## 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 http://www.math.rutgers.edu/~tumulka/teaching/fall11/325/script2.pdf
(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

SchrĂ¶dinger 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 http://arxiv.org/abs/0707.2832.

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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