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Robert A. Herrmann

Publications and source records attributed to Robert A. Herrmann.

At least 19 recordsLinked to original sources
arXiv2015

Solutions to the "General Grand Unification Problem," and the Questions "How Did Our Universe Come Into Being?" and "Of What is Empty Space Composed?"

Using mathematical techniques to model one of the most simplistic of human linguistic processes, it is rationally predicted that within the nonstandard physical world (NSP-world) there exists a force-like (logical) operator *S and an entity w' such that *S{w'} sequentially generates each of the Natural systems that comprise a Universe. This model shows specifically that within the NSP-world the behavior of each Natural world Natural system is related logically. Further, the model predicts the rational existence of a single type of entity within the NSP-world's substratum that can be used to construct, by means of an exceptionally simple process, all of the fundamental Natural world particles used within particle physics. In section 11.2, it is shown how (Natural law) allowable perturbations in Natural system behavior are also included within this mathematical model. These results solve the pre-geometry problem of Wheeler. In general, the model predicts that when the behavior of these Universe creating processes is viewed globally, it can be described as apparently mirroring the behavior of an infinitely powerful computer or mind.

astro-ph↗
arXiv2014

General Logic-Systems that Determine Significant Collections of Consequence Operators

In this paper, general logic-systems and a necessary and sufficient algorithm are used to substantiate significant consequence operator properties. It is shown, among other results, that, in certain cases, (1) if the number of steps in a deduction is restricted, then such deduction does not yield a consequence operator. (2) In general, for any non-organized infinite language L, there is a special class of finite consequence operators that is not meet-complete. (3) For classical deduction, three different examples of modified propositional deduction yield collections of finite consequence operators that are not meet-complete. Other general logic-system examples are given. In a final section, the notion of potentially finite is investigated.

math.GM↗
arXiv2014

Nonstandard Analysis Applied to Special and General Relativity - The Theory of Infinitesimal Light-Clocks

Nonstandard analysis and electromagnetic propagation properties are used to derive all of the fundamental results for the Special Theory of Relativity. Infinitesimal modeling via infinitesimal light-clocks is used to derive two general line-elements (metrics) without the use of Riemannian geometry. By substituting potential velocities, the Schwarzschild, quasi and modified Schwarzschild, de Sitter, Robertson-Walker and similar line-elements are derived. New black hole and quasi-white hole investigations are presented. A new fixed method using separating operators is used to obtain the major predictions for the relativistic alterations in natural-system behavior. The major conclusion is that all such changes are related to electromagnetic properties and that Riemannian geometry is but an analogue model for natural-system behavior.

math.GM↗
arXiv2013

Probability Models and Ultralogics

In this paper, we show how nonstandard consequence operators, ultralogics, can generate the general informational content displayed by probability models. In particular, a probability model that predicts that a specific single event will occur and those models that predict that a specific distribution of events will occur.

quant-ph↗
arXiv2013

Nonstandard Consequence Operators

In this paper, we investigate the algebras of consequence operators and finite consequence operators on a fixed language. Significant new collections of consequence operators are defined and shown to be complete and distributive sublattices. Further, the collection of consequence operators is shown to be almost atomic. Other lattice theoretic properties are investigated and useful chain properties are obtained. In the last section, natural languages, and associated consequence operators, are encoded and embedded into a nonstandard structure. The entire basic theory of nonstandard consequence operators is developed in this last section.

math.LO↗
arXiv2012

The Theory of Ultralogics Part I

As of the date of this version, this monograph (parts I and II) contains all of the known technical results relative to the Robinson-styled nonstandard modeling of natural languages and certain associated linguistic processes such as deduction via consequence operators among other concepts. These results have direct application to the construction of the GGU-model, the GID-model, the GD-model, the MA-model and also apply to philosophy, psychology, properton theory and other aspects of the Nonstandard Physical World (NSP-world).

math.GM↗
arXiv2012

The Theory of Ultralogics Part II

As of this date of this version, this monograph (part I and II) contains most of the technical results relative to the Robinson-styled nonstandard modeling of natural languages and certain associated linguistic processes such as deduction via consequence operators among other concepts. These results have direct application to the construction of the GGU-model, GID-model, D-world model, MA-model and also apply to philosophy, psychology, properton theory and other aspects of the Nonstandard Physical World (NSP-world).

math.GM↗
arXiv2010

The Encoding of Quantum State Information Within Subparticles

A method is given by which the descriptive content of quantum state information can be encoded into subparticle coordinates. This method is consistent with the MA-model solution to the general grand unification problem. Subparticle mechanisms via affine or linear transformations are also discussed.

quant-ph↗
arXiv2010

Nonstandard Analysis - A Simplified Approach

In this monograph, nonstandard characteristics for many notions from real analysis are obtained and applied. However, only two simple types of atomic formula are used and almost all of the characteristics are shown to hold for a simple ultrapower styled structure generated by any free ultrafilter over the natural numbers.

math.GM↗
arXiv2010

Standard and Hyperfinite Unifications for All Physical Theories

In this paper, the set of all physical theories is represented by a countable subset of the lattice of consequence operators defined on a language L. It is established that there exists a unifying injection U defined on the set of significant representations for natural-systems M. If W is a member of M, then U selects an ultralogic C such that C(*W) restricted to L is a unification for the set of all physical theories as each is applied to W. There also exists a standard injection S that for each W in M selects a standard unifying consequence operator D, where C(*W) is a subset of *D(*W). It is also shown how to use these unifying operators and obtain a product operator that has the same effect but, in a practical sense, this operator is applied to every natural-system within our universe simultaneously.

physics.gen-ph↗
arXiv2009

An Operator Equation and Relativistic Alterations in the Time for Radioactive Decay

In this paper, using concepts from the nonstandard physical world, the linear effect line element is derived. Previously this line element was employed to obtain, with the exception of radioactive decay, all of the experimentally verified special theory relativistic alterations in physical measures. In this paper by means of an operator equation and separation of variables, the relativistic alteration in decay time for radioactive material is obtained by applying a hypercontinuous microeffect that gives the appearance of a discrete alteration in the amount of radioactive material present.

math-ph↗
arXiv2009

A Nonstandard Derivation for the Special Theory of Relativity

Using properties of the nonstandard physical world, a new fundamental derivation for all of the effects of the Special Theory of Relativity is given. This fundamental derivation removes all the contradictions and logical difficulties in the original derivation and leads to the fundamental expressions from which Prokhovnik derives the basic transformations. However, it is shown that the correct interpretation is completely distinct from Prokhovnik's. It is shown that the Special Theory effects are but manifestations of the interaction between our natural world and a nonstandard substratum. This derivation eliminates the controversy associated with any physically unexplained universal time dilation and length contraction. It is shown that there is no such thing as a universal time dilation and length contraction but, rather, there are alterations in pure numerical quantities associated with an electromagnetic interaction with a NSP-world substratum.

physics.gen-ph↗
arXiv2009

A Hypercontinuous Hypersmooth, Scharzschild Line Element Transformation

In this paper, the Eddington-Finkelstein transformation is used as an illustration of how the problem of singularities or infinities can be removed by application of nonstandard analysis to the Schwarzschild line element (metric). The evolution of a gravitationally collapsing spherical body with radius greater than but near to the Schwarzschild radius is also investigated.

math-ph↗
arXiv2008

Modeling the Dialectic

Three formal first-order finite dialectical schemes are investigated. It is shown that schemes 1 and 2 have significantly different finite models. Further, an infinite natural number model for schemes 1, 2, 3 is constructed, and it is shown that scheme 3 has no finite model.

math.GM↗