![]() | This article has multiple issues. Please help improve it or discuss these issues on the talk page . (Learn how and when to remove these messages)
|
In relativistic physics, Lorentz invariance states that the laws of physics should remain unchanged under Lorentz transformation. In quantum gravity, Lorentz invariance measures the universal features in the hypothetical loop quantum gravity universes; which is a hypothetical theory that explains the quantum theory of gravity based on a geometrical interpretation of the theory of relativity. The various hypothetical design models for the universe, multiverse, and loop quantum gravity could have various general covariant principle results.
Because loop quantum gravity can model universes, space-gravity theories are contenders to build and answer unification theory. The Lorentz invariance helps grade the spread of universal features throughout a proposed multiverse in time.
The Grand Unification Epoch is the era in time in the chronology of the universe where no elementary particles existed; the three gauge interactions of the Standard Model, which define the electromagnetic and weak and/or strong interactions or forces, are merged into one singular force. Scientific consensus suggests that 3 minutes after the Big Bang: protons and neutrons began to come together to form the nuclei of simple elements. [1] Loop quantum gravity theories, in contrast, place the origin and subsequently, the age of elementary particles, and the age of Lorentz invariance, beyond 13.799 ± 0.021 billion years ago.
The permanence of Lorentz invariance constants is based on elementary particles and their features. There are eons of time before the Big Bang to build the universe from black holes and older multiverses. There is a selective process that creates features in elementary particles, such as accepting, storing, and giving energy. Lee Smolin's books about loop quantum gravity posit that this theory contains the evolutionary ideas of "reproduction" and "mutation" of universes, elementary particles, as well as being formally analogous to models of population biology.[ citation needed ]
In the early universes before the Big Bang, there are theories that ''loop quantum gravity" and "loop quantum structures'' formed space. The Lorentz invariance and universal constants describe elementary particles that do not yet exist.
A fecund universe is a multiverse theory by Lee Smolin about the role of black holes. The theory suggests that black holes and loop quantum gravity connected early universes together; that loop quantum gravity can be pulled into black holes, and that within Fecund universes each new universe has slightly different laws of physics. Because these laws are only slightly different, each is assumed to be like a mutation of the early universes.
Loop quantum gravity (LQG) is a quantization of a classical Lagrangian classical field theory. It is equivalent to the Einstein–Cartan theory in that it leads to the same equations of motion describing general relativity with torsion.
Global Lorentz invariance is broken in LQG as it is broken in general relativity (with the exception of Minkowski spacetime, which is one particular solution of the Einstein field equations). Alternatively, there has been much talk about possible local and global violations of Lorentz invariance beyond those expected in straightforward general relativity.
Further research into whether the LQG analogue of Minkowski spacetime breaks or preserves global Lorentz invariance is needed and Carlo Rovelli and coworkers have recently been investigating the Minkowski state of LQG using spin foam techniques. It is expected that these questions will all remain open as long as the classical limits of various LQG models (see below for the sources of variation) cannot be calculated.
Mathematically, LQG is local gauge theory of the self-dual subgroup of the EXPANDED Lorentz group, which is related to the action of the Lorentz group on Weyl spinors commonly used in elementary particle physics. This is partly a matter of mathematical convenience, as it results in a compact group SO(3) or SU(2) as gauge group, as opposed to the non-compact groups SO(3,1) or SL(2.C). The compactness of the Lie group avoids some thus-far unsolved difficulties in the quantization of gauge theories of noncompact lie groups, and is responsible for the discreteness of the area and volume spectra. The theory involving the Immirzi parameter is necessary to resolve an ambiguity in the process of complexification. These are some of the many ways in which different quantizations of the same classical theory can result in inequivalent quantum theories, or even in the impossibility to carry quantization through.
