Three Roads to Quantum Gravity
by Lee Smolin read in 2006
4 QM changed observer/observed relationship and held space/time relationship equal to Newton's. GR did the reverse.
17 "But if it is knowledge we desire, if we wish to understand what the universe is and how it came to be that way, we need to seek answers to questions about the things we see when we look around us."
18 Space is like a sentence; geometry like a grammar. I say this is closer than Smolin might think: all are concepts.
20 "There is nothing beyond the world except what we see, no background to it except its particular history."
22 "Points of space have no existence in themselves -- the only meaning a point can have is as a name we give to a particular feature in the network of relationships between the three sets of field lines."
31 Topos theory
32 George Soros: Theory of reflexivity
35 "a state consists of all the information needed to completely describe a system at an instant of time." OK. Now does 'describe' have any meaning in any context that excludes consciousness?
40 Wheeler-DeWitt equations define a quantum theory of cosmology.
40 Smolin, Jacobson, and Rovelli found exact solutions to these equations in 1986.
43 Consistent histories; Fay Dowker; Adrian Kent
44 "It is almost as if the questions bring reality into being. If one does not first ask for a history of the world that includes the question of whether dinosaurs roamed the Earth a hundred million years ago, one may not get a description in which the notion of dinosaurs -- or any other big 'classical objects' -- has any meaning."
45 The meaning of the word 'is'
45 "different observers see partly different, partial views of the universe."
47 Fotini Markopoulou-Kalamara's context-dependent theory: a context turns out to be the past of an observer at a given moment.
47 "In all these [context-dependent] theories there are many quantum descriptions of the same universe. Each of them depends on a way of splitting the universe into two parts such that one part contains the observer and the other part contains what the observer wishes to describe."
48 "One universe, seen by many observers, rather than many universes, seen by one mythical observer outside the universe." Supports my notion of one PC following all world lines.
56 "...the universe as a kind of computer. But it is a computer in which the circuitry is not fixed, but can evolve in time as a consequence of the information flowing through it."
59 "The causal structure is not fixed for all time. It is dynamical: it evolves, subject to laws."
59 "...gravitational ...waves travel through the causal structure"
60 "Einstein's theory of gravity is a theory of causal structure. It tells us that the essence of spacetime is causal structure and that the motion of matter is a consequence of alterations in the network of causal relations."
61 The universe might be finite and discrete.
62 "The Planck scale can be established in terms of known fundamental principles."
63 "What caused our world to exist was probably not so much an explosion as an event that caused a region of the universe to cool drastically and freeze."
63 Reality is a network of relationships of properties.
64 Elementary particles are really like elementary computer operations.
64 "The whole history of the world is then nothing but the story of huge numbers of these processes, whose relationships are continually evolving."
64 "What is mystical is the picture of the world as existing in an eternal three-dimensional space, extending in all directions as far as the mind can imagine. The idea of space going on and on for ever has nothing to do with what we see."
65 "When we imagine we are seeing into an infinite three-dimensional space, we are falling for a fallacy in which we substitute what we actually see for an intellectual construct. This is not only a mystical vision, it is wrong."
72 Plato, objectivity, observer independence, and knowability
72 "'objectivity' is not the same as 'knowable by all'" The troublesome 'all'.
74 "horizons [of black holes] are themselves surfaces of light....a curtain made of photons."
81 Acceleration causes the appearance of particles and an increase in temperature.
83 Heisenberg's Uncertainty Principle implies zero point motion.
83 Quantum fluctuations of the vacuum
84 Entropy, disorder, randomness, heat -- all derived from lack of information!
86 The position and motion info of random gas molecules is "thrown away" only in the context of our conversations (upward info) it is still present informing the behavior of the particles themselves (downward info).
86 "The entropy of a gas is a measure of this information -- it is equal to the number of yes/no questions that would have to be answered to give a precise quantum theoretic description of all the atoms in the gas."
86 "Unruh's law: Accelerating observers see themselves as embedded in a gas of hot photons at a temperature proportional to their acceleration.
Berkenstein's Law: With every horizon that forms a boundary separating an observer from a region which is hidden from them, there is associated an entropy which measures the amount of information which is hidden behind it. This entropy is always proportional to the area of the horizon."
90 Gerard 't Hooft says a black hole horizon is like a computer screen with one pixel for each four Planck areas.
91 Misuse of analogy characterizes the thinking of novices.
91 Hawkings Law: T = k/m
93 "in most circumstances entropy is a measure of missing information." Missing from what or whom?
96 "the world around us [is] nothing but a network of evolving relationships...among the events that make up the history of the world. The relationships define the space, not the other way round."
98 "the laws of thermodynamics are not absolute: they describe what is most likely to happen, but there will always be a small probability of the laws being violated."
99 Wittgenstein switched from physics to philosophy after Boltzmann's suicide.
99 Laws of thermo are exactly true for infinite systems: Einstein realized they could be broken for finite systems.
100 "But Planck was one of those physicists who believed neither in atoms nor in Boltzmann's work."
