Theory of everything

A theory of everything (or ToE for its acronym in English, Theory of Everything) is a hypothetical theory of theoretical physics that it would explain and connect into a unified theoretical scheme the fundamental physical interactions. Initially, the term was used with an ironic connotation, to refer to various overgeneralized theories. It was later popularized in quantum physics by describing several theoretical proposals that could unify or explain through a consistent model all the fundamental interactions found in quantum field theory. Other terms, not quite synonymous, used to refer to the same concept are unified theory, grand unified theory, unified field theory, and unified field theory.

One could conceive an intellect that at any given moment knew all the forces that animate the nature and positions of the beings that make up it; if this intellect were vast enough to subject the data to analysis, it could condense in a simple formula the movement of the great bodies of the universe and of the lightest atom; for such intellect nothing could be uncertain and the future as well as the past would be in front of their eyes.

Pierre-Simon Laplace

The concept of a "theory of everything" it is rooted in the principle of causality and its discovery is the enterprise of bringing us closer to seeing through the eyes of Laplace's demon. Although said possibility can be considered as deterministic, in a "simple formula" can fundamentally probabilistic physics still survive, as some current quantum mechanical positions propose. This is because even if the mechanisms that govern the particles are intrinsically random, we can know the rules that govern that randomness and calculate the probabilities of occurrence for each possible event. However, other interpretations of the Schrödinger equation give little importance to chance: it would only have importance within the atom and would be diluted in the macroscopic world. Others, however, completely deny it and consider it a wrong interpretation of quantum laws. Consequently, the greatest difficulty in discovering a unified theory has been to correctly harmonize laws that govern only a small area of nature and transform them into a single theory that explains it in its entirety, both in its microscopic and macroscopic world and explains the existence of all fundamental interactions: the gravitational, electromagnetic, strong nuclear, and weak nuclear forces.

During the 20th century, there were numerous theories of everything proposed by theoretical physicists. Until now, none have been able to pass an experimental test, they have had tremendous difficulties for their theories to have stable experimental results. The first problem in producing a theory of everything is that accepted theories, such as quantum mechanics and general relativity, are radically different in their descriptions of the universe: simple ways of combining them quickly lead to "renormalization"; of the problem, where the theory does not give us finite results for quantitative experimental data.

Historical background

Since the time of the ancient Greeks, philosophers have speculated that the apparent diversity of appearances conceals an underlying unity, and therefore that the list of forces may be shortened, indeed may have only one entry. For example, the mechanical philosophy of the 17th century proposed that all forces could ultimately be reduced to a contact force between small particles. solid. This was abandoned after the acceptance of long-distance gravitational forces proposed by Isaac Newton; but at the same time Newton's work on his Principia provided the first dramatic empirical evidence for the unification of forces that at the time seemed different: Galileo's work on terrestrial gravitation, Kepler's laws of planetary motion and tidal phenomena were all quantitatively explained by a simple law, called universal gravitation.

In 1820, Hans Christian Oersted discovered a connection between electricity and magnetism; many decades of work culminated in James Clerk Maxwell's theory of electromagnetism. Also during the 19th and 20th centuries, many examples of contact forces, elasticity, viscosity, friction, pressure - the results of electrical interactions between very small particles of matter - gradually appeared. In the late 1920s, the new quantum mechanics showed that chemical bonds between atoms were examples of electrical (quantum) forces, corroborating Dirac's boast that "the underlying physical laws necessary for a mathematical theory for a large part of physics and all of chemistry [already] are completely known". It was therefore a question of associating these fundamental forces in a single totalizing model that would effectively explain complex interactions of apparently diverse and uncorrelated forces.

Attempts to unify gravity with magnetism date back to the 1849-50 experiments of Michael Faraday. After Einstein's theory of gravitation (general relativity) published in 1915, the search for a unified field theory combining gravity with electromagnetism it became more serious. At the same time, it became plausible to say that no more fundamental forces existed. Prominent contributions were made by Gunnar Nordstrom, Hermann Weyl, Arthur Eddington, Theodor Kaluza, Oskar Klein, and most notably by Einstein and his associates. None of these proposals was successful.

The search was interrupted by the discovery of the weak and strong forces, which could not be aggregated into gravity or electromagnetism. Another obstacle was the acceptance that quantum mechanics had to be incorporated from the start, it did not emerge as a consequence of the deterministic unified theory, as Einstein expected. Gravity and Electromagnetism can always coexist peacefully as types of Newtonian forces, but for many years it has been observed that gravity cannot be incorporated into the quantum picture, leaving it alone to unify with other fundamental forces. For this reason this unification work in the 20th century focused on understanding the three "quantum": electromagnetism and the weak and strong nuclear forces. The first two were unified in 1967-8 by Sheldon Glashow, Steven Weinberg, and Abdus Salam. The strong and electroweak forces coexist in the Standard Model of particles, but remain distinct. Many unified theories (or GUTs for its acronym in English) have been proposed to unify them. Although the simplicity of GUTs has been ruled out in experience, the general idea, especially when linked to supersymmetries, remains firmly in favor of the theoretical physics community.

