{"id":859,"date":"2021-01-22T17:49:50","date_gmt":"2021-01-22T16:49:50","guid":{"rendered":"https:\/\/acircleisround.com\/?p=859"},"modified":"2022-12-15T09:33:38","modified_gmt":"2022-12-15T08:33:38","slug":"quantum-gravity-in-the-making","status":"publish","type":"post","link":"https:\/\/acircleisround.com\/nl\/2021\/01\/22\/quantum-gravity-in-the-making\/","title":{"rendered":"Quantum Gravity in the Making"},"content":{"rendered":"<p class=\"graf graf--p\">We always appreciate it when explanations add up. There is a sort of soothing and satisfying effect that comes along and suffuses us when things make sense.<\/p>\n<p class=\"graf graf--p\">Precisely for those reasons, what has irked many theoretical physicists for already several decades is the absence of <em class=\"markup--em markup--p-em\">the<\/em> theory of quantum gravity, which intends to put gravitational and quantum behaviour under one coherent roof regardless of the energy scale.<\/p>\n<p class=\"graf graf--p\">This article sketches a brief overview of the quantum gravity landscape and a couple of its leading candidate theories, namely M-theory, loop quantum gravity, causal dynamical triangulations, and asymptotically safe gravity.<\/p>\n<h3 class=\"graf graf--h3\"><strong class=\"markup--strong markup--h3-strong\">The Outline of the\u00a0Marriage<\/strong><\/h3>\n<p class=\"graf graf--p\">Quantum mechanics is the ensemble of the laws of physics that accurately account for the kinetics of atomic and subatomic particles as well as radiation (light) at minute distance scales. The theory explains behaviour that we do not normally observe in our macroscopic world, for instance, establishing an instantaneous connection over large distances (<a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/phys.org\/news\/2020-09-quantum-entanglement-distant-large.html\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/phys.org\/news\/2020-09-quantum-entanglement-distant-large.html\">quantum entanglement<\/a>), crossing barriers otherwise impenetrable to larger objects (<a class=\"markup--anchor markup--p-anchor\" href=\"http:\/\/hyperphysics.phy-astr.gsu.edu\/hbase\/quantum\/barr.html\" target=\"_blank\" rel=\"noopener\" data-href=\"http:\/\/hyperphysics.phy-astr.gsu.edu\/hbase\/quantum\/barr.html\">quantum tunnelling<\/a>), and taking different paths at the same time (<a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/jqi.umd.edu\/glossary\/quantum-superposition\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/jqi.umd.edu\/glossary\/quantum-superposition\">quantum superposition<\/a>).<\/p>\n<p class=\"graf graf--p\">It is this theory\u200a\u2014\u200amore correctly, it is <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/www.ias.edu\/sites\/default\/files\/sns\/What%20is%20QFT%20long.pdf\" target=\"_blank\" rel=\"noopener\">quantum field theory<\/a>, which is quantum mechanics intertwined with classical field theory and special relativity\u200a\u2014\u200athat explicates the dynamics of the most fundamental building blocks of our Universe, collectively captured in the <a class=\"markup--anchor markup--p-anchor\" href=\"http:\/\/electron6.phys.utk.edu\/phys250\/modules\/module%206\/standard_model.htm\" target=\"_blank\" rel=\"noopener\">Standard Model<\/a> of particle physics. In addition to fermions, such as the electron, the quarks, and the neutrinos, that model also contains bosons, including the photon and the Higgs boson.<\/p>\n<p class=\"graf graf--p\">In contrast, gravitation is not described within the contours of the Standard model, but by Albert Einstein\u2019s theory of general relativity, which posits that the curvature of spacetime is what we experience as gravity. In the words of physicist <a class=\"markup--anchor markup--p-anchor\" href=\"http:\/\/stanford.edu\/~maehwee\/SPCS\/Relativity2019\/\" target=\"_blank\" rel=\"noopener\" data-href=\"http:\/\/stanford.edu\/~maehwee\/SPCS\/Relativity2019\/\">John Wheeler<\/a>: \u201cSpacetime tells matter how to move; matter tells spacetime how to curve.\u201d<\/p>\n<p class=\"graf graf--p\">Theories of quantum gravity look at regimes where <em class=\"markup--em markup--p-em\">both<\/em> gravitational fields and quantum effects grow very strong. This usually occurs <em class=\"markup--em markup--p-em\">beyond<\/em> the <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/www.symmetrymagazine.org\/article\/the-planck-scale\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/www.symmetrymagazine.org\/article\/the-planck-scale\">Planck scale<\/a>\u200a\u2014\u200athis is the smallest known physical distance scale\u200a\u2014\u200awhere the equivalent energies are much <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/arxiv.org\/pdf\/hep-th\/9812104.pdf\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/arxiv.org\/pdf\/hep-th\/9812104.pdf\">higher<\/a> than those probed in the Standard Model\u200a\u2014\u200athe energy region beyond the Planck scale is often figuratively labelled as the ultraviolet (UV) regime or UV limit. In particular, the said regime becomes relevant in the vicinity of the most inner part of a black hole and at the moment of the Big Bang (the early Universe).<\/p>\n<p class=\"graf graf--p\">The ultimate purpose of a theory of quantum gravity is to duly spell out the physics beyond the Planck scale in such a way that at lower energies the theory can still reproduce the core tenets of quantum mechanics plus general relativity.<\/p>\n<p class=\"graf graf--p\">Due to the fact that the energy scales associated with quantum gravity are much higher than the upper limits of our current experimental technologies, e.g., the <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/home.cern\/science\/accelerators\/large-hadron-collider\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/home.cern\/science\/accelerators\/large-hadron-collider\">Large Hadron Collider<\/a>, which we use to test the Standard Model, the proposed theories of quantum gravity remain out of scope of such tests. Given the <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/backreaction.blogspot.com\/2016\/05\/how-can-we-test-quantum-gravity.html\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/backreaction.blogspot.com\/2016\/05\/how-can-we-test-quantum-gravity.html\">lack<\/a> of direct observational data in those regimes, it is thorny to rule out some of the theories and thus to progress towards <em class=\"markup--em markup--p-em\">the<\/em> theory of quantum gravity.<\/p>\n<p class=\"graf graf--p\">At the conceptual side, two difficulties stand out in the attempt to merge quantum mechanics with gravity in the UV limit, to which different theories have different answers.