Heisenberg's Uncertainty Principle?

[pivoxa15]

Would it be correct to conclude from the Uncertainty Principle that the Newtonian mechanics of being able to exactly determine the velocity of a particle from its displacement (and vice versa) through differential equations is only an approximation?

Many fundalmental things in the Universe is quantised from the QM view but why than are differential equations so widely used in physics and do people see them getting less and less used in physics? Are they popular in the newer theories like string theory?

 

[dextercioby]

Dynamics usually involves the concept of continuity (of time & space) and evolution (we're interested in time evolution), so our fundamental equations need to be (integro)-differential equations.

I don't know what you mean by "getting less & less used" ? Most of them cannot be solved exactly and that's why perturbative or numerical methods are used to get the physical information.

Daniel.

 

[Dr.Brain]

Newtonian methods degree of precision increases as the size of dealt-with objects increases and it is quite precise when dealing with general object , it is only when dimensions of the object decrease to that of atomic-dimensions , the Newtonian-methods deviate from reality, that is when QM comes into play .

BJ

 

[selfAdjoint]

Perturbative methods still use differential equations, it's just that the solutions are understood to be approximate. Schroedinger's and Dirac's equations are differential equations. In Lagrangian field theory you get down to equations of motion. The propagators, or Green's functions, that loom so large in field theory are techniques for solving differential equations, look 'em up.