Do randomness and indeterminacy in Quantum Physics mean the same?

Question

I have been trying to learn about the randomness in Quantum Physics. But of the many sources I referred to, some say about "Randomness in Quantum physics" and some others say about "Quantum indeterminacy". So my question is do these two mean the same or are they completely different? Is randomness because of that indeterminacy or that randomness is actually "there" and that causes the indeterminacy in Quantum Physics? Or are they just two ways of referring to the same thing and if yes then what are they actually referring to?

Answer 1

You might be interested in this question or this question (and some others I cannot track down now).

The basic problem is this: It is not clear what we exactly mean by "deterministic". If you mean that we can in principle determine the future state of a system solely from initial conditions, then the time evolution given by the Schrödinger equation is indeed deterministic.¹ However, if you prescribe that "deterministic" means that we can in principle determine the result of any measurement ahead of time, then you run into Bell's theorem: Either your theory is non-deterministic in this sense or it has non-local dependencies.

The or is the vexing thing here, since it means that saying "QM is non-deterministic" could always be countered by "Or it is deterministic and non-local!" (the latter theory constructions are called non-local hidden variable theories).

So, the answer to your question is: These terms are not used perfectly consistently. Determinacy of time evolution is something different from determinacy of measurement results, and whether or not you think QM is deterministic/non-deterministic depends on your interpretation of it.

Randomness is encapsulated by non-determinacy of measurement results, since the Born rule of the Copenhagen interpretation gives you probabilities for each possible result. Non-determinacy of time evolution would not be random, since collapses of the wave function occur during sharp events, i.e. interactions/measurement processes, at not according to a probability distribution in collapsy interpretations.

¹There's another pitfall here, namely if you subscribe to a collapse or a non-collapse interpretation of QM. Some collaspy types may say that QM is not deterministic even in the time evolution sense.

Answer 2

To say the least, they are inseparable. The "indeterminacy" is meant to be a synonym of the "uncertainty" (original in German: Unschärfe oder Unbestimmtheit), e.g. the nonzero values of $\Delta x$ (uncertainty of position) and $\Delta p$ (uncertainty of momentum) that obey $$ \Delta x \cdot \Delta p \geq \frac\hbar 2$$ This is a consequence of the nonzero commutator $xp-px = i\hbar$ in the more mathematical formulation of the theory. It directly follows that $x,p$ cannot have exact values at the same moment, and the only thing that this can mean for the actual measured values is that they are not exactly determined before the measurement. They have some unavoidable intrinsic inaccuracy, an error margin, and what result is actually obtained by a particular single measurement is a random decision of Nature.