<\/p>\n<p class=\"graf graf--p\">First, when treating gravitation dynamically as a quantum field, an <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/physics.stackexchange.com\/questions\/488955\/why-is-quantum-gravity-non-renormalizable\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/physics.stackexchange.com\/questions\/488955\/why-is-quantum-gravity-non-renormalizable\">infinite number<\/a> of terms show up in the calculations which makes it evidently hard for a theory to be predictable. Even so, a boson (underpinned by a quantum field) is expected to exist for the gravitational field, i.e., the <a class=\"markup--anchor markup--p-anchor\" href=\"http:\/\/snst-hu.lzu.edu.cn\/zhangyi\/ndata\/Graviton.html\" target=\"_blank\" rel=\"noopener\" data-href=\"http:\/\/snst-hu.lzu.edu.cn\/zhangyi\/ndata\/Graviton.html\">graviton<\/a>, although it has not yet been detected up to this point.<\/p>\n<p class=\"graf graf--p\">Bear in mind that if you would put an upper limit on the energy scale\u200a\u2014\u200aa so-called UV cut-off\u200a\u2014\u200ayou would as a matter of fact be able to design a quantum field theory of gravitation (more specifically, this is <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/arxiv.org\/pdf\/1209.3511.pdf\" target=\"_blank\" rel=\"noopener\">referred<\/a> to as an effective field theory approach to quantum gravity). Nonetheless, a <em class=\"markup--em markup--p-em\">full<\/em> theory of quantum gravity should not need to be cut off at some energy level in order to be consistent but, rather, should be finite-dimensional, and thus predictive, within the entire UV regime. Once coherently describing the dynamics at high energies, such theory would be designated as the <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/www.researchgate.net\/post\/What_does_UV_Completion_mean_and_what_is_meant_by_a_theory_is_IR_free\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/www.researchgate.net\/post\/What_does_UV_Completion_mean_and_what_is_meant_by_a_theory_is_IR_free\">UV completion<\/a> of quantized gravity.<\/p>\n<p class=\"graf graf--p\">The second difficulty is that spacetime in the Standard Model is a priori defined\u200a\u2014\u200athat is, spacetime is fixed and the theory is categorized as background-dependent\u200a\u2014\u200awhereas in general relativity the specific spacetime structure comes out of the equations\u200a\u2014\u200athat is, spacetime is dynamic and the theory is considered <a class=\"markup--anchor markup--p-anchor\" href=\"http:\/\/citeseerx.ist.psu.edu\/viewdoc\/download?doi=10.1.1.749.1271&amp;rep=rep1&amp;type=pdf\" target=\"_blank\" rel=\"noopener\" data-href=\"http:\/\/citeseerx.ist.psu.edu\/viewdoc\/download?doi=10.1.1.749.1271&amp;rep=rep1&amp;type=pdf\">background independent<\/a>. This geometric difference causes an incompatibility between general relativity and quantum mechanics that quantum gravity aims to smooth out.<\/p>\n<p class=\"graf graf--p\">Let us now have an introductory glimpse at some of the competing theories within the field of quantum gravity.<\/p>\n<h3 class=\"graf graf--h3\"><strong class=\"markup--strong markup--h3-strong\">M-Theory<\/strong><\/h3>\n<p class=\"graf graf--p\">Arguably, one of the top contenders is M-theory, which is an overarching theoretical framework that provides shelter not just to the five <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/acircleisround.com\/nl\/2020\/05\/30\/in-theory-can-we-string-the-universe-together\/\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/acircleisround.medium.com\/in-theory-can-we-string-the-universe-together-bed803a6e0a9?sk=716acf4590fdf17d66899886d2839ac7\">superstring theories<\/a>\u200a\u2014\u200aType I, Type IIA, Type IIB, Heterotic E\u2088xE\u2088, and Heterotic SO(32)\u200a\u2014\u200abut also to supergravity. The prefix \u2018super\u2019 hints at the idea of <a class=\"markup--anchor markup--p-anchor\" href=\"http:\/\/hitoshi.berkeley.edu\/public_html\/susy\/susy.html\" target=\"_blank\" rel=\"noopener\" data-href=\"http:\/\/hitoshi.berkeley.edu\/public_html\/susy\/susy.html\">supersymmetry<\/a>, a hypothesized symmetrical relationship between fermions and bosons. <a class=\"markup--anchor markup--p-anchor\" href=\"http:\/\/abyss.uoregon.edu\/~js\/glossary\/supergravity.html\" target=\"_blank\" rel=\"noopener\" data-href=\"http:\/\/abyss.uoregon.edu\/~js\/glossary\/supergravity.html\">Supergravity<\/a> is a kind of quantum theory that relies on supersymmetry and naturally includes gravity.<\/p>\n<p class=\"graf graf--p\">Various relations are discovered between all these theories. For one, at lower energy scales, the superstring theories and M-theory can be <a class=\"markup--anchor markup--p-anchor\" href=\"http:\/\/edu.itp.phys.ethz.ch\/hs11\/strings\/Chapter10.pdf\" target=\"_blank\" rel=\"noopener\">approximated<\/a> by supergravity in 10 and 11 dimensions, respectively\u200a\u2014\u200ain other words, 1 time dimension and 9 or 10 spatial dimensions. Not only that, the five superstring theories each represent a separate limiting case of M-theory and are coupled to one another through special symmetries called <a class=\"markup--anchor markup--p-anchor\" href=\"http:\/\/web.physics.ucsb.edu\/~strings\/superstrings\/duality.htm\" target=\"_blank\" rel=\"noopener\" data-href=\"http:\/\/web.physics.ucsb.edu\/~strings\/superstrings\/duality.htm\">dualities<\/a> (see Fig. 1).<\/p>\n<p class=\"graf graf--p\">One of the reasons that M-theory is branded as a theory of quantum gravity is because the superstring theories spontaneously supply us with the graviton, the quantum-mechanical particle description of the gravitational field. In these theories, the fundamental entities of the Universe are 1-dimensional vibrating strings (not particles), whereby the different modes of vibration give birth to the different particles.<\/p>\n<figure class=\"graf graf--figure\">\n<p><div style=\"width: 1154px\" class=\"wp-caption aligncenter\"><img data-recalc-dims=\"1\" decoding=\"async\" class=\"graf-image lazyload\" title=\"Overview of M-theory, supergravity, and the five superstring theories as well as their connecting dualities.\" data-src=\"https:\/\/i0.wp.com\/cdn-images-1.medium.com\/max\/1600\/1%2APns1R0-Fn61I7QEF4gyqXA.png?resize=629%2C361&#038;ssl=1\" alt=\"Overview of M-theory, supergravity, and the five superstring theories as well as their connecting dualities.\" width=\"629\" height=\"361\" data-image-id=\"1*Pns1R0-Fn61I7QEF4gyqXA.png\" data-width=\"1144\" data-height=\"656\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 629px; --smush-placeholder-aspect-ratio: 629\/361;\" \/><p class=\"wp-caption-text\">Fig. 1. Overview of M-theory, supergravity, and the five superstring theories as well as their connecting dualities. (Source: adapted from <a href=\"https:\/\/universe-review.ca\/R15-18-string04.htm\" target=\"_blank\" rel=\"noopener\">universereview<\/a>).