The measurement process in the quantum universe

The traditional interpretation of quantum mechanics divides the world into small quantum systems and large measurement devices, and restricts itself to making statistical statements about measured results.

On the other hand there is a consensus that quantum mechanics should be valid for the universe as a whole. (Otherwise the search for a quantum theory of gravity, for example, would be futile.) Thus the whole universe is also a quantum system, and the traditional interpretation is no longer applicable.

Clearly we measure the universe, so we need a better theory of the measurement process. In this case the measuring device is part of the measured system. Thus one needs to generalise or modify the traditional formalism.

This has lead to a number of alternatives being discussed (many worlds, decoherence, consistent histories) all of which have their problems, and which I will not discuss here. My opinion about them can be found in

http://www.mat.univie.ac.at/~neum/manyworlds.txt

http://www.mat.univie.ac.at/~neum/zeh.txt

Here I will restrict myself to discussing my own interpretation.

In short, the thermal interpretation says the following about measurements in the universe:

The universe is the only closed system existing in our vicinity. It is impossible to guarantee that no photons escape from a system, that there is no energy exchange with the container, etc. It is exactly these things that ensure that one cannot view the system as deterministic, because the external influences are uncontrollable. (Even if this seems negligible at first sight, it is only so if one is investigating macroscopic phenomena. Microscopic phenomena are extremely sensitive to their environment. This is discussed in more detail in the literature about decoherence.)

Since the universe is closed, it obeys a deterministic dynamics.

Because we only prepare a small part of the universe when we do experiments, it is no surprise that we observe apparently inexplicable randomness. This is simply a corollary of our limitedness and the sloppy traditional modes of argumentation.

In other words, as soon as we observe only a subsystem of an arbitrary deterministic system, we lose information and can for this reason only describe the subsystem stochastically. The phenomena observed in practice can be modelled by diffusion and jump processes, which are derived from the deterministic dynamics with the help of the projection formalism of statistical mechanics (but only rigorously and under extremely restrictive conditions).

Naturally this also applies to subsystems of the universe, and thus completely explains random behaviour. If one knew the exact state of the universe, one would be able to predict anything that one can measure.

That measured values are nevertheless not 100% certain is thus not the result of irreducible quantum randomness, but a consequence of the fact that measurements use one many-particle system to measure another.

Uncertain measurement results and irreducible quantum randomness do not necessarily have anything to do with one another. This is because measurement values are also uncertain classically if one measures one many-particle system with another. This is in spite of the fact that all events (including measurement values) are classically determined by the state of the universe.

The thermal interpretation thus postulates a deterministic dynamics for the universe as a whole, and deduces an approximate stochastic dynamics for each subsystem.

The thermal interpretation thus reinstates (only) determinism. Uncertainty in measurements is not avoided, but related back to the philosophically unproblematic concept of mass which was in currency before 1900.

Arnold Neumaier (Arnold.Neumaier@univie.ac.at) A theoretical physics FAQ