The Born rule may be stated mathematically as the rule that probabilities in quantum theory are expectation values of a complete orthogonal set of projection operators. This rule works for single laboratory settings in which the observer can distinguish all the different possible outcomes corresponding to the projection operators. However, theories of inflation suggest that the universe may be so large that any laboratory, no matter how precisely it is defined by its internal state, may exist in a large number of very distantly separated copies throughout the vast universe. In this case, no observer within the universe can distinguish all possible outcomes for all copies of the laboratory. Then normalized probabilities for the local outcomes that can be locally distinguished cannot be given by the expectation values of any projection operators. Thus the Born rule fails and must be replaced by another rule for observational probabilities in cosmology. The freedom of what this new rule is to be is the measure problem in cosmology. A particular volume-averaged form is proposed.
Journal of Cosmology and Astroparticle Physics
- Pub Date:
- July 2009
- High Energy Physics - Theory;
- General Relativity and Quantum Cosmology;
- Quantum Physics
- LaTeX, 16 pages, typos in Eqs. (4.3) and (6.2) corrected