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A Real Lorentz-FitzGerald Contraction

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Abstract

Many condensed matter systems are such that their collective excitations at low energies can be described by fields satisfying equations of motion formally indistinguishable from those of relativistic field theory. The finite speed of propagation of the disturbances in the effective fields (in the simplest models, the speed of sound) plays here the role of the speed of light in fundamental physics. However, these apparently relativistic fields are immersed in an external Newtonian world (the condensed matter system itself and the laboratory can be considered Newtonian, since all the velocities involved are much smaller than the velocity of light) which provides a privileged coordinate system and therefore seems to destroy the possibility of having a perfectly defined relativistic emergent world. In this essay we ask ourselves the following question: In a homogeneous condensed matter medium, is there a way for internal observers, dealing exclusively with the low-energy collective phenomena, to detect their state of uniform motion with respect to the medium? By proposing a thought experiment based on the construction of a Michelson-Morley interferometer made of quasi-particles, we show that a real Lorentz-FitzGerald contraction takes place, so that internal observers are unable to find out anything about their ‘absolute’ state of motion. Therefore, we also show that an effective but perfectly defined relativistic world can emerge in a fishbowl world situated inside a Newtonian (laboratory) system. This leads us to reflect on the various levels of description in physics, in particular regarding the quest towards a theory of quantum gravity.

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References

  1. Barceló, C., Liberati, S., Visser, M.: Analogue gravity. Liv. Rev. Relativ. 8, 12 (2005). http://www.livingreviews.org/lrr-2005-12

    ADS  Google Scholar 

  2. Novello, M., Visser, M., Volovik, G. (eds.): Artificial Black Holes. World Scientific, Singapore (2002)

    Google Scholar 

  3. Volovik, G.E.: The Universe in a Helium Droplet. Clarendon, Oxford (2003)

    MATH  Google Scholar 

  4. Michelson, A.A., Morley, E.W.: On the relative motion of the Earth and the luminiferous ether. Am. J. Sci. 34, 333 (1887)

    Google Scholar 

  5. Visser, M., Weinfurtner, S.: Massive Klein–Gordon equation from a BEC-based analogue spacetime. Phys. Rev. D 72, 044020 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  6. Jackson, J.D.: Classical Electrodynamics, 3rd edn. Wiley, New York (1998)

    Google Scholar 

  7. Bell, J.S.: How to teach special relativity. Prog. Sci. Cult. 1, 2 (1976). Reprinted in: J.S. Bell, Speakable and Unspeakable in Quantum Mechanics, Cambridge University Press, Cambridge (1987)

    Google Scholar 

  8. Liberati, S., Sonego, S., Visser, M.: Faster-than-c signals, special relativity, and causality. Ann. Phys. 298, 167 (2002)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  9. Lorentz, H.A.: Versuch einer Theorie der elektrischen und optischen Erscheinungen in bewegten Körpern. Brill, Leiden (1895)

    Google Scholar 

  10. FitzGerald, G.F.: The ether and the Earth’s atmosphere. Science 13, 390 (1889)

    Article  ADS  Google Scholar 

  11. Brush, S.: Note on the history of the FitzGerald–Lorentz contraction. Isis 58, 230 (1967)

    Article  Google Scholar 

  12. Holton, G.: Einstein, Michelson, and the ‘crucial’ experiment. Isis 60, 132 (1969)

    Article  Google Scholar 

  13. Lorentz, H.A.: Electromagnetic phenomena in a system moving with any velocity less than that of light. Proc. Acad. Sci. Amsterdam 6, 809 (1904). Reprinted in Sommerfeld, A. (ed.) The Principle of Relativity. Dover, New York (1952)

    Google Scholar 

  14. Einstein, A.: Zur Elektrodynamik bewegter Körper. Ann. Phys. 17, 891 (1905). Reprinted as “On the electrodynamics of moving bodies” in Sommerfeld, A. (ed.) The Principle of Relativity. Dover, New York (1952)

    Article  Google Scholar 

  15. Einstein, A.: Äther und Relativitätstheorie. Address delivered on May 5th, 1920, in the University of Leyden. Reprinted as “Ether and the theory of relativity” in: Einstein, A.: Sidelights on Relativity, Methuen and Co., London (1922)

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  1. Instituto de Astrofísica de Andalucía, (CSIC), Camino Bajo de Huétor 50, 18008, Granada, Spain

    Carlos Barceló & Gil Jannes

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  1. Carlos Barceló
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  2. Gil Jannes
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Correspondence to Gil Jannes.

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Barceló, C., Jannes, G. A Real Lorentz-FitzGerald Contraction. Found Phys 38, 191–199 (2008). https://doi.org/10.1007/s10701-007-9196-7

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  • DOI: https://doi.org/10.1007/s10701-007-9196-7

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