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Soumendra Nath Thakur

Soumendra Nath Thakur
Tagore's Electronic Lab. · Head

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148
Publications
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Introduction
He is an electronics and telecommunications engineer with decades of experience in the application, testing, and diagnosis of electronic devices. Currently, he researches theoretical physics. He has deep expertise from analogue to digital technologies and formerly ran Tagore's Electronic Lab in Kolkata. He holds a diploma in applied electronics and telecommunication and certifications in microprocessor, digital electronics, and programming, blending academic knowledge with practical expertise.

Publications

Publications (148)
Preprint
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The research paper provides a mathematical framework for understanding phase shift in wave phenomena, bridging theoretical foundations with real-world applications. It emphasizes the importance of phase shift in physics and engineering, particularly in fields like telecommunications and acoustics. Key equations are introduced to explain phase an...
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𝑨𝒃𝒔𝒕𝒓𝒂𝒄𝒕: Relative time emerges from relative frequencies. It is the phase shift in relative frequencies due to infinitesimal loss in wave energy and corresponding enlargement in the wavelengths of oscillations; which occur in any clock between relative locations due to the relativistic effects or difference in gravitational potential; result error...
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EasyChair:https://easychair.org/publications/preprint/9Vxm DOI:10.20944/preprints202409.1190.v3 _________________________________________________ This research paper explores the framework of Extended Classical Mechanics, with a focus on the Equivalence Principle, Mass, and Gravitational Dynamics. Volume 1 of this study re-examines the classical...
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This study presents an advanced extension of classical mechanics to examine photon dynamics and its parallels with cosmological phenomena, particularly dark energy. Central to this framework is the concept of effective mass (Mᵉᶠᶠ), a dynamic property uniting rest mass (Mᴍ) and apparent mass (Mᵃᵖᵖ). For photons, which have zero rest mass, their appa...
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A Symmetry and Conservation Framework for Photon Energy Interactions in Gravitational Fields by Soumendra Nath Thakur presents a conceptual and mathematical advancement in quantum mechanics, offering a novel approach that seeks to reconcile quantum mechanics with gravity. This study extends the framework for photon energy interactions within gravi...
Data
This study, Analytical Insights into Time Dilation and Time Distortion, provides a critical examination of the relativistic and conceptual interpretations of time, serving as a supplementary resource to the research titled Effect of Wavelength Dilation in Time-About Time and Wavelength Dilation. It investigates the distinction between time dilation...
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This study explores the foundational equations of Extended Classical Mechanics (ECM), offering a comprehensive framework for analysing energy and force interactions across distinct scenarios involving matter mass (Mᴍ), apparent mass (Mᵃᵖᵖ), and effective mass (Mᵉᶠᶠ). Key equations are presented, including the force equation, effective mass definiti...
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This research introduces an advanced framework in extended classical mechanics to explore photon dynamics and its connection to cosmological phenomena, particularly dark energy. Central to this framework is the concept of effective mass (Mᵉᶠᶠ), a dynamic property encompassing rest mass (Mᴍ) and apparent mass (Mᵃᵖᵖ). For photons, with zero rest mass...
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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,...
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This study presents a revised framework for understanding the photon-to-dark-energy transition, building upon Peter Rafay's hypotheses and integrating concepts from Extended Classical Mechanics (ECM). The research extends classical and quantum principles to provide a more mathematically consistent and theoretically robust model of photon behaviour...
Preprint
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This research explores the concept of photon dynamics, specifically focusing on the notion of effective mass (Mᵉᶠᶠ) and its implications for force interactions and energy-momentum exchanges in extended classical mechanics. While photons are traditionally considered massless, their energy (E = h·f) implies an equivalent mass via the famous equation...
Data
This study supplements A Symmetry and Conservation Framework for Photon Energy Interactions in Gravitational Fields by Soumendra Nath Thakur,[1][2] providing a deeper exploration of the distinctions between gravitational and anti-gravitational redshifts of light. It identifies two primary mechanisms: gravitational redshift (due to ΔEg), arising fro...
Preprint
Full-text available
This study supplements A Symmetry and Conservation Framework for Photon Energy Interactions in Gravitational Fields by Soumendra Nath Thakur, [1][2] providing a deeper exploration of the distinctions between gravitational and anti-gravitational redshifts of light. It identifies two primary mechanisms: gravitational redshift (due to ΔEg), arising fr...
Preprint
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This study advances the framework for understanding photon energy interactions within gravitational fields by delineating the distinct roles of intrinsic photon energy (E) and gravitational-interactional energy (Eg). Building on previous research into symmetrical energy and momentum exchanges, we explore how photons, while traversing gravitational...
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The study explores the universe's mass-energy composition, where 95% consists of dark energy and dark matter. Dark energy, with its distinctive property of negative pressure, drives the accelerated expansion of the universe. This work proposes an extended classical mechanics framework that integrates dark energy, dark matter, and effective mass as...
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This study highlights the transformative role of relativistic rest energy, extending our understanding beyond classical energy forms. Unlike kinetic, potential, and other classical energies, rest energy, expressed by E = m·c², reveals mass as intrinsic energy, crucial in nuclear reactions and high-energy physics.
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This study highlights the transformative role of relativistic rest energy, extending our understanding beyond classical energy forms. Unlike kinetic, potential, and other classical energies, rest energy, expressed by E = m·c², reveals mass as intrinsic energy, crucial in nuclear reactions and high-energy physics.
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This study investigates gravitational lensing as interpreted through general relativity (GR), which posits that massive celestial bodies induce curvature in spacetime, thereby bending light's path. In regions devoid of massive objects, spacetime remains relatively flat. However, the presence of such bodies disrupts this state, causing downward curv...
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This study investigates the fundamental equations governing photon behaviour in external gravitational fields due to electromagnetic-gravitational interaction, emphasizing their energy, momentum, and wavelength relationships. Building upon the pioneering contributions of Max Planck and Louis de Broglie, the analysis highlights key equations such as...
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The study explores the mathematical relationships between phase shifts in oscillatory wave frequencies, their corresponding time periods, and energy changes. It reveals that the time period associated with a 1° phase shift is directly proportional to the infinitesimal time shift Δt, and the change in energy ΔE is proportional to f₀ and inversely re...
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The study explores the mathematical relationships between phase shifts in oscillatory wave frequencies, their corresponding time periods, and energy changes. It reveals that the time period associated with a 1° phase shift is directly proportional to the infinitesimal time shift Δt, and the change in energy ΔE is proportional to f₀ and inversely re...
Data
The study explores the mathematical relationships between phase shifts in oscillatory wave frequencies, their corresponding time periods, and energy changes. It reveals that the time period associated with a 1° phase shift is directly proportional to the infinitesimal time shift Δt, and the change in energy ΔE is proportional to f₀ and inversely re...
Data
This supplement study explores how light, or photons, interacts with gravity when traveling through space. When a photon rises from a source deep in a gravitational field (like a star), it loses some energy, which causes its light to shift toward the red end of the spectrum—this is called redshift. However, the situation changes when the photon get...
Preprint
Full-text available
This study investigates the fundamental equations governing photon behaviour in external gravitational fields due to electromagnetic-gravitational interaction, emphasizing their energy, momentum, and wavelength relationships. Building upon the pioneering contributions of Max Planck and Louis de Broglie, the analysis highlights key equations such as...
Chapter
Full-text available
This study explores the piezoelectric and inverse piezoelectric effects on piezoelectric crystals, emphasizing their applications across various conditions. It discusses the fundamental principles governing piezoelectric crystals, including Newton's second law, Hooke's law, and the operation of piezoelectric accelerometers. The piezoelectric effect...
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This paper delves into the intricate relationships among potential energy (PE), mass, and kinetic energy (KE) within classical mechanics, advocating for a more nuanced understanding of these fundamental concepts. It highlights how changes in potential energy significantly influence mass and the generation of kinetic energy. The direct proportionali...
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DOI: http://dx.doi.org/10.13140/RG.2.2.25421.24808 This paper delves into the intricate relationships among potential energy (PE), mass, and kinetic energy (KE) within classical mechanics, advocating for a more nuanced understanding of these fundamental concepts. It highlights how changes in potential energy significantly influence mass and the g...
Chapter
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This unified study investigates the intricate relationships among gravitational mass, matter mass, and dark matter dynamics within the framework of extended classical mechanics. By addressing the roles of dark matter mass and negative apparent mass in gravitational forces and effective mass, this research delineates the distinctions between mechani...
Chapter
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Dark energy is often misunderstood as a mysterious substance permeating the universe. However, a deeper exploration reveals that dark energy is not a standalone entity but a consequence of the gravitational and kinetic dynamics of the universe. This paper presents a comprehensive analysis of the interplay between potential and kinetic energy during...
Preprint
Full-text available
This research paper explores the framework of Extended Classical Mechanics, with a focus on the Equivalence Principle, Mass, and Gravitational Dynamics. Volume 1 of this study re-examines the classical equivalence principle, which maintains the equivalence of inertial mass and gravitational mass (also referred to as gravitating mass) and extends th...
Preprint
Full-text available
This study investigates human perception of zero and hyper-dimensions, bridging physical and mathematical concepts. A point, symbolized as '.', denotes precise spatial location without dimensionality. Real numbers on a one-dimensional number line extend infinitely in both positive and negative directions from zero, the origin. Despite their concept...
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This resource serves as a supplementary guide for researchers investigating length deformation in classical and relativistic mechanics. It complements studies such as the 'Comparative Analysis of Length Deformation in Classical and Relativistic Mechanics' series,[₁,¹, ₂,²] 'Dynamics between Classical Mechanics and Relativistic Insights'[₃,³], and '...
Chapter
Full-text available
This study serves as a supplementary resource for researchers investigating length deformation in classical and relativistic mechanics. It complements existing studies such as the 'Comparative Analysis of Length Deformation in Classical and Relativistic Mechanics' series, 'Dynamics between Classical Mechanics and Relativistic Insights', and 'Advanc...
Preprint
Full-text available
This study, serving as Part-2 of the research titled "Comparative Analysis of Length Deformation in Classical and Relativistic Mechanics," investigates the behaviour of matter within gravitationally bound systems. Through meticulous examination of projected length alterations, the research highlights differences between classical and relativistic m...
Preprint
Full-text available
This study, serving as Part-2 of the research titled "Comparative Analysis of Length Deformation in Classical and Relativistic Mechanics," investigates the behaviour of matter within gravitationally bound systems. Through meticulous examination of projected length alterations, the research highlights differences between classical and relativistic m...
Preprint
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This study presents a comparative analysis of length deformation in Classical and Relativistic Mechanics, specifically investigating 10-gram objects accelerating to 1% of the speed of light. By employing Hooke's Law in Classical Mechanics and the Relativistic Lorentz Factor, the research explores the implications of acceleration dynamics and the li...
