Soumendra Nath Thakur
Tagore’s Electronic Lab, India
ORCiD: 0000-0003-1871-7803
postmasterenator@gmail.com
Date: 19-12-2023
http://dx.doi.org/10.13140/RG.2.2.15838.82245
Chapter: X-I
Embarking on a journey beyond the Planck scale involves transcending familiar temporal dimensions to explore spatial realms that extend beyond our observable limits. This endeavour requires employing theoretical frameworks and abstract mathematical models to predict phenomena outside our current grasp, much akin to how time representation relies on physics and mathematics theories.
The exploration navigates through non-eventful, timeless energetic potential existences in point forms, transcending imperceptible, eventful temporal existences beyond the Planck scale and progressing to observable, eventful temporal existence within the Planck scale's dimensions. The aim is to expand into higher dimensional spaces, offering mathematical hypotheses about realms devoid of conventional existence—an intricate lattice of infinite equilibrium points.
At the core of this exploration are fundamental principles in mathematics and physics, particularly those concerning the total energy of a system. In classical and quantum mechanics, the Hamiltonian operator (H) symbolizes the system's total energy (E), comprising kinetic energy (E₀ₖ) and potential energy (E₀ₚ). Oscillations, whether linear or harmonic, introduce restoring forces linked to displacement, shaping the dynamics of a system.
Furthermore,
delving into the essence of points in mathematical terms, these entities
signify exact locations devoid of physical presence or temporal attributes.
When initiating an oscillation from equilibrium, these points disrupt
surrounding potentials, signifying a transition from positional to vibrational
energy without the formation of time or space.
This investigation traverses beyond Planck time, aiming to explore cosmic origins and the pre-Big Bang landscape. It ventures into territories where human perception of existence, constrained by dimensions and time scales within the Planck limit, gives way to imperceptible existence encompassing energetic potential existences devoid of time and changing events.
The theoretical journey unfolds by transitioning from non-eventful, timeless energetic potential existences in point forms to imperceptible, eventful temporal existences beyond Planck limits. It proceeds to observable, eventful temporal existence within Planck scale dimensions and expands into imperceptible, eventful temporal existence within higher-dimensional spaces.
Drawing on conservation principles, dark matter observations, and gravitational forces, this pursuit navigates uncharted terrains, presenting a conjectural notion of a potentially non-eventful vibrational universe—where oscillatory dynamics within an array of equilibrium points give rise to multidimensional energetic spaces.
Mathematical Presentation:
In the initial 0ₜₕ-dimensional domain, a state where ∞E₀ₖ equals zero and is devoid of temporal reference, the absence of manifestations and events characterizes a noneventful condition of non-oscillating points. These points exist without disturbances or manifestations, displaying a state of equilibrium devoid of any disturbances or events.
Within this realm, the absence of disturbances or equilibrium states characterizes the infinitesimal potential energy (∞E₀ₚ). These points exist without any temporal attributes or progression, representing an infinite array of infinitesimal potential energy points in a perpetual state of equilibrium without temporal progression or events.
A
destabilization in the initial origin point, either due to an optimal
collection of potential points or the introduction of infinitesimal kinetic
energy, characterizes a noneventful oscillation of the origin point.
In a domain devoid of temporal reference and lacking events, where the absence of manifestations and events characterizes a noneventful oscillation of a point, devoid of time and disturbances, this point exists within a realm void of temporal attributes. It forms infinitesimal vibrational energy without temporal progression or events.
Following this context, consider the initial energetic point perturbing the associated potential points across various axes—up and down, front and back, left and right. The disturbance caused by this initial energetic point reverberates throughout the entirety of the system of potential points along these axes.
This disturbance in the equilibrium state disrupts the entire system of potential points, initiating a cascading effect through the domain, perturbing points in a 0ₜₕ-dimensional space. This perturbation leads to an initial formation where the infinite potential energy (∞E₀ₚ) equals the integral of incremental potential energy changes (∫ ΔE₀ₚ dx).
This conversion and perturbation process result in the diminishment of the infinite potential energy (∞E₀ₚ) to a state of manifestation, where the infinite kinetic energy (∞E₀ₖ) now equals the integral of incremental kinetic energy changes (∫ ΔE₀ₖ dx). This transformation signifies a state where the infinite total energy (∞E₀ₜₒₜ) equals the sum of kinetic and potential energies, with potential energy reduced to zero (∞E₀ₜₒₜ = E₀ₖ + E₀ₚ; E₀ₚ = 0).
This sequence outlines the progression from noneventful oscillation characterized by a destabilized origin point to disturbances and perturbations in a zero-dimensional space, illustrating the transformation from infinite potential to kinetic energy within a system of associated points in equilibrium.
Where, mathematical entities are used to describe and quantify the energy states, perturbations, and transformations within the described system, illustrating the progression and equilibrium of energy within the system.
• ∞E₀ₖ: Denotes
infinite kinetic energy.
• ∞E₀ₚ: Represents
infinite potential energy.
• 0ₜₕ-dimensional:
Specifies a zero-dimensional space.
• ∫
ΔE₀ₚ dx:
Indicates the integral of incremental potential energy changes over a domain.
• ∫
ΔE₀ₖ dx:
Represents the integral of incremental kinetic energy changes over a domain.
• ∞E₀ₜₒₜ: Signifies the
infinite total energy within the system.
• E₀ₖ + E₀ₚ: Represents the sum of kinetic and potential energies.
