Assuming that the universe is eternal, a question arises: How is it that thermodynamic equilibrium has not already been achieved?[4]
This theoretical paradox is directed at the then-mainstream strand of belief in a classical view of a sempiternal universe, whereby its matter is postulated as everlasting and having always been recognisably the universe. Heat death paradox is born of a paradigm resulting from fundamental ideas about the cosmos. It is necessary to change the paradigm to resolve the paradox.
The paradox was based upon the rigid mechanical point of view of the second law of thermodynamics postulated by Rudolf Clausius and Lord Kelvin, according to which heat can only be transferred from a warmer to a colder object. It notes: if the universe were eternal, as claimed classically, it should already be cold and isotropic (its objects should have the same temperature, and the distribution of matter or radiation should be even).[4] Kelvin compared the universe to a clock that runs slower and slower, constantly dissipating energy in impalpable heat, although he was unsure whether it would stop for ever (reach thermodynamic equilibrium). According to this model, the existence of usable energy, which can be used to perform work and produce entropy, means that the clock has not stopped - since a conversion of heat in mechanical energy (which Kelvin called a rejuvenating universe scenario) is not contemplated.[5][2]
According to the laws of thermodynamics, any hot object transfers heat to its cooler surroundings, until everything is at the same temperature. For two objects at the same temperature as much heat flows from one body as flows from the other, and the net effect is no change. If the universe were infinitely old, there must have been enough time for the stars to cool and warm their surroundings. Everywhere should therefore be at the same temperature and there should either be no stars, or everything should be as hot as stars. The universe should thus achieve, or asymptotically tend to, thermodynamic equilibrium, which corresponds to a state where no thermodynamic free energy is left, and therefore no further work is possible: this is the heat death of the universe, as predicted by Lord Kelvin in 1852. The average temperature of the cosmos should also asymptotically tend to Kelvin Zero, and it is possible that a maximum entropy state will be reached.[6]
Kelvin's solutionedit
In February 1862, Lord Kelvin used the existence of the Sun and the stars as an empirical proof that the universe has not achieved thermodynamic equilibrium, as entropy production and free work are still possible, and there are temperature differences between objects. Helmholtz and Rankine expanded Kelvin's work soon after.[2] Since there are stars and colder objects, the universe is not in thermodynamic equilibrium, so it cannot be infinitely old.
Modern cosmologyedit
The paradox does not arise in the Big Bang or its successful Lambda-CDM refinement, which posit that the universe began roughly 13.8 billion years ago, not long enough ago for the universe to have approached thermodynamic equilibrium. Some proposed further refinements, termed eternal inflation, restore Kelvin's idea of unending time in the more complicated form of an eternal, exponentially-expanding multiverse in which mutually-inaccessible baby universes, some of which resemble the universe we inhabit, are continually being born.
Related paradoxesedit
Olbers' paradox is another paradox which aims to disprove an infinitely old static universe, but it only fits with a static universe scenario. Also, unlike Kelvin's paradox, it relies on cosmology rather than thermodynamics. The Boltzmann Brain can also be related to Kelvin's, as it focuses on the spontaneous generation of a brain (filled with false memories) from entropy fluctuations, in a universe which has been lying in a heat death state for an indefinite amount of time.[7]
^ abc Thomson, William (1862). "On the Age of the Sun's Heat". Macmillan's Magazine. Vol. 5. pp. 388–393.
^ Smith, Crosbie; Wise, M. Norton (1989). Energy and Empire: A Biographical Study of Lord Kelvin. Cambridge University Press. p. 500. ISBN978-0-521-26173-9.
^ abCucic, Dragoljub A. (2008). "Astrophysical Paradoxes, long version". arXiv:0812.1679 [physics.hist-ph].
^Otis, Laura (2002). "Literature and Science in the Nineteenth Century: An Anthology". OUP Oxford. Vol. 1. pp. 60–67.
^Carroll, Sean (29 December 2008). "Richard Feynman on Boltzmann Brains". Retrieved 24 June 2019.
