A quantum mechanical principle due to Werner Heisenberg which states that the position and
momentum of a particle cannot be determined simultaneously with any arbitrary
accuracy. These quantities can be determined only with accuracies limited by the
relation Δx.Δp ≥ (1/2)ħ, where Δx is the error in the
determination of the position and Δp is the error in the momentum. A similar
relation holds for the energy of a particle and the time, ΔE.Δt ≥ (1/2)ħ.
Same as → Heisenberg uncertainty principle.

Any of the physical principles that indicate in what way the actual
motion of a state of a mechanical system differs from all of its
kinematically possible motions or states. Variational principles that
express this difference for the motion or state of a system in each
given instant of time are called → differential.
These principles are equally applicable to both → holonomic
and → nonholonomic systems.
Variational principles that establish the difference between
the actual motion of a system during a finite time interval and all of
its kinematically possible motions are said to be → integral.
Integral variational principles are valid only for holonomic systems. The main
differential variational principles are: the
→ virtual work principle and
→ d'Alembert's principle.

In logical positivism philosophy, the claim that
a statement is literally meaningful (it expresses a proposition) if and
only if it either actually has been verified or could at least in principle be verified.

In → analytical mechanics, a principle whereby
it is necessary and sufficient for the equilibrium of any material
system with ideal constraints that the sum of the elements of work,
performed by the applied forces acting on the system in any virtual
displacement, be equal to zero (if all constraints are bilateral) or
less than zero (if some of the constraints are unilateral).

The → world lines of galaxies form in the 4D space-time
a bundle of non-intersecting
→ geodesics orthogonal to a series of space-like hyperstructures
(e.g. Narlikar 2002, An Introduction to Cosmology,
3rd Edition, Cambridge Univ. Press). Expressed differently: The world lines of galaxies, or
"fundamental particles," form (on average) a space-time filling family of
non-intersecting geodesics converging toward the past (Rugh & Zinkernagel, 2010,
astro-ph/1006.5848). The statement is sometimes denoted postulate, assumption, or
hypothesis. The importance of Weyl's principle is that it asserts that cosmic matter
moves according to certain regularity requirements. See also
→ cosmological principle.

First introduced by the German mathematician Hermann Weyl (1885-1955)
in 1923 in his Raum, Zeit, Materie; → principle.

work-energy principle

پروَز ِ کار-کاروژ

parvaz-e kâr-kâruž

Fr.: principe travail-énergie

The → work of the resultant force exerted on a particle equals
the change in kinetic energy of the particle.