Background independence is a condition in theoretical physics, that requires the defining equations of a theory to be independent of the actual shape of the spacetime and the value of various fields within the spacetime. In particular this means that it must be possible not to refer to a specific coordinate system —the theory must be coordinate-free. In addition, the different spacetime configurations (or backgrounds) should be obtained as different solutions of the underlying equations.
Background independence is a loosely defined property of a theory of physics. Roughly speaking, it limits the number of mathematical structures used to describe space and time that are put in place "by hand". Instead, these structures are the result of dynamical equations, such as Einstein field equations, so that one can determine from first principles what form they should take. Since the form of the metric determines the result of calculations, a theory with background independence is more predictive than a theory without it, since the theory requires fewer inputs to make its predictions. This is analogous to desiring fewer free parameters in a fundamental theory.
So background independence can be seen as extending the mathematical objects that should be predicted from theory to include not just the parameters, but also geometrical structures. Summarizing this, Rickles writes: "Background structures are contrasted with dynamical ones, and a background independent theory only possesses the latter type—obviously, background dependent theories are those possessing the former type in addition to the latter type."
In general relativity, background independence is identified with the property that the metric of spacetime is the solution of a dynamical equation.In classical mechanics, this is not the case, the metric is fixed by the physicist to match experimental observations. This is undesirable, since the form of the metric impacts the physical predictions, but is not itself predicted by the theory.
Manifest background independence is primarily an aesthetic rather than a physical requirement. It is analogous and closely related to requiring in differential geometry that equations be written in a form that is independent of the choice of charts and coordinate embeddings. If a background-independent formalism is present, it can lead to simpler and more elegant equations. However, there is no physical content in requiring that a theory be manifestly background-independent – for example, the equations of general relativity can be rewritten in local coordinates without affecting the physical implications.
Although making a property manifest is only aesthetic, it is a useful tool for making sure the theory actually has that property. For example, if a theory is written in a manifestly Lorentz-invariant way, one can check at every step to be sure that Lorentz invariance is preserved. Making a property manifest also makes it clear whether or not the theory actually has that property. The inability to make classical mechanics manifestly Lorentz-invariant does not reflect a lack of imagination on the part of the theorist, but rather a physical feature of the theory. The same goes for making classical mechanics or electromagnetism background-independent.
Because of the speculative nature of quantum-gravity research, there is much debate as to the correct implementation of background independence. Ultimately, the answer is to be decided by experiment, but until experiments can probe quantum-gravity phenomena, physicists have to settle for debate. Below is a brief summary of the two largest quantum-gravity approaches.
Physicists have studied models of 3D quantum gravity, which is a much simpler problem than 4D quantum gravity (this is because in 3D, quantum gravity has no local degrees of freedom). In these models, there are non-zero transition amplitudes between two different topologies,or in other words, the topology changes. This and other similar results lead physicists to believe that any consistent quantum theory of gravity should include topology change as a dynamical process.
String theory is usually formulated with perturbation theory around a fixed background. While it is possible that the theory defined this way is locally background-invariant, if so, it is not manifest, and it is not clear what the exact meaning is. One attempt to formulate string theory in a manifestly background-independent fashion is string field theory, but little progress has been made in understanding it.
Another approach is the conjectured, but yet unproven AdS/CFT duality, which is believed to provide a full, non-perturbative definition of string theory in spacetimes with anti-de Sitter asymptotics. If so, this could describe a kind of superselection sector of the putative background-independent theory. But it would be still restricted to anti-de Sitter space asymptotics, which disagrees with the current observations of our Universe. A full non-perturbative definition of the theory in arbitrary spacetime backgrounds is still lacking.
Topology change is an established process in string theory.
A very different approach to quantum gravity called loop quantum gravity is fully non-perturbative, manifest background-independent: geometric quantities, such as area, are predicted without reference to a background metric or asymptotics (e.g. no need for a background metric or an anti-de Sitter asymptotics), only a given topology.
General relativity, also known as the general theory of relativity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time or four-dimensional spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations.
M-theory is a theory in physics that unifies all consistent versions of superstring theory. Edward Witten first conjectured the existence of such a theory at a string-theory conference at the University of Southern California in the spring of 1995. Witten's announcement initiated a flurry of research activity known as the second superstring revolution.
Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics, and where quantum effects cannot be ignored, such as in the vicinity of black holes or similar compact astrophysical objects where the effects of gravity are strong, such as neutron stars.
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interact with each other. On distance scales larger than the string scale, a string looks just like an ordinary particle, with its mass, charge, and other properties determined by the vibrational state of the string. In string theory, one of the many vibrational states of the string corresponds to the graviton, a quantum mechanical particle that carries gravitational force. Thus string theory is a theory of quantum gravity.
A theory of everything, 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.
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 an observer-independent maximum energy scale and minimum length scale.
In theoretical physics, the anti-de Sitter/conformal field theory correspondence, sometimes called Maldacena duality or gauge/gravity duality, is a conjectured relationship between two kinds of physical theories. On one side are anti-de Sitter spaces (AdS) which are used in theories of quantum gravity, formulated in terms of string theory or M-theory. On the other side of the correspondence are conformal field theories (CFT) which are quantum field theories, including theories similar to the Yang–Mills theories that describe elementary particles.
The history of loop quantum gravity spans more than three decades of intense research.
In particle physics, quantum field theory in curved spacetime is an extension of standard, Minkowski space quantum field theory to curved spacetime. A general prediction of this theory is that particles can be created by time-dependent gravitational fields, or by time-independent gravitational fields that contain horizons.
In general relativity, the hole argument is an apparent paradox that much troubled Albert Einstein while developing his famous field equations.
Conformal gravity are gravity theories that are invariant under conformal transformations in the Riemannian geometry sense; more accurately, they are invariant under Weyl transformations where is the metric tensor and is a function on spacetime.
In physics, event symmetry includes invariance principles that have been used in some discrete approaches to quantum gravity where the diffeomorphism invariance of general relativity can be extended to a covariance under every permutation of spacetime events.
The causal sets program is an approach to quantum gravity. Its founding principles are that spacetime is fundamentally discrete and that spacetime events are related by a partial order. This partial order has the physical meaning of the causality relations between spacetime events.
In mathematical physics, de Sitter invariant special relativity is the speculative idea that the fundamental symmetry group of spacetime is the indefinite orthogonal group SO(4,1), that of de Sitter space. In the standard theory of general relativity, de Sitter space is a highly symmetrical special vacuum solution, which requires a cosmological constant or the stress–energy of a constant scalar field to sustain.
In loop quantum gravity, the Kodama state is a zero energy solution to the Schrödinger equation.
Standard-Model Extension (SME) is an effective field theory that contains the Standard Model, general relativity, and all possible operators that break Lorentz symmetry. Violations of this fundamental symmetry can be studied within this general framework. CPT violation implies the breaking of Lorentz symmetry, and the SME includes operators that both break and preserve CPT symmetry.
Asymptotic safety is a concept in quantum field theory which aims at finding a consistent and predictive quantum theory of the gravitational field. Its key ingredient is a nontrivial fixed point of the theory's renormalization group flow which controls the behavior of the coupling constants in the ultraviolet (UV) regime and renders physical quantities safe from divergences. Although originally proposed by Steven Weinberg to find a theory of quantum gravity, the idea of a nontrivial fixed point providing a possible UV completion can be applied also to other field theories, in particular to perturbatively nonrenormalizable ones. In this respect, it is similar to quantum triviality.
In theoretical physics, the problem of time is a conceptual conflict between general relativity and quantum mechanics in that 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. For macroscopic systems the directionality of time is directly linked to first principles such as the Second law of thermodynamics.
Dynamical dimensional reduction or spontaneous dimensional reduction is the apparent reduction in the number of spacetime dimensions as a function of the distance scale, or conversely the energy scale, with which spacetime is probed. At least within the current level of experimental precision, our universe has three dimensions of space and one of time. However, the idea that the number of dimensions may increase at extremely small length scales was first proposed more than a century ago, and is now fairly commonplace in theoretical physics. Contrary to this, a number of recent results in quantum gravity suggest the opposite behavior, a dynamical reduction of the number of spacetime dimensions at small length scales.