The Born Rule Dies
arXiv:0903.4888 · doi:10.1088/1475-7516/2009/07/008
Abstract
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 dies 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.
LaTeX, 16 pages, typos in Eqs. (4.3) and (6.2) corrected
References in corpus (43)
- Inflationary Cosmology
- The Mathematical Universe
- The Measure Problem in Cosmology
- The Classical Universes of the No-Boundary Quantum State
- TASI Lectures on the Cosmological Constant
- The No-Boundary Measure of the Universe
- Predicting the Cosmological Constant from the Causal Entropic Principle
- Predicting the cosmological constant with the scale-factor cutoff measure
- Properties of the scale factor measure
- Is Our Universe Likely to Decay within 20 Billion Years?
- The cosmic microwave background temperature bispectrum from scalar perturbations induced by primordial magnetic fields
- Are We Typical?
- Hurdles for Recent Measures in Eternal Inflation
- Holographic Multiverse
- Boltzmann babies in the proper time measure
- Prediction and explanation in the multiverse
- A global picture of quantum de Sitter space
- Complementarity in the Multiverse
- Return of the Boltzmann Brains
- Predictions in eternal inflation
- (No) Eternal Inflation and Precision Higgs Physics
- Landscape Predictions from Cosmological Vacuum Selection
- Geodesic measures of the landscape
- Stationary Measure in the Multiverse
- Is Our Universe Decaying at an Astronomical Rate?
- Many lives in many worlds
- Cosmological Measures without Volume Weighting
- Evidence for a bound on the lifetime of de Sitter space
- Boltzmann Brains--I'd Rather See Than Be One
- A volume-weighted measure for eternal inflation
- Volume Weighted Measures of Eternal Inflation in the Bousso-Polchinski Landscape
- Multiverses and Cosmology: Philosophical Issues
- Measures on transitions for cosmology from eternal inflation
- Entropy and initial conditions in cosmology
- Observational Selection Effects in Quantum Cosmology
- Black holes, information, and locality
- Limitations of anthropic predictions for the cosmological constant : Cosmic Heat Death of Anthropic Observers
- Some Late-time Asymptotics of General Scalar-Tensor Cosmologies
- Volume Weighting in the No Boundary Proposal
- Reheating-volume measure for random-walk inflation
- Typicality Derived
- Reheating-volume measure in the landscape
- Typicality, Freak Observers and the Anthropic Principle of Existence