Everything about Observable totally explained
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're 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's
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.
Further Information
Get more info on 'Observable'.
|
External Link Exchanges
Do you know how hard it is to get a link from a large encyclopaedia? Well we're different and will prove it. To get a link from us just add the following HTML to your site on a relevant page:
<a href="http://observable.totallyexplained.com">Observable Totally Explained</a>
Then simply click through this link from your web page. Our crawlers will verify your link, extract the title of your web page and instantly add a link back to it. If you like you can remove the words Totally Explained and embed the link in article text.
As long as your link remains in place, we'll keep our link to you right here. Please play fair - our crawlers are watching. Your site must be closely related to this one's topic. Any kind of spamming, dubious practises or removing the link will result in your link from us being dropped and, potentially, your whole site being banned. |
