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Foundations of Physics

, Volume 45, Issue 12, pp 1537–1560 | Cite as

A Comparison Between Models of Gravity Induced Decoherence

  • Sayantani Bera
  • Sandro Donadi
  • Kinjalk Lochan
  • Tejinder P. Singh
Article

Abstract

It has been suggested in the literature that spatial coherence of the wave function can be dynamically suppressed by fluctuations in the spacetime geometry. These fluctuations represent the minimal uncertainty that is present when one probes spacetime geometry with a quantum probe. Two similar models have been proposed, one by Diósi (D-model) and one by Karolyhazy and collaborators (K-model), based on apparently unrelated minimal spacetime bounds. The two models arrive at somewhat different expressions for the dependence of the localization coherence length on the mass and size of the quantum object. In the present article we compare and contrast the two models from three aspects: (i) comparison of the spacetime bounds, (ii) method of calculating decoherence time, (iii) comparison of noise correlation. We show that under certain conditions the minimal spacetime bounds in the two models can be derived one from the other. We argue that the methods of calculating the decoherence time are equivalent. We re-derive the two-point correlation for the fluctuation potential in the K-model, and confirm the earlier result of Diósi and Lukács that it is non-white noise, unlike in the D-model, where the corresponding correlation is white noise in time. This seems to be the origin of the different results in the two models. We derive the non-Markovian master equation for the K-model. We argue that the minimal spacetime bound cannot predict the noise correlation uniquely, and additional criteria are necessary to accurately determine the effects of gravitationally induced decoherence.

Keywords

Decoherence Gravity Quantum theory 

Notes

Acknowledgments

The authors are grateful to Lajos Diósi for bringing Ref. [69] to their attention, and for helpful correspondence.The work of TPS is supported by Grant # 39530 from the John Templeton Foundation. SD acknowledges support from NANOQUESTFIT, the COST Action MP1006 and INFN, Italy. SD and KL acknowledge the hospitality of the Tata Institute of Fundamental Research (Mumbai) where part of this work has been done. TPS would like to thank Aniket Agrawal for collaboration during the early stages of this work.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Sayantani Bera
    • 1
  • Sandro Donadi
    • 2
    • 3
  • Kinjalk Lochan
    • 4
  • Tejinder P. Singh
    • 1
  1. 1.Tata Institute of Fundamental ResearchMumbaiIndia
  2. 2.Department of PhysicsUniversity of TriesteTriesteItaly
  3. 3.Istituto Nazionale di Fisica NucleareTriesteItaly
  4. 4.IUCAAPuneIndia

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