User:Boris Tsirelson/Sandbox1: Difference between revisions

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The [[Heisenberg Uncertainty Principle|Heisenberg uncertainty principle]] for a particle does not allow a state in which the particle is simultaneously at a definite location and has also a definite momentum. Instead the particle has a range of momentum and spread in location attributable to quantum fluctuations.


==Measurement and influence==
An uncertainty principle applies to most of quantum mechanical operators that do not commute (specifically, to every pair of operators whose commutator is a non-zero scalar operator).
 
In classical physics an ideal measurement exerts no influence on the
object. It only reveals some properties of the object to the
experimenter. The experimenter is able to choose an observable (a
variable to be measured), or to measure all possible observables at
once, and still, the subject may be treated as a closed system.
 
Quantum physics is strikingly different. The influence of a
measurement on the object is almost inevitable. If a macroscopic
measuring device together with some environment is treated as a part
of the quantum system (the object), and the experimenter only observes
the reading of the device, then in some sense the experimenter does
not influence the object. This is a subtle point related to
[[decoherence]]. Typically, macroscopic devices are not included into
the quantum system, which implies that every measurement inevitably
exerts a substantial influence on the object.
 
In general, two measuring devices cannot be applied simultaneously to
the same object. Thus, in general, two observables are
incompatible. For exapmle, the coordinate <i>q<sub>x</sub></i> and the
momentum <i>p<sub>x</sub></i> of a particle are incompatible (but
<i>q<sub>x</sub></i> and <i>p<sub>y</sub></i> are compatible). The
experimenter may choose one of the two observables, coordinate and
momentum, and measure it, thus exerting a substantial influence on the
other observable.
 
==Local causality and influence==
 
Local causality negates action on a distance. Basically it states that
if two objects A, B are far apart in space then any external influence
on A has no direct influence on B.
 
A strict relativistic interpretation states that a signal cannot
propagate faster than light. More exactly, let A, B be two domains in
space-time. (For example, A may be a given space ship during a given
one-second time interval (according to its local clock), and B another
space ship, 1,000,000 km apart, during its time interval.) Assume that
a light ray emitted from A cannot reach B. (For example, because it
can travel only 300,000 km during the given second.) Then any external
influence exerted within A is of no consequence within B. (For
example, a sudden explosion on the first space ship during its
interval cannot cause anxiety on the second space ship before the end
of its time interval.)

Latest revision as of 03:25, 22 November 2023


The account of this former contributor was not re-activated after the server upgrade of March 2022.


The Heisenberg uncertainty principle for a particle does not allow a state in which the particle is simultaneously at a definite location and has also a definite momentum. Instead the particle has a range of momentum and spread in location attributable to quantum fluctuations.

An uncertainty principle applies to most of quantum mechanical operators that do not commute (specifically, to every pair of operators whose commutator is a non-zero scalar operator).

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