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Email: Margaret R. Kelso

Introduction to Pythagorean Physics
Todd Mathews Kelso

Pythagorean Physics postulates the existence of a basic unit of matter, the Pythagorean atom. It deals with discreteness in favor of continuity. It considers both time and space to be absolute. Motion is a function of space and time. Unlike classical mechanics, Pythagorean Physics considers mass to be a variable and has a different concept of what a particle is. Pythagorean Physics employs an axiomatic system that incorporates both philosophy and science in order to achieve meaning.

Scientists sometimes have a difficult time understanding the limits and validity of what they think they know. Neither the theory of relativity nor quantum mechanics employs an axiomatic system that can guard against such errors. Rather, they both superimpose notions for convenience. Pythagorean Physics follows an axiomatic system that starts with definitions and proceeds step by step from there in a logical fashion that provides meaning in a way that other approaches can not.

Integration of Philosophy and Science
Specialization has tended to separate concepts that are really interconnected. In order to understand better how the universe works, it is necessary to understand more than just one small portion of it. A comprehensive overview that honors the interconnectedness of all existence is required. Unfortunately, particular aspects of science are becoming more and more esoteric without a broader view. It even becomes necessary at times for a scientist to accept on faith the work developed in a different area of science. This practice can add credence to ideas that should be challenged. Pythagorean Physics challenges multiple ideas from multiple disciplines.

The Contribution of Pythagoras
Pythagoras lived roughly between 569 and 475 BC and headed up a secret society that was partly philosophical (religious), partly musical, partly astronomical, but essentially mathematical. He was influenced by Thales and his pupil Anaximander, Egyptian priests, and the Babylonians. Pythagoras believed that reality is mathematical in nature and he had a symbolic method of teaching. His interest in the principles of mathematics led him to the abstract idea of a proof. He examined the principles of science by probing theorems in an immaterial and intellectual manner. Each new theorem set up a platform toward new understandings. He believed that exercising logical proofs improved the human condition. Pythagorean Physics honors this legacy.

An Introductory Critique of the Theory of Relativity

Confusion about Space as a Continuum
The general theory of relativity is commonly praised for having incorporated geometry into physics, but it is classical mechanics that uses geometry correctly. The “incorporation” of geometry into physics by the general theory of relativity amounts to treating space-time and thus both space and time as if these were continuous physical substances that can be stretched and compressed and that expand or contract. The physical substances that can be stretched and compressed are not continua. The physical substances that can be stretched and compressed owe this mutability to the fact that they are not continua. It makes no sense to say of something that it has changed either its size or its shape unless there is some standard all parts of which retain forever the same size and shape with respect to which standard the size and shape of anything else is defined. This something is space, so it makes no sense to say of space or of any part of space that it changes its size or shape.

Confusion between Abstract Structures and Physical Objects
I note that incorporation means putting something into a body. All relativistic “thinking” involves a lack of understanding of the difference between abstract mathematical structures such as space and time and physical objects such as sheets of rubber and pools of water. This confusion is reminiscent of the ancient confusion of darkness with mist or empty space with air. There is no clarity of thought, for example, in Einstein’s statement that we must just assume that space has the properties of a medium (for electromagnetic waves) and not worry too much about what this statement means. The deformation of space and time by massive objects proposed by general relativity is also not anything that makes any sense. The same confusion is central and crucial in special relativity. Special relativity purports to deal with a set of spatial reference frames that move uniformly relative to each other. Spatial reference frames, however, are abstract sets rather than physical objects, while motion is exclusively a property of physical objects.

Lack of Definitions
Furthermore, motion, as the concept is understood in any context other than relativity theory, consists in having a variable location in space. If there is no space, then the relativists obviously must mean something different by such words as ‘motion’ and ‘uniform motion’ and ‘spatial reference frame’ from what everybody else means by these words. It is incumbent upon them to say what it is that they mean, but relativity theory comes with neither definitions of these concepts nor postulates sufficient to characterize them.

The notion of absolute space in classical mechanics provides a standard. If there is no standard that consists of things that are permanently the same distance from each other, then there is no meaningful content to the “proposition” that any two things are any specific distance from each other. There is a fortiori no meaningful content to the “proposition” that such a distance has changed and still more so no meaningful content to the “proposition” that such a distance is changing either at a uniform or at a non-uniform rate.

The notion of absolute time in classical mechanics provides a standard. If there is no standard that consists of something that happens everywhere and at a constant rate, then there is no meaningful content to the “proposition” that anything happens at any given rate. There is a fortiori no meaningful content to the “propositions” that such a rate changes and still more so no meaningful content to the “proposition” that such a rate changes either uniformly or non-uniformly.

The notion of absolute mass in classical mechanics similarly provides a standard. If there is no standard that consists of a set of masses that are always and everywhere in the same proportions to and having the same differences from each other, then there is no meaningful content to the “proposition” that any physical object has one mass rather than any other. There is a fortiori no meaningful content to the “proposition” that two physical objects have the same mass or have different masses, or that one physical object has either the same mass or two different masses at two different times, or that a physical object has a different mass for one observer from that which it has for another observer.

Confusion over What 'Understanding' Is
Each of the “propositions” that are taken to be the axioms of either the special or the general theory of relativity, and therefore also each of the “propositions” that are taken to be the theorems of either theory, is not actually a proposition at all. These “theories,” therefore, are not actually theories but are word salads. Those who think that they understand either of these theories are confused. The confusion is very deep, since it entails not understanding what ‘understanding’ means.

What Einstein and his progeny do is to hold the structure of space, time and mass in abeyance. They proceed to string together undefined and therefore meaningless words about uniform and accelerated motion as “postulates” and then deduce statements about the structure of space, time and mass as theorems. This is the misguided procedure that has yielded such theorems as that the length and mass of physical objects and the duration of physical processes depend on the relative speed of the objects and processes with respect to the observer making the measurements. It is not surprising that the theorems derived by such a confused and disorderly procedure as that used by relativists do not make any sense.

Diversion from Meaningful Approaches
The simplest hypothesis that is consistent with everything that is known is that space, time and mass are exactly as they are taken to be in classical mechanics. Space is three-dimensional and Euclidean, time one-dimensional and Euclidean and mass isometric to an open ray in either space or time, for example, the positive x-axis or the set of all instants later than a given instant. It is not logically necessary that space, time and mass be exactly as Newton said they were. Space could, for example, be seven-dimensional if the law of interaction between physical objects were such that only three-dimensional clusters of smaller objects could form. Space could be hyperbolic or elliptic rather than Euclidean. Mass could be the magnitude of a vector rather than being merely a scalar. Alternatively, there could be objects with negative masses.
What is logically necessary in order to have a mathematical theory of mechanics is that space, time and mass be metric spaces. A sensibly organized theory of mechanics must start by stating as an axiom what metric spaces space, time and mass are. This must be axiom number one, since any other axioms will concern themselves with how space, time and mass are related to each other or how physical objects or physical processes are to be described using these abstract concepts. The other axioms will thus need the mathematical structure of space, time and mass to be already at hand.

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