachers dispute and hate each other, and speculative men are esteemed unsound and frivolous. But to a sound judgment, the most abstract truth is the most practical. Whenever a true theory appears, it will be its own evidence. Its test is, that it will explain all phenomena. Now many are thought not only unexplained but inexplicable; as language, sleep, madness, dreams, beasts, sex.
 * Ralph Waldo Emerson, Nature (1849) Introduction, p. 2.


 * "[A]greement with observed facts" never singles out one individual theory. There is never only one theory that is in complete agreement with all observed facts, but several theories that are in partial agreement. We have to select the final theory by a compromise. The final theory has to be in fair agreement with observed facts and must also be fairly simple. If we consider this point, it is obvious that such a "final" theory cannot be "The Truth."
 * , Philosophy of Science: The Link Between Science and Philosophy (1957) p. 356.


 * [F]inding the T.O.E. would in no way mean that psychology, biology, geology, chemistry, or even physics had been solved or in some sense subsumed. The universe is such a wonderfully rich and complex place that the discovery of the final theory... would not spell the end of science. Quite the contrary: The discovery of the T.O.E.—the ultimate explanation of the universe at its most microscopic level, a theory that does not rely on any deeper explanation—would provide the firmest foundation on which to build our understanding of the world. Its discovery would mark the beginning, not the end. The ultimate theory would provide an unshakable pillar of coherence forever assuring us that the universe is a comprehensible place.
 * Brian Greene, The Elegant Universe (1999, 2003) Ch. 1 "Tied Up with a String."


 * We are all, in our own way, seekers of the truth... each generation stands firmly on the shoulders of the previous... Whether any of our descendants will ever take in the view from the summit and gaze out on the vast and elegant universe with a perspective of infinite clarity, we cannot predict. But... we are fulfilling our part, contributing our rung to the human ladder reaching for the stars.
 * Brian Greene, The Elegant Universe (1999, 2003) Ch. 15 "Prospects."


 * The clearest expression of this modern "religious" mission can be recognized wherever one encounters the ancient Pythagorean search for nature's mathematical symmetry and harmony. This Pythagorean religion was transformed by early mechanists into a search for the mind of the Christian God. That quest has been tempered since the seventeenth century by a concern to find more practical mathematical relationships in nature, but it has not disappeared. ...wherever the religious mission has been retained in its pure form, as, for example, in the quest for a Theory of Everything... fewer women scientists will be found.
 * Frederick Gregory, "Intersections of Physical Science in Western Religion in the Nineteenth and Twentieth Centuries," The Cambridge History of Science: Volume 5, The Modern Physical and Mathematical Sciences (2003) ed.,, p. 52-53.


 * Ever since Newton, and especially since Einstein, the goal of physics has been to find simple mathematical principles of the kind Kepler envisioned, and with them to create a unified theory of everything that would account for every detail of the matter and forces we observe in nature. ...The goal was to find not just a single theory that explains all forces but also one that explains the fundamental numbers... such as the strength of the forces and the masses and charges of the elementary particles. ...A unique theory would be unlikely to have the fine-tuning that allows us to exist. But if... we interpret Einstein's dream to be that of a unique theory that explains this and other universes, with their whole spectrum of different laws, then M-theory could be that theory.
 * Stephen Hawking, Leonard Mlodinow, The Grand Design (2010)

The concepts may, however, be sharply defined with regard to their connections. This is actually the fact when the concepts become part of a system of axioms and definitions which can be expressed consistently by a mathematical scheme. Such a group of connected concepts may be applicable to a wide field of experience and will help us to find our way in this field. But the limits of the applicability will in general not be known, at least not completely.
 * Any concepts or words which have been formed in the past through the interplay between the world and ourselves are not really sharply defined with respect to their meaning: that is to say, we do not know exactly how far they will help us in finding our way in the world. We often know that they can be applied to a wide range of inner or outer experience, but we practically never know precisely the limits of their applicability. This is true even of the simplest and most general concepts like "existence" and "space and time". Therefore, it will never be possible by pure reason to arrive at some absolute truth.
 * Werner Heisenberg, Physics and Philosophy: The Revolution in Modern Science (1958)

This theory of everything will be... a myth... a story that makes sense within its own terms, offers explanations for everything... but can be neither tested nor disproved... an explanation that everyone agrees on because it is convenient to agree on it, not because its truth can be demonstrated. This... will indeed spell the end of physics... not because physics has at last been able to explain everything... but because physics has reached the end of all things it has the power to explain.
 * The ideal theory of everything, in the minds of physicists... is a mathematical system of uncommon tidiness and rigor, which may, if all works out correctly, have the ability to accommodate the physical facts... Perhaps physicists will one day find a theory of such compelling beauty that its truth cannot be denied; truth will be beauty... because, in the absence of any means to make practical tests, what is beautiful is declared ipso facto to be the truth.
 * David Lindley, The End of Physics: The Myth of a Unified Theory (1993) p. 255.


 * Do quarks and galaxies play by the same rules? Physicists believe they should, even though they don't quite know why. For decades, physicists have been searching for a "theory of everything"—a comprehensive description of the laws of nature. In particular, they want to bridge the gap between the large and the small with a quantum theory of gravity—a reconciliation of general relativity with quantum mechanics. String theory appears to be the current best bet...
 * , Is God a Mathematician? (2009)


 * It can rightly be said that symmetry, gauge theories, and spontaneous symmetry breaking have been the three pegs upon which modern particle physics rests.
 * , "Quantum Field Theory: from QED to the Standard Model," The Cambridge History of Science: Volume 5, The Modern Physical and Mathematical Sciences (2003) ed.,, p. 388.


