13 found
Sort by:
Disambiguations:
Don N. Page [11]Don Page [4]
  1. Don N. Page, Generalized Jarzynski Equality.
    The Jarzynski equality equates the mean of the exponential of the negative of the work (per fixed temperature) done by a changing Hamiltonian on a system, initially in thermal equilibrium at that temperature, to the ratio of the final to the initial equilibrium partition functions of the system at that fixed temperature. It thus relates two thermal equilibrium quantum states.
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  2. Don Page, Exact Quantum-Statistical Dynamics of Time-Dependent Generalized Oscillators.
    Using linear invariant operators in a constructive way we find the most general thermal density operator and Wigner function for time-dependent generalized oscillators. The general Wigner function has five free parameters and describes the thermal Wigner function about a classical trajectory in phase space. The contour of the Wigner function depicts an elliptical orbit with a constant area moving about the classical trajectory, whose eccentricity determines the squeezing of the initial vacuum.
    Direct download  
     
    My bibliography  
     
    Export citation  
  3. Don Page, Insufficiency of the Quantum State for Deducing Observational Probabilities.
    It is usually assumed that the quantum state is sufficient for deducing all probabilities for a system. This may be true when there is a single observer, but it is not true in a universe large enough that there are many copies of an observer. Then the probability of an observation cannot be deduced simply from the quantum state (say as the expectation value of the projection operator for the observation, as in traditional quantum theory). One needs additional rules to (...)
    Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  4. Don N. Page, Born Again.
    A simple proof is given that the probabilities of observations in a large universe are not given directly by Born’s rule as the expectation values of projection operators in a global quantum state of the entire universe. An alternative procedure is proposed for constructing an averaged density matrix for a random small region of the universe and then calculating observational probabilities indirectly by Born’s rule as conditional probabilities, conditioned upon the existence of an observation.
    No categories
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  5. Don N. Page, Born's Rule is Insufficient in a Large Universe.
    Probabilities in quantum theory are traditionally given by Born’s rule as the expectation values of projection operators. Here it is shown that Born’s rule is insufficient in universes so large that they contain identical multiple copies of observers, because one does not have definite projection operators to apply. Possible replacements for Born’s rule include using the expectation value of various operators that are not projection operators, or using vari-.
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  6. Don N. Page, Do Our Observations Depend Upon the Quantum State of the Universe?
    Here I shall call elements (1)-(3) the quantum state (or the “state”), since they give the quantum state of the universe that obeys the dynamical laws and is written in terms of the kinematic variables, and I shall call elements (4)-(6) the probability rules (or the “rules”), since they specify what it is that has probabilities (here taken to be the results of observations, Oj, or “observations” for short), the rules for extracting these observational probabilities from the quantum state, and (...)
    Translate to English
    | Direct download  
     
    My bibliography  
     
    Export citation  
  7. Don N. Page, The Born Rule Dies.
    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 (...)
    Translate to English
    | Direct download (2 more)  
     
    My bibliography  
     
    Export citation  
  8. Don N. Page (2009). Quantum Mechanics as a Simple Generalization of Classical Mechanics. Foundations of Physics 39 (11):1197-1204.
    A motivation is given for expressing classical mechanics in terms of diagonal projection matrices and diagonal density matrices. Then quantum mechanics is seen to be a simple generalization in which one replaces the diagonal real matrices with suitable Hermitian matrices.
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  9. Don Page (2003). Mindless Sensationalism: A Quantum Framework for Consciousness. In Quentin Smith & Aleksandar Jokic (eds.), Consciousness: New Philosophical Perspectives. Oxford University Press. 468.
  10. Don N. Page (1996). Sensible Quantum Mechanics: Are Probabilities Only in the Mind? International Journal of Modern Physics D 5:583-96.
    Quantum mechanics may be formulated as Sensible Quantum Mechanics (SQM) so that it contains nothing probabilistic except conscious perceptions. Sets of these perceptions can be deterministically realized with measures given by expectation values of positive-operator-valued awareness operators. Ratios of the measures for these sets of perceptions can be interpreted as frequency- type probabilities for many actually existing sets. These probabilities gener- ally cannot be given by the ordinary quantum “probabilities” for a single set of alternatives. Probabilism, or ascribing probabilities to (...)
    Direct download (4 more)  
     
    My bibliography  
     
    Export citation  
  11. Don N. Page, Attaching Theories of Consciousness to Bohmian Quantum Mechanics. arXiv.
  12. Don N. Page (1991). Interpreting the Density Matrix of the Universe. In. In A. Ashtekar & J. Stachel (eds.), Conceptual Problems of Quantum Gravity. Birkhauser. 1--116.
    No categories
    Direct download  
     
    My bibliography  
     
    Export citation  
  13. Don N. Page (1986). Hawking's Wave Function for the Universe. In. In Roger Penrose & C. J. Isham (eds.), Quantum Concepts in Space and Time. New York ;Oxford University Press. 1--274.
    No categories
    Direct download  
     
    My bibliography  
     
    Export citation