Related papers: Quantum mechanics from invariance principles
The usual formulation of quantum theory is based on rather obscure axioms (employing complex Hilbert spaces, Hermitean operators, and the trace rule for calculating probabilities). In this paper it is shown that quantum theory can be…
Quantum mechanics is usually presented starting from a series of postulates about the mathematical framework. In this work we show that those same postulates can be derived by assuming that measurements are discrete interactions: that is,…
This paper can be seen as an exercise in how to adapt quantum mechanics from a strict relativistic perspective while being respectful and critical towards the experimental achievements of the contemporary theory. The result is a fully…
A suitable unified statistical formulation of quantum and classical mechanics in a *-algebraic setting leads us to conclude that information itself is noncommutative in quantum mechanics. Specifically we refer here to an observer's…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…
The concept of number is fundamental to the formulation of any physical theory. We give a heuristic motivation for the reformulation of Quantum Mechanics in terms of non-standard real numbers called Quantum Real Numbers. The standard axioms…
This paper deals with the foundations of quantum mechanics. We start by outlining the characterisation, due to Birkhoff and Von Neumann, of the logical structures of the theories of classical physics and quantum mechanics, as boolean and…
Relational quantum mechanics (RQM) proposes an ontology of relations between physical systems, where any system can serve as an `observer' and any physical interaction between systems counts as a `measurement'. Quantities take unique values…
In one-dimensional case, it is shown that the basic principles of quantum mechanics are properties of the set of intermediate cardinality.
Quantum theory's irreducible empirical core is a probability calculus. While it presupposes the events to which (and on the basis of which) it serves to assign probabilities, and therefore cannot account for their occurrence, it has to be…
Quantum mechanics led to spectacular technological developments, discovery of new constituents of matter and new materials. However there is still no consensus on its interpretation and limitations. Some scientists and scientific writers…
The idea that events obey a definite causal order is deeply rooted in our understanding of the world and at the basis of the very notion of time. But where does causal order come from, and is it a necessary property of nature? We address…
A general formulation of classical relativistic particle mechanics is presented, with an emphasis on the fact that superluminal velocities and nonlocal interactions are compatible with relativity. Then a manifestly relativistic-covariant…
The rules of quantum mechanics require a time coordinate for their formulation. However, a notion of time is in general possible only when a classical spacetime geometry exists. Such a geometry is itself produced by classical matter…
Decoherence may not solve all of the measurement problems of quantum mechanics. It is proposed that a solution to these problems may be to allow that superpositions describe physically real systems in the following sense. Each quantum…
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
Through a new interpretation of Special Theory of Relativity and with a model given for physical space, we can find a way to understand the basic principles of Quantum Mechanics consistently from Classical Theory. It is supposed that…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
In quantum gravity there is no notion of absolute time. Like all other quantities in the theory, the notion of time has to be introduced "relationally", by studying the behavior of some physical quantities in terms of others chosen as a…
Quantum mechanics marks a radical departure from the classical understanding of Nature, fostering an inherent randomness which forbids a deterministic description; yet the most fundamental departure arises from something different. As shown…