Preprint
Full-text available
This study presents a comparative analysis of length deformation in Classical and Relativistic Mechanics, specifically investigating 10-gram objects accelerating to 1% of the speed of light. By employing Hooke's Law in Classical Mechanics and the Relativistic Lorentz Factor, the research explores the implications of acceleration dynamics and the li...
Data
This supplementary resource {11-05-2024 (SR-1)} of the paper, titled, 'Dynamics between Classical Mechanics and Relativistic Insights:' DOI https://doi.org/10.20944/preprints202405.0706.v1, aims to expand upon this original study by incorporating additional insights into the role of piezoelectric materials and accelerometers within the framework of...
Preprint
Full-text available
This study is a comprehensive study exploring the intricate interplay of force, mass, and energy in physical systems. Beginning with Newton's foundational principles, the research delves into inertia, acceleration, and the force-motion relationship. Through mathematical formulations and conceptual analyses, it reveals how forces shape both inertial...
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This supplementary resource (11-05-2024 (SR-1) of the paper, titled, 'Dynamics between Classical Mechanics and Relativistic Insights:' DOI http://dx.doi.org/10.13140/RG.2.2.21005.96481/1, aims to expand upon this original study by incorporating additional insights into the role of piezoelectric materials and accelerometers within the framework of c...
Preprint
Full-text available
This study delves into the intricate dynamics of classical mechanics, exploring the interplay between force, mass, and energy. Through fundamental principles and mathematical formulations, it elucidates key relationships governing physical systems. Beginning with an overview of classical mechanics, the study establishes the foundational principles...
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Time, traditionally viewed as a linear, non-dynamic parameter, is re-envisioned in this study as a Hyperdimensional concept. This paper conducts a cross-disciplinary examination, critically analysing the conceptualization of time in classical mechanics, quantum mechanics, and cosmology to propose a ground breaking reconceptualisation that extends b...
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The text provides a detailed examination of equations and relationships governing phase shifts, time distortions, and energy changes in wave systems. It begins by establishing fundamental equations linking phase shift T(deg), time distortion (Δt), and energy change (ΔE), subsequently extending these equations to calculate energy changes based on fr...
Data
The text provides a detailed examination of equations and relationships governing phase shifts, time distortions, and energy changes in wave systems. It begins by establishing fundamental equations linking phase shift T(deg), time distortion (Δt), and energy change (ΔE), subsequently extending these equations to calculate energy changes based on fr...
Data
The text provides a detailed examination of equations and relationships governing phase shifts, time distortions, and energy changes in wave systems. It begins by establishing fundamental equations linking phase shift T(deg), time distortion (Δt), and energy change (ΔE), subsequently extending these equations to calculate energy changes based on fr...
Data
The text provides a detailed examination of equations and relationships governing phase shifts, time distortions, and energy changes in wave systems. It begins by establishing fundamental equations linking phase shift T(deg), time distortion (Δt), and energy change (ΔE), subsequently extending these equations to calculate energy changes based on fr...
Preprint
Full-text available
Time, traditionally viewed as a linear, non-dynamic parameter, is re-envisioned in this study as a Hyperdimensional concept. This paper conducts a cross-disciplinary examination, critically analysing the conceptualization of time in classical mechanics, quantum mechanics, and cosmology to propose a ground breaking reconceptualisation that extends b...
Data
This supplementary resource supports Soumendra Nath Thakur's paper, "Advancing Understanding of External Forces and Frequency Distortion: Part -1." It reinterprets the Lorentz transformation to show that potential energy, representing rest mass m₀ that changes under motion, equates to kinetic energy treated as 'effective mass' (mᵉᶠᶠ). Thakur descri...
Data
This supplementary resource supports Soumendra Nath Thakur's paper, "Advancing Understanding of External Forces and Frequency Distortion: Part -1." It reinterprets the Lorentz transformation to show that potential energy, representing rest mass m₀ that changes under motion, equates to kinetic energy treated as 'effective mass' (mᵉᶠᶠ). Thakur descri...
Preprint
Full-text available
The research paper delves into the intricate relationship between external forces, frequency distortion, and time measurement errors, offering insights into relativity theory. It highlights how differences in gravitational potential or relative velocities can impact the behavior of clocks and oscillatory systems. The analysis emphasizes the role of...
Preprint
Full-text available
This research paper delves into the complex relationship between external forces and frequency distortion, offering insights into relativity theory and its implications for time measurement. Through a meticulous examination of classical mechanics, relativistic physics, and wave mechanics, the paper unravels the mechanisms underlying frequency dis...
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The supplementary resource on "Complementary Refraction between Incident and Reflecting Photons" enriches the understanding of photon-mirror interaction dynamics as explored in the preprint paper "Relativistic Effects and Photon-Mirror Interaction – Energy Absorption and Time Delay." Authored by Soumendra Nath Thakur from Tagore’s Electronic Lab in...
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The supplementary resource on "Complementary Refraction between Incident and Reflecting Photons" enriches the understanding of photon-mirror interaction dynamics as explored in the preprint paper "Relativistic Effects and Photon-Mirror Interaction – Energy Absorption and Time Delay." Authored by Soumendra Nath Thakur from Tagore’s Electronic Lab in...
Preprint
Full-text available
The research paper Insights from M-Theory and the Concept of Multi-Dimensional Space' provides a comprehensive exploration of the intricate relationships between dimensions, drawing upon insights from M-Theory and the concept of multi-dimensional space. Through meticulous analysis and theoretical investigation, the paper elucidates how dimensions,...
Preprint
Full-text available
presents a revised research paper focusing on the complex interaction between photons and mirrors, aiming to elucidate the processes occurring during these interactions. Through meticulous analysis, the paper explores fundamental principles such as energy absorption, time delay, and relativistic effects. The optimization of mirror reflectivity by m...
Preprint
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This abstract presents a revised research paper focusing on the complex interaction between photons and mirrors, aiming to elucidate the processes occurring during these interactions. Through meticulous analysis, the paper explores fundamental principles such as energy absorption, time delay, and relativistic effects. The optimization of mirror ref...
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This study offers a simplified elucidation of the intricate connections between key elements in waveform analysis. Through concise explanations and clear mathematical expressions, this abstract distils complex concepts into easily digestible insights. Fundamental principles, such as the equivalence of time intervals and phase shifts, are elucidated...
Data
In this comprehensive exploration of photon dynamics within strong gravitational fields, Soumendra Nath Thakur delves into the intricate relationship between the initial photon energy (E) and the total photon energy in the gravitational field (Eg). By highlighting the algebraic equivalence derived from the condition E + ΔE = E − ΔE, Thakur elucidat...
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In this comprehensive exploration of photon dynamics within strong gravitational fields, Soumendra Nath Thakur delves into the intricate relationship between the initial photon energy (E) and the total photon energy in the gravitational field (Eg). By highlighting the algebraic equivalence derived from the condition E + ΔE = E − ΔE, Thakur elucidat...
Data
In this comprehensive exploration of photon dynamics within strong gravitational fields, Soumendra Nath Thakur delves into the intricate relationship between the initial photon energy (E) and the total photon energy in the gravitational field (Eg). By highlighting the algebraic equivalence derived from the condition E + ΔE = E − ΔE, Thakur elucidat...
Data
In this comprehensive exploration of photon dynamics within strong gravitational fields, Soumendra Nath Thakur delves into the intricate relationship between the initial photon energy (E) and the total photon energy in the gravitational field (Eg). By highlighting the algebraic equivalence derived from the condition E + ΔE = E − ΔE, Thakur elucidat...
Data
The article delves into the multifaceted nature of time, a fundamental dimension that governs the unfolding of events in the universe. Thakur embarks on a journey to elucidate the relationship between clocks and biological time perception, shedding light on the intricate mechanisms that shape our understanding of temporal reality. While clocks serv...
Preprint
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This paper delves into the intricate dynamics of time dilation and frequency shifts within quantum systems. This theoretical exploration integrates insights from diverse research endeavours, including the seminal study by Paige, A. J., Plato, A. D. K., & Kim, M. S. (2020), which investigated classical and nonclassical time dilation effects in quant...
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This abstract discusses the standardization of clock time, emphasizing its alignment with universal standard time. Clocks, whether quantum, classical, or atomic, adhere to a standardized time order known as "universal standard time," which is designed to be commensurate with the concept of "universal cosmic time." The objective is to ensure that al...
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This paper delves into the relationship between time dilation, entropy, and the consistency of the time scale. It discusses how entropy increases over time according to the second law of thermodynamics and emphasizes the constancy of the time scale despite variations in entropy across different systems. Insights from entropy highlight the inevitabi...
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"Re-examining Time Dilation through the Lens of Entropy" offers a thought-provoking exploration of the relationship between time dilation, entropy, and the uniformity of the time scale. Delving into the realms of physics and thermodynamics, the paper challenges conventional notions of time dilation by integrating insights from entropy theory. By el...
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This abstract provides an in-depth examination of photon interactions with external gravitational fields, building upon the principles discussed in the paper titled "Distinguishing Photon Interactions: Source Well vs. External Fields." The analysis elucidates how gravitational effects influence the properties of photons, including momentum and ener...
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This research delves into the fascinating realm of photon interactions within gravitational fields, particularly focusing on the nuanced dynamics of momentum changes and their symmetrical attributes. Through a meticulous exploration titled "Exploring Symmetry in Photon Momentum Changes: Insights into Redshift and Blueshift Phenomena in Gravitationa...
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This additional paper provides a detailed exploration of photon behaviour within gravitational fields, distinguishing between interactions occurring in source gravitational wells and external gravitational fields. The paper elucidates concepts such as energy expenditure, gravitational redshift, and momentum exchange, offering insights into astrophy...
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This study delves into the concept of the effective mass of the energetic pre-universe, exploring its composition, expansion, and fundamental particles. It provides insights into the constituents of the universe, including baryonic matter, dark matter, and dark energy, while emphasizing the constant energy-mass equivalence. The expansion of the uni...
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In the realm of modern physics, the comprehension of relativistic dynamics, encompassing concepts such as relativistic mass, mass transformation in special relativity, and Lorentz’s mass transformation, serves as a cornerstone for understanding the intricate interplay between mass and energy. This thesis presents a comprehensive exploration, spanni...
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This study delves into the nuanced interactions of photons or waves with gravitational fields, focusing on the distinction between their encounters with the gravitational wells of source objects and external massive bodies. When photons or waves escape a source gravitational well, such as that of a star or black hole, they expend energy, leading to...