Theory of Everything in Modern Physics

In current mainstream physics, the Theory of Everything could unify all the fundamental interactions of nature, which are considered as four: gravitation, the strong nuclear force, the weak nuclear force, and the electromagnetic. Since the weak force can transform elementary particles from one class to another, the theory of everything should produce a deep understanding of several different types of particles, as well as different forces. The predictable pattern of the theories is as follows:

In addition to the forces listed here, modern cosmology requires an inflationary force, dark energy, and also dark matter composed of fundamental particles outside the Standard Model scene.

The electroweak unification is a broken symmetry: electromagnetism and the weak force seem to be distinguished at low energies because the particles bring weak forces, the W and Z bosons have the mass of about 100 GeV/c², while the photon, which brings the electromagnetic force, has no mass. At high energies the W and Z bosons can easily create mass and the unified nature of the forces appears. Grand unification theory is expected to operate in a similar way, but energies on the order of 10¹⁶ GeV or much higher cannot be achieved by any particle accelerator on Earth. By analogy, the unification of the GUT forces with gravity is expected to be at a Planck energy, around 10¹⁹ GeV.

It might be premature to be looking for the theory of everything when there is no direct evidence for an electronuclear force and while there are many different proposals for GUTs in any case. Indeed the deliberate name is wrapped in Hubris. However, many physicists believe that unification is possible, due in part to the history of convergence towards the same theory. Supersymmetry looks plausible not only because of its "beauty" theoretical, but for its naturalness in producing large amounts of dark matter, and the inflationary force can be related to physical GUT (although it does not seem to be an inevitable part of the theory). And now GUTs are clearly not the final answer. Both the current standard model and the GUT proposal are quantum field theories that require the technical problem of renormalizing responses to sensitive fields. It is usual to take this as a sign that there is only one effective field theory omitting crucial phenomena only at very high energies. Furthermore, the inconsistency between quantum mechanics and general relativity implies that one of the two must be replaced by a theory that incorporates quantum gravity.

The only leading candidate for a theory of everything at the moment is superstring theory. Ongoing research on loop quantum gravity may eventually play a fundamental role in the theory of everything, but this is not the main goal. These theories try to deal with the renormalization problem by setting some to the lower limit of possible length scales. Superstring theory and supergravity (both believed to be special cases of an undefined theory M) assume that the universe actually has more dimensions than can be seen with the naked eye: three spatial and one temporal. The motivation behind this approach begins with the Kaluza-Klein theory, where it was noted that by applying general relativity in a 5-dimensional universe (one dimension plus a small folding dimension) it maintained the equivalent to general relativity, of 4 dimensions, with Maxwell's laws of electromagnetism (also in 4 dimensions). This has given rise to efforts to work with many-dimensional theories in which it is hoped that equations that are similar to those known in physics can be produced. The notion of extra dimensions also helps to solve the hierarchy problem, where the question of why gravity is weaker than any other force. The common answer says that gravity would be in an extra dimension to the other forces.

In the late 1990s it was noted that one of the problems with having many candidate theories of everything (but particularly with string theory) was that they did not contain the characteristics of predicting the universe. For example, many theories of quantum gravity can create universes with an arbitrary number of dimensions or with arbitrary cosmological constants. Even the "standard" 10-dimensional string theory allows the "spiralated" be compacted into many different paths (an estimate is 10⁵⁰⁰ where each corresponds to different collections of fundamental particles and low energy forces).

A speculative solution is that many of these possibilities are realizable in one or other of the possible universes, but only a small number of them are habitable, and therefore the fundamental universal constants are ultimately the result of an anthropic principle. as a consequence of a theory of everything. This anthropic approach is clearly criticized in that, as the theory is flexible enough to cover almost any observation, it could not make useful predictions (such as original, false or verifiable). From this point of view, string theory could be considered as pseudoscience, where an unfalsifiable theory is constantly adapted so that experimental results conform to it.

Expected Predictions of the Theory of Everything

There are several phenomena that a theory of everything should be able to explain:

• Contingent parameters. Although quantum theories of the electrodebil and strong interactions, they give phenomenologically correct descriptions and make valuable predictions, they contain a series of numerical parameters for whose value the theory itself gives more explanation and should be determined by experiment (although actually a broader theory might show that its value is not arbitrary). A theory of the whole could explain those parameters and predict their value from more fundamental parameters or relationships.
• The jars of general relativity. A theory of all should explain phenomena such as the Big Bang or the nature of the time-space singularities that the theories of general relativity and quantum mechanics do not explain.
• Philosophical satisfaction. The theoretical and philosophical motivations to find a theory of all include the Platonic belief that the ultimate nature of the Universe is simple and that the current models of Universe such as the standard model cannot be completed because they are too complex.

Outline Theories of Everything

Two theories have recently emerged that could one day evolve into the aforementioned unified theory. One is M-Theory, a variant of string theory based on 11-dimensional space. The second is the so-called loop quantum theory, which postulates that space-time itself would be dimensionally quantized, something that has not yet been proven.

