Geometric Generalization of the Structure of Nature

A theory of everything and a mathematical formulation of a philosophy

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1.
Introduction – Quick Overview ← Start Here
7.
Fundamental Forces and Gravity


2.
Philosophy and Methodology
8.
Quantum Mechanics


3.
Hypothesis
9.
Final Generalization ← You are here


4.
The Basis of Physical Reality
10.
Elementary Particles


5.
Formation of Mass and Energy
11.
The Universal Unit System


6.
Distance - Time - Relativity

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This section presumes that the reader has worked through the preceding sections and chapters.


It is recommended to start from Introduction - Quick Overview


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9.2. Basic Principles of the Structure of Nature
9.4. The Universe at Large Scale




9. Final Generalization

9.3. The Exact Meaning of Relativity
Connecting Gravity with Quantum Mechanics

According to Geometric Generalization, relativity is an empirical consequence of basic principles of Nature (the expanding space and the universal strain on the expansion). However, regarding the Theory of Relativity as one of the basic principles of laws of Nature led to many misunderstandings and hampered full comprehension of laws of Nature. As a result, misinterpretations on relativity obstruct the connection between the gravitation and quantum (strain) mechanics.

One of the most controversial and surprising conclusions of this paper is discussed in this section.
9.3.1. The postulate of relativity
First, let us review Galileo’s postulate on relativity:
“Any two observers moving at constant speed and direction with respect to one another will obtain the same results for all mechanical experiments”

Practically, this postulate, which can be also confirmed empirically, has a very important meaning. According to this postulate, there are no observational consequences of motion. Observers can only measure their velocity relative to another body. Therefore, observers cannot conclude if their inertial frame is in motion or not, and any observer may choose to believe that its inertial frame is motionless.

In fact, this postulate has also been the basis of Einsteinian relativity. Einstein’s principle is very not different from Galileo’s except that it adds the postulate of constancy of speed of light, and formulates relativistic transformations at high speeds.

Consequently, these postulates let observers choose arbitrary coordinate orientations, and formulate Lorentz Transformation Equations between arbitrary coordinate orientations.

It is interesting that Geometric Generalization’s hypothesis generates both postulates of relativity, and it derives Lorentz transformation equations (Section 6.6).
9.3.2. Relativity in wholeness of physical reality
On the other hand, Galileo’s postulate has been changed in Einsteinian relativity; its modern version is “The laws of physics are the same in any inertial frame of reference”.

However, modern version of this postulate makes a presumption on the laws of Nature, and relativistic abstraction of Nature has gone beyond its original meaning. In fact, this assumption implies that laws of Nature have a kind of arbitrariness (since laws of Nature are independent from the state of motion).

According to Geometric Generalization, the mechanism that ensures the original postulate and generates relativity as a phenomenon suggests a rather different physical reality than that which is presumed by the modern version of the postulate. This paper assumes wholeness in physical reality, its geometry, and its interactions, but not any kind of arbitrariness. Additionally, this paper rejects the absence of metric standards, and it concludes that the space-time geometry of physical reality suggests concrete intrinsic metric standards.

Please note that the expression “laws of Nature” itself is also incompatible with this paper’s unified point of view. This expression implies as if Nature is a coincidence of independently existing elements and there are laws to maintain interactions of these elements. This paper rejects this philosophy; instead, according to this paper, the entire Nature is a single active process, and we can talk about the principles of this process.
9.3.3. Derivation of relativistic transformations on absolute space
In Section 6.6, we have presented the derivation of Lorentz transformation equations (Lorentz gamma factor) from this paper’s hypothesis. We will skip this discussion now, but let us note that Section 6.6 confirms that relativity is a result of an integral and continuous mechanism in Nature (the flux of expanding spatial dimensions).

Additionally, this derivation has astonishing consequences; it demonstrates that relativistic transformations can be derived on absolute space. By the expression absolute space, we mean a space where it practically differs to be in motion.

According to our derivation, there should be a motionless state for matter in absolute space; although there is no absolute motion, and state of motion cannot be detected by local experiments.

In fact, the expanding closed space on which we constructed physical reality is exactly an absolute space (Section 4.2).
9.3.4. Absoluteness on spherical geometry
Geometric Generalization assumes that the geometry of the universe is (elliptical) spherical; this property is the result of the logical principles that cause physical reality (Section 4.3).

However, it differs to be static and to be in motion on spherical geometry, because if a body is moving on the surface of a sphere (space), it will feel a fictitious centrifugal force (as a function of the inertia of the object being pushed into the sphere) towards perpendicular time dimension. Hence, elliptic geometry does not allow orientation of accelerated coordinate systems on the 3D hypersphere.

Additionally, there needs to be an interaction between the moving body and sphere (space) to keep the moving body on the surface of the sphere. In fact, accelerated matter wraps space-time more and causes extra gravitational effect, due to the (relativistic) mass increase. Hence, the way that matter affects space-time geometry differs according to matter’s movement on spherical geometry.

However, there are surely no special locations on space (three-dimensional sphere) to orient a coordinate system, since the universe has a constant positive curvature (all spatial directions are curved towards the same hyper-direction). Therefore, observers are free to orient coordinate systems arbitrarily on any absolute (static) location.
9.3.5. Matter in the wholeness of physical reality
According to Geometric Generalization, quantum of matter is a local strain (energy) package on the expanding space-time geometry like knots on an inflating balloon (Section 5.3).

