Friday, June 5, 2015

A modern take on the old measurement problem

The measurement problem in quantum mechanics is the key to understand various interpretations. There are many approaches to it: some say it is not a real problem, or that parts of it are not real but pseudo-problems, some claim that Bohr had figured it out already, some state that since there are so many solutions to it is not really interesting anymore, or some think that if only they would have enough time (perhaps an afternoon) to think about it they will solve it.

Now the best way to explain it was done by Tim Maudlin in

In particular I like his quote from Feynman:

"[We] always have had (secret, secret, close the doors!) we always have had a great deal of difficulty in understanding the world view that quantum mechanics represents. At least I do, because I'm an old enough man that haven't got to the point that this stuff is obvious to me. Okay, I still get nervous with it... you know how it always is, every new idea, it takes a generation or two until it becomes obvious that there's no real problem. I cannot define the real problem, therefore I suspect there's no real problem, but I'm not sure there's no real problem."

Without expanding on all generality of Tim's well known paper, here is the basic "trilemma":
  1. The wavefunction specifies completely the physical properties of a physical system
  2. The wavefunction evolves linearly according to Schrodinger's equation
  3. Experiments have definite outcomes

Now any two statements from above contradict the third one. Denying number one corresponds to adding "hidden variables" and Bohmian's approach falls in here. Denying number two is the approach taken by collapse theories like GRW, and denying number three is the approach of MWI.

QBism stands apart from the three approaches above in that it denies the measurement problem altogether: and tries to convince us that "there is no real problem" as Feynman would put it.

Now to this "classical" approach to the measurement problem, efforts in quantum mechanics reconstruction point to a basic mathematical inconsistency which place the measurement problem in a new light. So there is a "real problem". One can obtain quantum mechanics from invariance of the laws of nature under composition and Leibniz identity: . In the algebraic approach to quantum mechanics it is well known that Leibniz identity corresponds to unitarity and hence any unitary violation renders the entire quantum formalism mathematically inconsistent: quantum formalism+collapse = contradiction.

So how can we solve this? Here are the existing quantum mechanics interpretation solutions:
  1. Extend the formalism: GRW
  2. Remove the collapse: Bohmian
  3. Provide contextual protection: MWI and QBism
For MWI the context is the world branch which results after the split, for QBism the context is the subjective experience of the experimenter in the sense of De Finetti: collapse is a mere update of information happening inside your mind.

There is another variant on extending the formalism. In spontaneous collapse theories the evolution is stochastic and outside quantum formalism. However the quantum formalism can be extended to include collapse and there is a unique mathematical way to do it. I will talk about this next week at the QTFT conference in Vaxjo and then I'll expand it here at this blog.

This predicts new physics and quantum mechanics interpretation will be put to an experimental test. 

My next post will be delayed a bit due to travel, but it will contain fresh insights from the conference. Please stay tuned. 

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