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There have been many theories of everything proposed by theoretical
physicists over the last century, but none have been confirmed experimentally.
The primary problem in producing a TOE is that the accepted theories of quantam
mechanics and general relativity are hard to combine. Based on theoretical holographic
principle arguments from 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 complete
theory of everything, although there is no widespread consensus.
Laplace famously
suggested that a sufficiently powerful intellect could, if it knew the velocity
of every particle at a given time, along with the laws of nature, calculate the
position of any particle at any other time:
Although modern quantum mechanics suggests that uncertainty
is inescapable, a unifying theory governing probabilistic assignments may
nevertheless exist.
Since ancient Greek
times, philosophers have speculated that the
apparent diversity of appearances conceals an underlying unity, and thus that
the list of forces might be short, indeed might contain only a single entry. For
example, the mechanical philosophy of the 17th century
posited that all forces could be ultimately reduced to contact forces between tiny solid particles.[3] This was abandoned
after the acceptance of Isaac
Newton's long-distance force of gravity; but at the same time, Newton's work
in his Principia
provided the first dramatic empirical evidence for the unification of apparently
distinct forces: Galileo's work on terrestrial gravity, Kepler's laws of
planetary motion, and the phenomenon of tides were all quantitatively explained by a single law of
universal gravitation.
In 1820, Hans Christian Řrsted discovered a
connection between electricity and magnetism, triggering decades of work that
culminated in James Clerk Maxwell's theory of electromagnetism. Also
during the 19th and early 20th centuries, it gradually became apparent that many
common examples of forces—contact forces, elasticity, viscosity, friction, pressure—resulted 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".[4]
Attempts to unify gravity with electromagnetism date back at least to Michael Faraday's
experiments of 1849–50.[5] After Albert Einstein's
theory of gravity (general relativity) was published in 1915,
the search for a unified field theory combining gravity
with electromagnetism began in earnest. At the time, it seemed plausible that no
other fundamental forces exist. Prominent contributors were Gunnar
Nordström, Hermann
Weyl, Arthur Eddington, Theodor Kaluza, Oskar Klein, and most notably, many attempts by
Einstein and his collaborators. In his last years, Albert Einstein was intensely
occupied in finding such a unifying theory. None of these attempts were
successful.[6]
The search for a unifying theory was interrupted by the discovery of the strong and
weak nuclear
forces, which could not be subsumed into either gravity or electromagnetism. A
further hurdle was the acceptance that 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 Newtonian 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 unified in 1967–68 by Sheldon
Glashow, Steven
Weinberg, and Abdus
Salam as the "electroweak" force.[7] However,
while the strong and electroweak forces peacefully coexist in the standard
model of particle physics, they remain distinct. Several Grand
Unified Theories (GUTs) have been proposed to unify them. Although the
simplest GUTs have been experimentally ruled out, the general idea, especially
when linked with supersymmetry, remains strongly favored by the
theoretical physics community. There is one GUT not linked to super symmetry
that has not been eliminated by experiment. That is the four universe theory of
George Ryazanov. It has been tested once in a lab at Hebrew University
informally. The results were reported to be positive. But the test has not been
repeated elsewhere. See http://george-ryazanov.com/book4/03-Physics_of_Unity.html.
However Ryazanov's theory does involve Lorentz violation. If the Fermi Glast
project does not find Lorentz violation, this will be a blow to the Ryazanov
Theory.
In current mainstream physics, a Theory of Everything would unify all the fundamental
interactions of nature, which are usually considered to be four in number:
gravity, the strong nuclear force, the weak nuclear force, and the electromagnetic
force. Because the weak force can transform elementary
particles from one kind into another, the TOE should yield a deep
understanding of the various different kinds of particles as well as the
different forces. The expected pattern of theories is:
In addition to the forces listed here, modern cosmology might require an inflationary
force, dark energy, and
also dark matter composed of
fundamental particles outside the scheme of the standard model. The existence of
these has not been proven and there are alternative theories such as modified Newtonian dynamics.
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 a mass of about 100 GeV, 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. Grand unification is expected to work in a similar way,
but at energies of the order of 1016 GeV,
far greater than could be reached by any possible Earth-based particle
accelerator. By analogy, unification of the GUT force with gravity is
expected at the Planck
energy, roughly 1019 GeV.
