Section III: Fundamental Principles in Mathematics and Physics:

3. I) Total Energy of a System: 

In classical mechanics and quantum mechanics, the Hamiltonian operator (H) represents the total energy of a system. For a particle or a wave, the total energy (E) is the sum of its kinetic energy (Eₖ) and potential energy (Eₚ). 

II) Restoring Forces in Classical and Quantum Oscillations: 

In classical mechanics, a linear oscillation vibrates with a single frequency; its movement is sinusoidal and regular. The harmonic oscillation encounters a restoring force (F) directly linked to the displacement (x) from its equilibrium position, where k represents a positive constant. In quantum mechanics, a harmonic oscillation is governed by a restoring force that varies proportionally to the displacement of the oscillation phase. 

III) Hamiltonian Operator and Total Energy of a System:

The Hamiltonian equation conveys that the kinetic energy (Eₖ) and potential energy (Eₚ) of a wave is equal to the wave's total energy (E). 

The expression, E = Eₖ + Eₚ.     

This equation signifies that the total energy of a wave (E) is the sum of its kinetic energy (Eₖ) and potential energy (Eₚ). It is a fundamental principle in classical mechanics and quantum mechanics.

IV ) Relationships in Harmonic Oscillation Frequencies and Time Intervals:

The time interval (T) of a harmonic oscillation with frequency (f), the phase angle (θ) = 360 degree of the signal phase, or a complete cycle of the frequency of the harmonic oscillation. The relationship between the angular frequency (ω), time interval (T), and phase angle (θ) for a harmonic oscillation, ω = T/θ. 

V) Frequency, Time, Energy, and Planck's Constant: Relationships:

The energy (E) of the the harmonic oscillation with frequency (f) can be represented by the Planck equation, E = hf, where h is Planck constant. The relationship between frequency (f), time interval (T), energy (E), and Planck's constant (h) can be expressed as:

f = 1/T = E/h. Therefore, T = h/E.

VII) The de Broglie relations:

The de Broglie relation conveys momentum ρ and the wavelength λ of the wave representation is given by Planck's constant. Expressed by the equation, 

λ = h/ρ. 

This equation denotes that the wavelength (λ) is inversely proportional to the momentum (ρ) of a wave, where h represents Planck's constant.

f = ρ/h. 

This equation demonstrates that the frequency (f) is directly proportional to the momentum (ρ), with h being Planck's constant.

VIII) Conservation of Total Energy in a Point:

The overall energy (E) of a point remains constant, as expressed by the equation: 

Eₜ = Eₖ + Eₚ.

Here:

Eₜ signifies the total energy possessed by the point.

Eₖ represents the kinetic energy associated with the point, usually connected to its motion or movement.

Eₚ denotes the potential energy linked to the point's position or configuration within a given system.

This equation, Eₜ = Eₖ + Eₚ, indicates that the summation of kinetic and potential energies remains steady over time for the considered point. Any alterations in either kinetic or potential energy are offset by opposite changes in the other form, ensuring that the total energy of the point, Eₜ, remains constant throughout its evolution.

IX) Conservation of Energy Analysis:

The differential analysis reveals that the increment in kinetic energy is equivalent to the decrement in potential energy:

ΔEₖ = - ΔEₚ

XI) Work-Energy Theorem and Differential Kinetic Energy:

As per the work-energy theorem, the relationship between force F and the differential distance Δx over which it acts produces a change in kinetic energy (ΔEₖ).

ΔEₖ = F ⋅ Δx → ΔEₖ = FΔx

X) Relationship between Force and Potential Energy Change:

This equation illustrates the connection between force (F) and the negative rate of change of potential energy (ΔEₚ) concerning displacement (Δx). 

F = - (ΔEₚ/Δx) 

XI) Relationship between Changes in Kinetic and Potential Energy with Respect to Position:

The expression (ΔEₖ / Δx) = -(ΔEₚ / Δx) signifies the inverse relationship between the rates of change of kinetic and potential energy concerning position.

The previous equation ΔEₖ = FΔx represents the relationship between the change in kinetic energy ΔEₖ and the force F acting over a displacement Δx. When this equation is rearranged, it shows that the rate of change of kinetic energy with respect to position (ΔEₖ / Δx) is equal to the negative rate of change of potential energy with respect to position (ΔEₚ / Δx). 

XII) Point Existence and Oscillations:

A point lacks physical presence. It does not have dimensions and is not connected to any event, space, or time. In mathematics, a point is utilized to indicate an exact location or position within or outside a space; it does not possess any length, width, height, or shape. A point acts as the initial reference for depicting any figure or shape and is denoted by a dot.

When a wave within a point initiates a linear oscillation from its equilibrium state or balanced position, its movement disrupts the surrounding potential due to its specific linear motion.