This definition indicates that matter is an ingredient of space-time geometry of physical reality, and there exists a mutual relationship between matter and space-time. Eventually, observable consequences of general relativity prove this relationship.

However, such a mutual relationship between matter and space-time in the wholeness of physical reality (knots and balloon’s surface) conflicts with the arbitrariness as suggested by the over interpretation of the relativity theorem.
9.3.6. Opposition between acceleration and deceleration
The concept of absolute space emphasizes dissimilarity between acceleration and deceleration. On absolute space, acceleration and deceleration are completely opposite actions for any relative observer. Hence, opposite effects of acceleration and deceleration on matter (relative mass increase or decrease) is concrete for any relative observers.

This point has been ignored in special relativity, which cause the twins paradox.

In this case, if we consider the finite history of (the wrinkling epoch of) our expanding universe, we can easily conclude that some matter has accelerated more and some are in less motion.
9.3.7. Motion in Hubble’s space
Observations confirm that Hubble’s expanding space is an absolute space in accordance with this paper’s integral space-time concept.

On earth, we observe that the universe expands towards all directions isotropically, and we assume that the distance between any points on space increases constantly. This phenomenon indicates that matter clusters (galaxy clusters) are approximately inert on the Hubble’s expanding space (ignoring regional rotating trajectories).

On the other hand, an observer who travels at very high speeds (very close to speed of light relatively to Earth) would measure different Hubble’s constants in different directions in relation to its motion. In other words, that observer would believe the universe expands less in its direction of travel and more in the opposite direction.

However, it will be illogical for the observer traveling at a high speed, if he assumes that he is motionless and the universe is expanding asymmetrically (since he will not be able to explain such an asymmetry in the whole universe). Additionally, it will be unreasonable too; if accelerated observer chooses to believe that, the whole matter content of the universe is in motion relatively to his motionless state. In fact, if our observer is wise enough, he can simply conclude that his frame is in motion in Hubble’s expanding (absolute) space.

It is interesting this discussion implies that even Galileo’s basic postulate can be criticized, since observers can decide if they are in motion or not by observing the universe at a large scale.
9.3.8. The exact meaning of relativity
Inert observers may not be able to decide if they are in motion or not by examining their states (by making local mechanical experiments), but it would be suspicious to value Galileo’s postulate beyond that.

In fact, in Nature, some very important changes happen in state of motion. Basic elements of matter (strain packages like knots or vortexes) significantly change after acceleration or deceleration. The confinement volume tightens, mass (energy content) increases with acceleration. Additionally, after a velocity increase, rate of clock-ticks and spatial distance metric contracts in accelerated body’s inert frame of reference (Section 6.1, and Section 6.3). Moreover, strength of interactions also varies (fine structure constant increases) at high energy levels.

On the other hand, these variations (in clock-ticks and distance metrics) occur in such a reciprocal way that any relative observer is right to believe that laws of Nature are not changing. In fact, the thing that is not changing is the constant ratio between the rate of clock-ticks and spatial distance metric; therefore, the speed of light becomes constant for any relative observer. This ratio is kept constant in any case, because both the rate of clock-ticks and the spatial distance metric are functions of the constituents of matter (the tightness of the confinement volume of the knots), which build that body. However, mass (energy content) of a body increases unilaterally with acceleration, since magnitude of mass is also a function of the tightness of the confinement volumes.

Geometric Generalization derives postulates of relativity and Lorentz transformation equations on an absolute space concept, where to be in motion differs. Additionally, this paper concludes that physical reality is a whole and there is a mutual relation between matter and space-time geometry (e.g. a balloon and knots tied on it).

Eventually, interpreting relativity as a law of Nature beyond its original (empirical) meaning implies that there is arbitrariness in Nature. This deceptive presumption disregards the wholeness and the logical consistency of Nature, and obstructs comprehending laws of Nature (The constant and continuous expansion of closed spatial dimensions…). Hence, postulates of relativity and relativistic transformations should be considered as a consequent property of matter’s action in Nature rather than a fundamental and independent law itself.

In fact, our conclusion confirms Einstein’s basic approach: he stated, "Relativity teaches us the connection between the different descriptions of one and the same reality.”
9.3.9. Connecting gravity with quantum mechanics
Geometric Generalization assumes that the wave function describes the physical existence at a location at a time (Section 8.2). Disregarding the improper probability interpretation, quantum mechanics (the wave function) seems to describe physical existence properly. On the other hand, the over-interpretation of relativity that is discussed in this section causes the inconsistency between the gravitation (described by general relativity) and quantum mechanics.

It seems that it is not possible to match the gravitation and quantum mechanics without involving the concept of absolute space. Eventually, the wave function that describes strain packages (quanta of matter and energy) is location dependent, since it describes a magnitude at a location at a time in space-time.

The concept of gravity that is suggested by this paper in Section 7.7 describes the mutual relation between the stress in local strain packages (the knots and vortexes) and strain in whole space-time. Hence, according to this paper, gravitational deformations on space-time are also location dependent.

Mathematically, regional restraint and compression on the expansion (curvature in space-time in general relativity) is defined by the contraction in Estring length at a location as we discussed in Section 7.7. Practically, the variation in photon wavelengths in gravitational fields (gravitational lensing by metric contraction) describes the regional restraint on the expansion at a location (gravitational metric contraction in space-time); and eventually, the regional restraint on the expansion (the effect of gravity) is location dependent on absolute space.



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9.2. Basic Principles of the Structure of Nature
9.4. The Universe at Large Scale


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