Fundamental Limits of Quantum Mechanics and Physical Laws in a Non-deterministic World

Quantum mechanics is fundamentally different from all that came before in almost every aspect. But, as far as I can see now, there is one property that stands above all when we try to understand what quantum mechanics is all about: quantum mechanics is our first theory of Nature that is non-deterministic at a fundamental level. Long considered an unpleasant aspect, non-determinism is anything but: Non-determinism enables new freedoms. Phenomena that could not occur in deterministic theories because they would violate some basic laws of nature become possible in non-deterministic theories, under the cover of randomness. A famous example is nonlocality. In a deterministic world, if something acting in one place would instantaneously produce effects somewhere else, it would violate relativity; non-determinism allows it. As in recent years nonlocality/entanglement came to be viewed as one of the main aspects of nature, and as its existence implies non- determinism but not vice-versa, non-determinism itself was seen as secondary. But non-determinism allows many more freedoms. The vision of this project is to change the paradigm, and put non-determinism at the core. The aim is to go well beyond the insights gained from nonlocality and focus on the other freedoms. It will explore very recently discovered situations with indefinite causal order; situations in which the future can affect the past without leading to paradoxes; evolutions subjected to both initial and final conditions; implications for conservations laws, and thermodynamics, the hitherto ignored dynamic nonlocality, etc. all fundamental aspects of nature in which non-determinism is the key. Finally, quantum mechanics may not be the ultimate theory of nature. The project aims to explore the full extent of the freedoms allowed by non-determinism in quantum mechanics as well as in arbitrary theories. By comparing what is possible in general to what is specifically quantum, I hope to better understand both.