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Old 25-November-2008, 02:54 AM
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Quote:
Originally Posted by jamesabrown View Post
Yikes, can you explain that further, please?
The Heisenberg uncertainty principle is a bit more fundamental than what is being called the observer effect. It is not just a statement that a physical measurement requires a physical interaction between the system being measured and the measuring device, but rather a fundamental statement that the operators that represent measurements in quantum mechanics do not commute. So if you measure position and then momentum you will get a different result than if you measure momentum and then position. This boils down to the simple fact that if x represents the operation of multiplication by x (the position operator in QM) and d/dx is the usual operation of differentiation (the momentum operator) then the operators x*d/dx and d/dx*x are different operators (this is just a result of the product rule for differentiation as you can see by applying the operators to an arbitrary function f).

The Heisenberg uncertainty principle results in the determination of a minimum error that results from attempts to simultaneously measure both position and momentum, and this minimum error cannot be reduced by refinement of measurement technique.

The uncertainty principle itself and the essential uniqueness of operators obeying the commutation relations have been studies extensively.

http://en.wikipedia.org/wiki/Uncertainty_principle

http://en.wikipedia.org/wiki/Stone%E...eumann_theorem
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