In physics, a unified field theory (UFT) is
a type of field theory that allows all that
is usually thought of as fundamental forces
and elementary particles to be written in
terms of a pair of physical and virtual fields.
According to the modern discoveries in physics,
forces are not transmitted directly between
interacting objects, but instead are described
and interrupted by intermediary entities called
fields.
Classically, however, a duality of the fields
is combined into a single physical field.
For over a century, unified field theory remains
an open line of research and the term was
coined by Albert Einstein, who attempted to
unify his general theory of relativity with
electromagnetism. The "Theory of Everything"
and Grand Unified Theory are closely related
to unified field theory, but differ by not
requiring the basis of nature to be fields,
and often by attempting to explain physical
constants of nature. Earlier attempts based
on classical physics are described in the
article on classical unified field theories.
The goal of a unified field theory has led
to a great deal of progress for future theoretical
physics and progress continues.
== Introduction ==
=== Fields ===
Governed by a global event
λ
{\displaystyle \lambda }
under the universal topology, an operational
environment is initiated by the scalar fields
ϕ
(
λ
)
∈
{
ϕ
+
(
x
^
,
λ
)
,
ϕ
−
(
x
ˇ
,
λ
)
}
{\displaystyle \phi (\lambda )\in \{\phi ^{+}({\hat
{x}},\lambda ),\phi ^{-}({\check {x}},\lambda
)\}}
of a rank-0 tensor, a differentiable function
of a complex variable in its domain at its
zero derivative, where a scalar function
ϕ
+
(
x
^
,
λ
)
⊂
Y
+
{\displaystyle \phi ^{+}({\hat {x}},\lambda
)\subset Y^{+}}
or
ϕ
−
(
x
ˇ
,
λ
)
⊂
Y
−
{\displaystyle \phi ^{-}({\check {x}},\lambda
)\subset Y^{-}}
is characterized as a single magnitude with
variable components of the respective coordinate
sets
x
^
{
x
0
,
x
1
,
⋯
}
{\displaystyle {\hat {x}}\{x^{0},x^{1},\cdots
\}}
or
x
ˇ
{
x
1
,
x
2
,
x
3
}
{\displaystyle {\check {x}}\{x_{1},x_{2},x_{3}\}}
.
Because a field is incepted or operated under
either virtual or physical primacy of an
Y
+
{\displaystyle Y^{+}}
or
Y
−
{\displaystyle Y^{-}}
manifold respectively and simultaneously,
each point of the fields is entangled with
and appears as a conjugate function of the
scalar field
ϕ
−
{\displaystyle \phi ^{-}}
or
ϕ
+
{\displaystyle \phi ^{+}}
in its opponent manifold. A field can be classified
as a scalar field, a vector field, or a tensor
field according to whether the represented
physical horizon is at a scope of scalar,
vector, or tensor potentials, respectively.
Therefore, at the scalar potentials, the effects
are stationary projected to and communicated
from their reciprocal opponent, shown as the
following conjugate pairs:
ϕ
+
(
x
^
,
λ
)
,
φ
−
(
x
ˇ
,
λ
)
{\displaystyle \phi ^{+}({\hat {x}}\,,\lambda
)\,,\varphi ^{-}({\check {x}}\,,\lambda )\qquad
}
:
φ
−
(
x
ˇ
,
λ
)
↦
ϕ
+
(
x
^
,
λ
)
∗
,
x
^
∈
Y
+
{\displaystyle \varphi ^{-}({\check {x}}\,,\lambda
)\mapsto \phi ^{+}({\hat {x}}\,,\lambda )^{*}\,,{\hat
{x}}\in Y^{+}}
ϕ
−
(
x
ˇ
,
λ
)
,
φ
+
(
x
^
,
λ
)
{\displaystyle \phi ^{-}({\check {x}}\,,\lambda
)\,,\varphi ^{+}({\hat {x}}\,,\lambda )\qquad
}
:
φ
+
(
x
^
,
λ
)
↦
ϕ
−
(
x
ˇ
,
λ
)
∗
,
x
ˇ
∈
Y
−
{\displaystyle \varphi ^{+}({\hat {x}}\,,\lambda
)\mapsto \phi ^{-}({\check {x}}\,,\lambda
)^{*}\,,{\check {x}}\in Y^{-}}
where * denotes a complex conjugate. A conjugate
field
ϕ
−
=
(
φ
+
)
∗
{\displaystyle \phi ^{-}=(\varphi ^{+})^{*}}
of the
Y
+
{\displaystyle Y^{+}}
scalar potential is mapped to a field in the
Y
−
{\displaystyle Y^{-}}
manifold, and vice versa that a conjugate
field
ϕ
+
=
(
φ
−
)
∗
{\displaystyle \phi ^{+}=(\varphi ^{-})^{*}}
of the
Y
−
{\displaystyle Y^{-}}
scalar potential is mapped to a field in the
Y
+
{\displaystyle Y^{+}}
manifold. In mathematics, if f(z) is a holomorphic
function restricted to the Real Numbers, it
has the complex conjugate properties of
f (z) = f *(z*), which leads to the above
equation when
x
^
∗
=
x
ˇ
{\displaystyle {\hat {x}}^{*}={\check {x}}}
is satisfied.
=== Forces ===
All four of the known fundamental forces are
mediated by fields, which in the Standard
Model of particle physics result from exchange
of gauge bosons. Specifically the four fundamental
interactions to be unified are:
Strong interaction: the interaction responsible
for holding quarks together to form hadrons,
and holding neutrons and also protons together
to form atomic nuclei. The exchange particle
that mediates this force is the gluon.