An idea is presented where the total potential energy (∞E₀ₚ) is considered to be equal to the sum of potential energy (∆E₀ₚ) at each individual point within a theoretical 0ₜₕ-dimensional space. This space is conceptualized as a collection of points, each lacking measurable size or dimensions. It's a concept involving an infinite sum of potential energy changes happening at numerous tiny, indivisible points without spatial extent. The equation below attempts to explain how the sum of these extremely small potential energy changes across all these theoretical points within this dimensionless space could potentially result in an overall infinite potential energy. However, it's important to note that such a theoretical framework is deeply rooted in abstract concepts and might not have direct real-world physical implications or practical interpretations.

∞E₀ₚ = ∫ ΔE₀ₚ dx (integral over the domain representing points in a 0ₜₕ-dimensional space). 

The equation ∞E₀ₚ = ∫ ΔE₀ₚ dx represents an abstract conceptualization involving potential energy (∞E₀ₚ) being equal to the integral (∫) of infinitesimal potential energy (ΔE₀ₚ) with respect to a differential element (dx), where the integral is taken over the domain representing points in a 0ₜₕ-dimensional space.

Such an oscillating point existence, in a 0ₜₕ-dimensional space with linear oscillation, signifies a noneventful energetic state devoid of time in the absence of changing events. 

The transition from ∞E₀ₚ = ∫ ΔE₀ₚ dx to ∞E₀ₖ = 0 embodies a transformative process wherein infinite or significant potential energy (∞E₀ₚ) diminishes to a state of non-manifestation (E₀ₖ = 0). This transformation signifies the absence of energy manifestation, denoting a noneventful state within a linear space devoid of time. Additionally, it describes how this transformation indicates an absence of energy manifestation, leading to a noneventful state within a linear space without time, where events don't occur and time doesn't progress. This transformation of energy from positional to vibrational energy highlights the concept of a noneventful existence within a linear space devoid of temporal progression.

∞E₀ₖ = 0 symbolize the transformation or conversion of infinite or substantial potential energy (∞E₀ₚ) into a state where energy ceases to manifest (E₀ₖ = 0) due to the non-eventful existence or lack of progression within the context of linear space without time. 

A sinusoidal oscillation transforms its potential energy (equilibrium position) into periodic energy. Such oscillations convert potential energy (ΔE₀ₚ) into vibrational energy (ΔE₀ₖ) within a periodic signal. This periodic signal possesses a specific frequency (f₀) and amplitude. This oscillation produces a periodic signal represented by a sinusoidal wave. Sinusoidal or harmonic oscillation is a type of oscillation that produces an output using a sine waveform.

An initiation of an energetic disruption or instability, represented by ΔE₀ₖ, at a specific location within an origin point. This disturbance leads the energetic point to commence oscillation, characterized by its linear motion that causes interference or disturbance in the surrounding potential.

∞E₀ₖ = ∫ ΔE₀ₖ dx to ∞E₀ₚ embodies a transformative process wherein infinite or significant potential energy (∞E₀ₚ = ∫ ΔE₀ₚ dx) diminishes to a state of manifestation (∞E₀ₖ = ∫ ΔE₀ₖ dx).

The equation ∞E₀ₖ = ∫ ΔE₀ₖ dx to ∞E₀ₚ portrays a transformative process where the manifestation of infinite or substantial potential energy (∞E₀ₚ) transitions or diminishes to a state of manifestation (∞E₀ₖ). This equation suggests a shift from a state of significant or boundless potential energy (∞E₀ₚ) to a state denoting a realized or manifested form of energy (∞E₀ₖ), representing the integration of changes in potential energy (∆E₀ₚ and ∆E₀ₖ) across a domain (dx).

XIII) Emergence of Existence and Dimensions in Events, Space, and Time:

A linear dimensional point, when vibrating within two-dimensional states, generates two-dimensional space upon entering two or three-dimensional spaces, thereby initiating events and the passage of time.                                   

To be continued ...

Section II: Energy Beyond the Planck Time:

2. A Journey into Existence: Energy Beyond the Planck Time:

The exploration of the extension of existing physical principles into mathematical abstraction, geometry, and multidimensional frameworks can be represented conceptually. Here's a concise abstraction of this research approach:

I) Mathematical Abstraction: The study seeks to transcend empirical observations into abstract mathematical models that can encapsulate and describe phenomena beyond the scope of conventional physical laws. These mathematical abstractions aim to provide a theoretical foundation for understanding energy dynamics beyond the Planck time.

II) Geometric Interpretations: Utilizing geometry as a tool, the research employs spatial representations and geometrical constructs to visualize and potentially model the behaviour of energy at extreme temporal scales. Geometric interpretations may aid in conceptualizing the interplay of forces or energies in higher-dimensional spaces.

III) Multidimensional Frameworks: By extending beyond traditional three-dimensional space, the study incorporates multidimensional frameworks to accommodate complexities inherent in hypothesized energy dynamics beyond the Planck time. These frameworks may involve mathematical spaces with dimensions beyond the familiar three spatial dimensions and one temporal dimension.