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This study investigates the direct influence of the gravitational field on object motion and its implications for our understanding of spacetime distortion. By scrutinizing the fundamental relationship between the gravitational field and object motion, we question the necessity of including spacetime distortion as a mathematical abstraction in grav...
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This study investigates the direct influence of the gravitational field on object motion and its implications for our understanding of spacetime distortion. By scrutinizing the fundamental relationship between the gravitational field and object motion, we question the necessity of including spacetime distortion as a mathematical abstraction in grav...
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The Research Paper in process, titled "Journey from Abstract Dimensions to Eventful Universes: Exploring Temporal-States from 0-Dimensional Beginnings to 3-Dimensional Realities." This paper combines several research chapters that meticulously analyse the coherent progression from the noneventful 0-dimensional state to the eventful three-dimensiona...
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"The framework uses the term effective mass (mᵉᶠᶠ) to describe the variability of mass and its impact on mass-energy equivalence." This research paper delves into the mathematical validation of energy equivalent equations, spanning classical energy formulations, energy frequency equivalences, and energy mass equivalences. Classical mechanics princ...
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"The framework uses the term effective mass (mᵉᶠᶠ) to describe the variability of mass and its impact on mass-energy equivalence." This research paper delves into the mathematical validation of energy equivalent equations, spanning classical energy formulations, energy frequency equivalences, and energy mass equivalences. Classical mechanics princ...
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In this article, the author delves into the intriguing concept that even within a 0-dimensional abstract state, there exists a conceptual notion of directions such as "up and down," "left and right," or "front and back." The author proposes that this conceptualization forms a valid approach to the mathematical abstraction of points, suggesting that...
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The theoretical exploration presented by Soumendra Nath Thakur on January 26, 2024, delves into the intricate dynamics of abstract dimensions and energy equivalence within a 0-dimensional state. Challenging conventional notions, the study asserts that even in a seemingly dimensionless state, conceptual directions and orientations can be attributed,...
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"The framework uses the term effective mass (mᵉᶠᶠ) to describe the variability of mass and its impact on mass-energy equivalence." The concept of relativistic mass can be understood as an effective mass: In the paper, the concept of relativistic mass is explored as an effective mass within the framework of special relativity. The analysis of the o...
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The research paper titled "Relativistic Effects on Phaseshift in Frequencies Invalidate Time Dilation II" explores an alternative perspective on time. The abstract posits that relative time is intricately connected to relative frequencies, introducing a novel interpretation of the observed phenomena. The key findings challenge the conventional unde...
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"The framework uses the term effective mass (mᵉᶠᶠ) to describe the variability of mass and its impact on mass-energy equivalence." This exploration delves into the nuanced relationship between relativistic mass (m′) and energy in the context of special relativity, treating m′ as an equivalent of an effective mass (mᵉᶠᶠ). The discussion unfolds by h...
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"The framework uses the term effective mass (mᵉᶠᶠ) to describe the variability of mass and its impact on mass-energy equivalence." This exploration delves into the captivating realm of special relativity, unravelling the intricate relationship between mass and energy. The foundational equation E = m₀c² establishes the inherent link between rest mas...
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"The framework uses the term effective mass (mᵉᶠᶠ) to describe the variability of mass and its impact on mass-energy equivalence." The case study delves into the energetic form of relativistic mass in special relativity, specifically focusing on the relationship between effective mass and the energetic implications of relativistic mass. Through a...
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This study delves into the theoretical framework of unified quantum cosmology, examining the non vanishing energy beyond the Planck limit and its potential transformations up to the beginning of the universe (Big Bang). The introduction of a constant k, aligned with the universal gravitation constant (G), adds a novel dimension to the exploration....
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"The framework uses the term effective mass (mᵉᶠᶠ) to describe the variability of mass and its impact on mass-energy equivalence." The summary of the research delves into the intricate relationship between mass and energy in special relativity and atomic processes. Rooted in Einstein's theories, it explores the relativistic mass equation, emphasiz...
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This comprehensive research study meticulously explores the intricate dynamics of relativistic mass, Lorentz's transformations, and the nuanced interplay between mass and energy within the realm of special relativity. The investigation delves into ten pivotal facets, contributing collectively to a nuanced understanding of these phenomena. Initiatin...
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"The framework uses the term effective mass (mᵉᶠᶠ) to describe the variability of mass and its impact on mass-energy equivalence." A comprehensive exploration into the transformative relationship between mass and energy in the realm of special relativity and atomic processes. Our study delves into Einstein's theories, illuminating the nuanced inte...
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Unified Quantum Cosmology: Exploring Beyond the Planck Limit with Universal Gravitational Constants" by Soumendra Nath Thakur delves into a theoretical framework that seeks to unravel the enigmatic relationship between quantum mechanics and cosmology. The study introduces a constant, denoted as 'k,' aligned with the universal gravitation constant (...
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The study delves into the significance of a 1° phase shift in relation to the Planck frequency within the realm of quantum mechanics. The study provides a comprehensive analysis and mathematical explanation of the minute interval's implications on the Planck scale. The study initiates by elucidating the energy associated with a 360° phase change o...
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The study delves into the interconnectedness of Planck units and their fundamental relationships among time, frequency, and wavelength in the realm of theoretical physics. It centers on the assertion that different Planck units, intricately woven from fundamental physical constants, inherently relate to each other significantly. In this context, P...
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The study explores the behaviour of hypothetical zero-dimensional systems within the realm of quantum mechanics. The abstract outlines the study's focus on quantum-scale behaviour, oscillatory dynamics, and energy conservation within zero-dimensional entities. The investigation integrates theoretical frameworks from quantum mechanics, developing ab...
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This study explores gravitational interactions and energy-force relationships within a hypothetical 0ₜₕ-dimensional realm, examining force, potential energy changes, and energy density in an abstract environment. By linking force and potential energy changes and introducing 0-dimensional energy density with collective volumetric oscillations, the s...
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Within the uncharted territories of abstract theoretical physics lies an intriguing inquiry into the intricate relationship between force and potential energy dynamics within a hypothetical 0ₜₕ-dimensional realm. This visionary exploration endeavours to unravel the theoretical fabric of micro gravitational forces, contemplating their conceivable ex...
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Chapter X-I: Energy Dynamics in a Noneventful Oscillation Realm This chapter ventures beyond the Planck scale, transcending familiar temporal dimensions to explore spatial realms beyond our observable limits. Employing theoretical frameworks and mathematical models, the exploration progresses from non-eventful, timeless energetic potential existen...
Research
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The study explores the possibility of energy existence beyond the Planck time, drawing insights from conservation principles, dark matter, and dark energy observations. The investigation integrates speculative hypotheses, theoretical conjectures, and abstract phenomena to propose a framework beyond empirical validation. It highlights the conceptual...
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We will try to show and to some extent predict the critical limits or stable points as considered regarding the variation of the probability depending upon the factor ∆ with minimum dissipation but not conservative in the flow.
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The investigation into the nature of clocks and their mechanisms provides insights into the intricate connection between time measurement, relativistic impacts, and the equation governing time dilation concerning speed's influence. This paper critically evaluates the widely accepted equation for time dilation, t' = t /√(1-v²/c²), highlighting its i...
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The odyssey from Einstein's cosmological constant to dark energy is a captivating narrative in cosmology's history. This paper navigates this transformative journey, charting the evolution of cosmological theories, pivotal contributions, and ethical considerations. Einstein introduced the cosmological constant in 1917, seeking a static universe. La...
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The research paper "Wave Dynamics - Interplay of Phase, Frequency, Time, and Energy" explores the relationships among phase, frequency, time, and energy in wave dynamics. The paper aims to contribute to a comprehensive understanding of wave behavior across scientific fields, particularly in physics, telecommunications, engineering, and quantum mech...

Questions

Questions (56)
Question
ORCiD: 0000-0003-1871-7803
February 10, 2025
Within Extended Classical Mechanics (ECM), photon dynamics describes dark energy by positing that photons, due to their unique properties within the framework, can exhibit a "negative apparent mass," causing them to effectively repel each other and contribute to the observed accelerating expansion of the universe, which is the primary characteristic of dark energy; this negative mass arises from the complex interaction of photon momentum and energy within the ECM equations, leading to an "effective acceleration" that counteracts gravitational pull.
Photon Dynamics and Dark Energy in the Framework of Extended Classical Mechanics (ECM)
In the framework of Extended Classical Mechanics (ECM), photon dynamics and dark energy are intricately linked through the concepts of effective mass (Mᵉᶠᶠ) and apparent mass (Mᵃᵖᵖ). This framework provides a novel perspective on how gravitational interactions can induce mass in initially massless particles, such as photons, and how these interactions relate to the observed phenomena of dark energy.
Photon Dynamics and Effective Mass
Effective Mass and Apparent Mass:
In ECM, the effective mass (Mᵉᶠᶠ) of a photon is a dynamic property that combines the rest mass (Mᴍ​) and the apparent mass (Mᵃᵖᵖ). For photons, which have zero rest mass, their apparent mass dictates their energy-momentum exchanges and response to forces. This leads to the reformulated force equation:
Fₚₕₒₜₒₙ =−Mᵃᵖᵖ aᵉᶠᶠ
The apparent mass (Mᵃᵖᵖ) can be negative, which is crucial for understanding antigravitational effects and dark energy.
Gravitational Redshift and Photon Energy:
The total energy of a photon is analysed as the sum of its inherent energy (E) and gravitational interaction energy (Eg​). As photons escape a gravitational field, they retain their inherent energy while gradually expending their gravitational energy. This leads to gravitational redshift, where the photon's frequency shifts due to the gravitational potential.
Dark Energy and Negative Effective Mass
Dark Energy as a Gravitational Interaction:
In ECM, dark energy is not treated as a conventional field or particle but as a gravitationally interactive background that influences mass distributions at intergalactic scales. It acts on cosmic scales by modifying the gravitational potential, leading to the observed cosmic acceleration.
Negative Effective Mass and Antigravitational Effects:
The negative effective mass (Mᵉᶠᶠ<0) is a key feature of ECM, particularly in the context of dark energy. This negative mass can lead to antigravitational effects, where objects experience repulsion rather than attraction. This phenomenon echoes the behaviour of dark energy, which accelerates the universe's expansion by generating antigravitational effects.
Gravitational Mass and Dark Energy:
The gravitational mass (Mg​) in ECM is given by:
Mɢ = Mᴍ + (-Mᵃᵖᵖ)
At intergalactic scales, the interaction of dark matter with dark energy results in an effective mass contribution (Mᴅᴇ​), which is represented by:
Mɢ = Mᴍ + Mᴅᴇ
This additional inferred mass component (Mᴅᴇ) is an emergent gravitational effect, not a fundamental mass term.
