Thursday, June 20, 2013

Quantum mechanics and unitarity (part 4 of 4)

Now we can put the whole thing together and attempt to solve the measurement problem. But is there a problem to begin with? Here is a description of the problem as written by Roderich Tumulka (see page 53):

Start with 3 assertions:

• In each run of the experiment, there is a unique outcome.
• The wave function is a complete description of a system’s physical state.
• The evolution of the wave function of an isolated system is always given by the
Schrödinger equation

Then in the standard formulation of quantum mechanics at least one of them has to be refuted. From the quantum mechanics reconstruction work, the last two bullets are iron-clad and cannot be violated without collapsing the entire theory. This means that GRW theory, and Bohmian interpretations are automatically excluded. Also the usual Copenhagen interpretation is not viable either because it makes use of classical physics (we know that we cannot have a consistent theory of classical and quantum mechanics). Epistemic approaches in the spirit of Peres are not the whole story either because while collapse is naturally understood as information update, this means that Leibniz identity is violated as well.

So what do we have left? Only the many-worlds interpretation (MWI), or its more modern form of Zurek’s relative state interpretation

However, I will argue for another fully unitary solution different than MWI/relative state interpretation (and I agree with Zurek that the old fashion MWI gives up too soon on finding the solution), but in the same spirit of Zurek’s approach. The basic idea is that measurement is not a primitive operation. The experimental outcome creates huge numbers of information copies. The key difference between Zurek’s quantum Darwinism and the new explanation is on who succeeds in creating the information copies: the full wavefunction (as in quantum Darwinism), or the one and only experimental outcome. In other words, the Grothendieck equivalence relationship is broken by the measurement amplification effects: only one equivalent representative of the Grothendieck group element succeeds in making information copies and statistically overwhelms all the other ones (for all practical purposes). The information in the “collapsed part of the wavefunction” is not erased, but becomes undetectable.

Of course there are still open problems of delicate technical nature to be solved in this new paradigm, but they do seem to get their full answer in this framework. Solving them is a work in progress, and the solution is not yet ready for public disclosure.

In subsequent posts I’ll show how the wavefunction is neither epistemological, nor ontological and I will touch on Bell’s theorem, and the recent PBR result among other things.

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