Does the wave function/density state actually exist? I have been reading with interest the debates here on whether the wave function/density state actually collapses or not, or whether it is subjective Bayesian or objective with actual complex numbered values for each component. I have been struck, though, by the implicit assumption made by all camps that something like the wave function/density state actually exists, whether subjective or objective. What if it does not? That would render all of these debates moot.
The wf/ds is a highly abstract theoretical inference of what is measured experimentally. All one measures are correlations between definite measured outcomes. Pragmatically, it has been found such correlations can pretty much only be calculated accurately within the Dirac/von Neumann two stage framework where one first postulates some abstract wf/ds evolving unitarily alternating with a collapse during measurement to the eigenspaces of some 'measured observable' according to the Born rule, whatever that really means. This makes no ontological assumptions per se; it is just what anyone needs to go through to calculate the measured correlations.
Many worlds people argue wf/ds is objective with no collapse and all the branches co-exist. Copenhagenists argue for collapse. But what if the wf/ds doesn't exist? Then they are both wrong and missing the point. Other than the fact the only time wf/ds shows up is in abstract symbolic calculations, why its existence be assumed?
Here, the situation differs from classical probability distributions. The probabilities are still linear for the density state, but not the wave function, but negative probabilities appear and that makes all the difference. In classical Bayesian updating, there is some leeway in when the updating happens because the different updates evolve independently and the original distribution always evolves as a nonnegative weighted sum of the individual independent contributions. In the quantum density state case, destructive interference due to oscillations between positive and negative 'probabilities' exist and the different outcomes can no longer be said to be in any way independent. Decoherence does not really explain it away because the suppression of interference is not exact, takes time, and is potentially reversible in principle. What if the density state does not exist? 
 A: You ask "Does the wave function/density state actually exist?" but this is a question that can't be answered. Quantum Mechanics is a mathematical model that gives an excellent description of the real world. QM is based upon the assumption that the wf/ds is a real object, but whether QM is a "real" description of the world is a question we need to leave to the philosophers.
In a comment to another question, Is there a mechanism for time symmetry breaking?, someone mentioned this paper. Although I'm not sure it revolutionises our understanding of the wavefunction it makes an interesting read in the context of this question.
A: There is a hidden assumption made here by most people including Pusey et al. The assumption is strict causality in time. Give me any particular instant in time, and realism combined with this assumption states that there is some complete set of information we can specify about the state at that time such that the probabilities for future outcomes can be determined to the best possible in principle based solely and uniquely upon the complete set of information at the given instant. This overlooks retrocausal interpretations where the actual observed outcome depends upon a transaction of alternations between forward causal influences and retrocausal influences. In such interpretations, the wavefunction need not exist. 
A: The answer all boils down to which interpretation you adopt. Obviously, the many worlds interpretation deals with an existing wave function. The consistent histories interpretation also requires an existing real wave function because one of its requirements is consistent families and what the permissible consistent families are is very sensitive to the actual values of the components of the physical density state. The opinion of the Copenhagen interpretation is the wave function is only a computational tool for getting the probabilities of measured outcomes. 
A: Theoretical Physics does not actually use the concept of 'existence'.  That word does not appear in the usual axioms of QM and does not appear (much) in normal Physics textbooks either (I just checked Sommerfeld's Mechanics: as is typical, it only uses the word for mathematical existence, in an informal way: there exists a solution to the equation, etc.).  How on earth would one define it, anyway?  (Mathematical Logic doesn't use our normal intuitive concept of existence, either, as one can see by the fact that what might seem to be something like that,
the existential quantifier, is in fact avoidable by using the universal quantifier and negation instead.)  
Physics is, on the other hand, full of such statements as 'If the system is in the quantum state psi_o at time t=0, then....'  
I think this certainly supports Mr. Rennie's point.  I myself have noticed the same thing about the word 'event', I don't recall seeing it even once in any Mechanics textbook I have looked at...
Then the real difference between Bayesians and more 'classic' Quantum theorists such as Dirac and Wigner is that the latter simply say 'The set of quantum states of a system are the set of rays in a Hilbert Space' and go on to say many statements such as 'If the system is in the quantum state $v$ at time $t=0$ then ...'  But Bayesians are forced to say 'The quantum state of a system encodes all our knowledge about the system' and they cannot avoid introducing subjective concepts like 'my' or 'knowledge'.  