<\/p><\/div><\/figure>\n<p>Superstring theory is coherent only when operating in 10 dimensions. In order to make sure that we still live in a macroscopic 4-dimensional Universe (1 time dimension and 3 spatial dimensions), physicists have <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/acircleisround.com\/nl\/2020\/05\/30\/in-theory-can-we-string-the-universe-together\/\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/acircleisround.medium.com\/in-theory-can-we-string-the-universe-together-bed803a6e0a9?sk=716acf4590fdf17d66899886d2839ac7\">conjectured<\/a> the possibility that every point in our 3-dimensional space consists at the smallest of scales\u200a\u2014\u200aand therefore invisible to us\u200a\u2014\u200aof a 6-dimensional topological space in which the strings dwell and which is entirely curled up on itself. The way in which this microscopic space is folded affects the strings\u2019 vibrations which in turn determine the type of particle that arises.<\/p>\n<p class=\"graf graf--p\">By postulating strings instead of particles as elementary building blocks, M-theory is able to solve the conceptual issue of insurmountable infinities when quantizing gravity in the UV regime (see above section \u201cThe Outline of the Marriage\u201d). The strength of M-theory lies furthermore in its ability to account for the Bekenstein-Hawking <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/arxiv.org\/pdf\/hep-th\/9601029.pdf\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/arxiv.org\/pdf\/hep-th\/9601029.pdf\">entropy<\/a> of black holes, to present a solution to the black hole <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/www.ias.edu\/ideas\/2011\/maldacena-black-holes-string-theory\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/www.ias.edu\/ideas\/2011\/maldacena-black-holes-string-theory\">information problem<\/a> with the assistance of the holographic principle, and to embrace the most favourite candidate for <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/arxiv.org\/pdf\/1912.09909.pdf\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/arxiv.org\/pdf\/1912.09909.pdf\">dark matter<\/a>.<\/p>\n<p class=\"graf graf--p\">Then again, M-theory is struggling with becoming background <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/io9.gizmodo.com\/the-trouble-with-string-theory-5890789\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/io9.gizmodo.com\/the-trouble-with-string-theory-5890789\">independent<\/a>, with exclusively predicting our Standard Model since it leaves the door <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/www.forbes.com\/sites\/startswithabang\/2020\/02\/26\/why-string-theory-is-both-a-dream-and-a-nightmare\/?sh=426abd543b1d\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/www.forbes.com\/sites\/startswithabang\/2020\/02\/26\/why-string-theory-is-both-a-dream-and-a-nightmare\/?sh=426abd543b1d\">open<\/a> for the existence of a gigantic number of other possible universes, with explaining the <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/ned.ipac.caltech.edu\/level5\/Sept02\/Padmanabhan\/Pad11.html\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/ned.ipac.caltech.edu\/level5\/Sept02\/Padmanabhan\/Pad11.html\">accelerated<\/a> rate of expansion of our Universe, and with formulating an <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/pirsa.org\/05100043\" target=\"_blank\" rel=\"noopener\">answer<\/a> to questions related to the origin of the Big Bang and the nature of the black hole singularity.<\/p>\n<h3 class=\"graf graf--h3\"><strong class=\"markup--strong markup--h3-strong\">Loop Quantum\u00a0Gravity<\/strong><\/h3>\n<p class=\"graf graf--p\">The theory of loop quantum gravity, which is often cited as one of M-theory\u2019s main opponents, encompasses the <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/arxiv.org\/pdf\/gr-qc\/0404018.pdf\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/arxiv.org\/pdf\/gr-qc\/0404018.pdf\">dynamic<\/a> properties of Einstein\u2019s general relativity: it is background independent. Moreover, it hitches quantum mechanics\u2019 essential feature of <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/ocw.mit.edu\/courses\/physics\/8-05-quantum-physics-ii-fall-2013\/video-lectures\/lecture-10-uncertainty-principle-and-compatible-observables\/\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/ocw.mit.edu\/courses\/physics\/8-05-quantum-physics-ii-fall-2013\/video-lectures\/lecture-10-uncertainty-principle-and-compatible-observables\/\">quantum uncertainty<\/a> to that background. That is, loop quantum gravity <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/arxiv.org\/abs\/1801.01351\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/arxiv.org\/abs\/1801.01351\">treats<\/a> spacetime itself as quantum mechanical. This ultimately means that, within the context of this theory, spacetime is fundamentally discrete and looks granular at the smallest of scales.<\/p>\n<p class=\"graf graf--p\">At these scales, loops are quantum-mechanical excitations of the gravitational field\u200a\u2014\u200awhich delineates the actual physical space\u200a\u2014\u200aand combined they form a network, baptized as the spin network. Put differently, this network is a means to describe the quantum geometry of space.<\/p>\n<p class=\"graf graf--p\">The most basic components in this theory are <a class=\"markup--anchor markup--p-anchor\" href=\"http:\/\/igpg.gravity.psu.edu\/people\/Ashtekar\/articles\/rovelli03.pdf\" target=\"_blank\" rel=\"noopener\" data-href=\"http:\/\/igpg.gravity.psu.edu\/people\/Ashtekar\/articles\/rovelli03.pdf\">quanta of space<\/a>\u200a\u2014\u200athe grains of space\u200a\u2014\u200awhich sit precisely at the points where the loops intersect\u200a\u2014\u200athe nodes of the network. A loop subsequently appears when taking a sequence of various links between the nodes\u200a\u2014\u200athe links are called connections.<\/p>\n<p class=\"graf graf--p\">Both the concept of volume and surface area, which are affiliated with the nodes and connections, respectively, are discrete in nature (see Fig. 2)\u200a\u2014\u200athis entails that the nodes and connections have quantum numbers attached to them. As a result, a certain region of physical space finds itself in a quantum superposition of the spin network states, which are expressed by these quantum numbers.<\/p>\n<figure class=\"graf graf--figure graf--layoutOutsetLeft\">\n<p><div style=\"width: 1108px\" class=\"wp-caption aligncenter\"><img data-recalc-dims=\"1\" decoding=\"async\" class=\"graf-image lazyload\" title=\"Each node in a spin network determines a cell, or an elementary grain of space.\" data-src=\"https:\/\/i0.wp.com\/cdn-images-1.medium.com\/max\/1200\/1%2AqWQsv8oUvx8t0YqIcCHEbw.png?resize=629%2C360&#038;ssl=1\" alt=\"Each node in a spin network determines a cell, or an elementary grain of space.