2. Philosophy and Methodology
2.1. Philosophy
Geometric Generalization is a physics theory of everything, which develops the Special and General Theory of Relativity and the Theory of Quantum Mechanics, and as a result, it suggests a formulation to a major philosophical movement.
At first, probably Heraclitus suggested this philosophical standpoint, and many thinkers from different cultures all over the world have shared it independently in history.
This realist philosophy recognizes physical reality as a complete continuum and unity. According to this philosophy, physical reality is not static, but it is a state of constant movement and change (process philosophy). This ongoing process of change is a consequence of balancing opposites (formed by deviations from nothingness-flatness state).
In fact, Geometric Generalization is the detailed formulation of this simple and compact idea. Not only it is easy to visualize, but also its mathematical formulation is viable.
However, Geometric Generalization may seem challenging to some readers, because concepts of mainstream physics are strongly under the influence of another philosophy, “atoms” of Democritus, which treats Nature as a coincidence of scattered existing building blocks (materialism).
The philosophical approach that is depicted here defines the general character of the paper. However, the following chapters will discuss the philosophical deductions of the paper in further detail.
2.2. Methodology
Modern scientific inquiry is commonly based on interpreting observable and measurable evidence. Surely, experimental testability and observability are the essential conditions to verify a hypothesis or a theory as scientific. It seems that Geometric Generalization does not have any contradictions with known experiments and observations. Additionally, it has some observable predictions, and it suggests solutions to some mysterious phenomena (e.g. dark matter mystery, locality issue in particle scale, etc.).
The modern empirical method may seem to be adequate to formulate the algorithm in Nature, because it has already provided some technological applications.
On the other hand, it has not been possible to answer the why question with this approach. Although mainstream physics formulates the relations of matter and energy and describes them in terms of the other, it seems to ignore the exact nature of these things (matter and energy) and the reason why they exist.
According to our philosophy, it is not surprising that empirical reductionism has not been able to solve the mystery of Nature, since there are no independently existing elementary building blocks in Nature like the bricks of a building. Instead, our philosophy proposes to focus our attention in order to comprehend the principles and the logic behind the whole unity.
Abstract principles of mathematics, geometry, etc. cannot be directly extracted from experiments, and concepts of unity and causality go much beyond. Not only is it not possible to observe causality as the cause of physical existence, but it is also impossible to monitor the exact process between cause and effect in physical activities (e.g. the process between the emission and the absorption of a photon).
Space-time, although it is a very fundamental concept, also cannot be observed directly. It is only the relations and the proportions of things in space-time that can be measured. (Please note that this paper neither considers space-time as an abstract a priori nor treats it as a kind of substance.)
Geometric Generalization originates space-time on certain abstract principles and concepts (of geometry and causality), and it derives the things of physical existence (matter and energy) as a natural result of its space-time concept (as knot-like, vortex-like, wrinkle-like deformations on space-time).
Primary source of our knowledge may come from observations and experiences. However, according to Geometric Generalization, the exact formulations of the principles of Nature should be based on a priori abstract principles, since the physical existence itself is a natural result of these principles. Eventually, derivations in this paper are logical, and initial elements of these derivations (abstract principles) cannot be extracted empirically.
Geometric Generalization, as a theory of everything, is not only about the formulations of the relations of physical things (matter and energy), but it is also about the nature of their existence (matter and energy). However, since it is about the theory of things, it does not discuss logical proofs of abstract a priori principles, and it does not examine why these abstract principles existed in the first place. In fact, the reality of these concepts (causality and unity) can be finally proven, only if the true theory of everything is built on these concepts, and if the theory of everything is not formulated without them.
Since Geometric Generalization assumes that physical existence is a natural result of abstract a priori principles, it respects logical self-consistency (rationalism) as much as empirical confirmations, suggesting that the rationality of a theory (of everything) should also be examined carefully. Considering its derivations, it concludes that physical reality exists, because there are these a priori principles (e.g. mathematics, geometry, causality, unity, etc.).
In order to formulate its dynamic Nature philosophy, this paper attempts to develop well-known, well-formulated theories of mainstream physics from a single unique hypothesis reflecting its philosophy. The following chapters will develop this hypothesis in order to formulate the briefest description of Nature.
Methodology of this paper may seem deductive. However, this powerful hypothesis, which seems to develop mainstream physics equations, has not been considered like a dogma. In fact, this theory has been derived through the process of both inductive and deductive reasoning, and a thorough examination of mainstream physics and well-known experiments-phenomena. Here, we must note that this paper has been written independently from its philosophical ancestors or other similar theories, and that the story surrounding the birth and growth of this theory and its hypothesis is beyond its scope.
Radical approach of Geometric Generalization may seem suspicious at a glance, when considered from the mainstream point of view. This concern has affected the recounting style and the chapter structure of Geometric Generalization. The simple and compact idea of Geometric Generalization has not been expressed in the briefest way, in order to establish its relevance to mainstream physics.
Next chapter is the “Hypothesis”, which will guide us in this adventure…
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