Theory of Everything in Philosophy

The status of physics in the ToE is open to philosophical debate. For a moment, if the physical is true, a physical theory of everything could coincide with a philosophical theory of everything. Some philosophers—Aristotle, Plato, Hegel, Whitehead—have tried to build all-encompassing systems. Others have had great doubts about the great possibility of being a simple exercise.

Relation to Gödel's incompleteness theorem

A small number of scientists suggest that Gödel's incompleteness theorem implies that any attempt to construct a theory of everything is bound to fail. Gödel's theorem says that any sufficiently complex mathematical theory is either inconsistent or incomplete. Stanley Jaki pointed out in his 1966 book "The Relevance of Physics" that any theory of everything must be a consistently non-trivial mathematical theory, so it must be incomplete. Jaki therefore considers that this fact ruins a genuine deterministic theory of everything Freeman Dyson for his part has stated that:

Gödel's theorem implies that pure mathematics is not exhaustive. No matter how many problems you can solve, there will always be other problems that cannot be solved by existing rules. [...] because of Gödel's theorem, physics is not exhaustive either. The laws of physics are finite setups of rules and include rules to make mathematics, so that the Gödel theorem applies to them.

Freeman DysonNYRB, May 13, 2004

Many have interpreted this quote to support Jaki's position.

Stephen Hawking was originally a believer in a Theory of Everything, but after considering Gödel's theorem, he concluded that it could not be obtained.

Many people will be very upset if there is no last theory, that can formulate a finite number of principles. I used to belong to that camp, but I've changed my mind.

Stephen HawkingGödel and the end of physics, July 20, 2002

This view has been argued against by Solomon Feferman and others.

Many scientists and mathematicians believe that Gödel's theorem is completely irrelevant when discussing the theory of everything. Gödel's theorem is a statement about which theorems eventually would result in mathematical systems, where "eventually" means after an arbitrary time. Gödel's theorem does not prevent a mathematician from computing what happens after any amount of time, or does not prevent a person who knows the rules from doing the calculations. All that Gödel's theorem says is that, even knowing all the rules, it would be impossible to predict what new patterns the rules will eventually produce.

To illustrate, consider Conway's book Game of Life. This cellular automaton is complete, meaning that a variation of Gödel's argument shows that the long-term behavior of the automaton could not be predicted from an arbitrary initial configuration. And therefore, a hypothetical creature that lived within the game of life could know all the rules. The rules of the automaton are the theory of everything, and it is known even to the creatures inside the automaton.

Current Perspectives on the Theory of Everything

No physical theory at the moment is believed to be precisely accurate. Instead, physics has proceeded by series of "successive approximations" allowing increasingly accurate predictions on a wide range of phenomena. Many physicists believe that there are many errors in confusing theoretical models with the real nature of reality and maintain that the series of approximations will never end in "truth". Einstein himself expressed his view at times.From his point of view, we can reasonably expect for "a" suffrage. theory of everything where consistent -in itself- incorporates all currently known forces, but we should not wait to have the final answer. Instead, he was open to the view that despite the apparent mathematical complexity in each theory, in a deep sense associated with its underlying Gaugian symmetry and the number of universal physical constants, the theories will simplify. If that happens, the simplification process cannot continue indefinitely.

There is a philosophical debate within the physics community as to whether or not a theory of everything exists and whether it should be called "la" fundamental law of the universe. One option is the hard reductionist position that the theory of everything is the fundamental law and that all other theories that apply in the universe are a consequence of the law of everything. Another view is that emergent laws (called 'free-floating laws' by Steven Weinberg) where behavior of complex systems governs should be equally fundamental. Examples are the second law of thermodynamics and the theory of natural selection. Point begins that across our universe those laws describe systems whose behavior can ("in principle") be predicted by a ToE, which will also be realized in a universe with different low-level laws, subject only to some very special conditions. Therefore it is not helpful, even in principle, to invoke a low level of laws to discuss the behavior of complex systems. Some argue that this attitude could violate Occam's Razor if the formulation of the theory of everything is completely valid. If it is not clear that there is any point at issue in this debate (for example between Steven Weinberg and Phillip Anderson that there is no right to apply the word "fundamental" that respects the issues of interest).

Although the name "theory of everything" suggest Laplace's quoted determinism, it gives a very misleading impression. Determinism is frustrated by the natural probability of quantum mechanical predictions, by the extreme sensitivity to initial conditions that lead to mathematical chaos, and by the extreme mathematical difficulty of applying it to theory. Thus, although the modern Standard Model of particle physics "in principle" predict all known non-gravitational phenomena, in practice only a few results have been derived from a complete theory (for example: the masses of some of the simple hadrons) and those results (especially the particle masses where most relevant for high energy physics) are less precise than current experimental measurements. A true theory of everything could hardly be applied. The main reason to investigate a ToE, apart from the sheer satisfaction of completing a century of searching, is that all the unifications successfully predict new phenomena, many of them (eg electric generators) have proven their great practical importance. As in other cases of reduction theories, the theory of everything could also allow us to define with certainty the domain of validity and the residual error of high-energy approximations for a complete theory from which practical calculations can be obtained.