\" width=\"629\" height=\"360\" data-image-id=\"1*qWQsv8oUvx8t0YqIcCHEbw.png\" data-width=\"1098\" data-height=\"628\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 629px; --smush-placeholder-aspect-ratio: 629\/360;\" \/><p class=\"wp-caption-text\">Fig. 2. Each node in a spin network determines a cell, or an elementary grain of space. (a) Nodes are represented by small black spheres and the links as black lines, while cells are separated by elementary surfaces shown in purple. Each surface corresponds to one link, and the structure builds up a 3D space. (b) When the surfaces are pulled away, we can see that the sequence of links form a loop. These are the \u201cloops\u201d of loop quantum gravity. (Source: <a href=\"http:\/\/igpg.gravity.psu.edu\/people\/Ashtekar\/articles\/rovelli03.pdf\" target=\"_blank\" rel=\"noopener\">Carlo Rovelli<\/a>).<\/p><\/div><\/figure>\n<p class=\"graf graf--p\">Given that in loop quantum gravity the concept of volume is quantized, the expansion of the Universe therefore suggests that this process should occur in discrete time steps. In other words, the existence of space<em class=\"markup--em markup--p-em\">time<\/em> implies a history of spaces. As space in loop quantum gravity exists of spin networks, the discrete (quantum) geometry of space<em class=\"markup--em markup--p-em\">time<\/em> is then constructed through a temporal evolution of these networks, a structure that in its entirety is named causal <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/arxiv.org\/pdf\/hep-th\/0507235.pdf\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/arxiv.org\/pdf\/hep-th\/0507235.pdf\">spin foam<\/a>. In so doing, spacetime can similarly be regarded as a quantum superposition of the spin foam states.<\/p>\n<p class=\"graf graf--p\">In terms of the theory\u2019s <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/arxiv.org\/pdf\/1607.05129.pdf\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/arxiv.org\/pdf\/1607.05129.pdf\">advantages<\/a>, not only does it get rid of the lingering infinities that rise to the surface when handling gravity as a quantum field in the UV limit (see above section \u201cThe Outline of the Marriage\u201d), but loop quantum gravity can also do without supersymmetry or extra spatial dimensions\u200a\u2014\u200aas yet undetected traits of M-theory\u200a\u2014\u200ato design a mathematically coherent theory of quantum gravity.<\/p>\n<p class=\"graf graf--p\">What is more, the theory ensures that, at lower energy approximations, the collective behaviour of loops at larger scales gives rise to <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/ui.adsabs.harvard.edu\/abs\/1992NuPhB.378..288Z\/abstract\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/ui.adsabs.harvard.edu\/abs\/1992NuPhB.378..288Z\/abstract\">gravitons<\/a>. In addition to that, loop quantum gravity dissolves aside from the Big Bang singularity (it is replaced by a <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/ui.adsabs.harvard.edu\/abs\/2006PhRvL..96n1301A\/abstract\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/ui.adsabs.harvard.edu\/abs\/2006PhRvL..96n1301A\/abstract\">Big Bounce<\/a>) also the black hole singularity (the black hole shrinks to a Planck star and <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/physics.aps.org\/articles\/v11\/127\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/physics.aps.org\/articles\/v11\/127\">bounces back<\/a> as a white hole). Also, it predicts the Bekenstein-Hawking <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/journals.aps.org\/prl\/abstract\/10.1103\/PhysRevLett.80.904\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/journals.aps.org\/prl\/abstract\/10.1103\/PhysRevLett.80.904\">entropy<\/a> of black holes (after fixing the Immirzi parameter) as well as the phenomenon of <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/ui.adsabs.harvard.edu\/abs\/2014APS..APRJ16001P\/abstract\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/ui.adsabs.harvard.edu\/abs\/2014APS..APRJ16001P\/abstract\">Hawking radiation<\/a>.<\/p>\n<p class=\"graf graf--p\">However, loop quantum gravity also comes with a couple of <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/arxiv.org\/pdf\/hep-th\/0507235.pdf\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/arxiv.org\/pdf\/hep-th\/0507235.pdf\">unresolved issues<\/a>. First, it is not clear yet how the theory can recover general relativity in the low energy limit. Second, there are some complications with background independence with respect to topology (the field that studies the properties of geometric objects that remain invariant under deformations). Finally, it struggles with the issue of <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/ui.adsabs.harvard.edu\/abs\/2012AnP...524..757A\/abstract\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/ui.adsabs.harvard.edu\/abs\/2012AnP...524..757A\/abstract\">time<\/a>; it grapples with reconciling two seemingly mutually exclusive notions: in quantum mechanics, time is addressed in an absolute fashion, whilst in general relativity it is considered a relative phenomenon.<\/p>\n<h3 class=\"graf graf--h3\"><strong class=\"markup--strong markup--h3-strong\">Causal Dynamical Triangulations<\/strong><\/h3>\n<p class=\"graf graf--p\">This background-independent (dynamical) theory takes discrete surfaces as the building blocks for the assembly of its quantum spacetime, whereby the background itself is <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/www.statphys.sissa.it\/download\/beria.pdf\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/www.statphys.sissa.it\/download\/beria.pdf\">subjected<\/a> to quantum fluctuations\u200a\u2014\u200aas in the case of loop quantum gravity. Sewing together the surfaces at the smallest of scales leads to the <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/iopscience.iop.org\/article\/10.1088\/1742-6596\/174\/1\/012015\/pdf\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/iopscience.iop.org\/article\/10.1088\/1742-6596\/174\/1\/012015\/pdf\">emergence<\/a> of our four-dimensional, continuous, curved spacetime structure at macroscopic dimensions (simply put, it gives us back general relativity).<\/p>\n<p class=\"graf graf--p\">Such a discrete, fundamental surface is called an <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/fais.uj.edu.pl\/documents\/41628\/84fd3b4a-b210-4ecb-8eb2-5d95e7f1f893\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/fais.uj.edu.pl\/documents\/41628\/84fd3b4a-b210-4ecb-8eb2-5d95e7f1f893\">n-simplex<\/a>, which is a generalization of a triangle to higher dimensions (in the case of an n-simplex, the number of dimensions are n). For example, a triangle is a 2-dimensional simplex (2-simplex) that consists of three vertices (0-simplices) and three links or edges (1-simplices). Triangulation then means subdividing a geometric object into n-simplices.