On the other hand, quantum mechanics is a theoretical framework that focuses primarily on three non-gravitational forces for understanding the universe in regions of both very small scale and low mass: subatomic particles, atoms, and molecules.
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.
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.
For example, a grandfather of Ijon Tichy – a character from a cycle of Stanisław Lem's science fiction stories of the 1960s – was known to work on the "General Theory of Everything".
[10] Physicist John Ellis claims[11] to have introduced the acronym "TOE" into the technical literature in an article in Nature in 1986.
In ancient Greek philosophy, the pre-Socratic philosophers speculated that the apparent diversity of observed phenomena was due to a single type of interaction, namely the motions and collisions of atoms.
[20] Newton achieved the first great unification in physics, and he further is credited with laying the foundations of future endeavors for a grand unified theory.
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 second great unification in physics.
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.
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,[25] Theodor Kaluza, Oskar Klein (see Kaluza–Klein theory), and most notably, Albert Einstein and his collaborators.
In the 20th century, the search for a unifying theory was interrupted by the discovery of the strong and weak nuclear forces, which differ both from gravity and from electromagnetism.
While the strong and electroweak forces coexist under the Standard Model of particle physics, they remain distinct.
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.
This is usually regarded as a sign that these are only effective field theories, omitting crucial phenomena relevant only at very high energies.
[6] The final step in the graph requires resolving the separation between quantum mechanics and gravitation, often equated with general relativity.
Furthermore, cosmological experiments also suggest the existence of dark matter, supposedly composed of fundamental particles outside the scheme of the standard model.
This lent credence to the idea of unifying 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.
[40] Current research on loop quantum gravity may eventually play a fundamental role in a theory of everything, but that is not its primary aim.
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.
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 model was expressly generalized for an infinite number of generations and for the weak force bosons (but not for photons or gluons) in a 2008 paper by Bilson-Thompson, Hackett, Kauffman and Smolin.
Causal dynamical triangulation does not assume any pre-existing arena (dimensional space), but rather attempts to show how the spacetime fabric itself evolves.
[46] 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.
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.
[50] In 2000, Schmidhuber explicitly constructed limit-computable, deterministic universes whose pseudo-randomness based on undecidable, Gödel-like halting problems is extremely hard to detect but does not prevent formal theories of everything describable by very few bits of information.
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".