Po8

Interpretation: Many Worlds

- Why are we rolling dice?
- Middle ground: controlled unknowns
- Limited solutions
- What do we lose?
- One final note (pedants' corner)

In our work, we attempt to "roll the dice for quantum mechanics". You'd be right to think that this has some bearing on the Copenhagen Interpretation, and the Many Worlds (or 'multiverse') hypotheses that accompany any attempt to think about how outcomes are defined by quantum mechanics.

We do not accept that there are infinite possible futures. Our view simplifies the interpretation, suggesting that there is only one future. We enable this interpretation by providing a way for nature to roll its own dice. This mechanism for physicality is deterministic and computable, because it uses known and quantifiable variables (provided a knowable initial state), along with a simple condition for wave collapse.

In other words, given complete knowledge of all variables and states in the system, future states can be determined using no other information. This means that there is no reason to assume that reality contains alternative futures that require a choice.

Conventionally, these choices present difficulties, because a non-deterministic theory requires that these futures are realised randomly, and need to be assessed statistically, i.e. the question changes from "What happens?" to "What *could* happen, and what are the probabilities that each of these alternative future outcomes could happen?". This approach requires that we assess all probable futures, and integrate them into a picture of "the future".

Back to our approach, and we find that there is a middle ground, where we admit that some of the states of variables may be unknown. We may choose to do this just to humour the theorists in a thought experiment, or we might have a practical situation where only a few parameters are truly known, are only known to a given confidence, or we want to map the outcomes of many initial conditions. There are many different approaches one could take.

The simplest case is where we choose to ignore (declare unknown) one of the states within the system. How do we interpret the many possible futures that this case presents? Quite simply, we look for solutions just as we would with the 'omniscient' case where everything is known, except we have more than one possible solution. Notice that I didn't say that there were infinite solutions, which would be the Many Worlds interpretation. Instead, for a fully-known propagating wave, there are only a few possible solutions for its collapse, and this might be manageable as a semi-deterministic set of solutions that may be integrated. The essential point is that where one piece of information is unknown, it's possible to piece it back together to find the missing solution, or at least get a probability spread of what the solutions might be, given appropriate statistics for the missing terms.

More simply, you could imagine a propagating wave as a sphere in Euclidean 3D space, expanding at constant rate with time. For this sphere to collapse, it has to meet with another sphere and fulfil a 'phase-matching' requirement at a unique point. So if we don't know *everything* about the system, then in the Many Worlds approach, we have to assume that there's a future on every possible point on the surface of that sphere as it evolves in space and time. Conversely, for our approach, the possible solutions are limited to just a few points on the sphere as it expands: perhaps there are only a handful of points to explore, depending on the initial conditions.

Is it any simpler having only a few options, rather than an infinity of options? One handy feature of an uninterrupted infinity of options, is that you can assume some symmetries, and get nearly all of them to cancel out, or make them uninteresting, leaving only an interesting solution. This doesn't happen so much with the deterministic approach, and complicated systems can quickly get out of hand. However, in the domain of fundamental physics, where we're wanting to explore what happens at the smallest scales, we think a deterministic approach is more useful: more so if an analytical approach is used to explore systems with only a limited quantity of unknowns.

In the above article, we've described spheres that expand in space. That's a small lie, to make it easier for our readers to picture the process. In our mechanism, we specify only that waves have a *phase interval* from their origin, and we do not require a specific background for it to work in. If applied to space and time, this would indeed look like an expanding bubble, but we don't insist on this structure: it's background-free, and creates its own background and causality.

On the subject of the formalism of the Copenhagen Interpretation, and the uncertainty principle ... we have it covered, and hope to write a future article on that. For now, the hint is that our physicality defines reality a little differently, which provides context for what is measurable, and the degree of confidence for which uncertainty-paired parameters may be known.

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