Newton's Warning and Einstein's Oversight: A Critique of Relativity’s Misinterpretations.

Soumendra Nath Thakur

10-10-2024

In a critical video, the creator references Sir Isaac Newton’s warning from his Principia Mathematica:  Relative quantities are not the quantities themselves, whose names they bear, but are the sensible measures of them. By the names time, space, place, and motion, their sensible measures are to be understood, and it is improper to mean the measured quantities themselves by these terms. Those who interpret these words as the measured quantities violate the accuracy of language, and those who confuse real quantities with their relations and sensible measures corrupt the purity of mathematical and philosophical truths.

Two centuries later, a 26 year old graduate from the Polytechnic Institute of Zurich—who was the only one in his class not to receive an assistant position—would precisely fail to heed this warning, plunging modern physics into a state of philosophical free fall. One hundred and twenty years later, Einstein’s theories would be scrutinized, and the price for disregarding Newton’s warning would eventually come due.

The video’s creator even humorously remarked, “I truly think Einstein is a practical joker, pulling the legs of his overly enthusiastic followers, who have become more 'Einsteinish' than him.

Seven years after the creation of this critique video, I offer my own commentary. The word “sensible,” as used here, refers to phenomena perceived through the senses, synonymous with "physical" or "empirical." Thus, a "sensible measure" would mean a "physical measure." Yet time, space, place, and motion are not physically measurable entities in themselves. They are frameworks for measuring events (in time), positions (in space), locations (in place), and changes in position (motion).

The warning presented in the video is both clear and accurate. It explains that relativity is a method for measuring quantities, not the quantities themselves. Einstein, however, violated this mathematical principle by presenting relativistic concepts like time as actual quantities—turning "sensible time" into "natural time" and thereby undermining the independence of absolute time.

Additionally, "sensible space" under relativity refers to "natural space," which is bendable, a direct violation of the fundamental concept of space as the dimension in which all events occur. Place, as a measure of distance from an origin, and motion, as the measure of how fast objects change location, are misrepresented within the relativistic framework.

While relativity aims to connect cosmic time to events in the universe, it cleverly redefines clock time as "natural time," implying that because the clock is a physical object, the time it measures must also be natural. This assumption is misleading—the very idea of "natural time" is a farce.

Relativity also disregards the broader understanding of wavelength dilation, which corresponds to clock time distortion. It falsely presents this as time dilation, even though time dilation cannot be measured on a standard clock, which is built to measure standardized time, not the flawed time dilation proposed by relativity.

The experiments conducted by biased proponents of relativity led to the erroneous conclusion that time itself is dilatable. In reality, they should have measured wavelength dilation, which occurs due to phase shifts in frequencies, leading to slight energy loss in an oscillator’s wave and corresponding so-called "time dilation."

Furthermore, the relativistic notion that gravity is a result of spacetime curvature is a flawed interpretation. Gravitational lensing experiments, which claim that light bends due to spacetime curvature, are biased. In truth, the bending of a photon’s path is caused by momentum exchange with the gravitating body, which results in curvature within the gravitational field—not spacetime.

Relativity’s theories are built upon fundamentally flawed concepts of time and space as "spacetime." Consequently, the entire relativistic framework is unreliable. Time, by nature, is cosmic and absolute, which negates any possibility of time dilation or the reduction of age in the returning twin, as described in the famous twin paradox.

In conclusion, the video rightfully exposes the flaws in relativity and shows how Einstein’s theories stand in contradiction to Newton’s prescient warning. 

The Nexus of Existence and Events: A New Perspective on Cosmic Structure

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

06-10-2024

Abstract

This work articulates a vision of the ultimate imperceptible existence preceding the universe—a pre-universe from which the primordial universe emerged through the Big Bang. This perspective emphasizes the interplay between existence and events, positing that events are the activators of time and space, rendering them measurable and relevant. The framework extends the traditional Big Bang theory by proposing that time, space, and matter are emergent phenomena arising from a foundational state of infinite energy density and gravity. By exploring the relationships among existence, events, quantum fluctuations, and key cosmic milestones, this study offers a coherent model that aligns with contemporary cosmology while inviting deeper inquiries into the origins and evolution of the universe.

