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arXiv:0712.2240

Observational Selection Effects in Quantum Cosmology

Don Nelson Page

Published Dec 13, 2007• 22 citations
arXivHTMLPDF

Abstract

Scientific theories need to be testable by observations, say using Bayes' theorem. A complete theory needs at least the three parts of dynamical laws for specified physical variables, the correct solution of the dynamical laws (boundary conditions), and the connection with observations or experience or conscious perceptions (laws of psycho-physical parallelism). Principles are proposed for Bayesian meta-theories. One framework that obeys these principles is Sensible Quantum Mechanics (SQM), which is discussed. In principle, it allows one to test between single-history and many-worlds theories, and to discuss threats to certain theories from fake universes and Boltzmann brains. The threat of fake universes may be dismissed if one doubts the substrate-independence of consciousness, which seems very implausible in the SQM framework. Boltzmann brains seem more problematic, though there are many conceivable solutions. SQM also suggests the possibility that past steps along our evolutionary ancestry may be so rare that they have occurred nowhere else within the part of the universe that we can observe.

DOI
10.48550/arxiv.0712.2240

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Scientific theories need to be testable by observations, say using Bayes' theorem. A complete theory needs at least the three parts of dynamical laws for specified physical variables, the correct solution of the dynamical laws (boundary conditions), and the connection with observations or experience or conscious perceptions (laws of psycho-physical parallelism). Principles are proposed for Bayesian meta-theories. One framework that obeys these principles is Sensible Quantum Mechanics (SQM), which is discussed. In principle, it allows one to test between single-history and many-worlds theories, and to discuss threats to certain theories from fake universes and Boltzmann brains. The threat of fake universes may be dismissed if one doubts the substrate-independence of consciousness, which seems very implausible in the SQM framework. Boltzmann brains seem more problematic, though there are many conceivable solutions. SQM also suggests the possibility that past steps along our evolutionary ancestry may be so rare that they have occurred nowhere else within the part of the universe that we can observe.
Quantum cosmology is the quantum theory of the entire universe. Although strange at first sight, it is appropriate because (1) our world appears to be fundamentally quantum, (2) the classical description of gravity breaks down at singularities it would give at the beginning of the universe, and (3) our universe has many properties that cannot be explained by a classical description of them. A quantum state of the universe should obey certain constraints, such as the Wheeler-DeWitt equations. One approach to interpreting such a state is {\it Sensible Quantum Mechanics} (SQM), in which nothing is probabilistic, except, in a certain frequency sense, conscious perceptions. Sets of these perceptions can be deterministically realized with measures given by expectation values of positive-operator-valued {\it awareness operators}. These may be defined even when the quantum state itself is not normalizable, though there still seem to be problems of divergences when one has an infinite amount of inflation, producing infinitely large spatial volumes with presumably infinite measures of perceptions. Ratios of the measures for sets of perceptions (if finite) can be interpreted as frequency-type probabilities for many actually existing sets rather than as propensities for potentialities to be actualized, so there is nothing indeterministic in a specific SQM. One can do a Bayesian analysis to test between different specific SQMs. One can also make statistical predictions of what one might perceive within a specific SQM by invoking the {\it Conditional Aesthemic Principle}: among the set of all conscious perceptions, our perceptions are likely to be typical.
Quantum mechanics may be formulated as Sensible Quantum Mechanics (SQM) so that it contains nothing probabilistic, except, in a certain frequency sense, conscious perceptions. Sets of these perceptions can be deterministically realized with measures given by expectation values of positive-operator-valued awareness operators in a quantum state of the universe which never jumps or collapses. Ratios of the measures for these sets of perceptions can be interpreted as frequency-type probabilities for many actually existing sets rather than as propensities for potentialities to be actualized, so there is nothing indeterministic in SQM. These frequency-type probabilities generally cannot be given by the ordinary quantum "probabilities" for a single set of alternatives. Probabilism, or ascribing probabilities to unconscious aspects of the world, may be seen to be an aesthemamorphic myth. No fundamental correlation or equivalence is postulated between different perceptions (each being the entirety of a single conscious experience and thus not in direct contact with any other), so SQM, a variant of Everett's "many-worlds" framework, is a "many-perceptions" framework but not a "many-minds" framework. Different detailed SQM theories may be tested against experienced perceptions by the typicalities (defined herein) they predict for these perceptions. One may adopt the Conditional Aesthemic Principle: among the set of all conscious perceptions, our perceptions are likely to be typical. An experimental test is proposed to compare SQM with a variant, SQMn.
Sensible Quantum Mechanics or Mindless Sensationalism is a framework for relating consciousness to a quantum universe. It states that each conscious perception has a measure that is given by the expectation value of a corresponding quantum "awareness operator" in a fixed quantum state of the universe. The measures can be interpreted as frequency-type probabilities for a large set of perceptions that all actually exist with varying degrees of reality, so detailed theories within this framework are testable. The measures are not propensities for potentialities to be actualized, so there is nothing indeterministic in this framework, and no free will in the incompatibilistic sense. As conscious perceptions are determined by the awareness operators and the quantum state, they are epiphenomena. No fundamental relation is postulated between different perceptions (each being the entirety of a single conscious experience and thus not in direct contact with any other), so SQM or MS, a variant of Everett's "many-worlds" framework, is a "many-perceptions" framework but not a "many-minds" framework.
Existing physical theories do not predict every feature of our experience but only certain regularities of that experience. That difference between what could be observed and what can be predicted is one kind of limit on scientific knowledge. Such limits are inevitable if the world is complex and the laws governing the regularities of that world are simple. Another kind of limit on scientific knowledge arises because even simple theories may require intractable or impossible computations to yield specific predictions. A third kind of limit concerns our ability to know theories through the process of induction and test. Quantum cosmology -- that part of science concerned with the quantum origin of the universe and its subsequent evolution -- displays all three kinds of limits. This paper briefly describes quantum cosmology and discusses these limits. The place of the other sciences in this most comprehensive of physical frameworks is described.
The ideas of Sensible Quantum Mechanics are expressed in lay terms for philosophers of consciousness and others. A framework is proposed and explained for the `psycho-physical-parallelism' between conscious experiences and the mathematical structures of quantum physics (e.g., a set of quantum operators obeying some algebra, and a quantum state giving the expectation value of each operator). In particular, it is proposed that each set of possible conscious experiences has a measure given by the expectation value of a corresponding operator (a positive-operator-valued measure). Then one has a generalization of the Weak Anthropic Principle named the Conditional Aesthemic Principle: given that we are conscious beings, our conscious experiences are likely to be typical experiences in the set of all conscious experiences with its measure.
Abstract I write as a physicist, with the knowledge that many physicists are studying the mathematical structure of our physical universe and hope to be able to find a ‘theory of everything’, or TOE, that will give a complete set of dynamical laws for this structure. This would essentially give the rules for how all the physical quantities in the universe evolve. Such a TOE would not by itself give the boundary conditions also necessary to determine the history of the universe, so it is a misnomer to say that it is a ‘theory of everything’, but it is convenient to retain the acronym TOE for this dynamical part of the laws of physics. Some physicists, such as Hartle and Hawking (1983), are also seeking to find rules specifying the boundary conditions (BC) of the universe. The combination of the TOE and the BC would then give a complete description of the mathematics of the state of the universe and its evolution.