In summary, the research employs mathematical abstraction, geometric visualization, and multidimensional frameworks to explore and possibly model the behaviour of energy beyond the Planck time, aiming to extend existing physical principles into abstract mathematical representations for a deeper understanding of fundamental forces and temporal scales.

Section I: Investigating Nonexistence and Existence in Cosmic Origins:

1. The Big Bang model suggests the universe originated as a single point expanding and stretching with infinite energy density, contradicting the steady state theory and causing its current size. The Planck scale represents the universe's smallest units, determined by constants. Pixelation, a term for fuzziness or blurry sections, is used to describe quantum gravity effects or when current theories fail to accurately describe reality. The Planck time, which is the time it takes for light to travel 1 Planck length to zero, is the first event after the Big Bang, and no current physical theory can describe periods shorter than this. Before the Big Bang event, a time classified as a Planck time, all four fundamental forces were unified into one force - gravity, and matter, energy, space, and time inflated outward from the original singularity. However, no physical knowledge exists about this location before the Big Bang event. The study aims to explore the position field before the Big Bang event using mathematical, geometry, and extra dimensions, guided by existing physical theories and structure. The goal is to find the conditions of the position field before the event, allowing for the mathematical hypothesis of non-existence represented by an array of infinite points in equilibrium positions. The above description conveys that (i) human perception perceives existence within the dimensions of the Planck scale, Planck time, or the threshold frequency, (ii) imperceptible existence lies beyond the limits of the Planck scale, Planck time, or the threshold frequency, and (iii) this imperceptible existence encompasses pre-big bang states, non-eventful energetic potential existences in point forms, and does not entail time in the absence of changing events.    

Therefore, embarking on a journey into existence would commence by transitioning from non-eventful, timeless energetic potential existences in point forms to imperceptible, eventful temporal existences lying beyond the boundaries of the Planck scale. It would then progress to observable, eventful temporal existence within the dimensions of the Planck scale, and eventually expand into imperceptible, eventful temporal existence within hyperspace.

A Journey into Existence, Oscillations, and the Vibrational Universe: Unveiling the Origin:

Bharat of the Universe 

DOI: http://dx.doi.org/10.13140/RG.2.2.12304.79361

08 December, 2023

Soumendra Nath Thakur⁺

1. Abstract:

This investigation delves into the prospect of energy existence beyond the Planck time, drawing insights from conservation principles and empirical observations of dark matter and dark energy. The study seeks to navigate uncharted territories within physics, mathematics, and cosmology, presenting a conjectural notion of a potentially non-eventful vibrational universe.

The hypothesis intertwines speculative hypotheses, theoretical conjectures, and abstract phenomena to postulate a framework beyond empirical validation. Fundamental concepts such as energy transformations, gravitational forces, oscillations, and dimensional formations constitute pivotal elements in this speculative model.

Central to this supposition is the conceptual linkage between oscillatory behaviour and the generation of dimensions, postulating an abstract correlation that might elucidate the emergence of space and time from non-eventual states.

Acknowledging its limitations, this theoretical framework rests upon non-experimental mathematical abstractions, detailing the conversion of positional to vibrational energy, hinting at the existence of a vibrational non-eventual universe lying beyond empirical observations.

Furthermore, the abstract contemplates the temporal evolution of the universe, contemplating the diminishing influence of initial vibrations as the universe expands and progresses. This introduces the notion of a "dead past," suggesting a phase where the universe transcends the impact of its initial vibrations.

This speculative abstract aims to provide a theoretical lens for contemplating fundamental questions about the universe's genesis and progression, albeit rooted in conjectures and abstract constructs, encouraging further theoretical exploration.

Keywords:

Origin of Universe, Vibrational Universe, Oscillations, Existence, Space-time Formation, Energetic Oscillations, Dimensional Evolution, Gravitational Forces, Point Existence, Planck Scale Exploration,

⁺ Tagore’s Electronic Lab, India

⁺ ORCiD: 0000-0003-1871-7803

The Author declares no conflict of interest.

2. Introduction:

The hypothesis delves into the intriguing realms of cosmic origins, seeking to explore the fundamental nature of existence, dimensional evolution, and the dynamics shaping the universe. It investigates the intricate interplay between vibrations, oscillations, and the formation of space-time, aiming to comprehend the emergence of our cosmos from a standpoint of energetic existence and non-eventual oscillations. This exploration navigates the hypothetical inception of the universe, from the ambiguous pre-Big Bang epoch to the manifestation of space, time, and energy through oscillatory phenomena. Leveraging mathematical, geometrical, and multidimensional concepts, this study unfolds an intricate narrative, bridging the abstract notions of existence, dimensional transitions, and gravitational forces that potentially orchestrate the evolution of our universe.

