Laplace's demon

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French scholar Pierre-Simon de Laplace (1749–1827)

In the history of science, Laplace's demon was a notable published articulation of causal determinism on a scientific basis by Pierre-Simon Laplace in 1814.[1] According to determinism, if someone (the demon) knows the precise location and momentum of every atom in the universe, their past and future values for any given time are entailed; they can be calculated from the laws of classical mechanics.[2]

A desire to confirm or refute Laplace's demon played a vital motivating role[citation needed] in the subsequent development of statistical thermodynamics, the first of several repudiations developed by later generations of physicists to the assumption of causal determinacy upon which Laplace's demon is erected.

English translation[edit]

We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.

— Pierre Simon Laplace, A Philosophical Essay on Probabilities[3]

This intellect is often referred to as Laplace's demon (and sometimes Laplace's Superman, after Hans Reichenbach). Laplace himself did not use the word "demon", which was a later embellishment. As translated into English above, he simply referred to: "Une intelligence ... Rien ne serait incertain pour elle, et l'avenir, comme le passé, serait présent à ses yeux." This idea seems to have been widespread around the time that Laplace first expressed it in 1773, particularly in France. Variations can be found in Maupertuis (1756), Nicolas de Condorcet (1768), Baron D'Holbach (1770), and an undated fragment in the archives of Diderot.[4] Recent scholarship suggests that the image of a super-powerful calculating intelligence was also proposed by Roger Joseph Boscovich in his 1758 Theoria philosophiae naturalis.[5]

Arguments against Laplace's demon[edit]

Thermodynamic irreversibility[edit]

According to chemical engineer Robert Ulanowicz, in his 1986 book Growth and Development, Laplace's demon met its end with early 19th century developments of the concepts of irreversibility, entropy, and the second law of thermodynamics. In other words, Laplace's demon was based on the premise of reversibility and classical mechanics; however, Ulanowicz points out that many thermodynamic processes are irreversible, so that if thermodynamic quantities are taken to be purely physical then no such demon is possible as one could not reconstruct past positions and momenta from the current state.

Maximum entropy thermodynamics takes a very different view, considering thermodynamic variables to have a statistical basis which is separate from the deterministic microscopic physics.[6] However, this theory has met criticism regarding its ability to make predictions about physics; a number of physicists and mathematicians, including Yvan Velenik of the Department of Mathematics for the University of Geneva, have pointed out that maximum entropy thermodynamics essentially describes our knowledge about a system but does not describe the system itself.[7]

Quantum mechanical irreversibility[edit]

Due to its canonical assumption of determinism, Laplace's demon is incompatible with the Copenhagen interpretation, which stipulates indeterminacy. The interpretation of quantum mechanics is still very much open for debate and there are many who take opposing views (such as the Many Worlds Interpretation and the de Broglie–Bohm interpretation).[8]

Chaos theory[edit]

Chaos theory is sometimes pointed out as a contradiction to Laplace's demon: it describes how a deterministic system can nonetheless exhibit behavior that is impossible to predict: as in the butterfly effect, minor variations between the starting conditions of two systems can result in major differences.[9] While this explains unpredictability in practical cases, applying it to Laplace's case is questionable: under the strict demon hypothesis all details are known—to infinite precision—and therefore variations in starting conditions are non-existent. Put another way: Chaos theory is applicable when knowledge of the system is imperfect[citation needed] whereas Laplace's demon assumes perfect knowledge of the system, therefore chaos theory and Laplace's demon are actually compatible with each other.

Cantor diagonalization[edit]

In 2008, David Wolpert used Cantor diagonalization to disprove Laplace's demon. He did this by assuming that the demon is a computational device and showed that no two such devices can completely predict each other.[10][11] Wolpert's paper was cited in 2014 in a paper of Josef Rukavicka, where a significantly simpler argument is presented that disproves Laplace's demon using Turing machines, under the assumption of free will.[12]

Recent views[edit]

There has recently been proposed a limit on the computational power of the universe, i.e. the ability of Laplace's demon to process an infinite amount of information. The limit is based on the maximum entropy of the universe, the speed of light, and the minimum amount of time taken to move information across the Planck length, and the figure was shown to be about 10120 bits.[13] Accordingly, anything that requires more than this amount of data cannot be computed in the amount of time that has elapsed so far in the universe.

See also[edit]

References[edit]

  1. ^ Hawking, Stephen. "Does God Play Dice?". Public Lectures.
  2. ^ Pierre-Simon Laplace, "A Philosophical Essay on Probabilities" (full text).
  3. ^ Laplace, Pierre Simon, A Philosophical Essay on Probabilities, translated into English from the original French 6th ed. by Truscott, F.W. and Emory, F.L., Dover Publications (New York, 1951) p.4
  4. ^ Marij (2014). "On the origins and foundations of Laplacian determinism" (PDF). Studies in History and Philosophy of Science. 45: 24–31. doi:10.1016/j.shpsa.2013.12.003. PMID 24984446.
  5. ^ Kožnjak Boris (2015). "Who let the demon out? Laplace and Boscovich on determinism". Studies in History and Philosophy of Science. 51: 42–52. doi:10.1016/j.shpsa.2015.03.002. PMID 26227230.
  6. ^ http://bayes.wustl.edu/etj/articles/theory.1.pdf
  7. ^ "Section de Mathématiques Université de Genève". www.unige.ch. 23 July 2017.
  8. ^ Sommer, Christoph (2013). "Another Survey of Foundational Attitudes Towards Quantum Mechanics". arXiv:1303.2719v1 [quant-ph].
  9. ^ Stanford Encyclopedia of Philosophy, "Causal Determinism"
  10. ^ David H. Wolpert (2008). "Physical limits of inference". Physica D. 237 (9): 1257–1281. arXiv:0708.1362. Bibcode:2008PhyD..237.1257W. doi:10.1016/j.physd.2008.03.040. S2CID 2033616. full text
  11. ^ P.-M. Binder (2008). "Theories of almost everything" (PDF). Nature. 455 (7215): 884–885. Bibcode:2008Natur.455..884B. doi:10.1038/455884a. S2CID 12816652.
  12. ^ Rukavicka Josef (2014), Rejection of Laplace's Demon, The American Mathematical Monthly [1]
  13. ^ Physical Review Focus (24 May 2002). "If the Universe Were a Computer". Physics. APS. 9.