Saturday, July 17, 2010

No-collapse quantum theory

What happens when you make a measurement on a quantum system?
Does one have to introduce additional axioms into quantum theory (as Born and Bohr) did to understand measurements?

On my last plane trip I read some of a really nice paper, Experimental motivation and emprical consistency in minimal no-collapse quantum mechanics, by Max Schlosshauer. Based on a review of experiments involving SQUIDs and molecular interferometry he argues that:

(i) the universal validity of unitary dynamics and the superposition principle has been confirmed far into the mesoscopic and macroscopic realm in all experiments conducted thus far;

(ii) all observed ‘‘restrictions’’ can be correctly and comple

tely accounted for by taking into account environmental decoherence effects;

(iii) no positive experimental evidence exists for physical state-vector collapse

"Ohhhhhhh. ... Look at that, Schuster. ... Dogs are so cute when they try to comprehend quantum mechanics."

What are the assumptions in this minimal theory?

First, a completely known (pure) state of an isolated quantum system is described by a normalized state vector in a Hilbert space.

Second, the time evolution of a state vector is given by the time-dependent Schrodinger equation.

No mention is made of measurements in this formulation. Instead, measurements are described without special axioms in terms of physical interactions between systems described by state vectors (wave functions) and governed by suitable interaction Hamiltonians. Observables then emerge as a derived concept.

Basically, I agree with these and it is nice to see the arguments set out so clearly. On the other hand, I don't follow some of Max's arguments about the amount of entanglement in the macroscopic states that he discusses.


  1. I believe it's in Feynman's lectures where rather than starting with single particle QM, he starts with a two-particle picture so as to introduce (de-)coherence. This circumvents any need for wavefunction collapse. Right?

  2. Skimming the paper, I cannot tell if this is a version of many-worlds or not. The question is pretty simple. When formally you have a superposition, do you actually have several disjoint possibilities realized at once, or just one of them? It's not enough just to say there's no violation of the superposition principle. If you are proposing to explain quantum theory, ultimately you have to say what's there. But Schlosshauer seems to be hiding behind the concept of decoherence. One world or many worlds, Dr Schlosshauer, which is it? And if it's just one world, then what is a superposition?