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A theory of everything (TOE or ToE), final theory, ultimate theory, or master theory is a hypothetical single, all-encompassing, coherent theoretical framework of physics that fully explains and links together all physical aspects of the universe. Finding a TOE is one of the major unsolved problems in physics. String theory and M-theory
have been proposed as theories of everything. Over the past few
centuries, two theoretical frameworks have been developed that,
together, most closely resemble a TOE. These two theories upon which all
modern physics rests are general relativity and quantum mechanics. General relativity is a theoretical framework that only focuses on gravity
for understanding the universe in regions of both large scale and high
mass: stars, galaxies, clusters of galaxies, etc. On the other hand,
quantum mechanics is a theoretical framework that only focuses on three
non-gravitational forces for understanding the universe in regions of
both small scale and low mass: sub-atomic particles, atoms, molecules,
etc. Quantum mechanics successfully implemented the Standard Model that describes the three non-gravitational forces – strong nuclear, weak nuclear, and electromagnetic force – as well as all observed elementary particles.
General relativity and quantum mechanics have been thoroughly
proven in their separate fields of relevance. 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. However, the two theories are considered incompatible in regions of extremely small scale – the Planck scale
– such as those that exist within a black hole or during the beginning
stages of the universe (i.e., the moment immediately following the Big Bang).
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: the TOE
is a single theory that, in principle, is capable of describing all
phenomena in the universe.
In pursuit of this goal, quantum gravity has become one area of active research. One example is string theory, which evolved into a candidate for the TOE, but not without drawbacks (most notably, its lack of currently testable predictions) and controversy. String theory posits that at the beginning of the universe (up to 10−43
seconds after the Big Bang), the four fundamental forces were once a
single fundamental force. According to string theory, every particle in
the universe, at its most microscopic level (Planck length),
consists of varying combinations of vibrating strings (or strands) with
preferred patterns of vibration. String theory further claims that it
is through these specific oscillatory patterns of strings that a
particle of unique mass and force charge is created (that is to say, the
electron is a type of string that vibrates one way, while the up quark is a type of string vibrating another way, and so forth).
Name
Initially, the term theory of everything was used with an ironic reference to various overgeneralized theories. 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". Physicist Harald Fritzsch used the term in his 1977 lectures in Varenna. Physicist John Ellis claims to have introduced the term into the technical literature in an article in Nature in 1986. Over time, the term stuck in popularizations of theoretical physics research.
Historical antecedents
Antiquity to 19th century
Ancient Babylonian astronomers studied the pattern of the Seven Classical Planets against the background of stars, with their interest being to relate celestial movement to human events (astrology),
and the goal being to predict events by recording events against a time
measure and then look for recurrent patterns. The debate between the
universe having either a beginning or eternal cycles can be traced back to ancient Babylonia.
The natural philosophy of atomism appeared in several ancient traditions. 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. The concept of 'atom' proposed by Democritus was an early philosophical attempt to unify phenomena observed in nature. The concept of 'atom' also appeared in the Nyaya-Vaisheshika school of ancient Indian philosophy.
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.
Following earlier atomistic thought, 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 not all
forces in nature result from things coming into contact. Newton's work
in his Mathematical Principles of Natural Philosophy dealt with this in a further example of unification, in this case unifying Galileo's work on terrestrial gravity, Kepler's laws of planetary motion and the phenomenon of tides by explaining these apparent actions at a distance under 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.
— Essai philosophique sur les probabilités, Introduction. 1814
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 has to be amended: a theory of
everything must include gravitation and quantum mechanics. Even ignoring
quantum mechanics, chaos theory is sufficient to guarantee that the future of any sufficiently complex mechanical or astronomical system is unpredictable.
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. 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.
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".
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 these last few
decades of his life, this quixotic quest isolated Einstein from the
mainstream of physics.
Understandably, the mainstream was instead far
more excited about the newly 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, Theodor Kaluza, Oskar Klein (see Kaluza–Klein theory),
and most notably, Albert Einstein and his collaborators. Einstein
intensely searched for, but ultimately failed to find, a unifying
theory.
More than a half a century later, Einstein's dream of discovering a
unified theory has become the Holy Grail of modern physics.
Late 20th century and the nuclear interactions
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 1967–68 by Sheldon Glashow, Steven Weinberg, and Abdus Salam into the "electroweak" force.
Electroweak unification is a broken symmetry: the electromagnetic and weak forces appear distinct at low energies because the particles carrying the weak force, the W and Z bosons, have non-zero masses of 80.4 GeV/c2 and 91.2 GeV/c2, whereas the photon, which carries the electromagnetic force, is massless. At higher energies Ws and Zs can be created easily and the unified nature of the force becomes apparent.
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' – 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 fundamental interactions of nature: gravitation, strong interaction, weak interaction, and electromagnetism. Because the weak interaction can transform elementary particles
from one kind into another, the TOE should also yield a deep
understanding of the various different kinds of possible particles. The
usual assumed path of theories is given in the following graph, where
each unification step leads one level up:
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 Planck energy, roughly 1019 GeV.
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 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).
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.
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 yet. 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.
