Member

Einstein built relativity theory upon foundational conceptual shapes such as a spherical wave and a hypercone. He created the hypercone by defining l, or light-time, as l = ct. Conceptually and mathematically, Einstein then used l, or light-time, as a replacement for Time, t, in his derivation. Here we find that light-time, l, is actually a measure of Distance, not Time, because the result of a Velocity multiplied by a Time is always a Distance. Because Time and Distance cannot be used interchangeably, its mistreatment as both a Time and a Distance invalidates Einstein's hypercone concept and the resulting mathematical and theoretical conclusions. The critical mistake represents a key characteristic of Einstein's theory because it enables him to objectify Time - or treat Time as if it were a Distance. This objectification of motion, a key unstated characteristic of Relativity theory, has led to incorrect theoretical conclusions for over a century.

The Physics 3.0 Framework emphasizes Type, Function, and Namespace Abstraction, 2D and 3D Geometric Transformations, and Reverse Engineering into the Physics Body of Knowledge. It offers unique techniques for analyzing physical and mathematical problems, derivations, and theories. It also creates a foundation for addressing many physical problems ranging from Quantum Mechanics to Gravity to Relativity. For example, the model of Complete and Incomplete Coordinate Systems, which is built using the Physics 3.0 Frameworks, and is an alternative to Special Relativity Theory, produces quantitatively better results than Einstein's original equations.

Einstein's transformation equations are believed to be mathematically correct in part due to the Spherical Wave Proof that Einstein offers in each of his derivations. Einstein asserts that if an electromagnetic wave is propagated as a Sphere in system K that the wave will also be represented as a Sphere in system K', where the values of the Sphere in K' are determined using the transformation equations. The proof asserts a one-to-one mapping between the points representing the Sphere in K and the points representing the Sphere in K'. Here we find that Einstein's proof shows that the transformed values conform to the general equation of a Sphere in K', but that his proof does not validate that all of the transformed points are part of the same Sphere in K'. We then show that the proof fails because the transformed K' values have different radii and represent points on multiple spheres in K', instead of on a single sphere.

Namespaces are commonly used in Computer Science, with namespace problems as a leading cause of very difficult to identify programming errors. While namespaces have not been extensively used in mathematics, they can be used to describe the variables, identifiers, and components associated with mathematical functions and matrices. Namespace Analysis can be used to evaluate the validity of mathematical derivations that involve functions and matrices; can help identify the source of variable naming problems in complex derivations, and can provide insight on how the problems can be corrected. Here we use namespace analysis to evaluate multiple derivations of the Einstein-Lorentz transformation equations, revealing mathematical problems in each. We show that, in his 1905 paper, Einstein overloads the ?t? variable between his global and function namespaces, while Lorentz, in his 1904 paper, overloads the ?x? variable between his function and matrix namespaces. This overloaded variable problem enabled them to each produce incorrect time transformation equations. This finding of a mathematical problem in each significant Einstein-Lorentz derivation will require that the Einstein-Lorentz equations be modified and that the continued validity of Special Relativity be reexamined.

Wavelength is generally accepted as the total length of one cycle of a given frequency. Conceptually this length, as measured along the X-axis, is the distance from the origin to the endpoint and extends in one direction, which means that the value for length also represents the value of the endpoint along the X-axis. Here we find that that wavelength is bi-directional in nature and that the total value assigned to length does not also represent the position of the endpoint along the X-axis. This bi-directional wavelength characteristic is inherent in the mathematical derivations of both Einstein and Lorentz, but is not incorporated into their resulting discussions. Not only does this lead them to incorrectly normalized their resulting equations, they also incorrectly conclude that their input and output values represent points rather than lengths. Once the equations are corrected to account for bi-directional wavelength, we summarize how the corrected equations yield equal, or better, experimental results for frequency- and wavelength-based experiments than the existing Einstein and Lorentz equations. This finding of bi-directional wavelength, along with the recognition that the equations transform lengths instead of points, will require a revised theoretical model such as the model of Complete and Incomplete Coordinate Systems.

The continued mathematical validity of the Einstein and Lorentz transformation equations has been mathematically challenged based on namespace analysis and on apparent violations of the rules of algebraic substitution. In addition, the Einstein-Lorentz Special Relativity equations do not properly incorporate frequency into the derivation because they overlook its bi-directional nature and do not account for superposition of waves principle. Furthermore, both Einstein and Lorentz use their equations to transform points instead of lengths. He we compare and contrast the essential characteristics of the Einstein-Lorentz models with the model of Complete and Incomplete Coordinate Systems, which introduces a revised set of length-based transformation equations, addresses the bi-directional nature of frequency, and adheres to the superposition of waves principles. The model of Complete and Incomplete Coordinate Systems is a wave medium (aether) based model that is generalize to apply to oscillating phenomena and moving systems, does not suffer from the same mathematical problems as the Einstein-Lorentz derivations, and uses equations that yield equal or better results that the existing Einstein-Lorentz equations.

The Michelson-Morley Interferometer experiment is commonly cited as experimental validation of Special Relativity. While Michelson and Morley concluded an Earth Orbital Velocity (EOV) of 5 to 7.5 km/s, their result is generally accepted as 0 km/s, with their observation attributed to experimental error. Here we find three specific problems in the Michelson-Morley analysis, principal of which is the recognition that their expected result equation does not mathematically compensate for interacting frequencies as governed by the superposition of waves principle. Once the expected result equation is corrected, their data is reevaluated to reveal an EOV of approximately 30 km/s, which was their expected result. This finding is confirmed by reanalyzing Miller?s 1933 repeat Interferometer experiment, also revealing an EOV of 30 km/s. These experimental findings support the presumption of an electromagnetic wave medium and challenge the validity of Special Relativity.

Special Relativity Theory (SRT) is one theory that accurately explains the results of the Ives-Stillwell atomic clock experiment. SRT has been challenged on mathematical grounds following the discovery of inconsistencies in the derivation of the transformation equations. The model of Complete and Incomplete Coordinate Systems (CICS) corrects the mathematical and theoretical problems with SRT, and defines a set of equations for oscillating waves in moving systems. Here we show that the CICS model offers better predictive capabilities than SRT in evaluating the Ives-Stillwell atomic clock experiment, as measured by the amount of error between the predicted and actual results. Importantly, this finding supports the use of one-half a wavelength in the CICS equations to account for the bi-directional nature of wavelength.

Einstein's Special Relativity Theory (SRT) defines four transformations equations that are generally accepted as resulting from mathematically correct derivations. In this paper, we re-examine Einstein's 1905 paper and perform a brute-force analysis of the Xi transformation, revealing a specific algebraic problem in its derivation. The difficulty in identifying and communicating this problem will be explained since the problem does not manifest itself in the validity of the Xi equation, but rather in the validity of the Tau equation. Specifically, the problem manifests itself as an incorrect numerator in the SRT Tau equation. Once the root cause is identified and Tau is corrected, the resulting system of equations will require that the theoretical underpinnings of SRT be re-examined.