Related papers: Origin of Complex Quantum Amplitudes and Feynman's…
Quantification starts with sum and product rules that express combination and partition. These rules rest on elementary symmetries that have wide applicability, which explains why arithmetical adding up and splitting into proportions are…
Feynman's formulation of quantum theory is remarkable in its combination of formal simplicity and computational power. However, as a formulation of the abstract structure of quantum theory, it is incomplete as it does not account for most…
The density operator of a quantum state can be represented as a complex joint probability of any two observables whose eigenstates have non-zero mutual overlap. Transformations to a new basis set are then expressed in terms of complex…
Real numbers provide a sufficient description of classical physics and all measurable phenomena; however, complex numbers are occasionally utilized as a convenient mathematical tool to aid our calculations. On the other hand, the formalism…
While complex numbers are essential in mathematics, they are not needed to describe physical experiments, expressed in terms of probabilities, hence real numbers. Physics however aims to explain, rather than describe, experiments through…
The quantum formalism is a ``measurement'' formalism--a phenomenological formalism describing certain macroscopic regularities. We argue that it can be regarded, and best be understood, as arising from Bohmian mechanics, which is what…
Complex numbers play a crucial role in quantum mechanics. However, their necessity remains debated: whether they are fundamental or merely convenient. Recently, it was claimed that quantum mechanics based on real numbers can be…
The new interpretation of Quantum Mechanics is based on a complex probability theory. An interpretation postulate specifies events which can be observed and it follows that the complex probability of such event is, in fact, a real positive…
We present a heuristic derivation of Born's rule and unitary transforms in Quantum Mechanics, from a simple set of axioms built upon a physical phenomenology of quantization. This approach naturally leads to the usual quantum formalism,…
We show that the quantum-mechanical probability distribution involving complex probability amplitudes can be derived from three natural conditions imposed on a relativistically invariant probability function describing the motion of a…
It is argued that there is no evidence for causality as a metaphysical relation in quantum phenomena. The assumption that there are no causal laws, but only probabilities for physical processes constrained by symmetries, leads naturally to…
Quantum theory is formulated as the only consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if there are two different ways to compute an amplitude the two answers must agree. This…
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…
Why does quantum theory need the complex numbers? With a view toward answering this question, this paper argues that the usual Hilbert-space formalism is a special case of the general method of Markovian embeddings. This paper then…
Quantum forces are long-range interactions originating from vacuum fluctuations of mediator fields. Such forces inevitably arise between ordinary matter particles whenever they couple to light mediator species. Conventional computations of…
Everettian Quantum Mechanics, or the Many Worlds Interpretation, lacks an explanation for quantum probabilities. We show that the values given by the Born rule equal projection factors, describing the contraction of Lebesgue measures in…
Realistic quantum mechanics based on complex probability theory is shown to have a frequency interpretation, to coexist with Bell's theorem, to be linear, to include wavefunctions which are expansions in eigenfunctions of Hermitian…
The quantum probabilistic convergence in measurement, distinct from mathematical convergence, is derived for indeterminate probabilities from the weak quantum law of large numbers. This is presented in three theorems. The first establishes…
This note is sketching a simple and natural mathematical construction for explaining the probabilistic nature of quantum mechanics. It employs nonstandard analysis and is based on Feynman's interpretation of the Heisenberg uncertainty…
The mathematical formalism of Quantum Mechanics is derived or "reconstructed" from more basic considerations of probability theory and information geometry. The starting point is the recognition that probabilities are central to QM: the…