Heisenberg's uncertainty principle

It is impossible to define both the parameter and its canonical conjugate to arbitrary accuracy. This means that two coordinates which are canonical conjugate of each other (whose canonical commutation is non-zero, or whose Poisson bracket is non-zero) can not be simultaneously measured with arbitrary accuracy.

Examples:

  1. \({x,p}!=0\), or \([x,p]=i\bar{h}\). So we can not define position and momenta to arbitrary accuracy.