March 18, 2024
heat, death, paradox, heat, death, paradox, also, known, thermodynamic, paradox, clausius, paradox, kelvin, paradox, reductio, absurdum, argument, that, uses, thermodynamics, show, impossibility, infinitely, universe, formulated, february, 1862, lord, kelvin, . The heat death paradox also known as thermodynamic paradox Clausius paradox and Kelvin s paradox 1 is a reductio ad absurdum argument that uses thermodynamics to show the impossibility of an infinitely old universe It was formulated in February 1862 by Lord Kelvin and expanded upon by Hermann von Helmholtz and William John Macquorn Rankine 2 3 Contents 1 The paradox 2 Kelvin s solution 2 1 Modern cosmology 3 Related paradoxes 4 See also 5 ReferencesThe paradox editAssuming that the universe is eternal a question arises How is it that thermodynamic equilibrium has not already been achieved 4 This theoretical paradox is directed at the then mainstream strand of belief in a classical view of a sempiternal universe whereby its matter is postulated as everlasting and having always been recognisably the universe Heat death paradox is born of a paradigm resulting from fundamental ideas about the cosmos It is necessary to change the paradigm to resolve the paradox The paradox was based upon the rigid mechanical point of view of the second law of thermodynamics postulated by Rudolf Clausius and Lord Kelvin according to which heat can only be transferred from a warmer to a colder object It notes if the universe were eternal as claimed classically it should already be cold and isotropic its objects should have the same temperature and the distribution of matter or radiation should be even 4 Kelvin compared the universe to a clock that runs slower and slower constantly dissipating energy in impalpable heat although he was unsure whether it would stop for ever reach thermodynamic equilibrium According to this model the existence of usable energy which can be used to perform work and produce entropy means that the clock has not stopped since a conversion of heat in mechanical energy which Kelvin called a rejuvenating universe scenario is not contemplated 5 2 According to the laws of thermodynamics any hot object transfers heat to its cooler surroundings until everything is at the same temperature For two objects at the same temperature as much heat flows from one body as flows from the other and the net effect is no change If the universe were infinitely old there must have been enough time for the stars to cool and warm their surroundings Everywhere should therefore be at the same temperature and there should either be no stars or everything should be as hot as stars The universe should thus achieve or asymptotically tend to thermodynamic equilibrium which corresponds to a state where no thermodynamic free energy is left and therefore no further work is possible this is the heat death of the universe as predicted by Lord Kelvin in 1852 The average temperature of the cosmos should also asymptotically tend to Kelvin Zero and it is possible that a maximum entropy state will be reached 6 Kelvin s solution editIn February 1862 Lord Kelvin used the existence of the Sun and the stars as an empirical proof that the universe has not achieved thermodynamic equilibrium as entropy production and free work are still possible and there are temperature differences between objects Helmholtz and Rankine expanded Kelvin s work soon after 2 Since there are stars and colder objects the universe is not in thermodynamic equilibrium so it cannot be infinitely old Modern cosmology edit The paradox does not arise in the Big Bang or its successful Lambda CDM refinement which posit that the universe began roughly 13 8 billion years ago not long enough ago for the universe to have approached thermodynamic equilibrium Some proposed further refinements termed eternal inflation restore Kelvin s idea of unending time in the more complicated form of an eternal exponentially expanding multiverse in which mutually inaccessible baby universes some of which resemble the universe we inhabit are continually being born Related paradoxes editOlbers paradox is another paradox which aims to disprove an infinitely old static universe but it only fits with a static universe scenario Also unlike Kelvin s paradox it relies on cosmology rather than thermodynamics The Boltzmann Brain can also be related to Kelvin s as it focuses on the spontaneous generation of a brain filled with false memories from entropy fluctuations in a universe which has been lying in a heat death state for an indefinite amount of time 7 See also editEntropy arrow of time Graphical timeline from Big Bang to Heat Death Heat death of the universe List of paradoxes Thermodynamic temperatureReferences edit Cucic Dragoljub Angelopoulos 2010 Paradoxes of Thermodynamics AIP Conference Proceedings 1203 1 1267 1270 arXiv 0912 1756 Bibcode 2010AIPC 1203 1267C doi 10 1063 1 3322352 a b c Thomson William 1862 On the Age of the Sun s Heat Macmillan s Magazine Vol 5 pp 388 393 Smith Crosbie Wise M Norton 1989 Energy and Empire A Biographical Study of Lord Kelvin Cambridge University Press p 500 ISBN 978 0 521 26173 9 a b Cucic Dragoljub A 2008 Astrophysical Paradoxes long version arXiv 0812 1679 physics hist ph Otis Laura 2002 Literature and Science in the Nineteenth Century An Anthology OUP Oxford Vol 1 pp 60 67 Laws of Thermodynamics Thompson and Clausius Oxford University Press 2015 Carroll Sean 29 December 2008 Richard Feynman on Boltzmann Brains Retrieved 24 June 2019 Retrieved from https en wikipedia org w index php title Heat death paradox amp oldid 1213218634, wikipedia, wiki, book, books, library,
