Related papers: From Heisenberg to Goedel via Chaitin
The Generalized Uncertainty Principle arises from the Heisenberg Uncertainty Principle when gravity is taken into account, so the leading order correction to the standard formula is expected to be proportional to the gravitational constant…
The position-momentum uncertainty-like inequality based on moments of arbitrary order for d-dimensional quantum systems, which is a generalization of the celebrated Heisenberg formulation of the uncertainty principle, is improved here by…
Quantum theory demands that, in contrast to classical physics, not all properties can be simultaneously well defined. The Heisenberg Uncertainty Principle is a manifestation of this fact. Another important corollary arises that there can be…
General relativity treats spacetime as dynamical and exhibits its breakdown at singularities. This failure is interpreted as evidence that quantum gravity is not a theory formulated within spacetime; instead, it must explain the very…
The notion of the quantum angle is introduced. The quantum angle turns out to be a metric on the set of physical states of a quantum system. Its kinematics and dynamics is studied. The certainty principle for quantum systems is formulated…
Heisenberg's uncertainty principle implies fundamental constraints on what properties of a quantum system can we simultaneously learn. However, it typically assumes that we probe these properties via measurements at a single point in time.…
We first partly develop a mathematical notion of stable consistency intended to reflect the actual consistency property of human beings. Then we give a generalization of the first and second G\"odel incompleteness theorem to stably…
The uncertainty principle lies at the heart of quantum physics, and is widely thought of as a fundamental limit on the measurement precisions of incompatible observables. Here we show that the traditional uncertainty relation in fact…
While the slogan "no measurement without disturbance" has established itself under the name Heisenberg effect in the consciousness of the scientifically interested public, a precise statement of this fundamental feature of the quantum world…
In 1931, G\"odel presented in K\"onigsberg his famous Incompleteness Theorem, stating that some true mathematical statements are unprovable. Yet, this result gives us no idea about those independent (that is, true and unprovable)…
We establish a rigorous quantitative connection between (i) the interferometric duality relation for which-way information and fringe visibility and (ii) Heisenberg's uncertainty relation for position and modular momentum. We apply our…
This is an article written in a popular science style, in which I will explain: (1) the famous Heisenberg uncertainty principle, expressing the experimental incompatibility of certain properties of micro-physical entities; (2) the Compton…
We show how G\"odel's first incompleteness theorem has an analog in quantum theory. G\"odel's theorem implies endless opportunities for appending axioms to arithmetic, implicitly showing a role for an agent, namely an agent that asserts an…
(A) The momentum density conjugate to a bosonic quantum field splits naturally into the sum of a classical component and a nonclassical component. It is shown that the field and the nonclassical component of the momentum density satisfy…
Heisenberg's uncertainty principle, exemplified by the gamma ray thought experiment, suggests that any finite precision measurement disturbs any observables noncommuting with the measured observable. Here, it is shown that this statement…
This paper deduces universal uncertainty principle in different quantum theories after about one century of proposing uncertainty principle by Heisenberg, i.e., new universal uncertainty principle of any orders of physical quantities in…
The Heisenberg inequality \Delta X \Delta P \geq \hbar/2 can be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty, which is valid for all wavefunctions. The statistics of complementary…
Heisenberg's uncertainty principle is formulated for a set of generalized measurements within the framework of majorization theory, resulting in a partial uncertainty order on probability vectors that is stronger than those based on…
In this essay it will be shown that the introduction of a modification to Heisenberg algebra (here this feature means the existence of a minimal obserlvable length), as a fundamental part of the quantization process of the electrodynamical…
Heisenberg's reciprocal relation between position measurement error and momentum disturbance is rigorously proven under the assumption that those error and disturbance are independent of the state of the measured object. A generalization of…