<\/p>\n<p class=\"graf graf--p\">In this theory, space comes in a foliation structure, whereby each triangulated spatial leave, i.e., a slice, is assigned a discrete time step and successive slices are connected by n-simplices (see Fig. 3). Stitching these n-simplices together in such a way that the accompanying arrow of time of the edges (links between vertices) corresponds in direction eventually results in the emergence of quantum spacetime (see Fig. 4).<\/p>\n<figure class=\"graf graf--figure\">\n<p><div style=\"width: 1142px\" class=\"wp-caption aligncenter\"><img data-recalc-dims=\"1\" decoding=\"async\" class=\"graf-image lazyload\" title=\"A visualization of fundamental building blocks of four-dimensional Causal Dynamical Triangulations.\" data-src=\"https:\/\/i0.wp.com\/cdn-images-1.medium.com\/max\/1600\/1%2Am9EnjmcVnvZQTKJ1280XWA.png?resize=629%2C362&#038;ssl=1\" alt=\"A visualization of fundamental building blocks of four-dimensional Causal Dynamical Triangulations.\" width=\"629\" height=\"362\" data-image-id=\"1*m9EnjmcVnvZQTKJ1280XWA.png\" data-width=\"1132\" data-height=\"652\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 629px; --smush-placeholder-aspect-ratio: 629\/362;\" \/><p class=\"wp-caption-text\">Fig. 3. A visualization of fundamental building blocks of four-dimensional Causal Dynamical Triangulations (4-simplices in solid line). The simplices join two successive slices t and t+1 and are divided in to two types: {4,1} and {3,2}. The simplices are equipped with the flat Minkowski metric imposing the light-cone structure (blue-coloured image). The dotted line illustrates the cross section of a simplex by a three-dimensional hyperplane placed between the slices, at time t+1\/2. (Source: <a href=\"https:\/\/fais.uj.edu.pl\/documents\/41628\/84fd3b4a-b210-4ecb-8eb2-5d95e7f1f893\" target=\"_blank\" rel=\"noopener\">Thesis by Andrzej G\u00f6rlich<\/a>).<\/p><\/div><\/figure>\n<p class=\"graf graf--p\">Importantly, because of this built-in discrete temporal system, the premise of causality is embedded and conserved within this geometric structure. This imposed causality condition subsequently <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/arxiv.org\/pdf\/1004.0352.pdf\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/arxiv.org\/pdf\/1004.0352.pdf\">prohibits<\/a> either <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/acircleisround.com\/nl\/2020\/10\/25\/see-you-maybe-on-the-other-side\/\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/medium.com\/discourse\/see-you-maybe-on-the-other-side-13cef1a0b1ff?sk=929101cbbcdf7d6e97d5d316879cb24c\">wormholes<\/a> (a sort of cosmic shortcut to other locations in spacetime) or <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/arxiv.org\/pdf\/2002.08950.pdf\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/arxiv.org\/pdf\/2002.08950.pdf\">baby universes<\/a> (parts of the universe that have branched off of it) to ever arise in this specific spacetime.<\/p>\n<p class=\"graf graf--p\">What is more, the resultant quantum spacetime resembles our physical spacetime; the causal dynamical triangulation algorithm generates a so-called de Sitter universe, which, much like ours, is characterized by a positive cosmological constant\u200a\u2014\u200athis constant refers to the energy density of space itself and a positive constant signals the accelerated expansion of the Universe\u200a\u2014\u200aunlike superstring theory, whose fixed background is an anti-de Sitter spacetime containing a negative cosmological constant.<\/p>\n<p class=\"graf graf--p\">Note that, even though space is locally flat within each discrete simplex, the entire spacetime in its continuum, macroscopic limit is globally curved (see Fig. 4). Furthermore, the curvature of spacetime always resides on the n-2 dimensional sub-simplices for an n-simplex. That is, the location of curvature can be traced back to vertices for 2-simplices and to triangles for 4-simplices.<\/p>\n<figure class=\"graf graf--figure\">\n<p><div style=\"width: 1114px\" class=\"wp-caption aligncenter\"><img data-recalc-dims=\"1\" decoding=\"async\" class=\"graf-image lazyload\" title=\"Individual n-simplices and smoothly curved spacetime when the n-simplices are stitched together.\" data-src=\"https:\/\/i0.wp.com\/cdn-images-1.medium.com\/max\/1600\/1%2AP2X-ZV4yAKtao2PEKG6fSg.png?resize=629%2C359&#038;ssl=1\" alt=\"Individual n-simplices and smoothly curved spacetime when the n-simplices are stitched together.\" width=\"629\" height=\"359\" data-image-id=\"1*P2X-ZV4yAKtao2PEKG6fSg.png\" data-width=\"1104\" data-height=\"630\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 629px; --smush-placeholder-aspect-ratio: 629\/359;\" \/><p class=\"wp-caption-text\">Fig. 4. Left: n-simplices for different numbers of n. For example, the 4-simplex contains 5 vertices and 10 edges or links. Right: A lattice geometry simplicial approximation. (Source: <a href=\"https:\/\/www.statphys.sissa.it\/download\/beria.pdf\" target=\"_blank\" rel=\"noopener\">Marco\u00a0Beria<\/a>).<\/p><\/div><\/figure>\n<p class=\"graf graf--p\">The fact that the quantum super-positioned elementary simplices arrange themselves dynamically (by an as yet unknown underlying mechanism) into a de Sitter-shaped spacetime has led <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/arxiv.org\/pdf\/1004.0352.pdf\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/arxiv.org\/pdf\/1004.0352.pdf\">Jurkiewicz et al.<\/a> to allude to this triangulated modelled spacetime as a \u2018<em class=\"markup--em markup--p-em\">self-organizing quantum universe<\/em>\u2019.<\/p>\n<p class=\"graf graf--p\">So, the causal dynamic triangulations theory\u2019s <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/arxiv.org\/pdf\/1004.0352.pdf\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/arxiv.org\/pdf\/1004.0352.pdf\">strong<\/a> suit is its ability to design a quantum (discrete) geometry which develops into a smooth <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/arxiv.org\/pdf\/hep-th\/0507235.pdf\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/arxiv.org\/pdf\/hep-th\/0507235.pdf\">classical<\/a> spacetime at cosmic scales by falling back on a minimum of principles from quantum field theory and general relativity.