PWT has an underlying dynamics, much like classical mechanics, that to compute the predictions exactly, one has to have perfect knowledge of the current state. Given that knowledge and a perfect computational environment, one could then determine the future for all time, at least ignoring creation and annihilation of particles.

Clearly this is useless if that is all it provided. But so was classical mechanics. For example, to compute the gravitational force on my finger, technically, one needs in Newtonian theory to know the position and masses of all particles in the whole universe. Equally clearly, that's neither practical nor relevant.

Instead, we use the well-defined dynamics to do a statistical analysis of the theory. What happens when we do that is that we get a quantum thermodynamics equivalent which is what the Copenhagen interpretation is. But Copenhagen suffers from being vague and undefined (what the heck is a macroscopic measurement?) It is very imprecise and not a theory at all. And yet, when it appears as a statistical framework from an underlying well-define theory, the measurement problem completely recedes.

And it is important to understand that it is the theory that ought to tell us what a measurement actually means.

The next point to raise is, what is the point if we just derive Copenhagen? Well, the point is that it allows to both understand the setup and thus extend it. If all questions were known and answered, it would be largely philosophical. But we have not resolved the problems (QM + relativity) in standard quantum theory after many decades of research.

What are a few things that PWT explain?

1) Identical particles. By having configurations of particles, one can investigate what a configuration is. And, after a moment's thought, identical particles are not labelled by nature. Choosing a configuration space of unlabelled particles, we end up with the identical particle choices of symmetric or antisymmetric wave functions. It gets more complicated with spin, but it turns out spin is best represented as a value of the wave function located at a spatial point, not an intrinsic part of the particle. And then the problems just disappear from that.

2) Arrival times. There is a time of arrival naturally enough in a theory with particles actually moving about. In most theories, the collapse or splitting of the universe, etc., does not really fit in with experiments of time arrival. That doesn't stop physicists from coming up with answers, of course, but a theoretical framework is conceptually trivial based on this.

3) Collapse of the wave function. This collapse is central to the whole business. There is no collapse in the fundamental theory. But in suitable situations (measurements), the environment can be conditioned on to get a local wave function for the system in question. When a measurement happens with the environment registering it, the environmental conditioning changes that local wave function and that appears as a collapse.

This also helps deal with the murkiness of a position measurement which is never some precise state to collapse into. It is all a bit wishy-washy which is a problem for a theory such as Copenhagen in which that is all there is. It is trivial shrug in PWT.

4) Creation and annihilation of particles. There are particles that exist and they can be born or destroyed. There are formulas that give a probabilistic form for the creation of particles. This makes the theory no longer deterministic, but that was never the point of PWT. The point was to be an actual theory, one which was well-defined. There is nothing wrong with randomness. So the creation and annihilation of particles is perfectly consistent with PWT. It requires wave functions defined on a disjoint union of configuration spaces of different number of particles. This is exactly what quantum field theory does.

5) Well-defined quantum field theory. It is legendary that QFT is not well-defined mathematically. Recent work, inspired by PWT, looks promising in finding a well-defined path in QFT. Essentially, the perturbation from a free evolution cannot work. Instead, one has to work with functions in which the different number of particles spaces are linked in such a way as to preserve the probability. Once that is done, divergences fade away. The mathematical work is still quite difficult and it is early days, but it has had successes in toy theories that were not workable before.

6) Relativity. This is the big one. By having a clear theory to work with, one can understand the nonlocality that is present in reality (Bell's theorem) [unless you deny the results of experiments when they happen as in MWI]. There are explorations of natural foliations of space-time which provides the kind of nonlocality needed. In terms of something that works mathematically, that exists. A theory that is philosophically satisfactory is still being pursued. Essentially, the foliation is needed but is not detectable which is kind of what is needed, but it is unsatisfactory.

PWT is not a return to determinism. It is a return to clearly defined theories, whether they are deterministic or not. PWT is a theory that one could envision a computer being fed data and then computing out without further intervention. Copenhagen is not like that. One needs to know what experiments and measurements are to be done which, of course, can't really be specified in advance since what experiments are done may rely on what happened in the past.