Quantum Information for Quantum Cats (4)

Quantum Theory at Its Minimum 1 : States and Observables

In this implobable statement that the obserbed result is in observer's discretion, there resides an essence of quantum mechanics. We shall now look into that quantum discretion in more detail.

In quantum mechanics, the state and the result of observations have to be considered as two distinct concepts. That is because Bob, the observer in quantum measurement, is a mortal existence less than a god, and his power of observation is rather limited. All he is permitted to do with his experiment is to decide which state the paticle is in among a pre-defined set of possible states. Concerning our quantum arrow, Bob can observe the spin to be either in two state, for example , in "up" or "down". Now what do I mean by "for example" here? can he observe it to be "right" and "left"? Here comes the discretion of Bob. Bob can decide which direction he places his observational device, which results in him observing the arrow to be in a preferred direction, let's say \phi, or in \phi+180 degree.

Putting the quantitative acessment later, we describe the situation in verbally. Suppose Alice places the arrow straight up, \theta=0. If Bob decides to observe it up or down, and set his observational tools accordingly, the result is that he observe the arrow heading up, \phi=0 deg all the time. Well, make sense, and no surprise here, right? Now if Bob decides to observe it side ways, and set his observational tools accordingly, the result is either he observe the arrow heading right, \phi=90 deg with 50 % probability, and heading left, \phi = 270 deg with rest of the probability! This means both the result is probablistic and the observer has certain control over the result. To make the story consistent, if, after observing the arrow heading right, he does another observation with the same settings of his tools, he should surely discover it heading right. In other word, the state changes after the observation by Bob. Observation is not a passive activity but it affects the state of the observed system!

Why on earth the result depends on the observer's will? This is certaily a legitimate question to ask. But just keep asking this all the time could result in noprogress. You could also suspend that question for a time being, and pretend to accept that as a given fact and see where that would lead us.