Loop quantum gravity
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.In 1986, Abhay Ashtekar reformulated Einstein's general relativity in a language closer to that of the rest of fundamental physics, specifically Yang–Mills theory.The canonical version of the dynamics was established by Thomas Thiemann, who defined an anomaly-free Hamiltonian operator and showed the existence of a mathematically consistent background-independent theory.The covariant, or "spin foam", version of the dynamics was developed jointly over several decades by research groups in France, Canada, UK, Poland, and Germany.In LQG this aspect of general relativity is taken seriously and this symmetry is preserved by requiring that the physical states remain invariant under the generators of diffeomorphisms.'s with derivatives give rise to different operators – the choice made is called the factor ordering and should be chosen via physical reasoning.It was in particular the inability to have good control over the space of solutions to Gauss's law and spatial diffeomorphism constraints that led Rovelli and Smolin to consider the loop representation in gauge theories and quantum gravity.The Standard Model's accuracy in describing the universe at the smallest scales relies heavily on the unique properties of chiral fermions.Therefore, resolving the fermion doubling problem is crucial for advancing our understanding of the universe at its most fundamental level and developing a complete theory that unites gravity with the quantum world.This then naturally gives rise to the two-complex (a combinatorial set of faces that join along edges, which in turn join on vertices) underlying the spin foam description; we evolve forward an initial spin network sweeping out a surface, the action of the Hamiltonian constraint operator is to produce a new planar surface starting at the vertex.We are able to use the action of the Hamiltonian constraint on the vertex of a spin network state to associate an amplitude to each "interaction" (in analogy to Feynman diagrams).Given the spin foam 'interaction' amplitudes for this simple theory, one then tries to implement the simplicity conditions to obtain a path integral for general relativity.Progress has been made with regard to this issue by Engle, Pereira, and Rovelli,[20] Freidel and Krasnov[21] and Livine and Speziale[22] in defining spin foam interaction amplitudes with better behaviour.The fabric of a T-shirt is analogous: at a distance it is a smooth curved two-dimensional surface, but on closer inspection we see that it is actually composed of thousands of one-dimensional linked threads.Markopoulou, et al. adopted the idea of noiseless subsystems in an attempt to solve the problem of the low energy limit in background independent quantum gravity theories.The spectrum of the master constraint may not contain zero due to normal or factor ordering effects which are finite but similar in nature to the infinite vacuum energies of background-dependent quantum field theories.[39][40][41][42] The Consistent Discretizations approach to LQG,[43][44] is an application of the master constraint program to construct the physical Hilbert space of the canonical theory.The no hair conjecture of general relativity states that a black hole is characterized only by its mass, its charge, and its angular momentum; hence, it has no entropy.[48] Work by Stephen Hawking and Jacob Bekenstein showed that the second law of thermodynamics can be preserved by assigning to each black hole a black-hole entropy where[53] It is possible to derive, from the covariant formulation of full quantum theory (Spinfoam) the correct relation between energy and area (1st law), the Unruh temperature and the distribution that yields Hawking entropy.[52] Loop-quantization does not reproduce the result for black hole entropy originally discovered by Bekenstein and Hawking, unless one chooses the value of the Immirzi parameter to cancel out another constant that arises in the derivation.However recently physicists, such as Jack Palmer, have started to consider the possibility of measuring quantum gravity effects mostly from astrophysical observations and gravitational wave detectors.In a 2003 paper "A Dialog on Quantum Gravity",[68] Carlo Rovelli regards the fact LQG is formulated in 4 dimensions and without supersymmetry as a strength of the theory as it represents the most parsimonious explanation, consistent with current experimental results, over its rival string/M-theory.It is possible to extend mainstream LQG formalism to higher-dimensional supergravity, general relativity with supersymmetry and Kaluza–Klein extra dimensions should experimental evidence establish their existence.Sundance Bilson-Thompson, Hackett et al.,[85][86] has attempted to introduce the standard model via LQGs degrees of freedom as an emergent property (by employing the idea of noiseless subsystems, a notion introduced in a more general situation for constrained systems by Fotini Markopoulou-Kalamara et al.)[87] Furthermore, LQG has drawn philosophical comparisons with causal dynamical triangulation[88] and asymptotically safe gravity,[89] and the spinfoam with group field theory and AdS/CFT correspondence.[91] Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result.On the other hand, the consequences of LQG are radical, because they fundamentally change the nature of space and time and provide a tentative but detailed physical and mathematical picture of quantum spacetime.This means it remains unproven that LQG's description of spacetime at the Planck scale has the right continuum limit (described by general relativity with possible quantum corrections).[92] Other technical problems include finding off-shell closure of the constraint algebra and physical inner product vector space, coupling to matter fields of quantum field theory, fate of the renormalization of the graviton in perturbation theory that lead to ultraviolet divergence beyond 2-loops (see one-loop Feynman diagram in Feynman diagram).ESA's INTEGRAL satellite measured polarization of photons of different wavelengths and was able to place a limit in the granularity of space[94] that is less than 10−48m or 13 orders of magnitude below the Planck scale.
Beyond the Standard ModelLarge Hadron ColliderHiggs bosonStandard ModelHierarchy problemDark matterDark energyQuintessencePhantom energyDark radiationDark photonCosmological constant problemStrong CP problemNeutrino oscillationBrans–Dicke theoryCosmic censorship hypothesisFifth forceF-theoryTheory of everythingUnified field theoryGrand Unified TheoryTechnicolorKaluza–Klein theory6D (2,0) superconformal field theoryNoncommutative quantum field theoryQuantum cosmologyBrane cosmologyString theorySuperstring theoryM-theoryMathematical universe hypothesisMirror matterRandall–Sundrum modelN = 4 supersymmetric Yang–Mills theoryTwistor string theoryDark fluidDoubly special relativityde Sitter invariant special relativityCausal fermion systemsBlack hole thermodynamicsUnparticle physicsGraviphotonGraviscalarGravitonGravitinoMassive gravityGauge gravitation theoryGauge theory gravityCPT symmetrySupersymmetrySupergravitySupersymmetry breakingExtra dimensionsLarge extra dimensionsQuantum gravityFalse vacuumSpin foamQuantum foamQuantum geometryLoop quantum cosmologyCausal dynamical triangulationCausal setsCanonical quantum gravitySemiclassical gravitySuperfluid vacuum theoryGran SassoSuper-KTevatronAlbert Einsteinspace and timespin networksPlanck lengthBig BangBig Bounceperiod of expansionBig CrunchHistory of loop quantum gravityAbhay AshtekarYang–Mills theoryTed JacobsonLee SmolinWheeler–DeWitt equationAshtekar variablesCarlo RovellinonperturbativeJorge PullinJerzy LewandowskigraphsoperatorsRoger PenroseHamiltonianclassical limitcosmological constantacceleration in the expansion of the Universebackground independenttopologygeneral relativitydiffeomorphismsHamiltonian constraintdynamicsproblem of timePoisson bracketgauge transformationsDirac observablesphase spacePoisson commuteArnowitt–Deser–Misner (ADM) phase spaceFrame fields in general relativitySelf-dual Palatini actionquantum operatorsrotationspin connectionHolonomyWilson loopKnot invariantloop representation in gauge theories and quantum gravityparallel transportPauli matricesirreducible representationsWilson loopsLoop representationPosition and momentum spaceknot invariantsknot theorycoplanarHamiltonian constraint of LQG