A rule to assign physical meaning to Lagrange multipliers is discussed. Examples from mechanics, statistical mechanics and quantum mechanics are given.

It is often stated that quantum mechanics only makes statistical predictions and that a quantum state is described by the various probability distributions associated with it. Can we describe a quantum state completely in terms of probabilities and then use it to describe quantum dynamics? What is the origin of the probability distribution for a maximally specified quantum state? Is quantum mec...

Chapter 1: Jeremy Butterfield, “On Symplectic Reduction in Classical Mechanics.” Chapter 2: Gordon Belot, “The Representation of Time and Change in Mechanics.” Chapter 3: David Malament, “Classical Relativity Theory.” Chapter 4: Michael Dickson, “Non-Relativistic Quantum Mechanics.” Chapter 5: Klaas Landsman, “Between Classical and Quantum.” Chapter 6: Jeffrey Bub, “Quantum Information and Comp...

M athematical models for deducing cause-effect relationships from statistical data have been successful in diverse areas of science (see Ref. [1] and references therein). Such models can be applied, for instance, to establish causal relationships between smoking and cancer or to analyze risks in construction projects. Can similar models be extended to the microscopic world governed by the laws ...

FOUNDATIONS ................................................................................................................ 456 Signals and Noise, Detectability and Discriminability ............................................... 456 Noise from Classical Statistical Mechanics ............................................................... 459 Noise from Quantum Mechanics .........................