The Theory of the Quantum World

Kim Joris Boström

A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions about objects in a multiplicity of worlds. In this logical framework, the continuum of worlds is treated in analogy to the continuum of time points; both “time” and “world” are considered as mutually independent modes of existence. The theory combines elements of Bohmian mechanics and of Everett’s many-worlds interpretation; it has a clear ontology and a set of precisely defined postulates from where the predictions of standard quantum mechanics can be derived. Probability as given by the Born rule emerges as a consequence of insufficient knowledge of observers about which world it is that they live in. The theory describes a continuum of worlds rather than a single world or a discrete set of worlds, so it is similar in spirit to many-worlds interpretations based on Everett’s approach, without being actually reducible to these. In particular, there is no splitting of worlds, which is a typical feature of Everett-type theories. Altogether, the theory explains (1) the subjective occurrence of probabilities, (2) their quantitative value as given by the Born rule, and (3) the apparently random “collapse of the wavefunction” caused by the measurement, while still being an objectively deterministic theory.

Berthold‐Georg Englert

Abner Shimony

Anthony Short

We consider how to define a natural probability distribution over worlds within a simple class of deterministic many-worlds theories. This can help us understand the typical properties of worlds within such states, and hence explain the empirical success of quantum theory within a many-worlds framework. We give three reasonable axioms which lead to the Born rule in the case of quantum theory, and also yield natural results in other cases, including a many-worlds variant of classical stochastic dynamics.

Takashi Sakai

A body of theory is completely different between relativity theory and quantum mechanics. Most targeting physical phenomena are different between them as well. Despite that both theories describe our time-space world, no one has succeeded in arriving at one of these theories by using the other one, deductively. Fusion of these two theories produced quantum field theory. However this theory impresses us as a theory that was made by merging the two theories by force. So this theory cannot indicate the reason why both relativity theory and quantum mechanics exist in this world at the same time. Here I show you that quantum mechanics can be led by the equation of Minkowski's metrics, which stands up in the relativistic world of space and time. This is the first report proving mathematically that quantum mechanics can be born reductively in our relativistic world.

Ted Bastin