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Less Decoherence and More Coherence in Quantum Gravity, Inflationary Cosmology and Elsewhere

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Abstract

In Crull (Found Phys 45:1019–1045, 2015) it is argued that, in order to confront outstanding problems in cosmology and quantum gravity, interpretational aspects of quantum theory can by bypassed because decoherence is able to resolve them. As a result, Crull (Found Phys 45:1019–1045, 2015) concludes that our focus on conceptual and interpretational issues, while dealing with such matters in Okon and Sudarsky (Found Phys 44:114–143, 2014), is avoidable and even pernicious. Here we will defend our position by showing in detail why decoherence does not help in the resolution of foundational questions in quantum mechanics, such as the measurement problem or the emergence of classicality.

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Notes

  1. Probably she meant to say “coupling” instead of “commuting.”

  2. In Sect. 2.1 of [5] Crull briefly discusses the role measurements play in quantum mechanics, but by doing so she only contributes to a long tradition of fallacious statements regarding the issue. She tries to define a measurement entity as something capable of gaining information about some system, such that the information can later be gathered. However, such definition is so vague that it is practically useless. Moreover, it is circular because in order to gather such information at a later time one, presumably, needs to somehow measure it!

  3. For any operator A, its trace is defined by \(Tr(A)=\sum _i \langle \phi _i|A|\phi _i\rangle \) with \(\{\phi _i\}\) any basis of the Hilbert space in question.

  4. In [5], the basis problem is associated with the following question: “Given the statistical improbability of always observing bases that are classical, why should such preferences for them appear in nature?” We find the decision to state the problem in terms of a statistical improbability quite curious since one does not expect the observed basis to be chosen at random.

  5. Given that the particular interpretation we consider in [2] is fundamentally indeterministic, we find it odd for Crull to claim that the urgency to consider a specific interpretation most often arises from a hesitation to accept that the world is indeterministic.

  6. Apparently, Crull finds our brief review of basic features of objective collapse models in [2], which she takes to be a definition of such models, unsatisfactory: “one might argue that the way in which [Okon and Sudarsky] define objective collapse theories introduces as many black boxes as it purports to explain.” It is unclear what is it that she finds in need of further explanation. Evidently, if one is looking for a completely viable collapse model compatible with relativistic quantum field theory, one will not find it in our work, nor elsewhere, since such a theory is still very much under construction. Therefore, one should not compare it directly with finished proposals, such as “decoherence” or the “Consistent Histories” approach. That is, one cannot compare directly programs under development, such as quantum gravity proposals, with well established theories such as general relativity, and demand the former to be as precisely formulated at this stage as is the latter. On the other hand, one must recognize the potential of the former to deal with evident shortcomings of the latter (i.e., the incompatibility of GR with quantum theory). At any rate, the literature on objective collapse models is of course large and of excellent quality (see e.g., [4] and references therein).

  7. It is worth mentioning that J. Hartle long ago noted the serious difficulties faced in attempting to apply quantum theory to cosmology, [20]. This lead him and his collaborators to conclude that some modified version of quantum theory was required. They turned to the Consistent Histories framework, about which we will say more later.

  8. Things get further complicated by the fact that these constructions turn out to be inequivalent. However, a careful analysis using the algebraic approach shows that these problems can be readily overcome [27].

  9. Strictly speaking, if the expansion of the universe is not exactly exponential, and the space-time is therefore not truly described by the de Sitter line element, the state is not the Bunch–Davies vacuum. However, the important point for our purposes is that in such scenario the vacuum is still homogeneous and isotropic.

  10. The simplicity of the structure of the previous argument can be illustrated with the following straightforward example: Suppose that we have a classical system, as complicated as you like, but such that, at \(t=0\), its total energy is zero. Suppose, moreover, that the Hamiltonian of the system is time-translation invariant. As a result, the total energy of the system, at any other time, and independently of the details of the evolution, will also be zero. The same is true of the symmetry of the Bunch–Davies state under standard evolution.

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Acknowledgments

We acknowledge partial financial support from DGAPA-UNAM Project IG100316.

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Authors and Affiliations

  1. Instituto de Investigaciones Filosóficas, Universidad Nacional Autónoma de México, Circuito Maestro Mario de la Cueva s/n, Mexico, DF, 04510, Mexico

    Elias Okon

  2. Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A. Postal 70-543, Mexico, DF, 04510, Mexico

    Daniel Sudarsky

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  1. Elias Okon
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Correspondence to Elias Okon.

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Okon, E., Sudarsky, D. Less Decoherence and More Coherence in Quantum Gravity, Inflationary Cosmology and Elsewhere. Found Phys 46, 852–879 (2016). https://doi.org/10.1007/s10701-016-0007-x

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