Effect upon universal order of Hubble expansion
The level of order R in a spherical system of radius r0 with a probability amplitude function ψ(x),x=r,θ,ϕ obeys R=(1/2)r02I, where I=4∫dx|∇ψ|2 is its Fisher information level. We show that a flat space universe obeying the Robertson–Walker metric has an invariant value of the order as it undergoes...
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Published in | Physica A Vol. 391; no. 1-2; pp. 410 - 413 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
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Elsevier B.V
01.01.2012
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Abstract | The level of order R in a spherical system of radius r0 with a probability amplitude function ψ(x),x=r,θ,ϕ obeys R=(1/2)r02I, where I=4∫dx|∇ψ|2 is its Fisher information level. We show that a flat space universe obeying the Robertson–Walker metric has an invariant value of the order as it undergoes either uniform Hubble expansion or contraction. This means that Hubble expansion per se does not cause a loss of universal order as time progresses. Instead, coarse graining processes characterizing decoherence and friction might cause a loss of order. Alternatively, looking backward in time, i.e. under Hubble contraction, as the big bang is approached and the Hubble radius r0 approaches small values, the structure in the amplitude function ψ(x) becomes ever more densely packed, increasing all local slopes ∇ψ and causing the Fisher information I to approach unboundedly large values. As a speculation, this ever-well locates the initial position of the universe in a larger, multiverse.
► We define a measure of order or complexity proportional to the Fisher information. ► The measure is applied to our flat-space, dust and gas dominated, universe. ► Despite the universe’s relentless, ever-accelerating Hubble expansion, its level of order is found to remain constant. |
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AbstractList | The level of order R in a spherical system of radius r0 with a probability amplitude function ψ(x),x=r,θ,ϕ obeys R=(1/2)r02I, where I=4∫dx|∇ψ|2 is its Fisher information level. We show that a flat space universe obeying the Robertson–Walker metric has an invariant value of the order as it undergoes either uniform Hubble expansion or contraction. This means that Hubble expansion per se does not cause a loss of universal order as time progresses. Instead, coarse graining processes characterizing decoherence and friction might cause a loss of order. Alternatively, looking backward in time, i.e. under Hubble contraction, as the big bang is approached and the Hubble radius r0 approaches small values, the structure in the amplitude function ψ(x) becomes ever more densely packed, increasing all local slopes ∇ψ and causing the Fisher information I to approach unboundedly large values. As a speculation, this ever-well locates the initial position of the universe in a larger, multiverse.
► We define a measure of order or complexity proportional to the Fisher information. ► The measure is applied to our flat-space, dust and gas dominated, universe. ► Despite the universe’s relentless, ever-accelerating Hubble expansion, its level of order is found to remain constant. The level of order R in a spherical system of radius r sub(0 with a probability amplitude function [inline image] obeys [inline image], where [inline image] is its Fisher information level. We show that a flat space universe obeying the Robertson-Walker metric has an invariant value of the order as it undergoes either uniform Hubble expansion or contraction. This means that Hubble expansion per se does not cause a loss of universal order as time progresses. Instead, coarse graining processes characterizing decoherence and friction might cause a loss of order. Alternatively, looking backward in time, i.e. under Hubble contraction, as the big bang is approached and the Hubble radius r) sub(0) approaches small values, the structure in the amplitude function [inline image] becomes ever more densely packed, increasing all local slopes (grad)Ieand causing the Fisher information I to approach unboundedly large values. As a speculation, this ever-well locates the initial position of the universe in a larger, multiverse. |
Author | Plastino, A.R. Plastino, A. Frieden, B.R. |
Author_xml | – sequence: 1 givenname: B.R. surname: Frieden fullname: Frieden, B.R. email: roy.frieden@optics.arizona.edu organization: College of Optics, University of Arizona, Tucson, AZ 85721, United States – sequence: 2 givenname: A. surname: Plastino fullname: Plastino, A. email: angeloplastino@gmail.com organization: National University La Plata, Physics Institute (IFLP-CCT-CONICET), C.C. 727, 1900 La Plata, Argentina – sequence: 3 givenname: A.R. surname: Plastino fullname: Plastino, A.R. email: arplastino@ugr.es organization: CREG-National University La Plata-CONICET, C.C. 727, 1900 La Plata, Argentina |
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Cites_doi | 10.1088/0253-6102/47/4/005 10.1016/j.physe.2009.06.048 10.1080/0010751052000297588 10.1142/S1230161209000311 10.1088/0305-4470/35/25/303 10.1063/1.3274387 10.1016/S0375-9601(96)00756-6 10.1016/j.physa.2010.01.043 10.1109/TIT.2008.2008142 10.1103/PhysRevE.82.066117 10.1146/annurev-physchem-032210-103458 10.1023/A:1021059118007 |
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Snippet | The level of order R in a spherical system of radius r0 with a probability amplitude function ψ(x),x=r,θ,ϕ obeys R=(1/2)r02I, where I=4∫dx|∇ψ|2 is its Fisher... The level of order R in a spherical system of radius r sub(0 with a probability amplitude function [inline image] obeys [inline image], where [inline image] is... |
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StartPage | 410 |
SubjectTerms | Amplitudes Coarse graining Fisher information Friction Granulation Hubble expansion Invariants Order and complexity Slopes Statistical mechanics Universe |
Title | Effect upon universal order of Hubble expansion |
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