2) An engineering approach that detects signal widths on certain relative levels and yields the uncertainty relations
in the limit value form
Below in the present work we will also offer another universal formulation of uncertainty relation
for the "train of pulses" case.
The Uncertainty Relations
(UR) enjoy a considerable popularity, due in a large measure to the so called Conventional (Copenhagen) Interpretation of UR (CIUR).
Kempf, "Uncertainty relation
in quantum mechanics with quantum group symmetry," Journal of Mathematical Physics, vol.
About Heisenberg's uncertainty relation
. Proceedings of The Prussian Academy of Sciences Physics-Mathematical Section, 1930, v.19, 296-303; English version in: Bulg.
Certainly, for the history of the [L.sup.z]--[partial derivative] problem, the first reference element was the Robertson Schrodinger uncertainty relation
(RSUR) introduced [25, 26] within the mathematical formalism of QM.
One can see that uncertainty relation
[GUP.sup.**] causes increasing of the black holes temperature in comparison with relations (18) and (20).
Although the advent of Schrodinger equation dates back to many decades ago [1-3], the interest in the study of the equation has been renewed due to the noncommutative phase space commutations relations and the so-called minimal length (alternatively called generalized) uncertainty relation
. The noncommutativity between space-time coordinates was first explained by Snyder  and provides us with motivating scenarios in string and M-theories [5, 6] as well as modern cosmology [7-9].
The time-energy uncertainty relation
can be obtained from the position-momentum uncertainty relation
by using p = E/c and t = x/c to give
According to (1), it can be referred to as a measurement uncertainty (i) or as an error-disturbance uncertainty relation
Gosson (University of Vienna) proposes new concepts from symplectic topology as the proper setup for a better understanding of the twilight zone between quantum and classical properties, and shows how symplectic geometry and its topological extensions allow physicists to state and prove a classical multi-dimensional uncertainty principle formally similar to the quantum uncertainty relations
. The opening chapters review the basics of Hamiltonian mechanics in its Hamiltonian formulation with a strong emphasis on the symplectic character of Hamiltonian flows.
Many contemporary humanists and theologians see in the uncertainty relations
of quantum mechanics a space in which mental causation might operate on the physical.