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.
Over the past few centuries, two theoretical
frameworks have been developed that, as a
whole, most closely resemble a TOE.
These two theories upon which all modern physics
rests are general relativity (GR) and quantum
field theory (QFT).
GR 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, QFT 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.
QFT successfully implemented the Standard
Model and unified the interactions (so-called
Grand Unified Theory) between the three non-gravitational
forces: strong, weak, and electromagnetic
force.Through years of research, physicists
have experimentally confirmed with tremendous
accuracy virtually every prediction made by
these two theories when in their appropriate
domains of applicability.
In accordance with their findings, scientists
also learned that GR and QFT, as they are
currently formulated, are mutually incompatible
– they cannot both be right.
Since the usual domains of applicability of
GR and QFT are so different, most situations
require that only one of the two theories
be used.
As it turns out, this incompatibility between
GR and QFT is apparently only an issue in
regions of extremely small scale and high
mass, 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 this conflict, a theoretical framework
revealing a deeper underlying reality, unifying
gravity with the other three interactions,
must be discovered to harmoniously integrate
the realms of GR and QFT into a seamless whole:
a single theory that, in principle, is capable
of describing all phenomena.
In pursuit of this goal, quantum gravity has
become an area of active research.
Eventually, string theory evolved into a candidate
for the ultimate theory of the universe, but
not without drawbacks 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).
== Historical antecedents ==
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 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.
=== From ancient Greece to Einstein ===
In ancient Greece, 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', introduced by Democritus,
was an early philosophical attempt to unify
all phenomena observed in nature.
Archimedes was possibly the first scientist
known to have described nature with axioms
(or principles) and then deduce new results
from them.
He thus tried to describe "everything" starting
from a few axioms.
Any "theory of everything" is similarly expected
to be based on axioms and to deduce all observable
phenomena from them.Following Democritean
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 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.
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.
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.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.
(But see:Einstein–Maxwell–Dirac equations.)
More than a half a century later, Einstein's
dream of discovering a unified theory has
become the Holy Grail of modern physics.
=== Twentieth 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 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 provides an attempt of identifying
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.
For example, no candidate theory 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.
== Philosophy ==
The philosophical implications of a physical
TOE are frequently debated.
For example, if philosophical physicalism
is true, a physical TOE will coincide with
a philosophical theory of everything.
The "system building" style of metaphysics
attempts to answer all the important questions
in a coherent way, providing a complete picture
of the world.
Aristotle is the first and most noteworthy
philosopher to have attempted such a comprehensive
system in his Metaphysics.
While Aristotle made important contributions
to all the sciences in terms of his method
of logic and his first principle of causality,
he was later demonized by later modern philosophers
of the Enlightenment like Immanuel Kant who
criticized him for his idea of God as first
cause.
Isaac Newton and his Mathematical Principles
of Natural Philosophy constituted the most
all encompassing attempt at a theory of everything
up until the twentieth century and Albert
Einstein's General Theory of Relativity.
After David Hume's attacks upon the inductive
method utilized in all the sciences, the German
Idealists such as Kant and G.W.F.
Hegel - and the many philosophical reactions
they inspired - took a decided turn away from
natural philosophy and the physical sciences
and focused instead on issues of perception,
cognition, consciousness and ultimately language.
== 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 expressive enough for
elementary arithmetical facts to be expressed
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, 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.
=== 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.
== See also
