Difference between revisions 23979775 and 23986510 on enwiki

'''[[Quantum mechanics]] and [[Theory of relativity|relativity]] theory''' comprise two of the foundation stones of [[theoretical physics]], and [[information theory]] is one of the most successful of all theories in [[applied mathematics]].

In quantum mechanics, one is obsessed with what one can hope to learn about a physical system (for example, according to the [[uncertainty principle]], one cannot hope to learn both the position and momentum of an electron to arbitrary accuracy).

In relativity theory, one learns that signals cannot be propagated faster than light, and that all observers measure the same value for this maximal speed (in a vacuum).  Put another way, given a particular [[event]] A in a given [[spacetime]] model (such as an [[exact solutions in general relativity|exact solution in general relativity]], there is a definite region, called the [[absolute future]] of this event,A, such that no events outside the absolute future can be causally affected by this event A.

Information theory is on the other hand a ''strictly statistical theory''. While this theory does have a clear (statistical) notion of causal relationship, ''it has no arrow of time''.  Specifically, the quantity <math>I(X,Y)</math> which measures the information about <math>X</math> which is supplied when one learns <math>Y</math>, ''or vice versa'', does not allow us to conclude that one event ''ca(contracted; show full)y-- but where something closely analogous to an event horizon occurs; this leads to the idea of [[analog gravity]], which includes the notions of [[optical black hole]]s and [[acoustic black hole]]s.)  In addition, in the last decade, the new concept of the [[qubit]] has been intensively developed in the new field sometimes called [[qauntum information theory]].  This work really does involve both information theory and quantum theory in essential ways.

Perhaps motivated by these developments, Carl Hewitt
 (Computer Science, University of Michigan, Emeritus) speculates there should be a new kind of 'information theory' which addresses questions such as these:
*Fundamentally, what is information in physics?
*How can information be obtained physically?
*By what means can information be transmitted?
*Can information be complete?
(contracted; show full)
* Christopher Fuchs, ''Quantum mechanics as quantum information (and only a little more)'' in A. Khrenikov (ed.) Quantum Theory: Reconstruction of Foundations (Växjo: Växjo University Press, 2002).
*Asher Peres and Daniel Terno. ''Quantum Information and Relativity Theory'' Rev.Mod.Phys. 76 (2004) 93.

{{relativity-stub}}