This is not a difference as to the probabilistic or statistical interpretation of the wave function, both a 'classic' QM-er and a Bayesian can both say that the interpretation of the wave function is that the modulus squared of its values are the probabilities that ....etc.
And a Bayesian could say the wave function or quantum state is 'real', depending on their philosphic notions of reality and existence, which like Mr. Rennie said, are a separate issue from Physics.  That is why I stated the real difference is between formally introducing subjective concepts like 'knowledge' or 'observer' or not introducing them.  Dirac carefully avoids using either word: he says 'result of a measurement process' just as if no one was 
watching or cared.  
A symptom of the difference between a Bayesian and a classic QMer is that the former expand the old idea of quantum state to include density matrices.  The classic axioms make a sharp distinction: quantum state is a primitive concept and its connection with the probabilities of the results of measurement processes are given by axioms.  Then the mixed states and density matrices are define in terms of these, and the rules for calculating probabilities of results of measurements applied to mixed states are derived as theorems.  For a logically careful classic QMer, all quantum states are pure and all systems are closed.  
If you ask me, it is Bayesians who are trying to make the concept of quantum state palatable to our everyday intuition by dragging in subjectivism and knowledge issues.  Dirac simply said one could only develop an intuition about quantum concepts by using them...  To me, it seems that it is Bayesians who are trying to interpret a quantum concept and include that interpretation in the axiom or formal system, whereas Dirac wanted it to stay uninterpreted.
A: I think you're misinterpreting the debates a bit. The wave function isn't real. It's a bookkeeping device. QM has these things called observables. Nothing else is posited to be real. The wave function is not an observable. If you go look at the development of QM in Schwinger's book, you see that the wave function shows up purely as a mathematical intermediate to make a lot of calculations straightforward.
Copenhagen posits that there is an act, "measurement", which forces a particle into a pure state. Many worlds folks say that there is an act, "measurement", which splits the universe into multiple paths. Neither of them claim any reality for the wave function. There are interpretations, such as the Bohm-de Broglie pilot wave, which imply reality for the wave function. They're worth knowing about because they have been a useful intuitive tool for folks like John Bell.
The two things that are really worth reading about foundations of quantum mechanics at this point are van Kampen's 'Ten Theorems on Quantum Mechanical Measurements' (let me know if you can't find a copy), and Griffiths's book 'Consistent Quantum Theory' (available online).
A: Let’s take a step backwards and ask whether numbers are real objects. Well, if we consider the number 7, we can ask what it’s energy is, where it is, how many 7’s are there in the universe. For a real object, such as an electron, these are sensible questions which can be answered, but when asked of the number seven, they are absurd and cannot be answered. I reckon that all numbers are non real, defined terms. That 5 + 2 = 7 is a purely analytic statement, made true by the definitions of its terms. It is not an objective statement about the world, even though it still rates  as being a discovery.
    Wavefunctions consist only of numbers without units, and so they can’t be real physical quantities.
A: There is only one universe with only one quantum state. Density states are statistical descriptions and do not and cannot possibly apply to only one universe. Only with an ensemble of many many copies of the same quantum state can we associate a density state according to the limiting ratios of frequencies of the measured values of observables. No ensemble, no density state and no wavefunction either.
A: Let me quote Zurek here. There is no information without representation. If the wave function or density state exists as some form of actual information, it has to be represented by matter in some physical way. It has to, in the colorful terminology of a very interesting character, be made of potatoes. Clearly, there is no such material representation within our universe, but it could be turtles all the way down and materially represented on some higher hypostatis. 
A: I want you to think computationally. Obviously, nature can and does compute quantum mechanics.  It remains to be asked how nature does it. The Copenhagenists will smugly tell you it does not matter how nature does it or what happens in between. Inputs go in, and then a miracle happens and we are supposed to stay hush hush about it and not peek inside, and outputs come out. Aren't you the least bit curious what happens in between? Do you want to listen to the Copenhagenists telling you nothing happens in between? Then, by implication, nature computes by magic and somehow get it right.
If the Church-Turing thesis is right, nature needs to compute with some scratch space and "registers" and "RAM"s. Otherwise, nature is some hypercomputational machine. The contents of the scratch space which happen in between are what Bell termed "beables". What are the minimal information needed for a beable? Some would say the wave function. Others the density state. Others the path integral. If it is not possible to do with any less, the beable has to be real, or do you still insist upon objecting and fighting? The beable has to be real.
