Originally Posted by

**Markus Hanke**
Unfortunately this isn't possible because there are limits to how exactly something can be determined in quantum mechanics ( look up "Heisenberg Uncertainty Principle" ). What this basically means is that you can measure only one variable at a time with arbitrary accuracy, but not all of them simultaneously

Actually Marcus, I believe you slightly overstate your case. This is only true of

*non-commuting* variables as follows.

To every variable in QM there corresponds an Hermitian operator acting on a complex Hilbert space of state vectors. These operators/variables may be thought of as "observables" if the only allowable range of measurement outcomes are simply the spectrum of eigenvalues for these operators. This makes sense because the eigenvalues of an Hermitian operator must be real, as, if course, must also be a if it to be measurement in the physical world.

The converse, surprisingly (to me at least), is true: every possible measurement outcome of a state is an eigenvalue for some Hermitian operator

So given 2 (or more) Hermitian

operators taking the same state vector as argument, one says that they commute iff

. One may just well (more informally) say that the

*variables* commute under this circumstance. This ramble is because it is not obvious to me that, in the more general case in mathematics it makes sense to talk about "commuting variables".

Whatever. The point being, it can be shown that the eigenvalues for different commuting operators acting on the same state can be combined according to simple arithmetic rules (these are real numbers, recall), so that two (or more) commuting variables can be simultaneously measured, and one can think of this being a single measurement with two (or more) real values, simultaneously obtained

So in other words, it just isn't possible to determine all variables at the same time,

From the above, the HUP refers ONLY to the non-commutative case. (Though it requires a bit more work to show this)