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Oxford Colloquium 27Nov2020

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Oxford Colloquium 27Nov2020 What is Spacetime made of? Fay Dowker Imperial College London Oxford 27th November 2020 The Party Bag: • Causal set theory is an approach to the problem of quantum gravity that proposes a fundamental atomicity or discreteness of spacetime. • The microscopic degrees of freedom are discrete causal relations. • This may help us to explain Black Hole Entropy • Causal sets were used to make a successful prediction in cosmology (and what a prediction!) with potential for more to come • Causal sets give us a new way to think about the passage of time What is Quantum Gravity? • The phrase is a shorthand that names the biggest obstacle we currently face in our search for a unified framework for physics: General Relativity, our best theory of spacetime, does not do justice to the quantum nature of matter • Scarcity of observational/experimental data has led to a wide range of different approaches to quantum gravity. • Many workers think that we need to create a new framework with novel concepts probably radically different from the physics we know now. • That’s all very well, but how to get there from here? Asking “what is spacetime made of?” is a heuristic that can help us and that leads to a proposal of the atomicity of space-time and the causal order of spacetime as fundamental The Laws of Black Hole Mechanics Bardeen, Carter, Hawking 1973 is the surface gravity of the horizon of a stationary black hole, A is the surface area of the horizon Thermo Black Hole Zeroth T is constant throughout system in is constant on horizon of stationary Law equilibrium black hole 1 1st Law dE = TdS work dM = dA work − 8⇡G − Hawking’s Area 2nd Law dS 0 dA 0 ≥ ≥ Theorem T cannot be reduced to zero in cannot be reduced to zero in 3rd Law a finite process a finite process A remarkable “analogy” ? The Laws of Black Hole Thermodynamics Bekenstein, Bardeen, Carter, Hawking, Gibbons, Perry 1. Bekenstein proposed: area of black hole horizon is physically an entropy 2. Hawking proved that a black hole has a quantum temperature <latexit sha1_base64="nOSMbWy4/NVYCRJW63F5vrBUY/E=">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</latexit> 1 A ~ SBH = 2 ,TBH = 4 lp 2⇡ This turns Black Hole Mechanics into Black Hole Thermodynamics Black holes are the epitome of General Relativity. It is striking that GR “knows” about quantum mechanics and thermodynamics: The broadest unity yet achieved in physics, but it raises a question Seeking the Statistical Mechanics of BH Thermodynamics • The BH entropy has a quantum gravitational value. Not only it is finite but its value sets a scale and suggests that spacetime itself is discrete Entropy of BH is the number Entropy of a box of gas of Planck sized plaquettes is equal to the number of tiling the horizon (up to molecules (up to factor of factor of order one) order one) • There’s nothing locally special about BH horizons. If horizons are discrete, so must spacetime itself be discrete. Spacetime, NOT space 4d Newtonian Spacetime: made of slices of space A finite chunk of infinite spacetime In Newtonian physics, physical time is “spatialised” as a “dimension” 4d Einsteinian Spacetime in GR: made of events (Geroch) FUTURE A finite chunk of spacetime PAST In GR, there is no such thing as 3d space, only 4d spacetime. Physical time is local and passes along worldlines. Hypothesis: spacetime is “atomic”, made of indivisible, identical, Planck scale events Causal Order is central to GR and Black Hole Thermo NOBEL PRIZE 2020 to Penrose! Theorem: The causal order — Q which events are to the causal past and γ future of which other events — and the R volume of any region of spacetime, tells you the full geometry P (Penrose, Hawking, Malament) A black hole horizon is the boundary of the causal past of an “eternal” worldline. Black hole thermodynamics is tied to the causal nature of the horizon So, we postulate that causal order is what binds together the discrete spacetime atoms, resulting in ………. Discrete causal order = causal set transitive, directed, acyclic graph Continuum approximation (fluid) = a causal set B Future B A C A C D Past D <latexit sha1_base64="8YGkbdeUa6rozMJ3nLavtPbljKY=">AAAB73icbVBNSwMxEJ2tX7V+VT16CRbBU8mWih6LXjxWsB/QriWbZtvQbHZNskJZ+ie8eFDEq3/Hm//GdLsHbX0w8Hhvhpl5fiy4Nhh/O4W19Y3NreJ2aWd3b/+gfHjU1lGiKGvRSESq6xPNBJesZbgRrBsrRkJfsI4/uZn7nSemNI/kvZnGzAvJSPKAU2Ks1HXxQ1qr49mgXMFVnAGtEjcnFcjRHJS/+sOIJiGThgqidc/FsfFSogyngs1K/USzmNAJGbGepZKETHtpdu8MnVlliIJI2ZIGZerviZSEWk9D33aGxIz1sjcX//N6iQmuvJTLODFM0sWiIBHIRGj+PBpyxagRU0sIVdzeiuiYKEKNjahkQ3CXX14l7VrVvajiu3qlcZ3HUYQTOIVzcOESGnALTWgBBQHP8ApvzqPz4rw7H4vWgpPPHMMfOJ8/uGiPGw==</latexit> Lorentz