Related papers: From Heisenberg to Goedel via Chaitin
In this paper we critically analyse W. Heisenberg's arguments against the ontology of point particles following trajectories in quantum theory, presented in his famous 1927 paper and in his Chicago lectures (1929). Along the way, we will…
Coherent states are required to form a complete set of vectors in the Hilbert space by providing the resolution of identity. We study the completeness of coherent states for two different models in a noncommutative space associated with the…
Despite provable unknowables in recursion theory, indeterminism and randomness in physics is confined to conventions, subjective beliefs and preliminary evidence. The history of the issue is very briefly reviewed, and answers to five…
The form and justification of inductive inference rules depend strongly on the representation of uncertainty. This paper examines one generic representation, namely, incomplete information. The notion can be formalized by presuming that the…
The field of algorithmic randomness studies what it means for infinite binary sequences to be random for some given uncertainty model. Classically, martingale-theoretic notions of such randomness involve precise uncertainty models, and it…
It is shown that the Einstein-Podolsky-Rosen conclusion concerning the `incompleteness' of Quantum Mechanics does not follow from the results of their proposed gedanken experiment, but is rather stated as a premise. If it were possible to…
Two central concepts of quantum mechanics are Heisenberg's uncertainty principle, and a subtle form of non-locality that Einstein famously called ``spooky action at a distance''. These two fundamental features have thus far been distinct…
The intrinsic multivaluedness of interaction process, revealed in Part I of this series of papers, is interpreted as the origin of the true dynamical (in particular, quantum) chaos. The latter is causally deduced as unceasing series of…
The quantum multiparameter estimation is very different from the classical multiparameter estimation due to Heisenberg's uncertainty principle in quantum mechanics. When the optimal measurements for different parameters are incompatible,…
It is shown that all the known uncertainty relations are the secondary consequences of Robertson's relation. The basic idea is to use the Heisenberg picture so that the time development of quantum mechanical operators incorporate the…
The fundamental principles of complementarity and uncertainty are shown to be related to the possibility of joint unsharp measurements of pairs of noncommuting quantum observables. A new joint measurement scheme for complementary…
The notion of nonlocality implicitly implies there might be some kind of spooky action at a distance in nature, however, the validity of quantum mechanics has been well tested up to now. In this work it is argued that the notion of…
The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal values are not the outcomes of simultaneous…
Motivated by the Generalized Uncertainty Principle, covariance, and a minimum measurable time, we propose a deformation of the Heisenberg algebra and show that this leads to corrections to all quantum mechanical systems. We also demonstrate…
Uncertainty relation for photons that overcomes the difficulties caused by the nonexistence of the photon position operator is derived in quantum electrodynamics. The photon energy density plays the role of the probability density in…
We study the consequences of the generalized Heisenberg uncertainty relation which admits a minimal uncertainty in length such as the case in a theory of quantum gravity. In particular, the theory of quantum harmonic oscillators arising…
Heisenberg's uncertainty principle forms a fundamental element of quantum mechanics. Uncertainty relations in terms of entropies were initially proposed to deal with conceptual shortcomings in the original formulation of the uncertainty…
A sharper uncertainty inequality which exhibits a lower bound larger than that in the classical N-dimensional Heisenberg's uncertainty principle is obtained, and extended from N-dimensional Fourier transform domain to two N-dimensional…
Recent philosophical discussions about metaphysical indeterminacy have been substantiated with the idea that quantum mechanics, one of the most successful physical theories in the history of science, provides explicit instances of worldly…
The locality issue of quantum mechanics is a key issue to a proper understanding of quantum physics and beyond. What has been commonly emphasized as quantum nonlocality has received an inspiring examination through the notion of Heisenberg…