Dimensional flow and fuzziness in quantum gravity: emergence of stochastic spacetime

We show that the uncertainty in distance and time measurements found by the heuristic combination of quantum mechanics and general relativity is reproduced in a purely classical and flat multi-fractal spacetime whose geometry changes with the probed scale (dimensional flow) and has non-zero imaginary dimension, corresponding to a discrete scale invariance at short distances. Thus, dimensional flow can manifest itself as an intrinsic measurement uncertainty and, conversely, measurement-uncertainty estimates are generally valid because they rely on this universal property of quantum geometries. These general results affect multi-fractional theories, a recent proposal related to quantum gravity, in two ways: they can fix two parameters previously left free (in particular, the value of the spacetime dimension at short scales) and point towards a reinterpretation of the ultraviolet structure of geometry as a stochastic foam or fuzziness. This is also confirmed by a correspondence we establish between Nottale scale relativity and the stochastic geometry of multi-fractional models.Comment: 25 pages. v2: minor typos corrected, references adde

Organising and managing the fuzzy front end of new product development

new product development

A Theory of Factfinding: The Logic for Processing Evidence

Academics have never agreed on a theory of proof. The darkest corner of anyone’s theory has concerned how legal decisionmakers logically should find facts. This Article pries open that cognitive black box. It does so by employing multivalent logic, which enables it to overcome the traditional probability problems that impeded all prior attempts. The result is the first-ever exposure of the proper logic for finding a fact or a case’s facts. The focus will be on the evidential processing phase, rather than the application of the standard of proof as tracked in my prior work. Processing evidence involves (1) reasoning inferentially from a piece of evidence to a degree of belief and of disbelief in the element to be proved, (2) aggregating pieces of evidence that all bear to some degree on one element in order to form a composite degree of belief and of disbelief in the element, and (3) considering the series of elemental beliefs and disbeliefs to reach a decision. Zeroing in, the factfinder in step #1 should connect each item of evidence to an element to be proved by constructing a chain of inferences, employing multivalent logic’s usual rules for conjunction and disjunction to form a belief function that reflects the belief and the disbelief in the element and also the uncommitted belief reflecting uncertainty. The factfinder in step #2 should aggregate, by weighted arithmetic averaging, the belief functions resulting from all the items of evidence that bear on any one element, creating a composite belief function for the element. The factfinder in step #3 does not need to combine elements, but instead should directly move to testing whether the degree of belief from each element’s composite belief function sufficiently exceeds the corresponding degree of disbelief. In sum, the factfinder should construct a chain of inferences to produce a belief function for each item of evidence bearing on an element, and then average them to produce for each element a composite belief function ready for the element-by-element standard of proof. This Article performs the task of mapping normatively how to reason from legal evidence to a decision on facts. More significantly, it constitutes a further demonstration of how embedded the multivalent-belief model is in our law

Violation of Bell's inequalities in a quantum realistic framework

We discuss the recently observed "loophole free" violation of Bell's inequalities in the framework of a physically realist view of quantum mechanics, which requires that physical properties are attributed jointly to a system, and to the context in which it is embedded. This approach is clearly different from classical realism, but it does define a meaningful "quantum realism" from a general philosophical point of view. Consistently with Bell test experiments, this quantum realism embeds some form of non-locality, but does not contain any action at a distance, in agreement with quantum mechanics.Comment: This article is closely related to arxiv:1409.2120, with some parts condensed and others expanded, in order to spell out how the present approach explains quantum non-locality. In v2 some clarifications and improvements following referees remark