State
of a System| State
of a System |
In General > s.a. fluid [equation
of state]; phase space; Position.
* Idea: A way to summarize the available information on a system,
which allows us to predict results of measurements (associates numbers with
observables)
and future evolution of the system (using dynamical equations).
* Steady state: A state
in which physical quantities don't depend on time; If the system in question
is isolated, it will also be in equilibrium; If the system is not isolated,
there
may be
non-zero velocities, flows (stationary vs static, or "non-equilibrium" vs
equilibrium, steady state).
@ General: Thirring 81 (v III: 81, 2.2); Ludwig FP(90); Folse qp/02-in
[N Bohr's concept].
@ Covariant notion: Rovelli gq/01.
In Classical Theory > s.a. poisson
structure [structure on space of states].
* Idea: A (t-dependent)
measure on phase space; Possibly 
-function
like, a specification of the value of q and p, or q and q·,
at a time t, otherwise a statistical distribution functiion.
@ References: Mashburn FP(08) [order model for infinite classical states].
> Specific theories: see states in statistical
mechanics.
In Quantum Theory > s.a. quantum
states [including space of states] and quantum
field theory states.
* Idea: A normed, positive
linear functional on the algebra of observables (often a wave function or state
vector in a Hilbert space).
* Most general: Of the
form a 
tr(
a),
a density matrix.
* Mohrhoff: Quantum states
are fundamentally algorithms for computing correlations between possible measurement
outcomes, rather than evolving ontological
states [@ Mohrhoff IJQI(04)qp].
* And experiments: Outcomes
of experiments do not correspond to states directly; They indicate properties
of
probability
distributions for outcomes; Probability distributions leave open a choice of
quantum states and operators and particles, resolvable only by a guess.
@ General references: Newton AJP(04);
Madjid & Myers AP(05)
[associating outcomes of experiments to states]; Domenech et al AdP(06)qp [actual
and possible properties].
@ Covariant notion: Reisenberger & Rovelli PRD(02)gq/01;
> s.a. relativistic quantum mechanics.
> Related topics:
see observable algebras; quantum
statistical mechanics [including paradox].
Main page – Abbreviations – Journals – Comments – Other
sites – Acknowledgements
Send feedback and suggestions to bombelli at olemiss.edu – Modified
21 jun 2008