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
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Thakur, S. N. Description of Planck Equation and Energy-Frequency Relationship.
https://www.researchgate.net/publication/375416343
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Thakur, S. N. (2024). Unified Quantum Cosmology: Exploring Beyond the Planck
Limit with Universal Gravitational Constants. Qeios, 26U31C
https://doi.org/10.32388/26u31c
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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
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Thakur, S. N. (2023). Quantum Scale Oscillations and Zero-Dimensional Energy
Dynamics: ResearchGate. https://doi.org/10.13140/RG.2.2.36320.05124
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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
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