Presumably the actual property is the state of the wavefunction.
So for instance we could have a Gaussian wavefunction… and that would be the determinate physical variable. It has no particular position or momentum, because there are nonzero amplitudes for various different positions and momenta. We could choose a different wavefunction to get a more determinate position, but then because it’s a Fourier transform the momentum would grow ever more indeterminate.
Presumably the actual property is the state of the wavefunction.
So for instance we could have a Gaussian wavefunction… and that would be the determinate physical variable. It has no particular position or momentum, because there are nonzero amplitudes for various different positions and momenta. We could choose a different wavefunction to get a more determinate position, but then because it’s a Fourier transform the momentum would grow ever more indeterminate.
Interestingly, there are apparently ways of working around this, by carefully choosing your observables to be operators that commute. http://arstechnica.com/science/2010/08/quantum-memory-may-topple-heisenbergs-uncertainty-principle/