Nonlocality, Lorentz invariance, and Bohmian quantum theory.

@article{Berndl1996NonlocalityLI,
  title={Nonlocality, Lorentz invariance, and Bohmian quantum theory.},
  author={Berndl and D{\"u}rr and Goldstein and Zangh{\`i}},
  journal={Physical review. A, Atomic, molecular, and optical physics},
  year={1996},
  volume={53 4},
  pages={
          2062-2073
        }
}
  • Berndl, Dürr, Zanghì
  • Published 26 October 1995
  • Mathematics
  • Physical review. A, Atomic, molecular, and optical physics
We discuss the problem of finding a Lorentz invariant extension of Bohmian mechanics. Due to the nonlocality of the theory there is (for systems of more than one particle) no obvious way to achieve such an extension. We present a model invariant under a certain limit of Lorentz transformations, a limit retaining the characteristic feature of relativity, the nonexistence of absolute time, i.e., of simultaneity. The analysis of this model exemplifies an important property of any Bohmian quantum… 

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References

SHOWING 1-10 OF 52 REFERENCES
Quantum non-locality and relativity
It is sometimes stated that composite quantum systems in entangled states are fundamentally ‘non-local’(i.e. a measurement on one component system can affect a spacelike separated system
Bohmian mechanics and quantum theory: an appraisal
Preface. I: Bohmian Mechanics: Background and Fundamentals. 1. The Causal Quantum Theory Program J.T. Cushing. 2. Bohmian Mechanics as the Foundation of Quantum Mechanics D. Durr, et al. 3.
Bell's theorem, quantum theory and conceptions of the universe
On a Theory of the Collapse of the Wave Function.- On the Measurement Problem of Quantum Mechanics.- A New Characteristic of a Quantum System Between Two Measurements - A "Weak Value".- Can the
Quantum Theory of Fields
To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject. But it is a very good and most useful book. The original was
The Undivided Universe: An ontological interpretation of Quantum Theory
Systematic Theology by Louis BerkhofSaint Bonaventure (Stanford Encyclopedia of Philosophy)Bohmian Mechanics (Stanford Encyclopedia of Philosophy)Dogmatic Constitution on the Church (Lumen
"J."
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)
The Quantum Theory of Motion
A lubrication and sealing system for the cylinder head of an internal combustion engine having a sleeve valve mounted for rotation therein, said sleeve valve having intake slots therethrough which
Speakable and Unspeakable in Quatum Mechanics
Hiley, The Undivided Universe: An Ontological Interpretation of Quantum Theory (Routledge
  • 1993
Phys
  • Lett. A 178, 22
  • 1993
...
...