3. Methodology:

The methodology adopted in this hypothesis revolves around a multidisciplinary approach, amalgamating concepts from physics, mathematics, geometry, and theoretical frameworks to probe the genesis and evolution of the universe. It employs both deductive reasoning and speculative exploration to unravel the complex dynamics governing cosmic origins and dimensional transitions. Here's a breakdown of the methodology:

Theoretical Framework Utilization: Leveraging existing physical theories and mathematical concepts, the hypothesis navigates through speculative landscapes, utilizing principles from quantum mechanics, gravitational theories, and fundamental forces to construct a plausible narrative of cosmic emergence.

Mathematical/Geometrical Exploration:

The methodology employs mathematical abstractions and geometrical models to conceptualize and describe the transition from an initial state of non-eventual existence to the formation of multidimensional space and time. It delves into dimensions beyond the traditional three spatial dimensions, exploring higher-dimensional constructs and their implications.

Conceptual and Abstract Reasoning: Using abstract concepts of vibrational energy, oscillations, and non-eventual existence, the methodology formulates hypothetical scenarios to explain the formation of space-time and the evolution of the universe. It intertwines theoretical reasoning with abstract notions to provide a coherent narrative.

Progressive - Interlaced Oscillation Paradigm:  Proposing the Progressive and Interlaced oscillations as a mechanism for dimensional progression, the methodology seeks to explain how linear, planar, and higher-dimensional spaces might have emerged from oscillatory phenomena.

Integration of Forces and Energy Transitions:  It explores the integration of forces, particularly gravitational forces, with energetic transitions, aiming to link energy changes with force manifestations, especially regarding the conversion of positional energy into vibrational energy and its implications for gravitational forces.

Temporal Evolution and Universe's Lifecycle: Analysing the impact of initial vibrations on the formation of the universe and considering the diminishing influence of these vibrations as the universe evolves, expands, and establishes its own dynamics over time.

Limitation Acknowledgment:

Acknowledging the speculative and theoretical nature of the methodology, the study recognizes the limitations of extrapolating beyond the observable or testable realms, grounding itself in the bounds of theoretical exploration.

The methodology amalgamates speculative reasoning, mathematical models, abstract concepts, and theoretical frameworks to weave a narrative explaining the cosmic genesis, dimensional evolution, and the interplay of forces and energies in shaping the universe.

4.1 Mathematical Presentation:

The mathematical, geometrical, and dimensional presentation within the hypothesis employs a blend of theoretical frameworks, abstract concepts, and geometric interpretations to explore the genesis of the universe, the formation of dimensions, and the transition from non-eventual existence to multidimensional space-time. Here's an analysis of its key components:

Mathematical Abstractions: The hypothesis utilizes mathematical abstractions to describe the transition from non-existence to existence, often relying on symbolic representation. For instance, it employs the equation ∞E = 0 to symbolize the transformation of infinite potential energy (∞E) to a state where energy ceases to manifest (E = 0), depicting the conversion of positional energy to vibrational energy without adherence to time.

Geometric Interpretations:

It incorporates geometric interpretations to visualize the formation of dimensions. The portrayal of points, oscillations, and vibrations in geometric contexts helps illustrate the emergence of linear, planar, and higher-dimensional spaces. This includes the visualization of linear oscillations as movements along axes, planar oscillations forming two-dimensional planes, and higher-dimensional oscillations creating multi-dimensional spaces.

Dimensional Progression: The hypothesis explores the notion of progressive and interlaced oscillations as mechanisms for dimensional progression. It describes the sequential formation of linear dimensions (D₁), followed by planar dimensions (D₂), and further interlaced oscillations resulting in higher-dimensional spaces (D₃, Dₜ, Dₙ). This progression is presented in both mathematical notation and geometric illustrations.

Temporal and Spatial Dimensions: It addresses the dimensional hierarchy by associating specific dimensions with spatial and temporal aspects. Linear dimensions (D₁) correspond to one-dimensional spatial events, while planar dimensions (D₂) represent two-dimensional spatial events. Temporal dimensions (Dₜ) are introduced as abstract time dimensions intertwined with spatial dimensions in a higher-dimensional framework.

Coordinate System Representation: The hypothesis utilizes coordinate systems to symbolically represent dimensions. It uses Cartesian coordinates, such as ℝ¹ for linear dimensions, ℝ² for planar dimensions, and extends this notation to higher dimensions (ℝ³, ℝ⁴, and beyond) to depict spatial and temporal constructs.

Energy-Force Equivalence: It attempts to establish a connection between energy changes and forces, particularly gravitational forces. The methodology suggests that energy changes associated with vibrations imply gravitational force, implying a potential link between energy transitions and force manifestations.

The mathematical, geometrical, and dimensional presentation within the hypothesis employs symbolic representations, geometric illustrations, and abstract concepts to elucidate the progression from non-existence to multidimensional space-time, offering a speculative framework for understanding the universe's genesis and dimensional evolution.