100 "the birth of quantum physics is more properly attributed to Einstein and Ehrenfest." than to Planck.
101 "The search for the meaning of temperature and entropy of matter led to the discovery of atoms. The search for the meaning of the temperature and entropy of radiation led to the discovery of quanta. In just the same way, the search for the meaning of the temperature and entropy of a black hole is now leading to the discovery of the atomic structure of space and time."
101 Black holes somehow balance information against the geometry of space.
103 "Both loop quantum gravity and string theory assert that there is an atomic structure to space."
103 "spacetime can be understood to be structured by processes which transmit information from the past to the future."
103 "the area of the surface is a measure of its capacity to transmit information. This is very suggestive." Yes. It suggests an observer at a CRT.
104 An argument that the world must be discrete.
104 "Many of the important principles in twentieth-century physics are expressed as limitations on what we can know." What is the definition of 'we'?
105 "there is an absolute limit to information which requires each region of space to contain at most a certain finite amount of information" - Berkenstein's Bound
106 "the attempt to measure a unit of volume smaller than the minimal size alters the geometry of the space in a way that allows more volume to be created"
113 Strings or fields may be ontologically fundamental.
113 The hypothesis of duality
119 Julian Barbour
123 Louis Crane and the hypothesis that the structure of spacetime is like a fractal at Planck distances.
125 Abhay Ashtekar found a simpler reformulation of GR
128 LQG "gave...an exact description of the physics of the Planck scale in which space is constructed from nothing but the relationships among a set of discrete elementary objects."
131 "One straightforward consequence [of LQG] is that quantum geometry is indeed discrete"
131 Infinities come from the erroneous assumption that the geometry of spacetime is fixed and non-dynamical.
137 "In the spin network picture, space only seems continuous -- it is actually made up of building blocks which are the nodes and edges of the spin network."
137 Renate Loll
138 "The spin networks do not live in space; their structure generates space. And they are nothing but a structure of relations"
139 The metric tensor of classical geometry is approximately equivalent to the spin network of LQG.
139 "the picture of spacetime given by loop quantum gravity agrees with the fundamental principle that in the theory of relativity there are no things, only processes."
139 Spin foam
142 "The predictions [of LQG] do not constrain what else there can be in the world, how many dimensions there are or what the fundamental symmetries are."
143 "Giovanni Amelino-Camelia, has pointed out that there is a way to test the predictions that the geometry of space is discrete on the Planck scale."
147 Grossmann told Einstein about the curvature tensor.
152 Perturbation theory - approximations in the absence of a true theory.
156 Renormalization - Forcing the right answers to the mass and charge of an electron rather than the infinities produced by the theory.
160 Compactified dimensions
160 String theory is simplest in 9D space
160 Each way of compactifying the hidden dimensions leads to a different geometry and topology and thus a different string theory.
160 "the geometry of the extra dimensions influences the masses and the strengths of the interactions of the elementary particles we observe.
160 Background dependence/independence is more important than existence/number of hidden dimensions.
163 This curled-up dimension picture is incomplete. To get the 2nd, hidden, dimension you actually need 2 more i.e. 3 in total. It is in this 3D space that R is defined.
173 "the Berkenstein bound is a consequence of the second law of thermodynamics."
174 Argument for the Berkenstein bound based on acceptance of the second law
174 "entropy is a count of answers to yes/no questions"
175 "Louis Crane...deduced ... that quantum cosmology must be a theory of the information exchanged between subsystems of the universe, rather than a theory of how the universe would look to an outside observer."
176 Screen Theory -- like my VR analogy. The missing element is the observer and a place for the observer.
177 "In such a [holographic] world, nothing exists except processes by which information is conveyed from one part of the world to another."
178 "the world is a network of relationships."
183 "In many areas of science we are paying for the consequences of an academic system that rewards narrowness of focus over exploration of new areas."
197 "If...something external to the universe made the choice [of which consistent theory applies to our world], then this is the exact point at which science will become religion."
197 The anthropic question: "given that there seem to be more than one possible consistent set of laws, why is it that the laws of nature are such that the parameters fall within the narrow ranges needed for life?"
197 God of the Gaps and the Strong Anthropic Principle
198 Martin Rees's "multiverse"
199 Popper's criterion of refutability. By referring to "at least one universe like ours" Smolin is departing from his original definition of 'universe' because some are outside ours. My suggestion is to call "our universe" the physical universe and admit the possible existence of Penrose's other two worlds: The Platonic and the Cartesian.
200 "The big bang would then be just be (sic) the most recent of a series of transitions the universe has passed through." This assumes the equivalency of cosmic time and Einsteinian time. I say it is a false assumption.
202 "second, that nothing acting from the outside could have imposed that organization on the system. In the case of our universe we are taking this second part as a principle." No -- Error. See note 199
210 "after a while [quantum theory] will be reformulated as a theory about the flow of information among events."
Ideas Home Page
Go To Home Page
©2006 Paul R. Martin, All rights reserved.