Conclusions of Part II [chapter]

Gerard 't Hooft
2016 Fundamental Theories of Physics  
We had three reasons for working out many of our technical exercises in the second part of this book. First, we wanted to show what techniques can be used to support our assertions made earlier, which state that there are many ways to link quantum mechanical models with completely deterministic ones. Most of these deterministic models were chosen just to demonstrate some points; these were too simple to show delicate structures of direct physical interest. Some of our models are
more » ... universal", which means that they contain sufficient amounts of complexity to investigate their physical interest [37, 61]. Secondly, we wish to demonstrate that conventional quantum mechanics contains extensive mathematical tools that can be employed here as well. Fourier expansions, Taylor expansions, unitary transformations in Hilbert space, perturbation expansions, the Noether theorem, and other well-known procedures, are all extremely useful here. We wish to sketch the picture that quantum mechanics, as we know it, should be looked upon as a powerful mathematical tool to handle statistical features of our theories. If the dynamical equations are too complex to allow us to solve them, the quantum statistical approach may be the only option we have. No other systematic mathematical machinery would allow us to examine statistical features of any non-trivial cellular automaton when stretched over scales a billion times a billion times as large as the elementary scale of the individual cells. In quantized field theories, the tool that makes such jumps over scales is called the renormalization group. Thirdly, we do not want to belittle the difficulties that are still there. A completely systematic strategy for constructing models as complex as the Standard Model, has not yet been found; instead, we found several procedures that could be considered as useful ingredients for such a strategy, even if still quite incomplete. We emphasise that "no-go" theorems, such as Bell's theorem and the CHSH inequalities, do contain the loopholes that have been pointed out repeatedly. "Super determinism", abhorred by a majority of researchers, becomes less fearsome if one realizes that it comes with its own conservation law, the conservation of the ontic nature of a quantum state. To describe our universe, we have to limit ourselves to the ontic states.
doi:10.1007/978-3-319-41285-6_23 fatcat:jd2uilgl6jh2zdj7lgqzwtg2sa