<\/p>\n<p class=\"graf graf--p\">Moreover, this approach provides insight into the physics beyond the Planck scale: Calculations suggest that at these high-energy scales physics takes place in a <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/arxiv.org\/pdf\/1004.0352.pdf\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/arxiv.org\/pdf\/1004.0352.pdf\">two<\/a>-dimensional spacetime (rather than our familiar four dimensions at macroscopic scales). Other approaches to quantum gravity, such as <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/iopscience.iop.org\/article\/10.1088\/1126-6708\/2005\/10\/050\/meta\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/iopscience.iop.org\/article\/10.1088\/1126-6708\/2005\/10\/050\/meta\">asymptotically safe gravity<\/a> and <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/journals.aps.org\/prl\/abstract\/10.1103\/PhysRevLett.102.161301\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/journals.aps.org\/prl\/abstract\/10.1103\/PhysRevLett.102.161301\">Lifshitz gravity<\/a>, have come to the same conclusion.<\/p>\n<p class=\"graf graf--p\">Not only that, additional information about the quantum dynamics of the system is made accessible through the possibility of running numerical computer simulations, which is a <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/arxiv.org\/pdf\/1004.0352.pdf\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/arxiv.org\/pdf\/1004.0352.pdf\">unique<\/a> aspect of the theory within the whole pool of candidate theories.<\/p>\n<p class=\"graf graf--p\">Nevertheless, some physicists argue that, by integrating macroscopic qualities (e.g., curvature) into the simplices, information about the microstructure might be <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/iopscience.iop.org\/article\/10.1088\/1742-6596\/174\/1\/012015\/pdf\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/iopscience.iop.org\/article\/10.1088\/1742-6596\/174\/1\/012015\/pdf\">obscured<\/a>. Further, it is not yet entirely clear how <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/fais.uj.edu.pl\/documents\/41628\/84fd3b4a-b210-4ecb-8eb2-5d95e7f1f893\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/fais.uj.edu.pl\/documents\/41628\/84fd3b4a-b210-4ecb-8eb2-5d95e7f1f893\">matter<\/a>, black holes, and the Big Bang cosmology <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/www.sciencedirect.com\/science\/article\/pii\/S2211379712000319#b0040\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/www.sciencedirect.com\/science\/article\/pii\/S2211379712000319#b0040\">fit<\/a> into this theory. Finally, a point of friction may be that causal dynamical triangulations <a class=\"markup--anchor markup--p-anchor\" href=\"http:\/\/backreaction.blogspot.com\/2019\/09\/the-five-most-promising-ways-to.html\" target=\"_blank\" rel=\"noopener\" data-href=\"http:\/\/backreaction.blogspot.com\/2019\/09\/the-five-most-promising-ways-to.html\">treats<\/a> space and time in a different manner whereas Einstein\u2019s general relativity puts them both on equal footing.<\/p>\n<h3 class=\"graf graf--h3\"><strong class=\"markup--strong markup--h3-strong\">Asymptotically Safe\u00a0Gravity<\/strong><\/h3>\n<p class=\"graf graf--p\">As introduced in the above section \u201cThe Outline of the Marriage\u201d, the approach to establish a theory of quantum gravity beyond the Planck scale by quantizing the theory of general relativity traditionally leads to the inability to come up with a finite number of physical parameters to describe the theory\u200a\u2014\u200athe technical term for this applied method is <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/physics.stackexchange.com\/questions\/336460\/meaning-of-perturbative-and-non-perturbative-renormalizability\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/physics.stackexchange.com\/questions\/336460\/meaning-of-perturbative-and-non-perturbative-renormalizability\">perturbative renormalization<\/a>.<\/p>\n<p class=\"graf graf--p\">Asymptotically safe gravity still wants to quantize general relativity, but instead of resorting to perturbative renormalization it uses a slightly distinct method, known as <a class=\"markup--anchor markup--p-anchor\" href=\"http:\/\/philsci-archive.pitt.edu\/16786\/1\/asymptoticsafetypaper.pdf\" target=\"_blank\" rel=\"noopener\" data-href=\"http:\/\/philsci-archive.pitt.edu\/16786\/1\/asymptoticsafetypaper.pdf\">non-perturbative renormalization<\/a>\u200a\u2014\u200amore specifically, it relies on the <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/arxiv.org\/abs\/2006.04853\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/arxiv.org\/abs\/2006.04853\">functional renormalization group<\/a> scheme. The concept of theory space, i.e., the theoretical space of all possible dynamics of a physical system, along with dimensionless couplings, i.e., the <a class=\"markup--anchor markup--p-anchor\" href=\"http:\/\/hyperphysics.phy-astr.gsu.edu\/hbase\/Forces\/couple.html\" target=\"_blank\" rel=\"noopener\" data-href=\"http:\/\/hyperphysics.phy-astr.gsu.edu\/hbase\/Forces\/couple.html\">parameter<\/a> that reflects the strength of particle or field interactions, take a central stage in this technique.<\/p>\n<p class=\"graf graf--p\">A theory is considered <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/inspirehep.net\/literature\/83667\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/inspirehep.net\/literature\/83667\">asymptotically <em class=\"markup--em markup--p-em\">free<\/em><\/a><em class=\"markup--em markup--p-em\">,<\/em> when all the dimensionless couplings become zero in the high-energy UV limit. Stated in another way, such a theory must contain a UV fixed point in theory space\u200a\u2014\u200aa fixed point can be interpreted as a consistent microscopic initial condition of the physical theory. One example includes the theory of <a class=\"markup--anchor markup--p-anchor\" href=\"http:\/\/hyperphysics.phy-astr.gsu.edu\/hbase\/Particles\/qbag.html\" target=\"_blank\" rel=\"noopener\" data-href=\"http:\/\/hyperphysics.phy-astr.gsu.edu\/hbase\/Particles\/qbag.html\">quantum chromodynamics<\/a>, which accounts for the strong nuclear force between quarks and gluons inside the nucleus of atoms, whereby the respective particles are non-interacting in the UV limit.<\/p>\n<p class=\"graf graf--p\">However, when the couplings are non-zero but still finite in the UV limit, a theory is deemed <a class=\"markup--anchor markup--p-anchor\" href=\"http:\/\/www.percacci.it\/roberto\/physics\/as\/faq.html\" target=\"_blank\" rel=\"noopener\" data-href=\"http:\/\/www.percacci.it\/roberto\/physics\/as\/faq.html\">asymptotically <em class=\"markup--em markup--p-em\">safe<\/em><\/a>. The corresponding fixed point is then referred to as a non-Gaussian fixed point. That is to say, the asymptotic safety-based approach to quantum gravity aims to be a quantum theory that accommodates a non-Gaussian UV fixed point in theory space and reduces to general relativity in the low-energy regime.