Implications for Photon Dynamics and Dark Energy
Unified Framework:
ECM provides a unified framework that bridges classical mechanics, quantum principles, and cosmological implications. By incorporating the concept of apparent mass, ECM offers a cohesive mechanism to reconcile classical, quantum, and cosmological phenomena.
Cosmic Acceleration:
The negative effective mass associated with dark energy explains the observed cosmic acceleration. This antigravitational effect is crucial for understanding the expansion of the universe and the role of dark energy in shaping cosmic dynamics.
Gravitational Collapse at the Planck Scale:
At the Planck scale, gravitational interactions can induce mass in massless particles, leading to gravitational collapse. This transition from massless to massive states is a direct consequence of ECM's mass induction principle, where increasing energy (via frequency) leads to mass acquisition.
Conclusion
The framework of Extended Classical Mechanics (ECM) offers a detailed and nuanced understanding of photon dynamics and dark energy. By incorporating the concepts of effective mass and apparent mass, ECM provides a unified perspective on gravitational interactions across quantum and cosmological scales. This approach not only aligns with fundamental principles but also offers potential explanations for cosmic-scale phenomena involving dark matter, dark energy, and exotic gravitational effects.
Question
ORCiD: 0000-0003-1871-7803
February 10, 2025
Absolute Collapse Condition
Mass Acquisition at Planck Frequency:
In Extended Classical Mechanics (ECM), any massless entity reaching the Planck frequency (fp) must acquire an effective mass (Mᵉᶠᶠ = hf/c² = 21.77 μg). This acquisition of mass is a direct consequence of ECM's mass induction principle, where increasing energy (via f) leads to mass acquisition.
Gravitational Collapse:
At the Planck scale, the induced gravitational interaction is extreme, forcing the entity into gravitational collapse. This is a direct consequence of the mass acquisition at the Planck frequency, where the gravitational effects become significant.
ECM's Mass-Induction Perspective
Apparent Mass and Effective Mass:
The apparent mass (−Mᵃᵖᵖ) of a massless entity contributes negatively to its effective mass. However, at the Planck threshold, the magnitude of the induced effective mass (|Mᵉᶠᶠ|) surpasses |−Mᵃᵖᵖ|, ensuring that the total mass is positive:
|Mᵉᶠᶠ| > |−Mᵃᵖᵖ|
This irreversible transition confirms that any entity at fp must collapse due to self-gravitation.
Implications for Massless-to-Massive Transition
Behaviour Below Planck Frequency:
Below the Planck frequency, a photon behaves as a massless entity with effective mass determined by its energy-frequency relation. However, at fp​, the gravitating mass (Mɢ​) and effective mass (Mᵉᶠᶠ) undergo a shift where induced mass dominates over negative apparent mass effects.
Planck-Scale Energy:
Planck-scale energy is not just a massive state—it is a self-gravitating mass that collapses under its own gravitational influence. This suggests that at Planck conditions, the gravitationally induced mass dominates over any negative mass contributions, maintaining a positive mass regime.
Threshold Dominance at the Planck Scale
Gravitational Mass Dominance:
At the Planck scale, gravitational mass (Mɢ​) is immense due to the fundamental gravitational interaction. Since |+Mɢ​| ≫|−Mᵃᵖᵖ|, the net effective mass remains positive:
Mᵉᶠᶠ = Mɢ = (−Mᵃᵖᵖ) ≈ +Mᵉᶠᶠ
This suggests that at Planck conditions, the gravitationally induced mass dominates over any negative mass contributions.
Transition Scenarios for Negative Effective Mass
Conditions for Negative Effective Mass:
The condition −Mᵃᵖᵖ > Mɢ could, in principle, lead to a transition where the effective mass becomes negative. This might occur under strong antigravitational influences, possibly linked to:
• Dark energy effects in cosmic expansion.
• Exotic negative energy states in high-energy physics.
• Unstable quantum fluctuations near high-energy limits.
Linking Effective Mass to Matter Mass at Planck Scale
Matter Mass Emergence:
Since Mᵉᶠᶠ ≈ Mᴍ, under these extreme conditions, it implies that matter mass emerges predominantly as a consequence of gravitational effects. This aligns with ECM’s perspective that mass is not an intrinsic property but rather a dynamic response to gravitational interactions.
Conclusion
This work on ECM provides a detailed and nuanced understanding of how gravitational interactions can induce mass in initially massless particles, leading to gravitational collapse at the Planck scale. This perspective not only aligns with fundamental principles but also offers potential explanations for cosmic-scale phenomena involving dark matter, dark energy, and exotic gravitational effects. The detailed mathematical foundations and the implications of apparent mass and effective mass in ECM further clarify how mass can dynamically shift between positive, zero, and negative values based on gravitational and antigravitational influences.
Question
February 09, 2025
Section -
Preliminary Introduction:
In the complete absence of gravitational interactions, massless particles such as photons would move without restriction, with their velocity determined solely by their frequency. In such a scenario, as frequency approaches infinity, speed would also tend toward infinity, while wavelength would contract indefinitely—yet the particles would remain massless. However, when gravitational influence is introduced, a fundamental threshold arises. At the Planck length (ℓᴘ), a massless particle acquires a mass of approximately 21.77 micrograms, altering its fundamental nature. This mass acquisition marks a transition where the particle can no longer sustain its inherent velocity and undergoes gravitational collapse. Extended Classical Mechanics (ECM) provides a mathematical framework to explain how gravitational effects can generate mass in initially massless entities. Conversely, ECM also explores how antigravitational interactions could reduce mass, potentially leading to negative effective mass under certain conditions. This perspective challenges traditional interpretations, offering deeper insights into cosmic-scale phenomena involving dark matter, dark energy, and extreme gravitational interactions. In our forthcoming discussions, we will explore the detailed mathematical foundations of apparent mass and effective mass in ECM, demonstrating how mass can dynamically transition between positive, zero, and negative states based on gravitational and antigravitational influences.
In a theoretical scenario where gravitational interactions are entirely absent, massless particles such as photons would travel without restriction. Their velocity would not be constrained by an external limit but instead governed by their frequency rather than the total energy they possess. In such a case, the speed of a massless particle follows the relation v=fλ. As the frequency f approaches infinity (∞), the velocity v also tends toward infinity, provided there is a complete absence of gravitational influence. Meanwhile, the wavelength λ shrinks toward an infinitesimally small value (1/∞λ), yet the particle remains massless.
However, in the presence of the universal gravitational constant (G), a critical threshold emerges. When the wavelength λ reaches Planck length (ℓᴘ =1.616255 × 10⁻³⁵ m), the particle can no longer remain massless. At this scale, it acquires a mass of 21.77 micrograms, fundamentally altering its behaviour. As a result, it can no longer maintain its inherent velocity, leading to a breakdown of the simple relation v=fλ. When the conditions satisfy f = fᴘ   and λ = ℓᴘ, the particle undergoes gravitational collapse, with extreme gravity dominating its dynamics.
The Transition from Massless to Massive: Gravitational Influence and the Role of ECM
When the Planck length (ℓᴘ) is set equal to the Schwarzschild radius, an intriguing consequence emerges—a massless particle at this fundamental scale gains a mass of approximately 21.77 micrograms. This result signifies that gravitational influence alone can induce mass, even in entities traditionally considered massless, such as photons. The derived Planck mass represents the natural threshold at which quantum gravitational effects become significant, hinting at the deep connection between mass, gravity, and fundamental physics.
Conversely, if gravitational interactions can cause mass to emerge, then antigravitational influences could, in principle, reduce mass. This suggests that a sufficiently strong repulsive gravitational effect might lead even a highly massive body to transition into a massless state. Extending this notion further, under specific conditions, the effective mass of an object could even become negative, leading to novel physical behaviours that challenge conventional mechanics.
In Extended Classical Mechanics (ECM), the concepts of apparent mass and effective mass provide a detailed mathematical framework to describe these transitions. ECM extends traditional gravitational dynamics by incorporating the effects of both positive and negative mass interactions, offering insights into how mass evolves under varying gravitational and antigravitational conditions. This perspective not only aligns with fundamental principles but also provides a potential explanation for cosmic-scale phenomena involving dark matter, dark energy, and exotic gravitational effects.
In our following work, we will delve deeper into these mathematical foundations and explore the implications of apparent mass and effective mass in ECM, further clarifying how mass can dynamically shift between positive, zero, and negative values based on the influence of gravitational and antigravitational forces.
Question
This study explores the extended dynamics of photon motion, challenging the conventional view that light speed (c) is always constant. We propose that at an infinitesimally small scale, a photon transitions from rest to c due to an inherent acceleration phase governed by its negative apparent mass. This acceleration generates a self-exerted force, distinct from external interactions, allowing the photon to maintain equilibrium while escaping gravitational influence. Furthermore, we analyse the continuous nature of photon frequency, distinguishing it from discrete digital signals. Unlike step-like binary transitions, a photon's wave packet exhibits a smooth, incremental frequency pattern, implying alternating cycles of acceleration and deceleration within its propagation. These insights suggest that photon motion and frequency dynamics involve fundamental, phase-dependent changes at quantum and relativistic scales.
Force Dynamics on Photons:
• Derive the force equation F = −Mᵃᵖᵖaᵉᶠᶠ for photons using apparent mass and associated acceleration.
• Explore how this equation governs the photon’s motion under varying energy-momentum conditions.
• The derivation of the effective acceleration aᵉᶠᶠ aligns with the methodological exploration of force and acceleration acting on photons. It would complement the discussion of the force equation F = −Mᵃᵖᵖaᵉᶠᶠ and further clarify the dynamics of photons as analysed through the extended classical mechanics framework. The constant effective acceleration: aᵉᶠᶠ = 6 × 10⁸ m/s².
Determination of Constant Effective Acceleration of Photons
The distance travelled by the photon in 1 second is 3 × 10⁸ m, and that the acceleration is constant. The expression for the distance travelled in the case of constant acceleration is given by:
Δd = v₀Δt + (1/2)aᵉᶠᶠ(Δt)²
Where:
• Δd is the distance travelled (3 × 10⁸ m in 1 second),
• v₀ is the initial velocity (0 m/s, at emission),
• Δt is the time (1 second),
• aᵉᶠᶠ is the effective acceleration, which we want to solve for.
Substituting the known values into the equation:
3 × 10⁸ m = 0•1 s + (1/2)aᵉᶠᶠ(1)²
aᵉᶠᶠ = 6 × 10⁸ m/s²
Extended Photon Dynamics and Phases of Motion: Transition from Rest to Constant Velocity
• When considering a photon's motion, its apparent mass is negative. As a result, its effective acceleration leads to a force with a negative value. This behaviour is different from that of ordinary matter, which always has a positive mass.
