There are good reasons to believe that we are classical algorithms run on (effectively) classical machines. However, the fact that a physical state of a system in a universe described by a classical deterministic model doesn't contain any information about the model's evolution laws, gives rise to deep philosophical paradoxes with this picture of what we are. We explain these paradoxes in detail and show that they can be resolved once we take into account that in the real world, classical behavior arises as a result of decoherence. We then show that this solution naturally leads to a variant of the idea of a mathematical multiverse, originally proposed by Tegmark.
There are good reasons to believe that we are classical algorithms run on (effectively) classical machines. However, the fact that a physical state of a system in a universe described by a classical deterministic model doesn't contain any information about the model's evolution laws, gives rise to deep philosophical paradoxes with this picture of what we are. We explain these paradoxes in detail and show that they can be resolved once we take into account that in the real world, classical behavior arises as a result of decoherence. We then show that this solution naturally leads to a variant of the idea of a mathematical multiverse, originally proposed by Tegmark.
Abstract A collection of classical universes — even if they interact — is still classical. For instance, it doesn't have entanglement; its elements don't have phases to their amplitudes; it doesn't have continuous motion of discrete observables. The multiverse is not classical: it consists of much more than universes. Research into what is there in addition has already been fruitful and promises to be more so. Progress in understanding the quantum world more deeply through such research is also the key to resolving the long-running scandal of the slow take-up of Everett's theory by physicists and philosophers.
The mathematical representation of the universe consists of sequences of symbols, rules and operators containing Gödel's undecidable propositions: information and its manipulation, also with Turing Machines. Classical information theory and mathematics, ideally independent from the medium used, can be interpreted realistically and objectively from their correspondence with quantum information, which is physical. Each representation of the universe and its evolution are, in any case, physical subsets of the universe, structured sets of observers and their complements in the universe made with spacetime events generated by local quantum measurements. Their description becomes a semantically closed structure without a global object-environment loss of decoherence as a von Neumann's universal constructor with a semantical abstract whose structure cannot be decided deterministically a priori from an internal observer. In a semantically closed structure, the realization of a specific event that writes the semantical abstract of the constructor is a problem of finding "which way" for the evolution of the universe as a choice of the constructor's state in a metastructure, like the many-world Everett scenario, from a specific result of any quantum measurement, corresponding to a Gödel undecidable proposition for an internal observer.
The article demonstrates how the properties of the quantum world can be noncontradictory explained without using mathematical apparatus. They are generally considered incompatible with the logic of classical macroscopic physics. Indeed, wave-particle duality, magnetic pulses, negative energy, non-locality, entanglement, and other phenomena are not fit into the usual picture of the world. However, just one assumption provides the key to understanding most quantum paradoxes. If we assume that there is real and equal forward and backward in time movement in the microcosm, then we can find a simple explanation that is compatible with the principles of causality, conservation and symmetry.
The descriptions of the quantum realm and the macroscopic classical world differ significantly not only in their mathematical formulations but also in their foundational concepts and philosophical consequences. When and how physical systems stop to behave quantum mechanically and begin to behave classically is still heavily debated in the physics community and subject to theoretical and experimental research. This dissertation puts forward an approach to the quantum-to-classical transition fully within quantum theory and conceptually different from already existing models: It neither needs to refer to the uncontrollable environment of a system (decoherence) nor to change the quantum laws itself (collapse models), but puts the stress on the limits of observability of quantum phenomena due to the imprecision of our measurement apparatuses. For a certain class of time evolutions it is this mere restriction to coarse-grained measurements which is sufficient to see the natural emergence of macroscopic realism and even the classical Newtonian laws out of the full quantum formalism. But there also exist "non-classical" Hamiltonians for which a classical spatiotemporal description of the system's time evolution remains impossible even under fuzzy measurements or decoherence. It is argued that such Hamiltonians are unlikely to be spontaneously realized in nature because of their high complexity. The last part addresses the question of the origin of quantum randomness and proposes a link with mathematical undecidability.
In quantum theory it is possible to explain time, and dynamics, in terms of entanglement. This is the timeless approach to time, which assumes that the universe is in a stationary state, where two noninteracting subsystems, the ``clock'' and the ``rest,'' are entangled. As a consequence, by choosing a suitable observable of the clock, the relative state of the rest of the universe evolves unitarily with respect to the variable labeling the clock observable's eigenstates, which is then interpreted as time. This model for an ``evolution without evolution'' (Page and Wootters, 1983), albeit elegant, has never been developed further, because it was criticized for generating severe ambiguities in the dynamics of the rest of the universe. In this paper we show that there are no such ambiguities; we also update the model, making it amenable to possible new applications.
Machine learning has gained in popularity over recent years.It shows great power in many real-world problems, including Computer Vision, Natural Language Processing and Speech Recognition.However, a clear theoretical mechanism is still lacked behind many machine learning algorithms, such as Deep Learning.Good theoretical analysis can not only explain the current success of machine learning, but also reveal new approaches to future advancements.In last few years, more and more physicists contributed good works that provided novel insights and philosophy for machine learning communities.Due to two reasons, we believe physical approaches can be very promising.First, we think machine learning share some similar theoretical mechanism with physical theories, particularly quantum physics and statistical physics.We may employ physical languages to study machine learning models in some physical frameworks.Second, real-world problems and information itself must obey some fundamental laws, which are often physical laws for our universe.Good physical prior knowledge which may be helpful to reduce model complexity and improve generalization.The physical perspective deserve more attention.In this thesis, we review a few related works on the physics based approach and related traditional machine learning.It helps us understand how physics may interact with machine learning.We propose quantum interpretations for machine learning and a class of original physics-inspired machine learning algorithms, named Quantum-Inspired Forest.Both theoretical proof and empirical analysis are presented in details.The success of quantum-inspired machine learning encourages us to pay attention to multiple physical viewpoints.Even without solid theoretical analysis, important prior knowledge and heuristics may be obtained from physical models.The proposed algorithm is an example that illustrates how to combine physics and machine learning together.We in particular discuss a physical perspective on machine learning.We hope our physical analysis on machine learning would inspire more novel works in near future.