It is not possible to distinguish between SO(3) and SU(2) or between SO(3,1) and SL(2,C) at this level: the respective Lie algebras are the same. All four groups have the same complexified Lie algebra and these subtleties are usually ignored in elementary particle physics. The physical interpretation of the Lie algebra is that of infinitesimally small group transformations, and gauge bosons (such as the graviton) are Lie algebra representations, not Lie group representations. This means for the Lorentz group that, for sufficiently small velocity parameters, all four complexified Lie groups are indistinguishable in the absence of matter fields.
Adding to the complexity, it can be shown that a positive cosmological constant can be realized in LQG by replacing the Lorentz group with the corresponding quantum group. At the level of the Lie algebra, this corresponds to what is called q-deforming the Lie algebra, and the parameter q is related to the value of the cosmological constant. The effect of replacing a Lie algebra by a q-deformed version is that the series of its representations is truncated. In the case of the rotation group, instead of having representations labelled by all half-integral spins, all representations with total spin j less than some constant remain.
It is possible to formulate LQG in terms of q-deformed Lie algebras instead of ordinary Lie algebras, and in the case of the Lorentz group, the result would, again, be indistinguishable for sufficiently small velocity parameters.
In the spin-foam formalism, the Barrett–Crane model, which was for a while the most promising state-sum model of 4D Lorentzian quantum gravity, was based on representations of the noncompact groups SO(3,1) or SL(2,C), so the spin foam faces (and hence the spin network edges) were labelled by positive real numbers as opposed to the half-integer labels of SU(2) spin networks.
These and other considerations, including difficulties interpreting what it would mean to apply a Lorentz transformation to a spin network state, led Lee Smolin and others to suggest that spin network states must break Lorentz invariance. Smolin and Joao Magueijo then went on to study doubly special relativity, in which not only there is a constant velocity c but also a constant distance l. They showed that there are nonlinear representations of the Lorentz Lie algebra with these properties (the usual Lorentz group being obtained from a linear representation). Doubly special relativity predicts deviations from the special relativity dispersion relation at large energies (corresponding to small wavelengths of the order of the constant length l in the doubly special theory). Giovanni Amelino-Camelia then proposed that the mystery of ultra-high-energy cosmic rays might be solved by assuming such violations of the special-relativity dispersion relation for photons. No confirmation has yet been found, and this idea is still hypothetical.
Phenomenological (hence, not specific to LQG) constraints on anomalous dispersion relations can be obtained by considering a variety of astrophysical experimental data, of which high-energy cosmic rays are one part.
Published in 2024, the Large High Altitude Air Shower Observatory Collaborative examined the gamma ray output from GRB 221009A and was unable to detect any invariance based on the color (wavelength) of light, something Loop Quantum Gravity predicts should happen. [2]
In theories of quantum gravity, the graviton is the hypothetical elementary particle that mediates the force of gravitational interaction. There is no complete quantum field theory of gravitons due to an outstanding mathematical problem with renormalization in general relativity. In string theory, believed by some to be a consistent theory of quantum gravity, the graviton is a massless state of a fundamental string.
Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics. It deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the vicinity of black holes or similar compact astrophysical objects, as well as in the early stages of the universe moments after the Big Bang.
Loop quantum gravity (LQG) is a theory of quantum gravity that incorporates matter of the Standard Model into the framework established for the intrinsic quantum gravity case. It is an attempt to develop a quantum theory of gravity based directly on Albert Einstein's geometric formulation rather than the treatment of gravity as a mysterious mechanism (force). As a theory, LQG postulates that the structure of space and time is composed of finite loops woven into an extremely fine fabric or network. These networks of loops are called spin networks. The evolution of a spin network, or spin foam, has a scale on the order of a Planck length, approximately 10−35 meters, and smaller scales are meaningless. Consequently, not just matter, but space itself, prefers an atomic structure.
Lee Smolin is an American theoretical physicist, a faculty member at the Perimeter Institute for Theoretical Physics, an adjunct professor of physics at the University of Waterloo, and a member of the graduate faculty of the philosophy department at the University of Toronto. Smolin's 2006 book The Trouble with Physics criticized string theory as a viable scientific theory. He has made contributions to quantum gravity theory, in particular the approach known as loop quantum gravity. He advocates that the two primary approaches to quantum gravity, loop quantum gravity and string theory, can be reconciled as different aspects of the same underlying theory. He also advocates an alternative view on space and time that he calls temporal naturalism. His research interests also include cosmology, elementary particle theory, the foundations of quantum mechanics, and theoretical biology.
