What is a microscopic measurement?
Physicists talk a lot about the measurement of microscopic quantities. But what are they really measuring?
Since my thermal interpretation argues for a different view than the traditional one, it is worth examining the latter more carefully.
Let us therefore look more closely at the claim that a physicist has measured the spin of a particle in an experiment. What has really happened?
What has been measured is a macroscopic quantity which is stable enough to be observed in a completely reproducible fashion. This is the raw measurement. From this, by means of theoretical considerations (all handwaving) we make deductions about the spin of a single particle, and conclude that we have measured the spin.
This is highly dubious, because of the many approximations that lead from the description of system+apparatus+environment to the assertion that we have measured the spin, and because of the sensitivity with which a small quantum system reacts to perturbations.
When one makes a more precise statistical mechanics calculation, one does not really arrive at a more secure basis for this claim, but only the proposition that one measures the average spin. In practice one also records fairly random individual observations, and only on average, a usable, reproducible observation that counts as a physically relevant fact.
With an appropriate experimental setup one can collect enough data to determine the density matrix of the source, and thereby all of the expectation values produced by it.
This is exactly what quantum opticians do in their experiments, they want to know no more and no less about a quantum system (that is, a stationary or slowly varying source).
They also make no statements about single particles; nor are they interested in such. The physically interesting measurement is not the single click in the apparatus, but the distribution of such clicks.
The results of a single measurement are of course clearly measurement results - but not of the particle, rather the measurement device.
They describe, for example, the position of a pointer or a silver particle. The corresponding macroscopic variable is a mass weighted sum of the positions of very many atoms, and what one measures is the expectation values of the position in the statistical mechanics sense.
To interpret a macroscopic spot of silver as an 'exact' measurement of the spin of a particle is an additional assumption which cannot really be justified, but which is responsible for the paradoxes of quantum mechanics.
In the thermal interpretation, single results of so-called 'measurements' of microscopic systems are no longer interpreted as that for which they are generally taken, namely statements about microscopic variables, but rather as what they are, as macroscopic expectation values of certain variables of a many-particle system (the detector). This is what they are at the fundamental level. Only in the mass, and with the precision with which one can show theoretically that this result agrees with the value of a microscopic variable, do they deserve their status as measurements of such.
Arnold Neumaier (Arnold.Neumaier@univie.ac.at) A theoretical physics FAQ