It may seem premature to be searching for a TOE when there is as yet no
direct evidence for an electronuclear force, and while in any case there are
many different proposed GUTs. In fact the name deliberately suggests the hubris involved. Nevertheless, most
physicists believe this unification is possible, partly due to the past history
of convergence towards a single theory. Supersymmetric GUTs seem plausible not
only for their theoretical "beauty", but because they naturally produce large
quantities of dark matter, and the inflationary force may be related to GUT
physics (although it does not seem to form an inevitable part of the theory).
And yet GUTs are clearly not the final answer. Both the current standard model
and 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. Furthermore, the inconsistency between quantum mechanics and general
relativity implies that one or both of these must be replaced by a theory
incorporating quantum
gravity.
The mainstream theory of everything at the moment is superstring
theory / M-theory; current
research on loop quantum gravity may eventually play a
fundamental role in a TOE, but that is not its primary aim. These theories
attempt to deal with the renormalization problem by setting up some lower bound
on the length scales possible. 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 (one estimate is 10500) 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
realised 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
criticised in that, because the theory is flexible enough to encompass almost
any observation, it cannot make useful (as in 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.
A small number of scientists claim that Gödel's incompleteness
theorem proves that any attempt to construct a TOE is bound to fail. Gödel's
theorem, informally stated, asserts that any sufficiently complex mathematical
theory that has a finite description is either inconsistent or incomplete. In
his 1966 book The
Relevance of Physics, Stanley Jaki 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.[8]
This view has been argued against by Jürgen Schmidhuber (1997), who pointed
out that Gödel's theorems are irrelevant even for computable physics.[9] 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.[10][11]
Related critique was offered by Solomon Feferman,[12] among others.
Douglas S. Robertson offers Conway's game of life as an
example:[13] 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", these researchers argue
that Gödel's Theorem does not mean that a TOE cannot exist. On the other
hand, the physicists 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.[14] This definitional
discrepancy may explain some of the disagreement among researchers.
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.[15] On this view, we
may reasonably hope for a theory of everything which self-consistently
incorporates all currently known forces, but 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 fundamental physical constants,
the theories are becoming simpler. If so, the process of simplification cannot
continue indefinitely.
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.[16] 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 (called "free floating laws" by Steven Weinberg), which
govern the behavior of complex systems, should be seen as equally
fundamental. Examples are the second law of thermodynamics and
the theory of natural selection. The point being that,
although in our universe these laws describe systems whose behaviour could ("in
principle") be predicted from a TOE, they would also hold in universes with
different low-level laws, subject only to some very general conditions.
Therefore it is of no help, even in principle, to invoke low-level laws when
discussing the behavior of complex systems. Some argue that this attitude would
violate Occam's Razor if a completely valid TOE were
formulated. It is not clear that there is any point at issue in these debates
(e.g., between Steven Weinberg and Philip Anderson) other than the right to apply
the high-status word "fundamental" to their respective subjects of interest.
Although the name "theory of everything" suggests the determinism of
Laplace's quote, 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, and by the extreme
mathematical difficulty of applying the theory. Thus, although the current
standard model of particle physics "in principle" predicts 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 true TOE
would almost certainly be even harder to apply. The main motive for seeking a
TOE, apart from the pure intellectual satisfaction of completing a
centuries-long quest, is that all prior successful unifications have predicted
new phenomena, some of which (e.g., electrical generators) have proved of
great practical importance. As in other cases of theory reduction, the TOE would
also allow us to confidently define the domain of validity and residual error of
low-energy approximations to the full theory which could be used for practical
calculations.
The status of a physical TOE is open to philosophical debate. For
example, if physicalism is
true, a physical TOE would coincide with a philosophical theory of everything.
Some philosophers (Aristotle, Plato, Hegel, Whitehead, et al) have attempted to
construct all-encompassing systems. Others are highly dubious about the very
possibility of such an exercise. The Roman Catholic Church has sought a Grand
unification theory of the universe for centuries and Aquinas was a
contributor to this thought. This is a theory of elementary forces that unites
the weak, strong, electromagnetic, and gravitational interactions into one field
theory and views the known interactions as low-energy manifestations of a single
unified interaction.
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