In physics, a spin network is a type of diagram which can be used to represent states and interactions between particles and fields in quantum mechanics. From a mathematical perspective, the diagrams are a concise way to represent multilinear functions and functions between representations of matrix groups. The diagrammatic notation can thus greatly simplify calculations.
Doubly special relativity (DSR) – also called deformed special relativity or, by some, extra-special relativity – is a modified theory of special relativity in which there is not only an observer-independent maximum velocity, but also an observer-independent maximum energy scale and/or a minimum length scale. This contrasts with other Lorentz-violating theories, such as the Standard-Model Extension, where Lorentz invariance is instead broken by the presence of a preferred frame. The main motivation for this theory is that the Planck energy should be the scale where as yet unknown quantum gravity effects become important and, due to invariance of physical laws, this scale should remain fixed in all inertial frames.
The Poincaré group, named after Henri Poincaré (1905), was first defined by Hermann Minkowski (1908) as the isometry group of Minkowski spacetime. It is a ten-dimensional non-abelian Lie group that is of importance as a model in our understanding of the most basic fundamentals of physics.
In particle physics, a gauge boson is a bosonic elementary particle that acts as the force carrier for elementary fermions. Elementary particles whose interactions are described by a gauge theory interact with each other by the exchange of gauge bosons, usually as virtual particles.
The Immirzi parameter is a numerical coefficient appearing in loop quantum gravity (LQG), a nonperturbative theory of quantum gravity. The Immirzi parameter measures the size of the quantum of area in Planck units. As a result, its value is currently fixed by matching the semiclassical black hole entropy, as calculated by Stephen Hawking, and the counting of microstates in loop quantum gravity.
The history of loop quantum gravity spans more than three decades of intense research.
In mathematics, the representation theory of the Poincaré group is an example of the representation theory of a Lie group that is neither a compact group nor a semisimple group. It is fundamental in theoretical physics.
In general relativity, the hole argument is an apparent paradox that much troubled Albert Einstein while he was developing his field equations.
The symmetry of a physical system is a physical or mathematical feature of the system that is preserved or remains unchanged under some transformation.
In physics, helicity is the projection of the spin onto the direction of momentum.
Asım Orhan Barut was a Turkish-American theoretical physicist.
Loop quantum cosmology (LQC) is a finite, symmetry-reduced model of loop quantum gravity (LQG) that predicts a "quantum bridge" between contracting and expanding cosmological branches.
In physics, a charge is any of many different quantities, such as the electric charge in electromagnetism or the color charge in quantum chromodynamics. Charges correspond to the time-invariant generators of a symmetry group, and specifically, to the generators that commute with the Hamiltonian. Charges are often denoted by , and so the invariance of the charge corresponds to the vanishing commutator , where is the Hamiltonian. Thus, charges are associated with conserved quantum numbers; these are the eigenvalues of the generator . A "charge" can also refer to a point-shaped object with an electric charge and a position, such as in the method of image charges.
In physics, a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, do not change under local transformations according to certain smooth families of operations. Formally, the Lagrangian is invariant under these transformations.
This page is a glossary of terms in string theory, including related areas such as supergravity, supersymmetry, and high energy physics.
In theoretical physics, the problem of time is a conceptual conflict between quantum mechanics and general relativity. Quantum mechanics regards the flow of time as universal and absolute, whereas general relativity regards the flow of time as malleable and relative. This problem raises the question of what time really is in a physical sense and whether it is truly a real, distinct phenomenon. It also involves the related question of why time seems to flow in a single direction, despite the fact that no known physical laws at the microscopic level seem to require a single direction.
{{cite journal}}
: Cite journal requires |journal=
(help)