The Distinction Between Newton’s Classical Mechanics and the Framework of Special Relativity

The difference between Newton’s theory and special relativity is profound, rooted in the fundamental approach to understanding physical phenomena. Newton’s physics is a mechanical apparatus assembled by Sir Isaac Newton and his contemporaries and predecessors, heavily influenced by Euclid and the Greek geometers.

Newton’s Mechanics and Euclidean Influence

Newton’s work on mechanics is deeply intertwined with the geometric principles established by Euclid. In his unpublished preface to the 'Principia', Newton highlighted the Euclidean influence, recognizing the role of Euclid’s Elements as the foundation on which he built his theory of mechanics. The principles of mechanics in Newton’s time were often described using a mechanical model, akin to the gears and cogs of an engineering analogy, where calculus provided the means to gear ratios. This precise machinery allowed for a more accurate description of physical phenomena, applicable to a wide range of situations.

The Greeks, especially in the context of the Antikythera mechanism, employed a similar geometric approach, albeit less powerful than Newton’s. This sophisticated use of geometry to explain mechanical and physical phenomena underscores the complexity and innovation in Newton’s methods. While the exact level of innovation remains subject to interpretation, there is no doubt that Newton’s mechanics provided a far more precise and comprehensive framework for understanding the physical world.

Special Relativity and its Evolution

Special relativity, on the other hand, builds upon the foundation of Newton’s classical mechanics. It enhances the precision of the Newtonian model by excluding irrelevant components and setting inviolable limits on infinite extension and division. This framework was developed to address the peculiarities of phenomena occurring on a scale beyond our everyday experience, such as high velocities approaching the speed of light.

Norman Gray’s 'Student’s Guide to Special Relativity' provides a clear understanding that while Newton’s mechanics is more than sufficient for most classical physics applications, special relativity becomes essential for the analysis of events beyond the classical scale. The judgment to use one framework over the other is often based on expert assessments and assumptions relevant to the specific problems being addressed.

Despite its importance, special relativity is underutilized in many practical applications. This underutilization is partly due to the lack of a widely accepted constructive outline for special relativity, making it harder for physicists and engineers to adopt and apply these concepts effectively.

The Science Establishment and Constructive Models

Michael Doran, in his work, has offered a basic constructive outline for special relativity, relying on a few assumptions and the geometric model of Cavalieri’s Principle. Doran suggests that Cavalieri’s Principle might also serve as a similar function for general relativity, although more research is required. Doran’s exploration has led him to question why the science establishment does not support the development and dissemination of such constructive models. He believes that the preference for an "indirect" approach in special relativity reflects a desire to reinforce cognitive biases and philosophical prejudices, often rooted in outdated ideas.

The enduring reluctance of the scientific community to embrace constructive models for special relativity is puzzling, given the potential to simplify and clarify the understanding of modern physics. Doran’s research points to a need for more transparent and accessible explanations of these fundamental concepts.

In conclusion, while Newton’s classical mechanics provided a robust and precise framework for most applications, special relativity offers critical insights into the behavior of the physical world at high velocities and other scales. The development of clear and accessible models for special relativity could significantly enhance its utility and adoption in scientific and practical contexts.