• The commonly referenced distance that light travels in one second does not represent the photon's actual path during that time. Instead, it marks the moment of emission, where the photon, initially at rest in an apparent sense, rapidly attains its full velocity within a brief interval.
• During this transition period, the effective acceleration is determined by the relationship between force and the negative apparent mass. The force involved does not come from an external source but is instead exerted by the photon itself due to its unique mass-energy properties. This results in the photon undergoing a continuous deceleration at twice the speed of light.
• The force generated by the photon serves a dual purpose. It counteracts the gravitational pull of its source while ensuring the photon maintains a constant speed as it escapes. The energy necessary for this process is provided by the photon itself, allowing it to sustain the required acceleration and remain in
Photon Dynamics: Returning to the Force Equation for Photons
• Since the apparent mass is negative (−Mᵃᵖᵖ), the constant effective acceleration aᵉᶠᶠ = 6 × 10⁸ m/s² results in a force term with a negative value. This contrasts with the behaviour of matter mass (Mᴍ), which always remains positive.
• The distance of 3 × 10⁸ m in one second does not represent a photon’s trajectory over that duration. Instead, it corresponds to the initial emission event, where the photon, initially at rest in an apparent sense (t₀, v₀), attains a velocity v₁ at time t₁, with Δt = t₁ − t₀ = 1 second and Δv = v₁ − v₀ = 3 × 10⁸ m/s².
• During this interval (t₁ − t₀), the effective acceleration is given by aᵉᶠᶠ = F/(−Mᵃᵖᵖ). The force F is not an external force but is instead exerted by the photon itself due to its negative apparent mass (−Mᵃᵖᵖ). This implies that the photon undergoes continuous deceleration at twice the speed of light (6 × 10⁸ m/s²).
• The exerted force (F) not only counteracts the gravitational attraction of the source (Fg) but also enables the photon to escape the gravitational well at a constant speed of 3 × 10⁸ m/s². The energy required for this escape is compensated by the photon itself, maintaining the necessary energy balance to sustain its effective acceleration of 6 × 10⁸ m/s².
Explanation of Phases of Motion: Transition from Rest to Constant Velocity
On a number line, there are infinitely many points between any two nearest numbers. When you say "1," you are actually referring to the difference between 0 and 1, with an infinite sequence of points in between.
Similarly, while the speed of light (c) appears constant on large scales, at an infinitesimally small scale, it has a beginning due to transmission delay. This delay occurs because motion progresses incrementally, however small, starting from absolute rest (v=0) before reaching c.
The first phase, where velocity increases from 0 to c, represents acceleration. Motion does not begin with an arbitrary velocity but transitions from rest. The first phase starts at zero (v = 0) and progresses to an initial velocity (v), whereas successive phases continue from an already established velocity (v = v) rather than starting anew from v = 0.
Mathematical Representation
Let v(t) represent the velocity of the object as a function of time. In the first phase of motion:
Initial Phase (Acceleration)
The motion begins from rest, so at t = 0, v(0) = 0. The velocity increases from v=0 to some initial velocity v₁ = c, over some time interval Δt₁. The acceleration a(t) in this phase is given by:
a(t) = dv(t)/dt, where v(t) = ∫a(t)dt
The velocity increases gradually from 0 to c, so during this phase, the object undergoes acceleration.
Subsequent Phases (Constant Velocity)
After reaching an initial velocity v₁ = c, successive phases of motion proceed at this established velocity. In these phases, the velocity remains constant, so for t > Δt₁, we have:
v(t) = v₁ = c, a(t) = 0
In the subsequent phases, the object continues with the velocity v = c, without starting from rest or accelerating further.
Photon Frequency: Continuous Analogous Waves vs. Discrete Digital Signals
Photon frequency is not a discrete, step-like, binary signal. Unlike digital frequencies, which exhibit distinct on-off states, photon frequency is continuous and behaves in an analogy manner. It follows a smooth, incremental, and decimal-like wave pattern within its energy packet.
While digital signals transition between fixed values, a photon's frequency remains constant within its wave-packet, forming an uninterrupted oscillatory motion. This continuous wave behaviour implies that every phase of a photon’s wave structure inherently represents alternating cycles of acceleration and deceleration, rather than discrete jumps between states.
This suggests that the wave characteristics of a photon are not just propagating in a static manner but involve intrinsic dynamical changes at the quantum scale, reinforcing the idea that photon energy and momentum continuously adjust within their wave structure.
Question
February 07, 2025
The foundation of Extended Classical Mechanics (ECM) is constructed upon classical mechanics principles, as formulated by Newton, Lagrange, and Hamilton, yet it aims to transcend the limitations encountered at quantum scales, relativistic speeds, and in complex systems.
A central innovation within ECM is the introduction of the concepts of apparent mass (Mᵃᵖᵖ) and effective mass (Mᵉᶠᶠ). These constructs extend the traditional framework to incorporate the effects of dark matter and dark energy, offering a more comprehensive understanding of gravitational dynamics.
The concept of apparent mass (Mᵃᵖᵖ) is established in classical mechanics, specifically through the fundamental relationship between force, mass, and acceleration (F = ma). However, it also integrates observational evidence from phenomena like dark energy, bridging classical principles with contemporary cosmological insights.
Extended classical mechanics offers a unified perspective on photon dynamics. It synthesizes classical principles with modern observations, emphasizing the conservation of photon energy (E) and the symmetry of gravitational interactions (Eg). This approach posits that photons maintain their intrinsic energy (E) while interacting with gravitational fields, dynamically exchanging gravitational interactional energy (Eg) during their trajectories.
In summary, ECM weaves together classical mechanics with modern astrophysical phenomena through the constructs of Mᵃᵖᵖ and Mᵉᶠᶠ. This cohesive model not only respects the heritage of classical mechanics but also embraces the complexities revealed by modern science, offering new avenues for exploring the cosmos.
Question
Soumendra Nath Thakur
February 05, 2025
Mᴏʀᴅ (Ordinary/Baryonic Matter): This is the mass of protons, neutrons, and electrons. It's the "normal" matter we're familiar with.
Mᴅᴍ (Dark Matter): This is non-luminous matter that interacts gravitationally but not through electromagnetic forces. It's included in the total matter mass.
Mᴍ (Total Matter Mass): Mᴍ = Mᴏʀᴅ + Mᴅᴍ. This is the total mass of ordinary and dark matter within a system.
Mᴅᴇ (Dark Energy Effective Mass): This represents the effective mass contribution from dark energy. It's important to note that this is not dark energy itself, but its effect on mass.
Mᵃᵖᵖ (Apparent Mass): This is a dynamic, non-physical quantity that reflects observed mass variations due to external forces. It can be negative.
Mᵉᶠᶠ (Effective Mass): Mᵉᶠᶠ = Mᴍ − Mᵃᵖᵖ = Mᴍ + Mᴅᴇ. This is the mass that governs gravitational interactions in ECM.
Mɢ (Gravitating Mass): Mɢ = Mᵉᶠᶠ. This is the mass that appears in the gravitational force equation in ECM.
Key Points and Clarifications:
Mᴅᴇ vs. Dark Energy: Mᴅᴇ is the effective mass contribution from dark energy, not dark energy itself. This distinction is crucial.
Apparent Mass as a Dynamic Term: Mᵃᵖᵖ is a dynamic and non-physical term. It reflects the observed mass variations, not a change in the actual physical mass.
Kinetic Energy in ECM: The equation (1/2) Mᴏʀᴅ⋅v² + (1/2)Mᴅᴍ⋅v² = −Mᵃᵖᵖ shows how the kinetic energy of ordinary and dark matter is related to the apparent mass.
Question
The concept of time is not an open question in physics—it is well established. Time emerges from existential events, as change cannot occur without existence and events. In this sense, time is an emergent property of the universe, manifesting through the changes that occur within it.
The widely accepted Big Bang model supports the idea that the universe has a definite beginning, whether it follows a cyclic pattern or originated from a singular event. This reinforces the notion that the universe, as we know it, did not always exist. The idea of a static, eternal universe has been discarded, and scientific progress must not be hindered by outdated assumptions about an ever-existing cosmos.
Even in cyclic universe models, the transition between existence and nonexistence implies a distinct demarcation. Within an existential state, events occur, leading to the emergence of time. However, within a nonexistent state, time has no meaningful interpretation. While there may be a temporal gap between successive phases of existence, the concept of time within a purely non-eventful state lacks significance for beings whose understanding is tied to event-driven existence.
This perspective highlights that time is meaningful only within an eventful existential state, as predicted by the Big Bang model, rather than as a continuously emerging entity in a noneventful state. At minimum, there should be a clear distinction between time in eventful and noneventful phases of existence.
Ultimately, the focus should be on understanding how time emerges within an eventful universe, rather than speculating about its presence in a noneventful existential state, where it would serve no purpose.
In summary, time emerges for existential events, and its absence in a noneventful state is best understood as a gap between successive periods of eventful existence. Rather than concerning ourselves with how long time ceases to exist in such a state, we should appreciate its presence within our eventful universe.
Question
February 05, 2025
Abstract
Extended Classical Mechanics (ECM) introduces the concept of negative apparent mass, redefining gravitational dynamics and acceleration in a novel framework. Unlike classical mechanics, ECM incorporates apparent mass, which dynamically alters the effective mass of a system. A reduction in apparent mass—especially when negative—leads to an increase in effective acceleration, offering a fresh perspective on cosmic expansion and gravitational interactions.
This framework challenges relativistic spacetime expansion, proposing that the observed accelerated recession of galaxies is a consequence of decreasing effective mass rather than the expansion of space itself. ECM provides an alternative explanation for Hubble’s Law, where galaxy recession velocities increase due to weakened gravitational binding rather than metric expansion. The model also establishes a deep connection between photon dynamics and dark energy, suggesting that both exhibit gravitational effects through apparent mass interactions rather than intrinsic rest mass.
By redefining the role of mass in gravitational equations, ECM aligns with empirical observations, such as those from Chernin et al. (2013) Dark energy and the structure of the Coma cluster of galaxies, and offers a consistent mathematical framework. This directly challenges the traditional reliance on spacetime curvature as the foundation of gravitational interactions and provides a new pathway to understanding cosmic acceleration, dark energy, and the fundamental nature of gravitational forces at interstellar and intergalactic scales.
Newton’s Second Law and Acceleration:
Newton's second law states that force is proportional to mass and acceleration. It implies that if mass increases, acceleration decreases, or if acceleration increases, mass must decrease to maintain the inverse relationship. Classical mechanics does not consider the concept of negative apparent mass, despite some observations suggesting it might be necessary in certain contexts.
