Is quantum mechanical randomness objective?

If a subsystem can be identified objectively, this identification and the projection necessitated by it are just as objective.

This applies also to certain canonically identified description levels (hydrodynamics = local equilibrium, kinetics = micro-local equilibrium) and assorted hybrids with quantum mechanical systems. (Of course one can also choose very subjective description levels, and randomness will be correspondingly subjective.)

Objective randomness is thus that which results from a reduced description at a well-defined description level. It is subjective at most in the restrictive sense that what counts as chance depends on the description level (identification of the subsystem by choosing the relevant variables) and that this level can be chosen in different ways, being in this way dependent on the describing agent.

But randomness is objectively determined by the description level, which in practice means the choice of spatial and temporal scales on which a phenomenon is to be resolved, and the algebra of observable quantities thereby implied, and could be predicted with sufficient knowledge of the universe. The approximations made in the projection (in order to arrive at a Markov process) reveal the distribution of all relevant variables to be expressions that can in principle be calculated from the state of the universe.

Imprecision of measurement naturally also gives rise to an additional random element, which has a purely statistical character.

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Arnold Neumaier (Arnold.Neumaier@univie.ac.at)

A theoretical physics FAQ