Facts, Values and Quanta

@article{Appleby2005FactsVA,
  title={Facts, Values and Quanta},
  author={David Marcus Appleby},
  journal={Foundations of Physics},
  year={2005},
  volume={35},
  pages={627-668}
}
  • D. M. Appleby
  • Published 3 February 2004
  • Mathematics, Physics
  • Foundations of Physics
Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the meaning of probability statements. The interpretation of probability has excited nearly as much philosophical controversy as the interpretation of quantum mechanics. 20th century physicists have mostly adopted a frequentist conception. In this paper it is argued… 
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References

SHOWING 1-10 OF 111 REFERENCES
Quantum probabilities as Bayesian probabilities
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper, we show that,…
Probabilities as Measures of Information
We analyze the notion that physical theories are quantitative and testable by observations in experiments. This leads us to propose a new, Bayesian, interpretation of probabilities in physics that…
Statistical Interpretation of Quantum Mechanics.
  • M. Born
  • Philosophy, Medicine
    Science
  • 1955
The published work for which the honor of the Nobel prize for the year 1954 has been accorded to me does not contain the discovery of a new phenomenon of nature but, rather, the foundations of a new…
Quantum Mechanics as Quantum Information (and only a little more)
In this paper, I try once again to cause some good-natured trouble. The issue remains, when will we ever stop burdening the taxpayer with conferences devoted to the quantum foundations? The suspicion…
Why Quantum Theory
The usual formulation of quantum theory is rather abstract. In recent work I have shown that we can, nevertheless, obtain quantum theory from five reasonable axioms. Four of these axioms are…
Betting on the Outcomes of Measurements: A Bayesian Theory of Quantum Probability
TLDR
It is shown how the rules of rational betting imply all the interesting features of quantum probability, even in such finite gambles, including the uncertainty principle and the violation of Bell's inequality among others.
Hidden Variables, Statistical Mechanics and the Early Universe
One of the central mysteries of quantum theory is that it seems to be fundamentally nonlocal—and yet the nonlocality cannot be used for practical signalling at a distance. The consistency of modern…
Quantum Dynamical Reduction and Reality: Replacing Probability Densities with Densities in Real Space
Consideration is given to recent attempts to solve the objectification problem of quantum mechanics by considering nonlinear and stochastic modifications of Schrodinger’s evolution equation. Such…
Quantum Theory From Five Reasonable Axioms
The usual formulation of quantum theory is based on rather obscure axioms (employing complex Hilbert spaces, Hermitean operators, and the trace formula for calculating probabilities). In this paper…
Scientific Inference
SCIENTISTS generally care so little for scientific principles that the title of this book may repel as many as its author's name attracts. Let it be, therefore, stated at once that it is not a formal…
...
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