Abstract
We have omitted a lot in our reconstruction of the current state of relativistic quantum theory. For instance, the path integral formalism that is often hailed as a manifestly relativistic version of quantum field theory while, in fact, it is merely a technical reformulation that has just as many problems. Neither did we speak about string theory and other approaches to a quantum theory of gravity that are beyond the scope of this book. On the other hand, our critical assessment of quantum field theory may have created the impression that we are insisting on pointless mathematical rigor in the formulation of physical theories. We are not. Throughout this book, we have deliberately stayed well clear of purely academic questions like, for instance, the domain of self-adjointness of observable operators. Whoever sees in those a key to understanding quantum mechanics is certainly wrong. What we insist on are physical laws that make sense. Laws that do not merely describe asymptotic scattering states (after enough massaging) but tell us how the universe might actually work.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Quoted from: M. Bell and S. Gao (Eds.), Quantum Nonlocality and Reality: 50 Years of Bell’s Theorem. Cambridge University Press, 2016, p. 369.
- 2.
More formally, we may say that the property of coexisting in a world is not transitive: Φ 1 and ψ 0 exist in the same world, Φ 2 and ψ 0 exist in the same world, yet Φ 1 and Φ 2 do not.
- 3.
See D. Wallace, The Emergent Multiverse: Quantum Theory According to the Everett Interpretation. Oxford University Press, 2012.
- 4.
This is just a convenient choice. The worldline can be parametrized arbitrarily, with the proportionality factor changing accordingly. The four-velocity only has to be parallel to the vector field on the right-hand side of the equation.
- 5.
For more details, see D. Drr, S. Goldstein, T. Norsen, W. Struyve, and N. Zanghì, Can Bohmian mechanics be made relativistic? Proceedings of the Royal Society A 470, 20130699 (2013).
- 6.
For a detailed discussion of why that is so, we refer to K. Berndl, D. Drr, S. Goldstein, N. Zanghì, Hypersurface Bohm–Dirac models, Phys. Rev. A 60, 2729–2736 (1999), arXiv:quant-ph/9801070; EPR-Bell nonlocality, Lorentz invariance, and Bohmian quantum theory, Phys. Rev. A 53, 2062–2073 (1996), arXiv:quant-ph/9510027.
- 7.
N. Gisin, Impossibility of covariant deterministic nonlocal hidden-variable extensions of quantum theory. Physical Review A 83, 020102 (2011).
- 8.
S. Goldstein and R. Tumulka, Opposite arrows of time can reconcile relativity and nonlocality. Classical and Quantum Gravity 20 (3), 557–564 (2003).
- 9.
See, e.g., R.I. Sutherland, Causally symmetric Bohm model, Studies in History and Philosophy of Modern Physics 39 (4), 782–805 (2008). See also B. Reznik and A. Aharonov, On a time symmetric formulation of quantum mechanics, Physical Review A 52, 2538–2550 (1995).
- 10.
R. Tumulka, A relativistic version of the Ghirardi–Rimini–Weber model, Journal of Statistical Physics 125 (4), 821–840 (2006).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Dürr, D., Lazarovici, D. (2020). Further Food for Thought. In: Understanding Quantum Mechanics . Springer, Cham. https://doi.org/10.1007/978-3-030-40068-2_12
Download citation
DOI: https://doi.org/10.1007/978-3-030-40068-2_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-40067-5
Online ISBN: 978-3-030-40068-2
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)