 * Back in the 1970s there was a simple dream about how physics would end. A unified theory would be found that incorporated quantum theory, general relativity, and the various particles and forces known to us. This would not only be a theory of everything, it would be unique. We would discover that there was only one mathematically consistent quantum theory that unified elementary particle physics with gravity. ...Because it was unique, this theory would have no free parameters—there would be no adjustable masses or charges. ...There would be only one scale, against which everything would be measured... the Planck scale. The theory would allow us to calculate the results of any experiment to whatever accuracy we desired. ...Looking back, it is clear that the assumption that a unified theory would be unique was no more than that—an assumption. ....we know that there can be no such theory.
 * Lee Smolin, Quantum Gravity (2000)


 * Our particular laws are not at all unique. ...they could change from place to place and from time to time. The Laws of Physics are much like the weather... controlled by invisible influences in space almost the same way as that temperature, humidity, air pressure, and wind velocity control how rain and snow and hail form. ...The Landscape... is the space of possibilities... all the possible environments permitted by the theory. ...[T]heoretical physicists ...have always believed that the laws of nature are the unique, inevitable consequence of some elegant mathematical principle. ...the empirical evidence points much more convincingly to the opposite conclusion. The universe has more in common with a Rube Goldberg machine than with a unique consequence of mathematical symmetry. ...Two key discoveries are driving the paradigm shift—the success of inflationary cosmology and the existence of a small cosmological constant.
 * Leonard Susskind, The Cosmic Landscape: String Theory and the Illusion of Intelligent Design (2005) pp. 12-13.

The foundation of my argument is the assumption that there exists an external physical reality independent of us humans. ...Our most successful theories, such as general relativity and quantum mechanics, describe only parts of this reality... In contrast, the holy grail of theoretical physics is a theory of everything—a complete description of reality.
 * I will... argue that... our universe is not just described by mathematics—it is mathematics. ...this hypothesis... should... be useful in narrowing down what an ultimate theory of everything can look like.
 * Max Tegmark, "Shut up and calculate" (Sep 25, 2007) arXiv:0709.4024


 * If we assume that reality exists independently of humans, then for a description to be complete, it must also be well-defined according to non-human entities—aliens or supercomputers, say—that lack any understanding of human concepts. Put differently, such a description must be expressible in a form that is devoid of any human baggage like “particle”, “observation” or other English words.
 * Max Tegmark, "Shut up and calculate" (Sep 25, 2007) arXiv:0709.4024


 * The true mathematical structure isomorphic to our world, if it exists, has not been found.
 * Max Tegmark, "The Mathematical Universe" (Oct 8, 2007) arXiv:0704.0646

If a future physics textbook contains the TOE, then its equations are the complete description of the mathematical structure that is the external physical reality. ...is rather than corresponds to...If our external physical reality is isomorphic to a mathematical structure, it therefore fits the definition of being a mathematical structure.
 * We need to distinguish between two different ways of viewing the external physical reality: the outside view or bird perspective of a mathematician studying the mathematical structure and the inside view or frog perspective of an observer living in it. ...a mathematical structure is an abstract, immutable entity existing outside of space and time. If history were a movie, the structure would therefore correspond not to a single frame of it but to the entire videotape. ...
 * Max Tegmark, "The Mathematical Universe" (Oct 8, 2007) arXiv:0704.0646


 * We are at the end of our extensive journey into the heart of matter. It has been marked as a relentless march toward Unity. As physics progressed, intimate connections were discovered between phenomena once thought to be completely distinct. A unified description of Nature, sometimes referred to a bit pompously as "the theory of everything," has become the holy grail of modern physics. Symmetry has constantly and reliably guided the physicists' first hesitant steps in this quest for Unity. ...becoming increasingly abstract. ...Now scientists routinely deal with "matter-light symmetry."
 * Trinh Zuan Thuan, Chaos and Harmony (2001)

Are we about to reach the goal? ...I am not convinced. It is, for the time being... to be verified experimentally, since it would require phenomenal energies. ...protons have displayed a longevity surpassing initial predictions. ...the unification of everything is predicted at energies that defy human imagination... the theory is shrouded in such a thick mathematical veil that it no longer has any connection with reality. ...as long as physics is not rooted in reality, it is no more than metaphysics.
 * The theory of superstrings... described the world as a vast symphony of vibrations of infinitesimal strings in a 10-dimensional spade-time. The world would then be governed by a single superforce, melding all four currently known forces, and whose rule would extend over the entire universe.
 * Trinh Zuan Thuan, Chaos and Harmony (2001)


 * It is possible that when we finally understand how particles and forces behave at energies up to 1018 GeV, we will just find new mysteries, with a final unification as far away as ever. But I doubt it. There are no hints of any fundamental energy scale beyond 1018 GeV, and string theory even suggests that higher energies have no meaning.
 * Steven Weinberg, (quote from p. 11)


 * I feel that we are so close with string theory that—in my moments of greatest optimism—I imagine that any day, the final form of the theory may drop out of the sky and land in someone's lap. But more realistically, I feel that we are now in the process of constructing a much deeper theory than anything we have had before and that well into the twenty-first century, when I am too old to have any useful thoughts on the subject, younger physicists will have to decide whether we have in fact found the final theory.
 * Edward Witten, Interview (March 4, 1998), as quoted by Brian Greene, The Elegant Universe (1999) Ch. 15 Prospects.