Classical Acceleration vs. Effective Acceleration in ECM:
In classical mechanics, acceleration is inversely proportional to mass. However, in Extended Classical Mechanics (ECM), the introduction of apparent mass changes the total mass dynamically, leading to an effective mass. If the apparent mass decreases or becomes negative, the effective mass becomes smaller than the classical mass, leading to an increase in effective acceleration.
Apparent Mass, Effective Mass, and Their Influence on Acceleration in ECM:
In ECM, the effective mass is modified by the presence of apparent mass. This leads to an equation where the force depends on the sum of matter mass and apparent mass. The effective mass changes based on the apparent mass, which influences the acceleration.
Reduction of Apparent Mass and Its Effects:
A decrease in the apparent mass results in an increase in the effective acceleration under constant force. This demonstrates that the acceleration can increase due to the reduction of apparent mass rather than an increase in matter mass.
Effects of Apparent Mass Reduction on Effective Acceleration and Cosmological Dynamics:
The total effective mass in ECM can be influenced by dark energy, which has a negative effective mass. A negative apparent mass reduces the total effective mass, resulting in increased acceleration. This has implications for cosmological models and the understanding of gravitational effects, particularly in the context of dark energy and its role in cosmic expansion.
Extended Classical Mechanics vs. Relativity: A Superior Framework:
The introduction of negative apparent mass in Extended Classical Mechanics (ECM) offers a new perspective on classical mechanics, extending its explanatory power beyond traditional frameworks. This shift provides better insights into gravitational interactions, especially at interstellar and intergalactic scales.
Relativistic mechanics, particularly the use of Lorentz transformations, has limitations because it:
Does not account for classical acceleration effects between rest and moving frames.
Treats the speed of light as the primary defining factor, without considering material stiffness and its role in physical interactions.
ECM addresses these limitations and provides an alternative that challenges certain aspects of relativistic mechanics.
Conclusion:
The introduction of negative apparent mass in ECM leads to a better understanding of force, acceleration, and gravitational interactions, offering a more comprehensive framework compared to relativity.
Effective Mass, Acceleration, and Cosmological Implications in ECM:
ECM offers a framework where effective acceleration is influenced by effective mass. The effective mass is dynamically defined, incorporating both matter mass and dark energy.
The gravitational force equation within ECM accounts for the negative contribution of dark energy, affecting the gravitational dynamics. A decrease in effective mass leads to a reduction in distance for gravitational interactions, leading to higher acceleration when effective mass decreases.
Cosmological Implications of Decreasing Effective Mass:
In cosmology, the reduction of effective mass within gravitational dynamics explains the accelerated recession of galaxies or galactic clusters. This acceleration occurs not because of relativistic space expansion but due to the reduction in effective mass in gravitational interactions.
This interpretation challenges the conventional model of spacetime expansion in relativity, suggesting that galactic recession is the actual cause of observed cosmic dynamics, and not the expansion of space. This calls for a re-evaluation of the current framework of relativistic spacetime expansion.
Hubble’s Law as a Consequence of Decreasing Effective Mass:
In a system where gravitational force remains constant, the observed recession of galaxies and clusters corresponds to an increase in the distance between them over time.
An increase in distance requires a decrease in effective mass, which leads to the accelerated recession of massive bodies with increasing distance.
This phenomenon aligns with Hubble’s Law, which states that the recession velocity of galaxies increases with distance.
The accelerated expansion of the universe is explained by the continuous decrease in effective mass, rather than the relativistic expansion of space itself.
The recession of galaxies is thus a physical effect due to the reduction in effective mass, not an expansion of spacetime, challenging the relativistic interpretation of cosmic expansion.
Cosmological Implications:
The decreasing effective mass provides a logical and empirical foundation for reconsidering gravitational dynamics in cosmology.
This framework offers a mathematical explanation for the observed accelerated recession of galaxies, reinforcing the validity of Extended Classical Mechanics (ECM) as an alternative for understanding cosmic expansion.
Empirical Validation Through Observations:
The approach is supported by Hubble’s Law, which is based on astronomical observations.
Studies, such as the one by Chernin et al. (2013), provide observational backing for the mass-energy interactions described in ECM, lending credibility to the framework.
Mathematical Consistency Across Motion & Gravitation:
The relationship between motion and gravitational dynamics is coherent. As galaxies recede and distance increases, the effective mass decreases, which follows the classical inverse relationship between mass and acceleration.
This mathematical consistency underscores the robustness of ECM as a theoretical framework.
Implications for Cosmic Expansion:
The interpretation suggests that the recession of galaxies is caused by a decrease in effective mass, rather than the relativistic expansion of spacetime.
This challenges a core assumption of modern cosmology and provides an alternative explanation for the observed accelerated recession of galaxies.
Introduction to Extended Classical Mechanics (ECM):
ECM revises the understanding of gravitational dynamics by introducing the concept of effective mass, which accounts for both matter mass and apparent mass.
Apparent mass can take negative values, leading to significant implications for motion and acceleration in gravitational systems.
This framework challenges the conventional relativistic interpretation of cosmic expansion and offers an alternative explanation based on classical mechanics.
Defining Effective Mass in ECM:
In ECM, effective mass includes the matter mass of an object and the contribution from dark energy, which is negative.
If the apparent mass is negative, the effective mass becomes smaller, which increases acceleration under an applied force.
This leads to the inverse relationship between acceleration and effective mass, where a decrease in effective mass increases acceleration.
These principles have important implications for cosmology, particularly for explaining galactic recession without needing relativistic spacetime expansion.
Observations, such as those by Chernin et al. (2013), support the idea that negative apparent mass effects manifest in large-scale gravitational structures.
Reinterpreting Cosmic Expansion Through ECM:
Conventional cosmology attributes the accelerated expansion of the universe to the relativistic expansion of spacetime.
ECM proposes that the observed expansion is instead due to the accelerated recession of galaxies, which is caused by the decreasing effective mass within cosmological gravitational dynamics.
The recession velocity of galaxies is related to their distance through Hubble’s Law, but ECM suggests that this acceleration is due to the continuous decrease of effective mass, not the expansion of space.
As the effective mass decreases, galaxies appear to recede faster with increasing distance, which is explained by the dynamics of mass and acceleration in ECM.
Therefore, the recession of galaxies is a physical effect due to the reduction of effective mass, rather than a result of spacetime expansion.
Mathematical Basis of ECM’s Explanation
The relationship between effective mass and cosmic expansion is established through gravitational interactions.
As effective mass decreases due to the negative contribution of dark energy mass, gravitational binding weakens.
If gravitational force remains constant, the increase in separation between galaxies requires a further decrease in effective mass.
This results in greater acceleration of galaxies, explaining their increasing recession velocities.
Cosmological Implications of Decreasing Effective Mass
The decrease in effective mass provides a fundamental reason for the accelerated recession of galaxies and galactic clusters.
Instead of being caused by relativistic expansion of space, galactic recession results from the reduced gravitational binding due to decreasing effective mass.
This interpretation offers observational evidence supporting effective mass reduction as the actual cause of galactic recession.
It challenges the conventional relativistic model of spacetime expansion, suggesting that the physical motion of galaxies—not space expansion—is the correct explanation of cosmic dynamics.
Photon Motion and Its Equivalence to Dark Energy in ECM
ECM proposes an equivalence between the gravitational behaviour of massless photons and that of dark energy, both arising from apparent mass contributions.
1. Photon Gravitational Interaction:
Photons have energy but no rest mass, yet they interact gravitationally due to their apparent mass.
Their gravitational influence is not from intrinsic mass but from their interaction within gravitational potentials.
2. Dark Energy and Its Negative Effective Mass:
Dark energy contributes to gravitational interactions via apparent mass, similar to photons.
The effective mass of dark energy is negative, influencing large-scale cosmic dynamics.
This suggests that the gravitational effects of dark energy could be interpreted similarly to those of photons but at a cosmic scale.
Implications for Cosmic Expansion and Photon Gravitational Dynamics
In ECM, photons and dark energy influence gravitational interactions through their apparent mass rather than intrinsic rest mass.
Dark energy’s negative effective mass significantly modifies gravitational interactions at intergalactic scales, driving cosmic acceleration.
The equivalence between photon motion and dark energy dynamics suggests that the observed redshift in Hubble’s Law might be linked to the apparent mass effects of light propagation, rather than spacetime expansion.
Conclusion
ECM integrates massless objects into gravitational dynamics and establishes the link between apparent mass, photons, and dark energy.
The acceleration of cosmic expansion is fundamentally tied to decreasing effective mass, challenging the conventional idea of expanding spacetime.
Observational data, such as studies by Chernin et al. (2013), reinforce ECM as a strong alternative framework for explaining cosmic dynamics.
Key Research Insights
Hubble’s Law and Recession Velocity
The recession velocity of galaxies increases with distance, following Hubble’s Law.
This velocity can exceed the speed of light due to cosmic expansion, leading to observable redshift.
Redshift and Photon Energy Loss
As galaxies move apart, photon wavelengths stretch, resulting in cosmological redshift.
This leads to a decrease in photon frequency and energy over large cosmic distances.
Energy Dissipation of Photons
Photons lose energy while traveling through expanding space.
At extreme redshifts, their energy eventually reaches zero, making them undetectable.
This hints the observable universe’s limit at approximately 46 billion light-years.
Cosmic Expansion and Hubble’s Law Consistency
Hubble’s Law remains valid when considering the dynamic separation of galaxies.
Dark energy’s repulsive effect aligns with observations without requiring additional space-stretching mechanisms.
Observable Universe and Horizon
The observable universe is limited by how far light has travelled in 13.8 billion years.
Expansion and photon energy loss contribute to defining this horizon.
Integration into ECM Framework
Comparing ECM Predictions to Hubble’s Law
If ECM attributes galactic recession to decreasing effective mass, its predictions should align with or diverge from Hubble’s Law.
The relationship between recession velocity and redshift could serve as a test for ECM’s validity.
Quantifying Photon Energy Loss in ECM
ECM’s approach to mass and apparent mass could influence photon energy dissipation.
Investigating whether ECM predicts similar energy depletion trends without invoking space expansion would be a valuable test.
Effective Mass and the Horizon
ECM’s alternative explanation for cosmic expansion may offer a different perspective on the universe’s horizon.
Comparing ECM’s predictions of maximum observable distance with current empirical limits could validate its framework.
Extended Classical Mechanics (ECM) and Gravitational Dynamics
The concept of effective mass and its role in gravitational interactions.
How ECM reinterprets the equivalence principle and mass-energy dynamics in gravitational fields.
Dark Energy and Galaxy Cluster Structures
Observational studies on the Coma cluster and its connection to dark energy.
Evidence supporting mass-energy interactions affecting large-scale cosmic structures.
Photon Dynamics and Effective Mass in ECM
The relationship between photons, effective mass, and negative inertia.
