Search results
Results from the WOW.Com Content Network
Time-translation symmetry is the law that the laws of physics are unchanged (i.e. invariant) under such a transformation. Time-translation symmetry is a rigorous way to formulate the idea that the laws of physics are the same throughout history. Time-translation symmetry is closely connected, via Noether's theorem, to conservation of energy. [1]
If a system is time-invariant then the system block commutes with an arbitrary delay. If a time-invariant system is also linear, it is the subject of linear time-invariant theory (linear time-invariant) with direct applications in NMR spectroscopy, seismology, circuits, signal processing, control theory, and other technical areas.
For translational invariant functions : it is () = (+).The Lebesgue measure is an example for such a function.. In physics and mathematics, continuous translational symmetry is the invariance of a system of equations under any translation (without rotation).
In linear algebra, linear transformations can be represented by matrices.If is a linear transformation mapping to and is a column vector with entries, then there exists an matrix , called the transformation matrix of , [1] such that: = Note that has rows and columns, whereas the transformation is from to .
Because translation is commutative, the translation group is abelian. There are an infinite number of possible translations, so the translation group is an infinite group . In the theory of relativity , due to the treatment of space and time as a single spacetime , translations can also refer to changes in the time coordinate .
To find the answer, translate the state by an infinitesimal amount in the -direction, calculate the rate that the state is changing, and multiply the result by . For example, if a state does not change at all when it is translated an infinitesimal amount the x {\displaystyle x} -direction, then its x {\displaystyle x} -component of momentum is 0.
Thus some translation invariant operations can be represented as convolution. Convolutions play an important role in the study of time-invariant systems, and especially LTI system theory. The representing function g S is the impulse response of the transformation S.
Time evolution is the change of state brought about by the passage of time, applicable to systems with internal state (also called stateful systems). In this formulation, time is not required to be a continuous parameter, but may be discrete or even finite .