<\/p>\n<p class=\"graf graf--p\">Asymptotically safe gravity indeed manages to identify such fixed point for one specific finite-dimensional subspace\u200a\u2014\u200acalled a truncation\u200a\u2014\u200aof theory space, namely the Einstein-Hilbert truncation (see Fig. 5).<\/p>\n<p class=\"graf graf--p\">In terms of the geometric characteristics beyond the Planck scale, <a class=\"markup--anchor markup--p-anchor\" href=\"http:\/\/philsci-archive.pitt.edu\/16786\/1\/asymptoticsafetypaper.pdf\" target=\"_blank\" rel=\"noopener\" data-href=\"http:\/\/philsci-archive.pitt.edu\/16786\/1\/asymptoticsafetypaper.pdf\">spacetime<\/a> under the asymptotic safety scenario appears to reveal fractal-like features (a <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/users.math.yale.edu\/public_html\/People\/frame\/Fractals\/\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/users.math.yale.edu\/public_html\/People\/frame\/Fractals\/\">fractal<\/a> is a geometric shape whose constituent parts are self-similar to the whole shape) and come in two dimensions (as in the theory of causal dynamical triangulations).<\/p>\n<figure class=\"graf graf--figure graf--layoutOutsetLeft\">\n<p><div style=\"width: 1158px\" class=\"wp-caption aligncenter\"><img data-recalc-dims=\"1\" decoding=\"async\" class=\"graf-image lazyload\" title=\"Diagram of the flow of the dimensionless Newton\u2019s constant g and cosmological constant \u03bb based on the E-H truncation.\" data-src=\"https:\/\/i0.wp.com\/cdn-images-1.medium.com\/max\/1200\/1%2AHxuIsNimtZur3vnDgZSyPQ.png?resize=629%2C358&#038;ssl=1\" alt=\"Diagram of the flow of the dimensionless Newton\u2019s constant g and cosmological constant \u03bb based on the E-H truncation.\" width=\"629\" height=\"358\" data-image-id=\"1*HxuIsNimtZur3vnDgZSyPQ.png\" data-width=\"1148\" data-height=\"654\" src=\"data:image\/svg+xml;base64,PHN2ZyB3aWR0aD0iMSIgaGVpZ2h0PSIxIiB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciPjwvc3ZnPg==\" style=\"--smush-placeholder-width: 629px; --smush-placeholder-aspect-ratio: 629\/358;\" \/><p class=\"wp-caption-text\">Fig. 5. Diagram of the flow of the dimensionless Newton\u2019s constant g and cosmological constant \u03bb based on the Einstein-Hilbert truncation. Arrows flow from UV to the infrared (IR). The origin corresponds to an infrared-attractive Gaussian fixed point and the non-Gaussian UV fixed point sits in the centre of the spiralling arrows. The green trajectory connects both fixed points and separates regions with positive and negative cosmological constant \u03bb at low energy scales from each other. The candidate trajectory to be realized in nature is extremely close to the right of the green trajectory. (Source: <a href=\"http:\/\/philsci-archive.pitt.edu\/16786\/1\/asymptoticsafetypaper.pdf\" target=\"_blank\" rel=\"noopener\">Paper Simon Friederich<\/a>).<\/p><\/div><\/figure>\n<p class=\"graf graf--p\">To its advantage, the theory of asymptotically safe gravity is <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/ui.adsabs.harvard.edu\/abs\/2009GReGr..41..983R\/abstract\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/ui.adsabs.harvard.edu\/abs\/2009GReGr..41..983R\/abstract\">background-independent<\/a>, does not appeal to new hypothetical objects (unlike superstring theory) <a class=\"markup--anchor markup--p-anchor\" href=\"http:\/\/philsci-archive.pitt.edu\/16786\/1\/asymptoticsafetypaper.pdf\" target=\"_blank\" rel=\"noopener\" data-href=\"http:\/\/philsci-archive.pitt.edu\/16786\/1\/asymptoticsafetypaper.pdf\">and<\/a> builds on existing theories (field theories and renormalization), seems to incorporate a procedure that explains the <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/journals.aps.org\/prd\/abstract\/10.1103\/PhysRevD.94.103514\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/journals.aps.org\/prd\/abstract\/10.1103\/PhysRevD.94.103514\">origin<\/a> of the Big Bang as well as <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/iopscience.iop.org\/article\/10.1088\/1475-7516\/2007\/08\/024\/meta\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/iopscience.iop.org\/article\/10.1088\/1475-7516\/2007\/08\/024\/meta\">cosmic inflation<\/a>, has predicted both the <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0370269309014579\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0370269309014579\">mass<\/a> of the Higgs boson and the <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/link.springer.com\/article\/10.1007%2FJHEP05%282011%29119\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/link.springer.com\/article\/10.1007%2FJHEP05%282011%29119\">value<\/a> of fundamental constants, finds a <a class=\"markup--anchor markup--p-anchor\" href=\"http:\/\/philsci-archive.pitt.edu\/16786\/1\/asymptoticsafetypaper.pdf\" target=\"_blank\" rel=\"noopener\" data-href=\"http:\/\/philsci-archive.pitt.edu\/16786\/1\/asymptoticsafetypaper.pdf\">relationship<\/a> between the questions of why there is a classical regime at all and why the cosmological constant in that low-energy limit is so small, and might provide an <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/journals.aps.org\/prd\/abstract\/10.1103\/PhysRevD.70.124028\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/journals.aps.org\/prd\/abstract\/10.1103\/PhysRevD.70.124028\">explanation<\/a> for the gravitational behaviour of rotating flat galaxies without invoking dark matter.<\/p>\n<p class=\"graf graf--p\">Concerning its points of improvement, this theory <a class=\"markup--anchor markup--p-anchor\" href=\"http:\/\/philsci-archive.pitt.edu\/16786\/1\/asymptoticsafetypaper.pdf\" target=\"_blank\" rel=\"noopener\" data-href=\"http:\/\/philsci-archive.pitt.edu\/16786\/1\/asymptoticsafetypaper.pdf\">requires<\/a> more robust mathematical groundwork, inasmuch as there is no math-based proof available yet for the presence of a non-Gaussian UV fixed point in <em class=\"markup--em markup--p-em\">any<\/em> truncation under observation, not just the Einstein-Hilbert truncation. Also, <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/arxiv.org\/abs\/0709.3555\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/arxiv.org\/abs\/0709.3555\">some physicists<\/a> highlight some inconsistencies between this approach to quantum gravity and the Bekenstein-Hawking formula for black hole entropy (<a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/journals.aps.org\/prd\/abstract\/10.1103\/PhysRevD.89.084002\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/journals.aps.org\/prd\/abstract\/10.1103\/PhysRevD.89.084002\">others<\/a> refute this criticism, pointing out that the inconsistency makes sense, since it is not expected that this formula should hold in the high-energy limit of the theory in the first place).