The Theory of Everything (TOE) refers to the attempted unification of several major theories of physics.

The four basic forces of nature are gravity, the strong nuclear force, the nuclear weak force, and the electromagnetic force. The theory of general relativity explains gravity, and quantum mechanics explains the other three forces. Right now, no one theory that everyone accepts can explain all four forces. String theory is a theory that could become the ‘theory of everything.’

The primary problem in producing a TOE is that general relativity and quantum mechanics are hard to unify. This is one of the unsolved problems in physics. Initially, the term ‘theory of everything’ was used with an ironic connotation to refer to various overgeneralized theories. Over time, the term stuck in popularizations of quantum physics to describe a theory that would unify or explain through a single model the theories of all fundamental interactions and of all particles of nature: general relativity for gravitation, and the standard model of elementary particle physics — which includes quantum mechanics — for electromagnetism, the two nuclear interactions, and the known elementary particles.

Archimedes was possibly the first scientist to describe nature with axioms (or principles) and then to deduce new results from them. He thus tried to describe ‘everything’ starting from a few axioms. Also the concept of ‘atom,’ introduced by Democritus, realized an aspect of unification: the concept unified all phenomena observed in nature as the motion of atoms. As part of the atomistic model of nature, already in ancient Greek times philosophers speculated that the apparent diversity of observed phenomena was due to a single type of interaction, namely the collisions of atoms. Following atomism, the mechanical philosophy of the 17th century posited that all forces could be ultimately reduced to contact forces between the atoms, then imagined as tiny solid particles.

In the late 17th century, Isaac Newton’s description of the long-distance force of gravity implied that the idea of exclusively contact forces in nature had to be amended. Nevertheless, Newton’s work in his Principia provided an example of unification on its own: the work unified Galileo’s work on terrestrial gravity, Kepler’s laws of planetary motion and the phenomenon of tides by explaining them with one single law: the law of universal gravitation.

In 1814, building on these results, Laplace famously suggested that a sufficiently powerful intellect could, if it knew the position and velocity of every particle at a given time, along with the laws of nature, calculate the position of any particle at any other time:

‘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.’

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

In 1820, Hans Christian Ørsted 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 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.’

After 1915, when Albert Einstein published the theory of gravity (general relativity), the search for a unified field theory combining gravity with electromagnetism started again with renewed intensity. At the time, it seemed plausible that no other fundamental forces exist. Einstein intensely searched for such a unifying theory during the last decades of his life. However, none of these attempts were successful.

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

Gravity and electromagnetism could always peacefully coexist as entries in a list of classical forces, but for many years it seemed that gravity could not even be incorporated into the quantum framework, let alone unified with the other fundamental forces. For this reason, work on unification, for much of the twentieth century, focused on understanding the three ‘quantum’ forces: electromagnetism and the weak and strong forces. The first two were combined in 1967 into the ‘electroweak’ force.

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

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 far greater than could be reached by any possible Earth-based particle accelerator.

Although the simplest GUTs have been experimentally ruled out, the general idea, 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).

Since the 1990s, many physicists believe that 11-dimensional M-theory, which is described in many sectors by matrix string theory, in many other sectors by perturbative string theory, is the theory of everything. However, there is no widespread consensus on this issue, because M-theory and superstring theory is not a completed theory but rather an approach for producing one.

String theories and supergravity (both believed to be limiting cases of the yet-to-be-defined M-theory) suppose that the universe actually has more dimensions than the easily observed three of space and one of time. The motivation behind this approach began with the Kaluza-Klein theory in which it was noted that applying general relativity to a five dimensional universe (with the usual four dimensions plus one small curled-up dimension) yields the equivalent of the usual general relativity in four dimensions together with Maxwell’s equations (electromagnetism, also in four dimensions).

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

In the late 1990s, it was noted that one problem with several of the candidates for theories of everything (but particularly string theory) was that they did not constrain the characteristics of the predicted universe. For example, many theories of quantum gravity can create universes with arbitrary numbers of dimensions or with arbitrary cosmological constants. Even the ‘standard’ ten-dimensional string theory allows the ‘curled up’ dimensions to be compactified in an enormous number of different ways, each of which corresponds to a different collection of fundamental particles and low-energy forces. This array of theories is known as the string theory landscape.

A speculative 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, 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. This anthropic approach is often criticized in that, because the theory is flexible enough to encompass almost any observation, it cannot make useful (i.e., original, falsifiable, and verifiable) predictions. In this view, string theory would be considered a pseudoscience, where an unfalsifiable theory is constantly adapted to fit the experimental results.

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