Is the wavefunction ontological or epistemological?
What is wrong with Copenhagen/standard interpretation?
Arguably, the standard interpretation is the best available interpretation, but it is not without blemishes. The big problem here is the usage of classical mechanics. Here is a nice exposition of why there cannot be a consistent mixed classical-quantum mechanics theory: http://arxiv.org/abs/quant-ph/0301044 Quantum and classical mechanics belong to different composability classes: quantum mechanics is a realization of elliptic composability and classical mechanics is the sole realization of parabolic composability. Physically, in a mixed classical-quantum system, there is no back reaction of the quantum system in the classical one. In other words, classical devices cannot measure anything from the quantum world, and the idea of a classical measuring apparatus is a nice fantasy.
However, the old Bohr interpretation got a nice instrumentalist upgrade from late Asher Peres. I highly recommend his book: “Quantum Theory: Concepts and Methods” (http://www.amazon.com/Quantum-Theory-Concepts-Fundamental-Theories/dp/0792336321) In the Preface, Peres famously states: “quantum phenomena do not occur in a Hilbert space, they occur in a laboratory”.
On pages 172-173 of the book, Peres addresses the question of the universality of quantum mechanics:
“Even if quantum theory is universal, it is not closed. […] While quantum theory can in principle describe anything, a quantum description cannot include everything. In every physical situation something must remain unanalyzed. This is not a flaw of quantum theory, but a logical necessity in a theory which is self-referential and describes its own means of verification. This situation reminds of Gödel’s undecidability theorem: the consistency of a system of axioms cannot be verified because there are mathematical statements that can neither be proved nor disproved by the formal rules of the theory; but may nonetheless be verified by metamathematical reasoning.”
For all practical purposes, the
interpretation works very well if we do not notice the logical inconsistencies
of using classical measurement devices. Shut
up and calculate said Mermin. But is Peres’ quote from above an
acceptable defense of why the “something” which “must remain unanalyzed” be a classical device? Not at all.
What is needed is to obtain the emergence of the classical world from quantum mechanics. Then we can embrace Peres’ position (although there is a sizable amount of handwaving there).
The first step is to see why we don’t observe superposition. The answer is simple: decoherence. But decoherence is not enough. The unique experimental outcome needs an explanation too. Quantum Darwinism shows that what succeeds to be recognized as the measurement outcome is what succeeds to make copies of itself (and this in turn explains the preferred basis). This copying and amplification effect shows that the measurement device is in an unstable situation. The first outcome to be realized from a potentiality of choices wins the day and gives rise to “objective reality” where all observers can agree on the outcome due to the zillions of information copies of the one and only outcome. But how can one explain the very first copying event, the very first ionized atom, the very first collapse of the wavefunction? And do this while preserving unitarity. Here is where Peres hit the nail on the head: “quantum phenomena do not occur in a Hilbert space, they occur in a laboratory”. A Hilbert space is only a mathematical realization of some (operator) algebra (via GNS construction), and if in that algebra one can naturally create two elements out of one (this is called a co-product), Hilbert spaces can pop up or vanish with no mathematical or conceptual problems.
I don’t think there are any conceptual problems with a Fock space and with particle creation and annihilation, but the very same mechanism happens in ordinary quantum mechanics during interaction/measurement. The mathematical structure behind is called a Hopf algebra and the current challenge is to show that a Hopf algebra arises naturally in the operator algebra for ordinary quantum mechanics too and not only in field theory due to the existence of the Lorentz group. The math is highly nontrivial, but there are no interpretation issues. The math proof is work in progress, but it is advanced enough to be able to present a new interpretation of quantum mechanics in the next post. Since this interpretation stems from the program of deriving quantum mechanics form natural physical principles, this is it. After all, how many physics conferences do you know which are dedicated to the interpretation of special relativity?