# Dictionary Definition

observable adj : capable of being seen or
noticed; "a discernible change in attitude"; "a clearly evident
erasure in the manuscript"; "an observable change in behavior"
[syn: discernible,
evident]

# User Contributed Dictionary

## English

### Adjective

#### Translations

able to be observed

- Czech: pozorovatelný

### Noun

# Extensive Definition

In physics, particularly in
quantum
physics, a system observable is a property of the system
state that can be determined by some sequence of physical
operations.
For example, these operations might involve submitting the system
to various electromagnetic
fields and eventually reading a value off some gauge. In
systems governed by classical
mechanics, any experimentally observable
value can be shown to be given by a real-valued
function
on the set of all possible system states. In quantum
physics, on the other hand, the relation between system state
and the value of an observable is more subtle, requiring some basic
linear
algebra to explain. In the
mathematical formulation of quantum mechanics, states are given
by non-zero vectors
in a Hilbert
space V (where two vectors are considered to specify the same
state if, and only if, they are scalar multiples of each other) and
observables are given by self-adjoint
operators on V. However, as indicated below, not every
self-adjoint operator corresponds to a physically meaningful
observable. For the case of a system of particles,
the space V consists of functions called wave
functions.

In quantum mechanics, measurement of observables
exhibits some seemingly unintuitive properties. Specifically, if a
system is in a state described by a vector in a Hilbert
space, the measurement process affects the state in a
non-deterministic, but statistically predictable way. In
particular, after a measurement is applied, the state description
by a single vector may be destroyed, being replaced by a statistical
ensemble. The irreversible
nature of measurement operations in quantum physics is sometimes
referred to as the measurement
problem and is described mathematically by quantum
operations. By the structure of quantum operations, this
description is mathematically equivalent to that offered by
relative state interpretation where the original system is
regarded as a subsystem of a larger system and the state of the
original system is given by the partial
trace of the state of the larger system.

Physically meaningful observables must also
satisfy transformation
laws which relate observations performed by different observers in different
frames
of reference. These transformation laws are automorphisms of the state
space, that is bijective transformations
which preserve some mathematical property. In the case of quantum
mechanics, the requisite automorphisms are unitary
(or antiunitary)
linear transformations of the Hilbert space V. Under Galilean
relativity or special
relativity, the mathematics of frames of reference is
particularly simple, and in fact restricts considerably the set of
physically meaningful observables.

## References

- S. Auyang, How is Quantum Field Theory Possible, Oxford University Press, 1995.
- G. Mackey, Mathematical Foundations of Quantum Mechanics, W. A. Benjamin, 1963.
- V. Varadarajan, The Geometry of Quantum Mechanics vols 1 and 2, Springer-Verlag 1985.

observable in Czech: Pozorovatelná
veličina

observable in German: Observable

observable in Spanish: Observable

observable in French: Observable

observable in Italian: Osservabile

observable in Hungarian: Megfigyelhető
mennyiség

observable in Polish: Obserwabla

observable in Finnish: Observaabeli

# Synonyms, Antonyms and Related Words

apparent, appreciable, beholdable, clear, clear as crystal,
crystal-clear, detectable, discernible, disclosed, distinct, evident, explicit, exposed, exposed to view,
express, hanging out, in
evidence, in full view, in plain sight, in view, indisputable, indubitable, insight, manifest, memorable, naked, notable, noticeable, obvious, open, open to view, open-and-shut,
outcropping,
palpable, patent, perceivable, perceptible, perspicuous, plain, plain as day, recognizable, red-letter,
revealed, rubric, seeable, self-evident,
self-explaining, self-explanatory, sensible, showing, tangible, to be seen, transparent, unclouded, unconcealed, undisguised, unhidden, unmistakable, viewable, visible, visual, witnessable