Can measurements change Hilbert space?

The CCR's of quantum fields admit inequivalent representations; a basic step in treating them is the construction of the physically appropriate representation, that is, the Hilbert space. Once this is done, in textbook treatments, all analysis takes place in that Hilbert space.

I show that there are physically plausible circumstances in which infinitely many commuting measurements may be made, which would alter the representation, and that it seems inescapable this behavior must occur in open cosmological models. In the most conservative scenarios, causality restricts the consequences of this to only gradually become apparent on any one worldline, the evidence for it accumulating at later and later events. But I will also describe a situation in which it would seem that the effects could become known at finite events.

It is, however, possible that this behavior is far more pervasive. While conventional quantum theory specifies what happens in a measurement, it is silent about which measurements are likely to occur in which circumstances. We should ask what measurements are likely to have occurred over the 14 Gy evolution of the Universe, and what their consequences on physics have been. It is possible that the Hilbert space of the Universe has been remade many times.