Soumendra Nath Thakur
ORCiD: 0000-0003-1871-7803
Correspondence: postmasterenator@gmail.com
DOI: http://dx.doi.org/10.13140/RG.2.2.29274.25285
December 08, 2024
Abstract:
This study investigates the applicability of micro-scale
equations for frequency phase shift and time shift, specifically the equation
T(deg) = x°/f·360°, which accounts for 1/360th of respective time periods,
wavelengths, or energy values in standard units. The equation highlights its
precision in analysing periodic phenomena at the Planck scale, with a focus on
the Planck time (Tₚₗₐₙₖ) and its reciprocal relationship
with Planck frequency and wavelength. By dividing the Planck time by a 1° phase
shift of Planck time (1.498×10⁻⁴⁶ seconds), a near-complete 360°
phase cycle is observed, offering insights into the temporal structure of the
universe and its origins from the Big Bang. This framework underscores the
interconnectedness between time, wavelength, and energy, emphasizing the
significance of phase relationships in cosmology.
Keywords:
Planck time, frequency phase shift, time shift, Big Bang,
micro-scale, periodicity, phase cycle, Planck units, wavelength, energy,
cosmology, temporal structure, phase relationships
The power of the derived equation for frequency phase
shift and time shift:
The applicability of the micro scale derived equations for
frequency phase shift and time shift, capable of accounting for 1/360th of the
respective time period, wavelength, or energy values when measured in standard
units:
T(deg) = Δt = x°/f·360°
This derived equation showcases its power by providing a
framework to calculate precise phase relationships in terms of time,
wavelength, or energy values. This equation is applicable at the micro scale
and is capable of accounting for 1/360th of these respective values when
measured in standard units. This precision highlights its versatility in
analysing the periodic nature of fundamental physical phenomena.
The Planck time (Tₚₗₐₙₖ) is a cornerstone of this
framework, with its value defined as 5.391247(60) × 10⁻⁴⁴ seconds. The divisor, 1.498×10⁻⁴⁶ seconds, represents a 1° phase shift of Planck time,
emphasizing its relevance at the Planck scale. Within the domain of Planck units,
fundamental constants interrelate in a profound manner, allowing the Planck
time to act as the smallest meaningful unit of time, while the Planck frequency
(fP) serves as the highest possible frequency. This reciprocal relationship
underscores the fundamental periodicity and interconnectedness of these units.
In this context, the equation demonstrates that 1/360th of
Planck time (Tₚₗₐₙₖ) aligns with 1/360th of the
Planck wavelength (λₚₗₐₙₖ) and corresponds to 1/360th of
the time period of Planck frequency. This alignment reinforces the inherent
periodic structure embedded within the Planck units.
When dividing 5.391247(60) × 10⁻⁴⁴ seconds by 1.498×10⁻⁴⁶ seconds, the exact quotient is
approximately 359.8963°, leaving a remnant of approximately 1.3427 × 10⁻⁴⁶ seconds. This remnant, being nearly equal to the divisor, suggests
that it can be divided approximately 360 times, reflecting a complete 360°
phase cycle. This periodicity aligns closely with the foundational moment of
t₀, the beginning of the Big Bang, offering a phase-oriented perspective on the
temporal structure of the universe.
Human Perception of Zero and Hyper-Dimensions:
Human perception is inherently limited when dealing with
abstract mathematical constructs such as zero and hyper-dimensions. A point,
symbolized as '.', represents an exact spatial location without dimensionality,
serving as a cornerstone of mathematical abstraction. Real numbers, extending
infinitely in both positive and negative directions from zero on a
one-dimensional number line, reflect precise mathematical consistency. Yet,
translating these concepts into physical realities poses significant challenges.
For instance, humans struggle to perceive infinitesimally
small values such as the Planck length (ℓP), far beyond the thresholds of
perceptibility. Conversely, gamma rays, with detectable wavelengths of λ,
highlight the stark disparity in scales that humans can observe. This
limitation underscores the vast spectrum of physical phenomena lying outside
direct human experience.
Furthermore, exploring hyper-dimensions beyond the
familiar three-dimensional space introduces additional complexities. These dimensions
defy intuitive comprehension, existing beyond conventional spatial boundaries.
Despite these challenges, the interplay between zero, hyper-dimensions, and
Planck-scale phenomena provides crucial insights into the fabric of the
universe. By linking mathematical abstraction to physical realities, we gain a
deeper appreciation of the intricate relationship between the observable and
the imperceptible, paving the way for new frontiers in understanding the
cosmos.
Conclusion
The derived equation for frequency phase shift and time
shift underscores the periodicity inherent in Planck units. The calculation
demonstrates that the Planck time (Tₚₗₐₙₖ) can be divided by a 1° phase
shift of Planck time (1.498×10⁻⁴⁶ seconds) approximately 360
times, completing a near-perfect phase cycle. This result reveals a fundamental
periodic structure in the temporal framework of the universe, suggesting a profound
interconnectedness between time, wavelength, and energy. The alignment of this
framework with a 360° phase cycle offers a deeper understanding of the origins
of the universe and its temporal dynamics, reinforcing the significance of
phase relationships in cosmology.
