As far as I can tell (being a non-physicist), the Transactional Interpretation shares the mathematical simplicity of MWI. And here Kastner and Cramer argue that TI can derive the Born probabilities naturally, whereas MWI is said to need a detour through "the application of social philosophy and decision theory to subjectively defined ‘rational’ observers". So maybe TI is simpler.
The "possibilities" they posit seem quite parallel (pardon the pun) to the multiple worlds or bifurcated observers of MWI, so I don't see the philosophical ad...
I think the short version is that you don't need math that covers the wavefunction collapse, because you don't need the wave function to collapse.
For a longer version, you'd need someone who knows more QM than I do.
In non-relativistic MWI, the evolution of the quantum state is fully described by the Schrodinger equation. In most other interpretations, you need the Schrodinger equation plus some extra element. In Bohmian mechanics the extra element is the guidance equation, in GRW the extra element is a stochastic Gaussian "hit".
In Copenhagen, the extra element is ostensibly the discontinuous wavefunction collapse process upon measurement, but to describe this as complicating the math (rather than the conceptual structure of the theory) is a bit misleading. Whether you're working with Copenhagen or with MWI, you're going to end up using pretty much the same math for making predictions. Although, technically MWI only relies on the Schrodinger equation, if you want to make useful predictions about your branch of the wave function, you're going to have to treat the wave function as if it has collapsed (from a mathematical point of view). So the math isn't simpler than Copenhagen in any practical sense, but it is true that from a purely theoretical point of view, MWI posits a simpler mathematical structure than Copenhagen.
The thing that's always bugged me about the MWI is that it doesn't seem physically sensible. If something isn't physically sensible, than you need to check on your model. This happens all the time in physics - there are so many basic problems where you discard solutions or throw out different terms because they don't make sense. This is the path to successful understanding, rather than stubbornly sticking to your model and insisting that it must be correct.
The impression I get is that, if the math leads you to make a conclusion which seems like physical n...
As you say, matrix mechanics (or the Heisenberg formulation) is equivalent to the Schrodinger formulation, so it has exactly the same range of interpretations as the Schrodinger formulation.
If you want a concrete example of an experiment that would distinguish between MWI and Copenhagen, here it is:
Prepare an electron so that its z-spin state is the superposition |up> + |down> (I'm dropping the coefficients for ease of typing). Have a research assistant enter an appropriately isolated chamber with the electron and measure its z spin. If Copenhagen is correct, this will lead to the collapse of the superposition, and the electron's state will now be either |up> or |down>. If MWI is correct, the electron's state will become entangled with your research assistant's state, and the entire contents of the chamber will now be in one big superposition from your perspective.
Now have your research assistant record the state she measures by preparing another electron in that quantum state. So if she measures |up> she prepares the other electron in the state |up>. Again, if Copenhagen is correct, this new electron's state is either |up> or |down>, whereas if MWI is correct, its state is in an entangled superposition with the original electron and the research assistant. Call this entangled state predicted by MWI psi.
Now you (from outside the chamber) directly measure the difference between the x-spin (not the z-spin) of electron 2 (the one prepared by your assistant) and the x-spin of electron 1. I can't tell you off the top of my head how to operationalize this measurement, but the fact remains that it is a bona fide observable. If you do the math, it turns out that the entangled state psi is an eigenstate of this observable, with eigenvalue zero. So if MWI is right, whenever I make this measurement I should get the result zero. On the other hand, neither of the states predicted by Copenhagen are eigenstates of this observable, so if Copenhagen is right, if I keep repeating the experiment I will get a distribution of different results.
tl;dr: Basically, all I've done here is take advantage of the fact that there are observables that can distinguish between mixtures and superpositions by detecting interference effects.
Of course, in order for this experiment to be feasible, you need to make sure that the system consisting of the two electrons and the assistant doesn't decohere until you make your measurement. With current technology, we're not even close to making this happen, but that is a problem with the feasibility of the experiment, not its bare possibility.
You seem to conflate Copenhagen interpretation with objective collapse interpretations. Copenhagen doesn't make any committment to the existence and nature of both the wavefunction and the collapse process: it says they are just mathematical descriptions useful to predict empirical observations. While Copenhagen interpretation has itself multiple interpretations, it is typically understood as the instrumentalist "shut up and calculate!"
The thought experiment you describe appears to be flawed. According to the principle of deferred measurement,
http://www.scottaaronson.com/blog/?p=1103
Eliezer's gung-ho attitude about the realism of the Many Worlds Interpretation always rubbed me the wrong way, especially in the podcast between both him and Scott (around 8:43 in http://bloggingheads.tv/videos/2220). I've seen a similar sentiment expressed before about the MWI sequences. And I say that still believing it to be the most seemingly correct of the available interpretations.
I feel Scott's post does an excellent job grounding it as a possibly correct, and in-principle falsifiable interpretation.