4.2 Scientific Presentation:

The scientific presentation within the hypothesis integrates theoretical concepts from physics, cosmology, and mathematical principles to offer an exploratory framework for understanding the universe's genesis and evolution. Here's an analysis of its scientific elements:

Big Bang and Cosmological Theories: It references the Big Bang theory and steady-state theory to introduce the notion of the universe originating from a singular point with infinite energy density. The hypothesis contrasts these theories to highlight the expansion of the universe and the emergence of space, time, matter, and energy from a primordial singularity.

Planck Scale and Quantum Gravity: It delves into the Planck scale, the smallest unit that defines the fabric of the universe, indicating where current theories face limitations, often referred to as pixelation. The hypothesis connects these concepts to quantum gravity effects and the challenge of describing reality accurately at these scales.

Pre-Big Bang Universe: The study aims to explore the conditions and characteristics of the position field before the Big Bang event, a period classified as the Planck time, where all fundamental forces were unified. It acknowledges the absence of empirical knowledge about this pre-Big Bang state and proposes mathematical, geometrical, and extra-dimensional approaches guided by existing physical theories.

Energetic Transformations and Oscillations: The hypothesis emphasizes the transition from positional energy to vibrational energy through the oscillations of energetic points, without adherence to time or event. It explores how these oscillations generate non-eventual energetic existence, initiating a chain of synchronized oscillations leading to the creation of space, time, and multidimensional fields.

Gravitational Forces and Momentum: It suggests a relationship between energetic changes, momentum, and gravitational forces. It hypothesizes that energetic changes in oscillations potentially involve momentum and gravitational force, attempting to connect energy transformations to gravitational interactions.

Primordial Universe Formation: The hypothesis proposes a synchronized process involving progressive and interlaced oscillations in the formation of space-time. It speculates that these oscillations form various dimensional fields and suggestively defines the synchronization of event dimensions with other dimensions.

Abstract Phenomenon and Vibrational Universe: It introduces abstract concepts like the approximation of oscillations, non-experimental mathematical phenomena, and a vibrational universe beyond Planck time, aiming to explore energy existence beyond empirical observation based on conservation laws and observations of dark matter and dark energy.

Conceptual Frameworks: The hypothesis presents conceptual frameworks encompassing linear, planar, and higher-dimensional spaces and their interconnections through oscillations. It attempts to establish correlations between oscillatory behaviors, spatial dimensions, and the emergence of time.

The scientific presentation within the hypothesis amalgamates theoretical physics, cosmological concepts, and speculative mathematical frameworks to explore the nature of the pre-Big Bang universe, energetic transformations, and the possible evolution of dimensions and forces, thereby offering a conjectural perspective on the universe's origins and fundamental physical interactions.

5. Discussion:

The discussion within the hypothesis extends across various theoretical and conceptual realms, examining the implications and potential interpretations of its proposed ideas. Here's an analysis of the discussion:

Theoretical Synthesis: It synthesizes concepts from various theoretical frameworks in physics, cosmology, and mathematics to propose a speculative framework for understanding the universe's origins and evolution. The discussion attempts to integrate ideas from the Big Bang theory, quantum physics, Planck scale, and gravitational forces into a cohesive narrative.

Pre-Big Bang Universe: It critically addresses the limitations of current physical knowledge regarding the state of the universe before the Big Bang event. The discussion acknowledges the challenges in describing a pre-Big Bang era and aims to fill this gap using mathematical and geometrical approaches guided by existing physical theories.

Energy Transformations and Oscillations: The discussion delves into the nature of energetic transformations from positional to vibrational energy through oscillations. It explores the hypothetical creation of non-eventual existence through the oscillatory behaviour of energetic points, emphasizing the absence of time and events in this energetic conversion process.

Gravitational Forces and Momentum: It discusses the speculative relationship between energetic changes, momentum, and gravitational forces. The hypothesis suggests that energy changes during oscillations may involve momentum and gravitational forces, although this is presented as conjectural and speculative rather than empirically supported.

Primordial Universe Formation: The discussion revolves around the proposed synchronized process involving progressive and interlaced oscillations in the formation of space-time. It explores how these oscillations might have led to the creation of dimensions and their synchronization, suggesting the origins of space-time dimensions from energetic transformations.

Abstract Phenomena and Vibrational Universe: It explores abstract phenomena related to oscillations, non-experimental mathematical concepts, and a vibrational universe beyond the Planck time. The discussion attempts to speculate on the existence of energy beyond empirical observation, based on conservation laws and observations of dark matter and dark energy.

Conceptual Correlations: The discussion attempts to correlate conceptual frameworks related to linear, planar, and higher-dimensional spaces through oscillatory behaviors. It seeks to establish theoretical connections between oscillatory patterns, spatial dimensions, and the emergence of time, although these connections remain speculative and conjectural.

