相关论文: On a Final Theory of Mathematics and Physics

One of the outstanding problems of philosophy of science and mathematics today is whether there is just "one" unique mathematics or the same can be bifurcated into "pure" and "applied" categories. A novel solution for this problem is…

`How do our ideas about quantum mechanics affect our understanding of spacetime?' This familiar question leads to quantum gravity. The complementary question is also important: `How do our ideas about spacetime affect our understanding of…

The search for a theory of quantum gravity faces two great challenges: the incredibly small scales of the Planck length and time, and the possibility that the observed constants of nature are in part the result of random processes. A…

The central arguments for a generalised form of proper time as the basis for a unified theory, accounting for the Standard Model of particle physics and encompassing all four forces of nature including a consistent `quantum gravity', are…

Time, space, and matter are categories of our reasoning, whose properties appear to be fundamental. However, these require a scrutiny as in the extreme regime of the primordial universe these present quantum properties. What does it mean…

We discuss historical attempts to formulate a physical hypothesis from which Turing's thesis may be derived, and also discuss some related attempts to establish the computability of mathematical models in physics. We show that these…

Many novel quantum phenomena emerge in non-equilibrium relativistic quantum matter under extreme conditions such as strong magnetic fields and rotations. The quantum kinetic theory based on Wigner functions in quantum field theory provides…

The mathematical representation of the physical objects determines which mathematical branch will be applied during the physical analysis in the systems studied. The difference among non-quantum physics, like classic or relativistic…

Quantum theory describes our universe incredibly successfully. To our classically-inclined brains, however, it is a bizarre description that requires a re-imagining of what fundamental reality, or "ontology", could look like. This thesis…

Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…

Alongside the development of quantum algorithms and quantum complexity theory in recent years, quantum techniques have also proved instrumental in obtaining results in classical (non-quantum) areas. In this paper we survey these results and…

I shall discuss some "conditions of possibility" of a quantum theory of gravity, stressing the need for solutions to some of fundamental problems confronting any attempt to apply some method of quantization to the field equations of general…

We give a review of concepts related to connection of classical and quantum theories, from the phase space perspective. Quantum theory is described by non-commutative operators of coordinates and momenta, results in values having a certain…

We propose a geometric setting of the axiomatic mathematical formalism of quantum theory. Guided by the idea that understanding the mathematical structures of these axioms is of similar importance as was historically the process of…

There is a certainty that the modern (Copenhagen's) interpretation of quantum mechanics is correct. However, the some physicist had the opinion that the modern quantum mechanics is a phenomenological theory. The suggested theory is the new…

We pursue research leading towards the nature of causality in the universe. We establish the equation of the universe's evolution from the universe-state function and its series expansion, in which causes and effects connect together to…

Recent results suggest that quantum mechanical phenomena may be interpreted as a failure of standard probability theory and may be described by a Bayesian complex probability theory.

An age-old controversy in mathematics concerns the necessity and the possibility of constructive proofs. The controversy has been rekindled by recent advances which demonstrate the feasibility of a fully constructive mathematics. This…

The expansion of our universe, when followed backward in time, implies that it emerged from a phase of huge density, the big bang. These stages are so extreme that classical general relativity combined with matter theories is not able to…

Mathematical core of quantum mechanics is the theory of unitary representations of symmetries of physical systems. We argue that quantum behavior is a natural result of extraction of "observable" information about systems containing…