How photon interactions exhibit properties analogous to dark energy in ECM.
ECM’s Perspective on Dark Energy
A proposed alternative to the standard ΛCDM model.
How ECM explains cosmic expansion without invoking traditional spacetime stretching.
Photon Energy Interactions and Conservation Laws
A symmetry-based approach to photon energy exchanges in gravitational fields.
How ECM maintains consistency with conservation principles while modifying traditional interpretations.
Hubble Constant and Implications for Cosmology
Empirical studies refining the Hubble constant measurement.
Potential evidence for physics beyond the ΛCDM framework.
Alphabetical List of ECM Terms
• Apparent Mass (Mᵃᵖᵖ) – A dynamic mass term reflecting observed mass variations under external forces, which can become negative due to effective mass contributions.
• Baryonic Mass – The component of matter consisting of protons, neutrons, and electrons, distinguishable from dark matter.
• Cosmological Integration in ECM – The incorporation of empirical cosmological observations and principles, such as dark energy effects at intergalactic scales, into ECM’s gravitational framework.
• Dark Energy (Λ or DE) – A cosmological component influencing the large-scale structure of the universe but having no effect within gravitationally bound systems.
• Dark Matter (DM) – A non-luminous form of matter detectable through gravitational effects, which does not interact with dark energy within gravitational influence but may interact at intergalactic scales.
• Effective Acceleration (aᵉᶠᶠ) – The acceleration influenced by effective mass (Mᵉᶠᶠ) in ECM, distinct from classical acceleration.
• Effective Mass (Mᵉᶠᶠ) – The net mass contributing to gravitational and inertial effects, defined as the difference between matter mass (Mᴍ) and apparent mass (Mᵃᵖᵖ).
• Energy-Frequency Relation – A fundamental equation from Planck's theory, extended in ECM to incorporate refined momentum and mass relations.
• Extended Classical Mechanics (ECM) – A theoretical extension of classical mechanics incorporating negative apparent mass, dark energy, and their effects on motion and gravity.
• Gravitational Potential Energy in ECM – The potential energy formulation incorporating effective mass, distinguishing it from traditional Newtonian gravity.
• Hubble’s Law – The observational relationship between distance and recession velocity of galaxies, more precisely refined in ECM.
• Intergalactic Scale – A scale at which both dark matter and dark energy effects become noticeable, unlike within gravitationally bound systems.
• Lorentz Transformations – Mathematical formulations in relativity that ECM redefines due to their limitations in accounting for acceleration and material stiffness.
• Matter Mass (Mᴍ) – The total mass including both baryonic and dark matter, where dark matter effects become significant at intergalactic scales.
• Momentum in ECM – A refined momentum formulation incorporating effective mass and quantum mechanical principles such as de Broglie’s wavelength relation.
• Negative Apparent Mass (Mᵃᵖᵖ < 0) – A condition where the apparent mass term reduces the observable mass, emerging in high-velocity or strong gravitational field conditions.
• Quantum Mechanical Integration in ECM – The incorporation of principles such as Planck’s and de Broglie’s relations into ECM’s mass and motion framework.
• Refined Newtonian Gravity – A modification of classical gravity within ECM that incorporates effective mass and reinterprets gravitational interactions beyond the Newtonian framework.
Keywords:
Extended Classical Mechanics, ECM, Negative Apparent Mass, Effective Mass, Matter Mass, Dark Energy, Gravitational Dynamics, Acceleration & Force, Newton’s Second Law, Effective Acceleration, Cosmological Implications, Interstellar & Intergalactic Scales, Relativity vs. ECM, Lorentz Transformations, Spacetime Expansion, Hubble’s Law, Galactic Recession, Redshift & Photon Energy Loss, Photon Dynamics, Negative Inertia, Mass-Energy Interactions, Gravitational Binding, Observational Evidence, Cosmic Expansion, Mathematical Consistency in ECM, Alternative to ΛCDM Model, Empirical Validation, Reinterpreting Cosmic Expansion, Energy Dissipation in Photons, Observable Universe Limit, Horizon & Effective Mass, Gravitational Force Equation in ECM, Apparent Mass Effects, Material Stiffness in Physical Interactions, Redefining Gravitational Interactions, Comparison with General Relativity, Recession Velocity & Distance Relation, Hubble Constant Refinement, Gravitational Potential & Photon Motion, Negative Contribution of Dark Energy,
References
1. Thakur,  S. N. Extended Classical Mechanics: Vol-1 - Equivalence Principle, Mass and Gravitational Dynamics. Preprints 2024, 2024091190. https://doi.org/10.20944/preprints202409.1190.v2
2. Chernin, A. D., Bisnovatyi-Kogan, G. S., Teerikorpi, P., Valtonen, M. J., Byrd, G. G., & Merafina, M. (2013). Dark energy and the structure of the Coma cluster of galaxies. Astronomy and Astrophysics, 553, A101. https://doi.org/10.1051/0004-6361/201220781
3. Thakur,  S. N. Photon Dynamics in Extended Classical Mechanics: Effective Mass, Negative Inertia, Momentum Exchange and Analogies with Dark Energy. Preprints 2024, 2024111797. https://doi.org/10.20944/preprints202411.1797.v1
4. Thakur,  S. N. A Nuanced Perspective on Dark Energy: Extended Classical Mechanics. Preprints 2024, 2024112325. https://doi.org/10.20944/preprints202411.2325.v1
5. Thakur,  S. N. A Symmetry and Conservation Framework for Photon Energy Interactions in Gravitational Fields. Preprints 2024, 2024110956. https://doi.org/10.20944/preprints202411.0956.v1
5. Riess, A. G., et al. (2019). Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics beyond ΛCDM. The Astrophysical Journal, 876(1), 85. DOI: https://doi.org/10.3847/1538-4357/ab1422
Question
The concept of negative apparent mass in extended classical mechanics is a groundbreaking innovation. It marks a turning point in classical mechanics, introducing negative mass and expanding its capabilities beyond traditional frameworks. This extension enhances classical mechanics, making it more powerful than relativistic mechanics.
Furthermore, velocity-induced relativistic Lorentz's transformations are flawed because they neglect classical acceleration between the rest and moving frames. They also overlook material stiffness in calculations, relying solely on the speed of light as the defining dynamic factor. For these reasons, extended classical mechanics stands as a far superior framework compared to the flawed foundations of relativistic mechanics.
Effective Mass and Acceleration Implications of Negative Apparent Mass in Extended Classical Mechanics (ECM):
Newton's Second Law and Acceleration:
In classical mechanics, Newton's second law is typically expressed as:
F = ma
This shows that force (F) is directly proportional to acceleration (a) and mass (m).
As force F increases, acceleration a increases proportionally. However, the relationship a ∝ 1/m means that if mass m increases, acceleration a will decrease, assuming force is constant.
In this framework, if acceleration increases while force increases, it suggests that mass must decrease to maintain the inverse relationship between acceleration and mass.
Apparent Mass and Effective Mass in ECM:
In Extended Classical Mechanics (ECM), this relationship is reflected in the equation:
F = (Mᴍ − Mᵃᵖᵖ) aᵉᶠᶠ
The term (Mᴍ − Mᵃᵖᵖ) implies that the effective mass is the difference between matter mass and apparent mass, which is a dynamic concept.
Apparent mass reduction:
If the apparent mass Mᵃᵖᵖ decreases (or becomes negative), this results in an increase in effective mass, which in turn causes an increase in acceleration a when the force F remains constant.
Thus, in ECM, a reduction in apparent mass leads to a corresponding increase in acceleration, aligning with the inverse relationship a ∝ 1/m, where m is the effective mass. This supports the idea that acceleration can increase without an actual increase in matter mass Mᴍ but rather a reduction in apparent mass Mᵃᵖᵖ.
Supporting Observational Findings:
The expression Mᵉᶠᶠ = Mᴍ + Mᴅᴇ, where Mᴅᴇ is negative, aligns with this reasoning. If the apparent mass Mᵃᵖᵖ (which could be represented Mᴅᴇ in this framework) is negative, the effective mass becomes:
Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ)
This negative apparent mass Mᵃᵖᵖ or, effective mass of dark energy (Mᴅᴇ), reduces the total effective mass, causing an increase in acceleration when force is applied, consistent with the relationship a ∝1/m.
Conclusion:
In this framework, the concept of effective mass Mᵉᶠᶠ is key to understanding how acceleration behaves when apparent mass changes. When apparent mass decreases (or becomes negative), the effective mass also decreases, leading to an increase in acceleration. This theory not only aligns with the classical force-acceleration-mass relationship but also supports observational findings, particularly the role of negative apparent mass in cosmological models or exotic gravitational effects.
Question
This discussion critically examines the concept of time dilation as proposed by Einstein’s theories of relativity and maintains that it is fundamentally an error in clock readings rather than a physical reality of time itself. While Special and General Relativity suggest that time slows down due to relative motion and gravitational potential differences, this interpretation overlooks the principles of standardized timekeeping established by authoritative bodies such as the International Bureau of Weights and Measures (BIPM) and the International System of Units (SI).
Recent experimental findings on piezoelectric crystal oscillators and photon behaviour in gravitational fields indicate that factors such as heat, mechanical forces, motion, and energy dissipation lead to phase shifts and frequency variations in clock mechanisms, which result in erroneous time readings. This paper asserts that relative time is an artefact of physical changes in measurement devices and not an intrinsic property of the universe. Adhering to standardized guidelines for clock time measurement is essential to avoid misinterpretation of such discrepancies as time dilation.
According to Einstein’s theory of relativity, time dilation is considered a fundamental aspect of spacetime behaviour, arising from relative motion and differences in gravitational potential.
Special Relativity states that time slows down for objects moving at high velocities relative to an observer.
General Relativity states that clocks in stronger gravitational fields tick slower than those in weaker fields.
However, the theory not only disregarded classical interpretations of time but also overlooked the prevailing standards for clock time measurement at the time.
Standardized Timekeeping and Its Importance:
Standardized timekeeping aims to achieve a single, consistent reference time across different locations and conditions, following the guidelines set by authoritative bodies such as the International System of Units (SI). In standardized time systems, such as Coordinated Universal Time (UTC), discrepancies in measurements due to environmental factors—including heat, mechanical forces, motion, and gravitational effects—are considered errors, as they cause deviations from the expected standardized value.
Nonetheless, all scientific disciplines, including relativity, must adhere to standardized time measurement principles. Organizations such as the International Bureau of Weights and Measures (BIPM), which existed prior to the introduction of the time dilation concept, and current standards such as the SI second—defined by atomic transitions—ensure precise definitions of time.
Furthermore, the constancy of the time scale in relation to entropy is a well-established principle.