Electromagnetic interaction: the familiar
interaction that acts on electrically charged
particles. The photon is the exchange particle
for this force.
Weak interaction: a short-range interaction
responsible for some forms of radioactivity,
that acts on electrons, neutrinos, and quarks.
It is mediated by the W and Z bosons.
Gravitational interaction: a long-range attractive
interaction that acts on all particles. The
postulated exchange particle has been named
the graviton.Modern unified field theory attempts
to bring these four interactions together
into a single framework.
== History ==
=== Classic theory ===
The first successful classical unified field
theory was developed by James Clerk Maxwell.
In 1820 Hans Christian Ørsted discovered
that electric currents exerted forces on magnets,
while in 1831, Michael Faraday made the observation
that time-varying magnetic fields could induce
electric currents. Until then, electricity
and magnetism had been thought of as unrelated
phenomena. In 1864, Maxwell published his
famous paper on a dynamical theory of the
electromagnetic field. This was the first
example of a theory that was able to encompass
previously separate field theories (namely
electricity and magnetism) to provide a unifying
theory of electromagnetism. By 1905, Albert
Einstein had used the constancy of the speed
of light in Maxwell's theory to unify our
notions of space and time into an entity we
now call spacetime and in 1915 he expanded
this theory of special relativity to a description
of gravity, general relativity, using a field
to describe the curving geometry of four-dimensional
spacetime.
In the years following the creation of the
general theory, a large number of physicists
and mathematicians enthusiastically participated
in the attempt to unify the then-known fundamental
interactions. In view of later developments
in this domain, of particular interest are
the theories of Hermann Weyl of 1919, who
introduced the concept of an (electromagnetic)
gauge field in a classical field theory and,
two years later, that of Theodor Kaluza, who
extended General Relativity to five dimensions.
Continuing in this latter direction, Oscar
Klein proposed in 1926 that the fourth spatial
dimension be curled up into a small, unobserved
circle. In Kaluza–Klein theory, the gravitational
curvature of the extra spatial direction behaves
as an additional force similar to electromagnetism.
These and other models of electromagnetism
and gravity were pursued by Albert Einstein
in his attempts at a classical unified field
theory. By 1930 Einstein had already considered
the Einstein–Maxwell–Dirac System [Dongen].
This system is (heuristically) the super-classical
[Varadarajan] limit of (the not mathematically
well-defined) quantum electrodynamics. One
can extend this system to include the weak
and strong nuclear forces to get the Einstein–Yang–Mills–Dirac
System. The French physicist Marie-Antoinette
Tonnelat published a paper in the early 1940s
on the standard commutation relations for
the quantized spin-2 field. She continued
this work in collaboration with Erwin Schrödinger
after World War II. In the 1960s Mendel Sachs
proposed a generally covariant field theory
that did not require recourse to renormalisation
or perturbation theory. In 1965, Tonnelat
published a book on the state of research
on unified field theories.
=== Modern progress ===
In 1963 American physicist Sheldon Glashow
proposed that the weak nuclear force, electricity
and magnetism could arise from a partially
unified electroweak theory. In 1967, Pakistani
Abdus Salam and American Steven Weinberg independently
revised Glashow's theory by having the masses
for the W particle and Z particle arise through
spontaneous symmetry breaking with the Higgs
mechanism. This unified theory modeled the
electroweak interaction as a force mediated
by four particles: the photon for the electromagnetic
aspect, and a neutral Z particle and two charged
W particles for weak aspect. As a result of
the spontaneous symmetry breaking, the weak
force becomes short-range and the W and Z
bosons acquire masses of 80.4 and 91.2 GeV/c2,
respectively. Their theory was first given
experimental support by the discovery of weak
neutral currents in 1973. In 1983, the Z and
W bosons were first produced at CERN by Carlo
Rubbia's team. For their insights, Glashow,
Salam, and Weinberg were awarded the Nobel
Prize in Physics in 1979. Carlo Rubbia and
Simon van der Meer received the Prize in 1984.
After Gerardus 't Hooft showed the Glashow–Weinberg–Salam
electroweak interactions to be mathematically
consistent, the electroweak theory became
a template for further attempts at unifying
forces. In 1974, Sheldon Glashow and Howard
Georgi proposed unifying the strong and electroweak
interactions into the Georgi–Glashow model,
the first Grand Unified Theory, which would
have observable effects for energies much
above 100 GeV.
Since then there have been several proposals
for Grand Unified Theories, e.g. the Pati–Salam
model, although none is currently universally
accepted. A major problem for experimental
tests of such theories is the energy scale
involved, which is well beyond the reach of
current accelerators. Grand Unified Theories
make predictions for the relative strengths
of the strong, weak, and electromagnetic forces,
and in 1991 LEP determined that supersymmetric
theories have the correct ratio of couplings
for a Georgi–Glashow Grand Unified Theory.
Many Grand Unified Theories (but not Pati–Salam)
predict that the proton can decay, and if
this were to be seen, details of the decay
products could give hints at more aspects
of the Grand Unified Theory. It is at present
unknown if the proton can decay, although
experiments have determined a lower bound
of 1035 years for its lifetime.
=== Current status ===
Theoretical physicists have not yet formulated
a widely accepted, consistent theory that
combines general relativity and quantum mechanics
to form a theory of everything. Trying to
combine the graviton with the strong and electroweak
interactions leads to fundamental difficulties
and the resulting theory is not renormalizable.
The incompatibility of the two theories remains
an outstanding problem in the field of physics