The discussion within the hypothesis synthesizes various theoretical and speculative ideas to propose a conceptual framework for understanding the pre-Big Bang universe, energetic transformations, and the potential relationships between dimensions, forces, and time. However, it's important to note that the discussion predominantly relies on hypothetical and speculative constructs, lacking empirical evidence or experimental validation.

6. Conclusion:

The exploration into the theoretical landscape of a potentially non-eventful vibrational universe presents an abstract and speculative framework that delves into the genesis and fundamental structure of the cosmos. Rooted in mathematical and conceptual abstractions, this hypothesis postulates the existence of a pre-observable state of energy, beyond the confines of empirical validation.

The conjectural model highlights the transformative potential of oscillatory behavior, suggesting a correlation between vibrational energy, dimensional formations, and the emergence of space and time. Despite its speculative nature, this hypothesis offers a theoretical lens to contemplate the genesis of the universe, threading together concepts of energy transformations, gravitational forces, and oscillations.

A critical aspect introduced in this conjecture is the temporal evolution of the universe, proposing that the influence of initial vibrations may diminish as the universe evolves and expands. This notion of a "dead past" signifies a phase where the universe transcends the impact of its primordial vibrations, establishing its own dynamics and evolving beyond the initial perturbations.

While this speculative framework operates in the realms of abstraction and mathematical inference, it beckons further theoretical explorations, encouraging a deeper contemplation of the universe's origins and potential dimensions beyond empirical observations. The hypothesis opens avenues for discussions and future inquiries, stimulating theoretical investigations into the fabric of the universe and its enigmatic genesis.

This speculative hypothesis prompts a reconsideration of the fundamental aspects of cosmic existence, offering a conceptual canvas for ongoing discourse and theoretical reflections into the profound mysteries of the universe.

7. References:

These references aim to provide a comprehensive understanding of the various scientific concepts that are touched upon. The following references are suggested based on the general themes mentioned and may or may not be directly related to the hypothesis.

[1] Thakur, S. N. (2023, October 21). A Pure Mathematical Perspective: Dimensions, Numbers, and Mathematical Concepts. ResearchGate. https://doi.org/10.13140/RG.2.2.25942.01607

[2] The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory by Brian Greene

[3] Thakur, S. N. (2023, October 21). The Human Brain, Mind, and Consciousness: Unveiling the Enigma. ResearchGate. https://doi.org/10.13140/RG.2.2.29992.14082

[4] The Fabric of the Cosmos: Space, Time, and the Texture of Reality by Brian Greene

[5] Thakur, S. N., Samal, P., Modrzejewski, T., & Frederick, O. (2023, October 22). Energy Persistence Beyond Planck Scale. ResearchGate. https://doi.org/10.13140/RG.2.2.24267.57120

[6] A Brief History of Time by Stephen Hawking

[7] Thakur, S. N. (2023, October 27). A Pure Mathematical Perspective: Dimensions, Numbers, and Mathematical Concepts. https://doi.org/10.32388/msdjfa

[8] The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos by Brian Greene

[9] Thakur, S. N. (2023, November 3). Dimensional Analysis Demystified — Navigating the Universe through Dimensions. https://doi.org/10.32388/hnfbgr.2

[10] Gravitation by Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler

[11] Thakur, S. N., Samal, P., Bhattacharjee, D., & Frederick, O. (2023, November 7). Energy Persistence Beyond Planck Scale. ResearchGate. https://www.researchgate.net/publication/375488896_Energy_Persistence_Beyond_Planck_Scale

[12] The Quantum Universe: Everything That Can Happen Does Happen by Brian Cox and Jeff Forshaw

[13] Thakur, S. N. (2023, November 16). Wave Dynamics -Interplay of Phase, Frequency, Time, and Energy. ResearchGate. https://doi.org/10.13140/RG.2.2.16473.70242

[14] The Nature of Space and Time by Stephen Hawking and Roger Penrose

[15] Thakur, S. N. (2023, November 22). The Journey from Einstein’s Cosmological Constant to Dark Energy: ResearchGate. https://doi.org/10.13140/RG.2.2.28823.14242

[16] Cosmos by Carl Sagan

[17] Malek, A. (2023, November 24). QUASARS – POINTERS TO AN INFINITE, ETERNAL AND DIALECTICAL UNIVERSE AND A REPUDIATION OF THE BIG BANG COSMOLOGY. Journal of Advances in Physics. https://doi.org/10.24297/jap.v21i.9551

[18] The Physics of the Universe by Richard Fitzpatrick

[19] Scientific papers and publications on quantum physics, cosmology, and string theory from journals like Physical Review Letters, Nature, and Science.

*-*-*-*-*

The hypothesis titled 'A Journey into Existence' is presented in sectional summaries:

Summary: A Journey into Existence:

Item 1 delves into the investigation of diverse forms of existence and non-existence in the context of cosmology. It addresses the theoretical exploration of the universe's origins, specifically focusing on the Big Bang theory's proposal of the universe originating from a single point. This idea contradicts the steady-state theory and highlights the universe's current expansion from an infinitesimally dense state. The study aims to employ mathematical, geometric, and extra-dimensional approaches to understand the state preceding the Big Bang and potentially hypothesize a mathematical model portraying non-existence through an array of infinite equilibrium points.