Experimental Findings and Observational Evidence:
Recent experimental findings on piezoelectric crystal oscillators, along with observational data on photon behaviour within curved gravitational fields—distinct from the concept of curved spacetime—and the constancy of entropy in the time scale, collectively support the conclusion that time dilation is fundamentally an error in clock readings. These findings suggest that infinitesimal energy loss leads to frequency shifts and phase changes in clock oscillations, which have been misinterpreted as time dilation.
The Reinterpretation Against Time Dilation:
Through these experimental and observational findings, it is maintained that energy dissipation within clock mechanisms results in phase shifts and frequency variations, ultimately leading to perceived discrepancies in time that are mistakenly attributed to relativistic effects.
This research scientifically asserts that relative time is not an intrinsic property of the universe but rather an artefact of physical changes—such as heat, mechanical forces, motion, and gravitational effects—within clock mechanisms. It further emphasizes that any valid scientific approach must align with standardized guidelines for clock time measurement to ensure accuracy and consistency.
In essence, relative time emerges from relative frequencies. The phase shift in relative frequencies, caused by infinitesimal energy loss and the corresponding elongation of oscillation wavelengths, occurs in any clock operating between different relative locations due to relativistic effects or variations in gravitational potential. These shifts result in errors in clock time readings, which have been incorrectly interpreted as time dilation.
Soumendra Nath Thakur
January 21, 2025
Question
ORCiD: 0000-0003-1871-7803
1. The Concept of a Static Universe
Historically, the static universe model was considered a viable alternative but was ultimately disproven by observational evidence. Albert Einstein initially proposed a static, isotropic, and homogeneous universe, introducing the cosmological constant (Λ) to counteract gravitational collapse and maintain stability. However, in 1929, Edwin Hubble's discovery of the redshift of galaxies provided definitive evidence of an expanding universe. Hubble's law demonstrated that the redshift of galaxies is proportional to their distance, signifying that galaxies are receding from each other at speeds increasing with distance.
In light of this discovery, Einstein abandoned the static universe model, calling his introduction of the cosmological constant "the biggest blunder of my life." Consequently, the expanding universe model became the cornerstone of modern cosmology, and no reasonable alternative to it has been validated since.
2. Mass Loss and Gravitational Redshift
The claim that mass loss from stars or galaxies should result in a decreasing gravitational redshift is not scientifically accurate. Gravitational redshift, also known as the Einstein shift, depends on the gravitational potential of the source and the intrinsic and interactional energy of the photon at the point of emission, not on gradual mass changes over time.
3. Photon energy is a key parameter influenced by gravitational and cosmological phenomena during its journey through space. At emission, a photon’s total energy includes:
Eₜₒₜₐₗ,ₚₕₒₜₒₙ = E + Eg
• Intrinsic Energy (E): The inherent energy of the photon, proportional to its frequency.
• Interactional Energy (Eg): The energy gained from gravitational interaction with the source's gravitational potential.
Within the gravitational influence of massive bodies, photons expend Eg to escape the gravitational well, leading to gravitational redshift. However, the intrinsic energy (E) of the photon remains intact, as this component is unaffected by gravitational interactions.
Therefore, as the photon escapes the gravitational influence of the source, it does not lose its intrinsic energy (E); instead, it expends its interactional energy (Eg). The observed gravitational redshift arises from this expenditure, leading to a decrease in the total energy (Eₜₒₜₐₗ,ₚₕₒₜₒₙ) of the photon as it climbs out of the gravitational well.
4. Why Mass Loss Does Not Affect Gravitational Redshift:
• Gravitational redshift is determined by the gravitational potential at the point of photon emission. For a star or galaxy, this potential remains effectively constant over short timescales compared to the gradual mass loss caused by electromagnetic radiation or particle emissions.
• A photon's interaction with gravity is independent of the source's gradual mass changes, as long as the emission conditions remain unchanged.
5. Doppler and Relativistic Contributions:
Gravitational redshift is distinct from the relativistic Doppler effect, which arises due to the relative motion between the photon source and the observer. The Doppler factor, which relates the source and observed frequencies, is given by:
Doppler Factor = √(1−β)/(1+β), β = v/c
Here, v is the relative velocity of the source, and c is the speed of light. The Doppler effect affects photon frequency (f) and wavelength (λ) based on relative motion, whereas gravitational redshift results solely from energy interactions with the gravitational potential.
Illustration:
For a typical photon with intrinsic energy E = 4.0 × 10⁻¹⁹ J, its emission frequency corresponds to f = 6.0368 × 10¹⁴ Hz. The gravitational redshift arises as the photon expends its interactional energy (Eg) while escaping the gravitational field, leading to an observed decrease in frequency (fr) and a proportional increase in wavelength (λr).
In summary, a photon retains its intrinsic energy (E) as it escapes the gravitational influence of a massive object, while the redshift results from the loss of interactional energy (Eg). Gradual mass loss from stars or galaxies has no direct impact on this process, as gravitational redshift is governed by the gravitational potential at the point of emission and the photon's total energy interaction with that potential.
6. Photon Behaviour in Dark-Energy-Dominated Cosmic Space
As a photon exits the zero-gravity sphere of gravitationally bound systems and enters dark-energy-dominated intergalactic space, its energy behaviour changes due to the increasing distances between receding galaxies. In this interpretation, the increased separation of galaxies is treated as a physical increment of distances rather than an expansion of the natural spacetime fabric. The implications for photon energy are as follows:
Loss of Intrinsic Energy (E):
In contrast to its behaviour within gravitationally bound regions, a photon traveling through intergalactic space experiences a permanent loss of intrinsic energy (E). This energy loss is caused by the photon having to traverse additional physical distances created by the increasing separation of galaxies. The longer the photon’s journey, the greater the energy it expends to cover these growing distances, manifesting as a reduction in frequency (cosmological redshift).
Physical Increment of Distance:
Rather than attributing this phenomenon to the relativistic expansion of spacetime, the interpretation focuses on the physical increase in distances between galaxies driven by dark energy. The receding galaxies contribute to a lengthening of the photon’s travel path, resulting in greater energy expenditure.
Comparison with Gravitational Redshift:
• Gravitational Redshift: Results from a photon expending Eg while escaping a gravitational well, with E remaining unaffected.
• Cosmological Redshift (Revised): Results from the photon losing intrinsic energy (E) due to the extended physical travel distance required in intergalactic space dominated by dark energy.
7. Implications for Photon Energy Dynamics
This interpretation of distance increment between galaxies provides an alternative framework for understanding cosmological redshift. It underscores that the photon's energy loss during its journey is linked to the physical realities of increasing galaxy separations rather than the relativistic notion of spacetime fabric expansion. The observed redshift is thus a direct consequence of the photon's traversal of additional, physically real distances, reinforcing the role of dark energy in driving the universe's large-scale structure.
Conclusion
In summary, photons retain their intrinsic energy (E) within the gravitational influence of massive bodies, expending only their interactional energy (Eg) to escape gravitational wells. This ensures that the photon’s inherent properties remain intact. However, in dark-energy-dominated intergalactic space, the photon loses intrinsic energy due to the physical increment of distances between receding galaxies. This energy loss, observed as cosmological redshift, arises not from a relativistic expansion of spacetime but from the tangible elongation of the photon’s travel path in an evolving universe.
Addressing the broader question, "Is there a reasonable alternative to the theory of the expanding universe?"—the overwhelming observational evidence, including the cosmic microwave background (CMB), large-scale galaxy distributions, and redshift-distance relationships, firmly supports the theory of increasing distances between galaxies driven by dark energy. The notion of a static universe, previously proposed as an alternative, has been empirically invalidated by Hubble’s discoveries and subsequent advancements in astrophysical observations.
While interpretations of cosmic expansion may vary, such as the preference for framing the phenomenon as physical distance increments rather than spacetime fabric expansion, these distinctions do not undermine the fundamental premise of an evolving, dynamic cosmos. As of now, no alternative model has provided a comparable explanatory and predictive framework for the observable universe. Thus, while scientific exploration should always remain open to novel ideas, the theory of increasing distances between galaxies—whether interpreted as spacetime expansion or physical separation—remains the most reasonable and well-supported explanation for the universe’s large-scale behaviour.
Question
Author Comment:
This study synthesizes key conclusions derived from a series of research papers on extended classical mechanics. These papers provide a fresh perspective on established experimental results, challenging traditional interpretations and highlighting potential inaccuracies in previous theoretical frameworks. Through this reinterpretation, the study aims to refine our understanding of fundamental physical phenomena, opening avenues for further exploration and validation.
Keywords: Photon dynamics, Gravitational interaction, Negative mass, Cosmic redshift, Extended classical mechanics,
Reversibility of Gravitational Interaction:
A photon’s interaction with an external gravitational force is inherently reversible. The photon maintains its intrinsic momentum throughout the process and eventually resumes its original trajectory after disengaging from the gravitational field.
Intrinsic Energy (E) Preservation:
The photon's intrinsic energy E, derived from its emission source, remains unaltered despite gaining or losing energy (Eg) through gravitational interaction within a massive body's gravitational influence.
Contextual Gravitational Energy (Eg):
The gravitational interaction energy Eg is a localized phenomenon, significant only within the gravitational influence of a massive body. Beyond this influence, in regions of negligible gravity, the photon retains only its intrinsic energy E.
Cosmic Redshift and Energy Loss (ΔE):
In the context of cosmic expansion, the recession of galaxies causes a permanent loss of a photon's intrinsic energy ΔE due to the cosmological redshift. This energy loss is independent of local gravitational interactions and reflects the large-scale dynamics of the expanding universe.
Negative Apparent Mass and Antigravitational Effects:
The photon's negative apparent mass Mᵃᵖᵖ,ₚₕₒₜₒₙ generates a constant negative force −F, which manifests as an antigravitational effect. This behaviour parallels the characteristics attributed to dark energy in its capacity to resist gravitational attraction.
Wave Speed Consistency (c):
The constant negative force −F, arising from the photon's energy dynamics, ensures the photon’s ability to maintain a constant wave propagation speed c, irrespective of gravitational influences.
Negative Effective Mass:
The photon’s negative effective mass Mᵉᶠᶠ,ₚₕₒₜₒₙ allows it to exhibit properties akin to those of a negative particle. This feature contributes to its unique interaction dynamics within gravitational fields and reinforces its role in antigravitational phenomena.
Constant Effective Acceleration:
From the moment of its emission at an initial velocity of 0m/s, the photon experiences a constant effective acceleration, quantified as aᵉᶠᶠ,ₚₕₒₜₒₙ = 6 × 10⁸ m/s². This acceleration underpins the photon’s ability to achieve and sustain its characteristic speed of light (c), reinforcing its intrinsic energy and momentum dynamics.

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