invariant 10240 Statistical Order + Number = Geometry The Causal Set Quantum Gravity Programme (Rafael Sorkin) Continuum spacetime is an approximation to a discrete order/causal set (’t Hooft; Myrheim; Bombelli, Lee, Meyer and Sorkin) • Kinematics: study the substance. Can a causal set hold enough data to be the underpinning of a (more or less unique) continuum spacetime? • Dynamics: on causal sets, and of causal sets. The quantum theory of causal sets will be based on the path integral or sum- over-histories: iS(g) Z = e Z = eiS(C) spacetime geometries g X causetsX C • Phenomenology: how could the discrete substructure reveal itself to us? Kinematics: Gibbons-Hawking boundary term 7 + + C M } 5 6 ⌃ 3 4 M − } C− 1 2 <latexit sha1_base64="tgIc+AB6VU5O17ENdE2UfXdCcgQ=">AAACCXicbVDNS8MwHE3n15xfVY9egkPwNFpR9DjmRfAycV+wlpKm2RaWpiFJhVF29eK/4sWDIl79D7z535h1Pejmg5DHe78fyXuhYFRpx/m2Siura+sb5c3K1vbO7p69f9BRSSoxaeOEJbIXIkUY5aStqWakJyRBcchINxxfz/zuA5GKJrylJ4L4MRpyOqAYaSMFNmy0oCdkInQCPcp14N3TYYxg5Kn8vg3sqlNzcsBl4hakCgo0A/vLixKcxoRrzJBSfdcR2s+Q1BQzMq14qSIC4TEakr6hHMVE+VmeZApPjBLBQSLN4Rrm6u+NDMVKTeLQTMZIj9SiNxP/8/qpHlz5GeUi1YTj+UODlEETe1YLjKgkWLOJIQhLav4K8QhJhLUpr2JKcBcjL5POWc29qDl359V6o6ijDI7AMTgFLrgEdXADmqANMHgEz+AVvFlP1ov1bn3MR0tWsXMI/sD6/AFQpJl0</latexit> <latexit sha1_base64="x3HM+pB9SXvBBS+YfC5gAfR4Bwk=">AAACEHicbVDLTgIxFO34RHyhLt00EiPEQGaMRpcENq4MJrwSwEmndKCh7UzajpFM+AQ3/oobFxrj1qU7/8YysFDwJE3OPefe3N7jhYwqbdvf1tLyyuraemojvbm1vbOb2dtvqCCSmNRxwALZ8pAijApS11Qz0golQdxjpOkNKxO/eU+kooGo6VFIuhz1BfUpRtpIbuakUq7BTiiDUAfwxo05ehjnKneFPCwkJRWT8jTvZrJ20U4AF4kzI1kwQ9XNfHV6AY44ERozpFTbsUPdjZHUFDMyTnciRUKEh6hP2oYKxInqxslBY3hslB70A2me0DBRf0/EiCs14p7p5EgP1Lw3Ef/z2pH2r7oxFWGkicDTRX7EoDl+kg7sUUmwZiNDEJbU/BXiAZIIa5Nh2oTgzJ+8SBpnReeiaN+eZ0vlWRwpcAiOQA444BKUwDWogjrA4BE8g1fwZj1ZL9a79TFtXbJmMwfgD6zPHzhsmss=</latexit> + BT dσK CBT N (C−) N (C ) / / max − min Z⌃ ⇡d(d + 1) Buck, FD, Jubb, Surya cd = 2 2 2 d d d 2(d + 2)Γ( d )Γ( 2 + 1) d Black Hole Entropy: horizon molecules 7 + + C M } M + 5 6 ⌃ ⌃ 3 4 M − } C− 1 2 • If Sigma intersects a horizon and we consider only elements below Sigma then counting the number of causal links (nearest neighbour relations) that straddle the horizon near Sigma gives a number equal to the area in fundamental Planckian units up to a factor of order one. • Think of these links as horizon molecules c.f. entropy of box of gas • Statistical mechanics of the horizon state: can this come from a proper state counting of the horizon? Barton, Counsell, FD, Gould, Jubb, Taylor Phenomenology: Causal sets used to predict Lambda • In the late 1980’s/early 1990’s Rafael Sorkin predicted the value of the Cosmological “Constant” Lambda today using a heuristic argument based on expectations of quantum causal set theory. • Since Number ~ Volume, it is natural in a path integral for causal set quantum gravity to fix N for the causal sets summed over (Note: a justification for “unimodular” gravity c.f. Weinberg) • Because the Number/Volume relationship is statistical, fixing N means there are fluctuations in V of order ∆V pN pV ⇠ ⇠ • V and Lambda are canonically conjugate (c.f. Time and Energy) so ∆V ⇥ 1 ⇠ 1 2 120 ⇥ H 10− ⇠ ∆V ⇠ ⇠ If Lambda fluctuates about zero, then what we see is only the fluctuation Everpresent Lambda (Ahmed, Dodelson, Greene & Sorkin; Ahmed & Sorkin) There are homogeneous cosmological models realising Sorkin’s idea — stochastic models, not GR. The value of Lambda fluctuates, on a Hubble timescale, between positive and negative values that are of the same order of magnitude as the ambient matter density (Lambda is “everpresent”). Confrontation with observations (Nosiphiwo Zwane, Afshordi, Sorkin) • Run the stochastic model to get a history of Omega_Lambda(z) and a(z) • Calculate perturbations using CAMB: model spatial fluctuations in rho_Lambda as a quintessence field (different potential depending on history a(z), Omega_Lambda(z)), • Input into CosmoMC, Monte Carlo Markov Chain parameter estimation • Looked at CMB, BAO, H_0, Nucleosynthesis (Li-7 problem), Ultramassive black holes at high z. Headline: There are (“not atypical”) runs that do just as well as LambdaCDM in matching the data and do better at alleviating the “H0 tension” An ancient Dichotomy about Time Time is an illusion vs Time really passes Being vs Becoming Block Universe vs Growing Block • The main reason physicists support the Block is GR and the absence of the notion of 3d space and a Global Now • Within current physics, there is no way to resolve this dichotomy, but it
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