**classical vs QM**

Of course, if position x and momentum p are both determined at the same time, it will be classical physics.

Look at the simplest wave function for free particle in QM (or the “glass” in this topic):

Ψ = A exp( i(p•x– Et )) omit “h-” and vector marks for convenience of observation.

When position x and momentum p are both determined at the same time, it will no longer be a wave function, instead, an oscillation function. It seems that the “wave character” should disappear either.

What interesting is it could be considered as a special situation and the calculation of probability is still applicable. “A” is a constant. ｜A｜² is a constant. It means the probability of appearance of the particle in any space point is the same. In turn, it means the position of the free particle can not be determined.

Contradiction…

Classical physics vs QM, who is wrong?

Or, it demonstrates that a coin has two aspects and classical physics describes the certain aspect while QM describes the uncertain aspect?

How to solve the “seems” contradiction? The fourth (special) spacial dimension is needed to accommodate the uncertainty (probability of appearance).