Does Quantum Mechanics Force us to give up Determinism?
1. Definition of terms and endeavor
1.1 Unpredictability versus Indeterminacy
Consider a pendulum and assume we describe its state s(t) at time t solely by the position of its bob . For simplicity suppose also that time is quantized in multiples of the basic time unit 1. If kept unperturbed, the pendulum’s motion is periodic ; thus any state s(t) will be be achieved infinitely many times. Assume for instance that s(t1)=s(t2). Does this imply s(t1+1)=s(t2+1) ? Clearly, there can be no such implication, since we do not know the velocity of the bob at the two times in question. Therefore, the system as described here is indeterministic. We might, however, imagine a description of the state in terms of more parameters ; with respect to this more extensive characterization the system might turn out to be deterministic. In that case, if we were given the parameters q1,q2, q3,...qn-1 qn,we would be able to predict the state s(q1,q2, q3,...qn-1 qn, t+1) at time t+1 from our knowledge of the state s(q1,q2, q3,...qn-1 qn,t) at time t.
1.2 The difficulty of establishing non-determinism
The example illustrates the difference between unpredictability and non-determinism. If insufficiently characterized, the pendulum’s motion is unpredictable. However, this does not preclude the existence of a complete description s(q1,q2, q3,...qn-1 qn,t) of the pendulum’s states that will make the system deterministic. Unfortunately this means that it is very difficult to prove that a system is truly non-deterministic. Proving that a process is deterministic requires the more straightforward (though possibly very difficult) task of specifying the complete set of descriptive parameters for a state together with the rules by which we can obtain one state from the preceding ; proving that a process is non-deterministic, however, requires us to prove that no such complete description and set of rules can be found, whether in practice or in theory.
Due to this difficulty, our philosophy of physics professor would be unlikely to ask his students to write an essay discussing whether or not the world behaves deterministically, or, whether or not an accurate deterministic description of the world could be found. What we can discuss, is whether or not, given some theory X, the acceptance of X as a correct description of the world entails that the world described by this theory X behaves deterministically.
1.3 Assumptions made
All discussion in this essay is based on the assumption that we take
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