Discussion
This study presents a ground breaking perspective on the
temporal framework of the universe by leveraging micro-scale equations for
frequency phase shift and time shift. This discussion delves into the
implications, potential applications, and limitations of the research.
Implications for Cosmology
The equation offers a novel approach to understanding
periodic phenomena at the Planck scale, where the foundational units of time,
frequency, and wavelength are intricately interrelated. The study reveals that
the Planck time (Tₚₗₐₙₖ) can be divided approximately 360
times by a 1 phase shift of Planck time, culminating in a near-complete 360
phase cycle. This finding introduces a periodic structure within the Planck
units, aligning closely with the initial moments of the universe's existence,
specifically the Big Bang.
This periodicity challenges traditional notions of
continuous time by suggesting a discrete, cyclic framework at micro scales.
Such a framework could refine our understanding of early-universe physics,
offering insights into the transition from quantum-scale phenomena to
macroscopic cosmological dynamics.
Bridging Mathematical Abstraction and Physical Realities
By integrating the analysis of hyper-dimensions and
infinitesimal values with Planck-scale phenomena, the study addresses the
inherent disconnect between human perception and abstract mathematical
constructs. Human perceptual limitations hinder the direct observation of
Planck-scale phenomena, yet the study bridges this gap by linking these
imperceptible scales to observable cosmic phenomena, such as gamma rays. This
connection underscores the importance of mathematical abstraction in unveiling
the universe's hidden structures.
Exploring hyper-dimensions introduces additional
complexity but offers a richer tapestry for understanding the interplay between
time, space, and energy. The study’s findings, rooted in precise phase
relationships, could inspire advancements in theoretical physics and quantum
cosmology, enabling deeper insights into dimensions beyond our
three-dimensional experience.
Applications in Modern Physics
1. Quantum Mechanics and Cosmology: The derived
equation and its implications for phase cycles could enhance our understanding
of quantum oscillations and their influence on large-scale cosmic phenomena.
2. Energy Distribution in Early Universe: The
periodic structure of Planck time may inform models of energy distribution
during the Big Bang, refining simulations of the universe’s origins.
3. Gravitational Wave Analysis: Insights from phase
relationships could aid in the detection and interpretation of gravitational
waves, particularly those originating from the early universe.
Limitations and Future Directions
While the study presents a compelling framework, its
reliance on the precision of Planck-scale constants requires meticulous
validation. The near-complete but imperfect 360 phase cycle raises questions
about residual discrepancies and their physical interpretations. Additionally,
extending this framework to include hyper-dimensional dynamics necessitates
further exploration to ensure coherence with existing physical theories.
Future research could:
• Expand on the implications of the residual remnant (1.3427
× 10⁻⁴⁶) in
phase cycle calculations.
• Integrate these findings with quantum gravity theories
to explore the unification of forces.
• Investigate experimental approaches for observing phase
shifts at infinitesimal scales, potentially leveraging advancements in
high-energy physics.
Conclusion
This study contributes significantly to our understanding
of the temporal and periodic structure of the universe at its most fundamental
level. By elucidating the interconnectedness between Planck units, time, and
energy, it lays the groundwork for further exploration of the universe's
origins and the profound relationship between mathematical abstraction and
physical reality. The findings invite continued inquiry into the intricate
dance of periodicity, energy, and dimensionality that defines the cosmos.
Reference:
[1]
Thakur, S. N., & Bhattacharjee, D. (2023). Phase shift and infinitesimal
wave energy loss equations - [v1]. www.preprints.org/manuscript/202309.1831/v1
[2]
Thakur, S. N. Description of Planck Equation and Energy-Frequency Relationship.
https://www.researchgate.net/publication/375416343
[3]
Thakur, S. N. (2024). Unified Quantum Cosmology: Exploring Beyond the Planck
Limit with Universal Gravitational Constants. Qeios, 26U31C
https://doi.org/10.32388/26u31c
[4]
Thakur, S. N. (2024). Why is 1° time interval (T) the smallest meaningful
mathematical expression of the Planck frequency? ResearchGate
https://doi.org/10.13140/RG.2.2.32358.40001
[5]
Thakur, S. N. (2023). Quantum Scale Oscillations and Zero-Dimensional Energy
Dynamics: ResearchGate. https://doi.org/10.13140/RG.2.2.36320.05124
[6]
Thakur, S. N. (2023) et al. Energy Persistence Beyond Planck Scale.
ResearchGate https://www.researchgate.net/publication/375488896/
[7]
Thakur, S. N. Human's Imperceptions of Zero and Hyper-Dimension: Mathematical
Abstraction and Physical Realities https://www.researchgate.net/publication/381514768
#Plancktime, #frequency #phaseshift, #timeshift, #BigBang, #microscale, #periodicity, #phasecycle, #Planckunits, #wavelength, #energy, #cosmology, #temporalstructure, #phaserelationships,