<\/p>\n<p class=\"graf graf--p\">In addition, asymptotically safe gravity does <a class=\"markup--anchor markup--p-anchor\" href=\"http:\/\/philsci-archive.pitt.edu\/16786\/1\/asymptoticsafetypaper.pdf\" target=\"_blank\" rel=\"noopener\" data-href=\"http:\/\/philsci-archive.pitt.edu\/16786\/1\/asymptoticsafetypaper.pdf\">not<\/a> offer any solution to the <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/www.informationphilosopher.com\/problems\/measurement\/\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/www.informationphilosopher.com\/problems\/measurement\/\">measurement problem<\/a> in quantum mechanics and must show\u200a\u2014\u200a<a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/journals.aps.org\/prl\/abstract\/10.1103\/PhysRevLett.106.251302\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/journals.aps.org\/prl\/abstract\/10.1103\/PhysRevLett.106.251302\">except<\/a> for the Einstein-Hilbert truncation, as it has done so already\u200a\u2014\u200athat the abovementioned results continue to apply in a spacetime that carries a causal structure in it (technically, it has to demonstrate that the results are valid in a spacetime not only with a Euclidean signature but also with a Lorentzian one). In other words, it is <a class=\"markup--anchor markup--p-anchor\" href=\"http:\/\/backreaction.blogspot.com\/2019\/09\/the-five-most-promising-ways-to.html\" target=\"_blank\" rel=\"noopener\" data-href=\"http:\/\/backreaction.blogspot.com\/2019\/09\/the-five-most-promising-ways-to.html\">not<\/a> immediately obvious that asymptotically safe gravity constitutes a quantum theory in the UV regime.<\/p>\n<h3 class=\"graf graf--h3\"><strong class=\"markup--strong markup--h3-strong\">Closing the\u00a0Deal<\/strong><\/h3>\n<p class=\"graf graf--p\">Apart from the four main contenders for assembling <em class=\"markup--em markup--p-em\">the<\/em> theory of quantum gravity discussed in this article, still many other attempts are out there, such as <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/arxiv.org\/abs\/0903.0878\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/arxiv.org\/abs\/0903.0878\">emergent gravity<\/a>, <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/pos.sissa.it\/292\/078\/pdf\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/pos.sissa.it\/292\/078\/pdf\">infinite derivative gravity<\/a>, <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/link.springer.com\/article\/10.1007\/s41114-019-0023-1\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/link.springer.com\/article\/10.1007\/s41114-019-0023-1\">causal set theory<\/a>, background independent <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/arxiv.org\/abs\/1806.08704\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/arxiv.org\/abs\/1806.08704\">versions<\/a> of string theory, <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0370269317304100\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0370269317304100\">non-commutative geometry<\/a>, <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/link.springer.com\/chapter\/10.1007\/978-3-319-44418-5_25\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/link.springer.com\/chapter\/10.1007\/978-3-319-44418-5_25\">topos theory<\/a>, and new approaches that <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/abcbde\/meta\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/iopscience.iop.org\/article\/10.1088\/1361-6382\/abcbde\/meta\">mix<\/a> <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/arxiv.org\/abs\/1909.06340\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/arxiv.org\/abs\/1909.06340\">various<\/a> theories.<\/p>\n<p class=\"graf graf--p\">Perhaps our recent memory about the importance of <a class=\"markup--anchor markup--p-anchor\" href=\"https:\/\/journals.sagepub.com\/doi\/full\/10.1177\/2380084420976358\" target=\"_blank\" rel=\"noopener\" data-href=\"https:\/\/journals.sagepub.com\/doi\/full\/10.1177\/2380084420976358\">trust<\/a> in science might give a new impetus to bringing closure to this almost century-old challenge. Be that as it may, time will surely tell which one of the candidates will eventually succeed in officially marrying quantum mechanics to gravity all the way to UV completion.<\/p>\n<p class=\"graf graf--p\">In the meantime, all bets are open.<\/p>\n<hr \/>\n<p class=\"graf graf--p\" style=\"text-align: right;\"><a href=\"https:\/\/acircleisround.com\/nl\/articles\/\">Back to Articles<\/a><\/p>","protected":false},"excerpt":{"rendered":"<p>We always appreciate it when explanations add up. There is a sort of soothing and satisfying effect that comes along and suffuses us when things make sense. Precisely for those reasons, what has irked many theoretical physicists for already several decades is the absence of the theory of quantum gravity, which intends to put gravitational [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":860,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_uf_show_specific_survey":0,"_uf_disable_surveys":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[84],"tags":[64,17,63,28,50,62],"class_list":["post-859","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-theoretical-physics","tag-general-relativity","tag-integration","tag-quantum-gravity","tag-quantum-physics","tag-science","tag-theoretical-physics"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Quantum Gravity in the Making - A Circle Is Round - Science Writing<\/title>\n<meta name=\"description\" content=\"What are the leading theories that present themselves as candidates for the theory of quantum gravity? 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We wait for that insight, for that click, for that new perspective, for that shift to happen so that everything just makes sense. And when it does click, it feels as if the solution was right there all along. Everything feels familiar and we feel so much lighter. Only this time, we are wearing a new and more experienced jacket. While circling through life one step at a time, the key insight lies in the fact that we are all connected. My name is Olivier and I write in circles to eventually come back to the same point. In the meantime, at every step, I write an article. 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We wait for that insight, for that click, for that new perspective, for that shift to happen so that everything just makes sense. And when it does click, it feels as if the solution was right there all along. Everything feels familiar and we feel so much lighter. Only this time, we are wearing a new and more experienced jacket. While circling through life one step at a time, the key insight lies in the fact that we are all connected. My name is Olivier and I write in circles to eventually come back to the same point. In the meantime, at every step, I write an article. 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