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Pages: 109
Publisher: Arxiv
Year: 1995
Nonstandard Analysis Applied to Special and General Relativity: The Theory of Infinitesimal Light-Clocks

Robert A. Herrmann
  • Article 1. Foundations and Corrections to Einstein\'s Special and General Theories of Relativity, Part 1.
    1. Introduction
    2. Some Ether History
    3. The Calculus
    4. Relativity and Logical Error
    5. A privileged Observer
    6. The Fock Criticism and Other Significant Matters
    7. Why Different derivations?
    8. A Corrected Derivation; References for part 1
  • Article 2. A Corrected Derivation for the Special Theory of Relativity
    1. The Fundamental Postulates
    2. Pre-derivation Comments
    3. The Derivation
    4. The Time Continuum
    5. Standard Light-clocks and c
    6. Infinitesimal Light-clock Analysis
    7. An Interpretation
    8. A Speculation
    9. Reciprocal Relations
    10. Notes; References
  • Article 3. Foundations and Corrections to Einstein\'s Special and General Theories Relativity, Part 2
    1. Some Special Theory Effects
    2. General Effects
    3. Relativistic Alterations
    4. Gravitational Alterations
    5. Substratum Analysis
    6. Minimizing Singularities
    7. Speculative Applications
    8. Prior to Expansion, Expansion and Pseudo-White Hole Effects
    9. Notes; References to part 2
    10. Index

from the Preface

It is actually dangerous for me to present the material that appears within this book due to the usual misunderstandings. Any scientist who claims that there are fundamental errors within the foundational methods used to obtain Einstein?s General and Special Theories of relativity may be greatly ridiculed by his colleagues who do not read carefully. The reason for this has nothing to do with science but has everything to do with scientific careers, research grants and the like. Thousands upon thousands of individuals have built their entire professional careers upon these two theories and their ramifications. The theoretical science produced is claimed to be ?rational? since it follows the patterns of a mathematical structure. As a mathematician who produces such structures, it is particular abhorrent to the scientific community if I make such a claim. Mathematicians seem to have an unsettling effect upon some members of the physical science community, especially when a mathematician delves into a natural science. After all, it was the mathematician Hilbert who, without any great effort, was actually the first to present, in a public form, the so-called Einstein gravitational field equations.

Now please read the following very carefully. The results presented here and in my published papers on this subject are not intended to denigrate those scientists who have, in the past, contributed to these Einsteinian theories or who continue to do so. The corrections I have made are in the foundations for these theories. The corrections are totally related to how the results are interpreted physically. These corrections do not contradict the results obtained when the Einsteinian approach and the language used are considered as models for behavior. These corrections are based upon newly discovered rules for rigorous infinitesimal modeling. These results may also be significant to those that hold to the belief that many events within the natural world are produced classically by a zero-point radiation field.

Many unqualified individuals continue to present their own alternatives to these Einstein theories, some claiming that the results are but an exercise in high-school algebra. Certain scientific groups tend to categorize any and all criticisms of the Einstein theories as coming from the unqualified and lump such criticisms into the same unworthy category. However, many highly qualified scientists of the past such as Builder, Fock, Ives and Dingle have made such claims relative to the foundations of these two theories. For Ives, the fundamental approach was to assume that such a thing as length contraction, and not time dilation, is a real natural effect and it is this that leads to the Einstein conclusions. In order to eliminate these criticisms, Lawden states the ?modern? interpretation that length contraction has no physical meaning, and only ?time dilation? is of significance. This modern assumption is certainly rather ad hoc in character. Further, many theory paradoxes still appear within the literature and are simply ignored by the scientific community. There is, however, a reason for this...