Keywords: Cosmology, Big Bang theory, Universe's origins, Expansion, Equilibrium points, 

Items 2 and 3 collectively explore the nature of a point within a theoretical context. They outline that a point, devoid of physical existence or dimensions, symbolizes a location in space, serving as a starting reference for drawing shapes in mathematics. These items delve into the concept of an energetic point oscillating from its equilibrium state, converting positional energy into vibrational energy in a noneventful, linear space devoid of time. They emphasize the absence of physical attributes associated with points and their oscillations, presenting a theoretical scenario outside conventional physics, rooted in abstract mathematical principles.

Keywords: Nature of a point, Energetic point, Oscillating point, Noneventful space, Abstract mathematical principles, 

A combined summary of items 4, 4.1, and 4.2: These items delineate the emergence of existence, space, and time from energetic and material perspectives. The emergence of events, space, and time arises when linear dimensional points undergo vibrational energy, initiating two-dimensional spaces and progressing into three-dimensional spaces. The "Energetic Universe" item discusses sinusoidal oscillations in three-dimensional space and the transformation of positional energy into periodic energy, while the "Material Universe" item focuses on linear oscillations and harmonic motion governed by restoring forces proportional to displacement. Both energetic and material aspects underscore the synchronization of energetic oscillations among points, forming potent energetic-gravitational fields attributed to these oscillations. These items collectively illustrate the interconnectedness between oscillations and the consequential emergence of multi-dimensional spaces within the universe.

Keywords: Emergence of existence, Vibrational energy, Energetic Universe, Material Universe, Multi-dimensional spaces, 

A combined summary of items 5, 5.1, 5.2, 5.3, and 5.4: These items collectively explore the emergence of existence through energetic oscillations, progressing from linear to multi-dimensional fields. They depict how oscillating points generate vibrational energy, leading to an infinitesimal existence without adherence to time (∞E = 0). The discussions of progressive and interlaced oscillations describe the sequential development and synchronization of oscillations, forming multi-dimensional energetic fields. Furthermore, these oscillations play a crucial role in the emergence of space and time within the universe. The concept of disrupted equilibrium points emphasizes the interconnectedness of points within the chain, demonstrating how perturbations impact the entire system, ultimately leading to the formation of a three-dimensional robust field with infinite energy (∞E) and gravitational form.

Keywords: Energetic oscillations, Multi-dimensional fields, Space and time emergence, Disrupted equilibrium points, Infinite energy, 

Item 6 delves into the coordinated process behind the genesis of the early universe. It highlights how the establishment of space and time involves synchronized occurrences through progressive and interlaced oscillations. These oscillations sequentially create two-dimensional energetic domains and subsequently higher-dimensional energetic fields, encapsulating space and time. The text emphasizes that temporal dimensions consistently form as linear dimensions above spatial or hyper spatial dimensions in this coordinated process of universe formation.

Keywords: Coordinated process, Genesis of the early universe, Progressive and interlaced oscillations, Higher-dimensional energetic fields, Temporal dimensions, 

Item 7 delves into the conceptual framework of dimensions and the formation of the primordial universe. It elaborates on space as a linear dimensional continuum containing positions and directions. Describing planes as coordinate systems specifying points through pairs of real numbers, it elucidates the uniqueness of points in multi-dimensional Euclidean spaces. This item establishes a foundational understanding of abstract and real events within different dimensional frameworks in the early universe.

Keywords: Conceptual framework, Dimensions, Primordial universe, Euclidean spaces, Multi-dimensional, 

Items 8 and its sub-items introduce the expression of physical quantities as functions of fundamental dimensions. It details the representation of a physical quantity (Q) as a function of its fundamental dimensions (L, W, H, T). Subsequently, it elaborates on these dimensions: L¹ (Linear Dimension), L² (Planar Dimension), L³ (Spatial Dimension), and L⁴ (Hyper spatial Dimension), outlining their individual roles and significances within the dimensional framework.

Keywords: Physical quantities, Fundamental dimensions, Linear dimension, Planar dimension, Spatial dimension,

Items 9 and its sub-items delve into oscillation dynamics and the formation of dimensions in an abstract sense. It elaborates on the movements and behaviours of oscillating points: how they move from their original positions and synchronize to create various energetic planes. Progressive oscillation represents planar movements, synchronizing horizontal and vertical movements to form two-dimensional energetic planes. Interlaced oscillation involves synchronizing linear oscillations between two two-dimensional energy planes. Moreover, synchronized movements forward and backward, along with up and down, generate additional two-dimensional energetic planes. Interlaced oscillation unites all energetic planes, ultimately culminating in the creation of a three-dimensional energetic space. As the original point's oscillation impacts the interconnected equilibrium points, the entire system oscillates, rapidly expanding, and initiating the formation of a robust three-dimensional field with infinite energy and gravitational form.