A surprising property of string/M-theory
is that extra dimensions are required for the theory's consistency. In
this regard, string theory can be seen as building on the insights of
the Kaluza–Klein theory,
in which it was realized that applying general relativity to a
five-dimensional universe (with one of them small and curled up) looks from the four-dimensional perspective like the usual general relativity together with Maxwell's electrodynamics. 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 four-dimensional spacetime, an idea that has been
realized with explicit stringy mechanisms.
Research into string theory has been encouraged by a variety of
theoretical and experimental factors. On the experimental side, the
particle content of the standard model supplemented with neutrino masses fits into a spinor representation of SO(10), a subgroup of E8 that routinely emerges in string theory, such as in heterotic string theory or (sometimes equivalently) in F-theory. String theory has mechanisms that may explain why fermions come in three hierarchical generations, and explain the mixing rates between quark generations. On the theoretical side, it has begun to address some of the key questions in quantum gravity, such as resolving the black hole information paradox, counting the correct entropy of black holes and allowing for topology-changing processes. It has also led to many insights in pure mathematics and in ordinary, strongly-coupled gauge theory due to the Gauge/String duality.
In the late 1990s, it was noted that one major hurdle in this
endeavor is that the number of possible four-dimensional universes is
incredibly large. The small, "curled up" extra dimensions can be compactified in an enormous number of different ways (one estimate is 10500 ) each of which leads to different properties for the low-energy particles and forces. This array of models is known as the string theory landscape.
One proposed solution is that many or all of these possibilities
are realised in one or another of a huge number of universes, but that
only a small number of them are habitable. Hence what we normally
conceive as the fundamental constants of the universe are ultimately the
result of the anthropic principle rather than dictated by theory. This has led to criticism of string theory, arguing that it cannot make useful (i.e., original, falsifiable, and verifiable) predictions and regarding it as a pseudoscience. Others disagree, and string theory remains an active topic of investigation in theoretical physics.
Loop quantum gravity
Current research on loop quantum gravity may eventually play a fundamental role in a TOE, but that is not its primary aim. 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. 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.
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.
Other attempts
Among other attempts to develop a theory of everything is the theory of causal fermion systems, giving the two current physical theories (general relativity and quantum field theory) as limiting cases.
Another theory is called Causal Sets.
As some of the approaches mentioned above, its direct goal isn't
necessarily to achieve a TOE but primarily a working theory of quantum
gravity, which might eventually include the standard model and become a
candidate for a TOE. Its founding principle is that spacetime is
fundamentally discrete and that the spacetime events are related by a partial order. This partial order has the physical meaning of the causality relations between relative past and future distinguishing spacetime events.
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.
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 gauge symmetry of the Standard Model of particle physics, U(1)×SU(2)×SU(3), with the three Reidemeister moves of knot theory by equating each elementary particle to a different tangle of one, two, or three strands (selectively a long prime knot or unknotted curve, a rational tangle, or a braided tangle respectively).
Another attempt may be related to ER=EPR, a conjecture in physics stating that entangled particles are connected by a wormhole (or Einstein–Rosen bridge).
Present status
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. Most particle physicists expect that the outcome of the ongoing experiments – the search for new particles at the large particle accelerators and for dark matter – are needed in order to provide further input for a TOE.
Arguments against
In parallel to the intense search for a TOE, various scholars have seriously debated the possibility of its discovery.
Gödel's incompleteness theorem
A number of scholars claim that Gödel's incompleteness theorem
suggests that any attempt to construct a TOE is 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.
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.
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."
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."
Jürgen Schmidhuber (1997) has argued against this view; he points out that Gödel's theorems are irrelevant for computable physics. 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 at all prevent formal TOEs describable by very few bits of information.
Related critique was offered by Solomon Feferman, among others. Douglas S. Robertson offers Conway's game of life as an example:
The underlying rules are simple and complete, but there are formally
undecidable questions about the game's behaviors. Analogously, it may
(or may not) be possible to completely state the underlying rules of
physics with a finite number of well-defined laws, but there is little
doubt that there are questions about the behavior of physical systems
which are formally undecidable on the basis of those underlying laws.
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. 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. 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 gauge symmetry and the number of dimensionless physical constants, the theories are becoming simpler. If this is the case, the process of simplification cannot continue indefinitely.
Lack of fundamental laws
There is a philosophical debate within the physics community as to whether a theory of everything deserves to be called the fundamental law of the universe. One view is the hard reductionist
position that the TOE is the fundamental law and that all other
theories that apply within the universe are a consequence of the TOE.
Another view is that emergent laws, which govern the behavior of complex systems, should be seen as equally fundamental. Examples of emergent laws are the second law of thermodynamics and the theory of natural selection.
The advocates of emergence argue that emergent laws, especially those
describing complex or living systems are independent of the low-level,
microscopic laws. In this view, emergent laws are as fundamental as a
TOE.
The debates do not make the point at issue clear. Possibly the
only issue at stake is the right to apply the high-status term
"fundamental" to the respective subjects of research. A well-known
debate over this took place between Steven Weinberg and Philip Anderson.
Impossibility of being "of everything"
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. 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,
apart from the pure intellectual satisfaction of completing a
centuries-long quest, is that prior examples of unification have
predicted new phenomena, some of which (e.g., electrical generators)
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. This would imply an infinite sequence of physical theories.
Impossibility of calculation
Weinberg
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.
