I want to write a computer program.
The input to the program is:
- A description of an experimental device (for instance a Stern-Gerlach apparatus, or a laser and a polarizer)
- What the experimenter will do with the device (e.g., fire an electron, fire a photon)
And the output of the program is a sequence of yes/no answers to the following questions:
- Does this experiment correspond to a position measurement?
- Does this experiment correspond to a momentum measurement?
- Does this experiment correspond to an angular momentum measurement?
- Does this experiment correspond to a spin measurement?
- Does this experiment correspond to an energy measurement?
What I want to know is:
What is the algorithm the program uses to determine the result "yes" or "no" to each of the above questions?
Why am I asking such a weird question? Because I've never gotten a clear understandable answer on what constitutes a measurement type. Note, I am not asking what constitutes a measurement; I am asking what constitutes the type of measurement. The answers I get are always hand-wavy and subjective. But it can't possibly be subjective, because otherwise the experimental results would not match those computed with quantum mechanics, e.g., if I compute the eigenvalues of the wrong observable, the values aren't going to match up with those obtained from experiment.
So to give you a concrete example, suppose I shoot an electron at a flat board. I can measure the board's recoil to get the momentum of the electron, or I can measure the location the electron struck the board to get its position. But that's a hand-wavy explanation! I just "decided" that I'd call the first experiment a momentum measurement because it sounds like one, and similarly I simply decided to call the other one a position measurement. I want an exact procedure to categorize whether it is a position-determining or momentum-determining experiment.