Keywords: Oscillation dynamics, Energetic planes, Progressive oscillation, Interlaced oscillation, Three-dimensional space,

Item 10 explores the concept of chain synchronized energetic oscillation originating from an equilibrium state. It delves into how a series of synchronized energetic oscillations emerge when an energetic point moves from its equilibrium state, inducing a coherent synchronized oscillation among corresponding points. This phenomenon results in the formation of a robust energetic-gravitational field due to the energetic oscillation.

Keywords: Chain synchronized oscillation, Equilibrium state, Synchronized energetic oscillations, Robust energetic-gravitational field, Energetic point,

Items 11 and its sub-items collectively explore the formation of imperceptible existence through the intricate mechanisms of progressive and interlaced oscillations. They elucidate how interlaced oscillations, whether continuous or abstract, contribute to the creation and development of dimensions, leading to the emergence of complex spatial and temporal frameworks within the universe.

Keywords: Imperceptible existence, Progressive oscillations, Interlaced oscillations, Spatial and temporal frameworks, Emergence of dimensions,

Items 12, 13 and 14: These items delve into the exploration of a noneventful vibrational universe and its probable existence, examining the impact of initial vibrations on the evolution of the universe beyond its formation. They aim to understand how these vibrations, albeit non-eventual, potentially shaped the universe's past and influenced its evolutionary trajectory.

Keywords: Noneventful vibrational universe, Probable existence, Initial vibrations, Evolution of the universe, Evolutionary trajectory,

Answered the question, 'Is there a reasonable alternative to the theory of the expanding universe?':

<<Is there a reasonable alternative to the theory of the expanding universe?>>

(1) The question itself is not reasonable because, Einstein had already abandoned his alternative concept of a static universe. Einstein used a cosmological constant Λ to represent the constants of the universe. He modelled the universe on the basis that the universe is stationary, isotropic and homogeneous.

The theory of the expansion of the universe developed from the observed redshift of celestial objects, the space between which galaxies are increasing, so that the relevant galaxies appear to be moving away from us at a speed that increases with their distance. Hubble's brilliant observation that the redshift of galaxies, announced in 1929, was directly proportional to the galaxy's distance from Earth.

Therefore, Einstein's cosmological constant was abandoned after Edwin Hubble's confirmation that the universe was expanding. Einstein called the idea of cosmic repulsion 'the biggest blunder of my life'. Thus, the only reasonable alternative to the theory of an expanding universe was a static universe. Reply @ResearchGate

<<We know that our star, the Sun loses about 10⁻¹⁴ (unit?) of its mass per year as a result of electromagnetic radiation and particle emission. That reduction in mass should show up as a decreasing gravitational red shift. Same thing should happen to entire galaxies.>>

(2) It is not a valid statement that mass loss should show up as a decreasing gravitational redshift. The mass loss of stars and galaxies does not affect the known gravitational redshift.

The reasons:

As we know that the gravitational redshift, also known as Einstein shift, is the phenomenon that electromagnetic waves or photons traveling out of a gravitational well lose energy. While the energy of a photon, at emission form a star, corresponds to its frequency, which are the same for from any stars, regardless from the Sun or from a star in any galaxy. This loss of energy corresponds to a decrease in the wave frequency and increase in the wavelength, generally known as a redshift.

Gravitational redshift can be explained as a consequence of the equivalence principle that gravity and acceleration are equivalent and the redshift is due to the Doppler effect. The relativistic Doppler effect is a change in the frequency, wavelength, and amplitude of light caused by the relative motion of the source and observer, as in the classical Doppler effect, when considering the effects described by the special theory of relativity. Where, relative Doppler effect = λᵣ/λₛ = fₛ/fᵣ = Doppler factor = √{(1-β)/(1-β)}, where β = v/c > 0. The initial energy of an emitted photon from any star is (E) = 4.0 × 10⁻¹⁹ J. Hence the corresponding frequency of an emitted photon is (f) = 6.0368 × 10¹⁴ Hz.

From the above explanations, we can see that the Doppler factor (fₛ/fᵣ) causes the red shift due to the speed of the (photon) wave, because the emission frequency of the photon is the source frequency (fₛ) which is always 6.0368 × 10¹⁴ Hz and the received frequency (fᵣ) is the corresponding distance's speed, causes red shift. The photon loses energy (ΔE) due to the gravitational effect of the photon source, which corresponds to a change in frequency (Δf) = (fₛ - fᵣ), a corresponding redshift due to the increase in photon wavelength (λᵣ/λₛ). The photon is massless, its interaction with the gravitational source or the emission source, remains the same regardless of gravitational intensity. Doppler redshift depends more on the distance between the source and the receiver. Reply @ResearchGate

- Soumendra Nath Thakur