Keywords: Existence, Events, Big Bang, Cosmic Structure, Quantum Fluctuations,

Presentation:

The primary objective is to articulate a vision of the ultimate imperceptible existence preceding the universe—a pre-universe from which, in accordance with the principle of conservation of energy, the primordial universe emerged into physical existence through the event of the Big Bang. This moment marked the initiation of the universe's expansion, the birth of time, and the formation of matter, through a cascade of events that continue to this day and will persist indefinitely into the future.

This interpretation of the Big Bang theory, combined with a conceptualization of the ultimate existence preceding the universe, presents a cohesive framework that aligns with modern cosmology. The pre-universe is envisioned as a state of infinite energy density and gravity, akin to the classical singularity described in the Big Bang model. In this view, time and space are not intrinsic properties of existence but rather emergent phenomena, activated by events. Without events, time stands still (t₀), and space collapses to a point, as shown in the following equations:

Equation 1:

existence − events = 0⋅time = t₀

 

This equation implies that in the absence of events, time becomes irrelevant—frozen in a state where progression ceases.

Equation 2:

space(x,y,z) = 0

Here, space, too, collapses to a zero state when events do not occur, reflecting the interdependence of time, space, and events.

Equation 3:

time(t) + space(x,y,z) = >0 when events occur in existence

Events within existence activate time and space, making both measurable.

Equation 4:

existence + events = time(t) + space(x,y,z) = >0

Existence, when coupled with events, gives rise to spacetime.

This vision emphasizes the dynamic nature of space and time, which only "activates" in response to events occurring within existence. In this framework, the Big Bang can be seen as the pivotal event that initiated the unfolding of space and time, giving rise to the observable universe's structures. The pre-universe, while imperceptible and beyond current empirical scrutiny, serves as the source of the energy that formed all known matter and energy in the universe, consistent with the principle of conservation of energy.

Furthermore, this interpretation builds upon established principles, such as the conservation of energy and the relational nature of space and time. It asserts that the mass-energy content of the universe—comprising dark energy, dark matter, and normal matter—emerges from the infinite energy housed in the pre-universe. This aligns with contemporary cosmology, even though the characteristics of the pre-universe remain conceptual.

The model underscores that time and space are contingent on the occurrence of events within existence. Without these events, both time and space would remain collapsed, devoid of relevance. The unfolding of the universe, from its initial singularity-like state, leads to the expansion and structure we observe today, consistent with the Big Bang theory, while extending into deeper theoretical territory regarding pre-Big Bang conditions and the nature of space and time itself.

In conclusion, this comprehensive vision offers a scientifically coherent and conceptually rich extension of the Big Bang theory. By exploring the emergence of time, space, and matter from an imperceptible pre-universe, this model resonates with key principles of modern physics while pushing the boundaries of cosmological inquiry.

Supportive Alignment of the Pre-Universe Vision with the Emergence and Evolution of the Universe:

In the context of cosmology, existence serves as the fundamental prerequisite for all subsequent events. Without existence, no events can occur, and consequently, time would have no meaning. This idea directly corresponds to the vision of a pre-universe—an imperceptible state of existence from which events such as the Big Bang and subsequent cosmic evolution emerged. As outlined in The Emergence and Evolution of the Universe, events are essential activators of time. Time gains relevance only in the presence of events, which, as illustrated in Equation 1, cause time and space to “activate” within existence.

This emphasis on events as activators of time and space is also evident in the notion that without events, time progression halts—a concept consistent with the interpretation of t₀, where time becomes frozen in the absence of events. This static state reflects the same fundamental relationship between events and the emergence of time discussed in the pre-universe model.

Existence as a Prerequisite for Events and Cosmic Structure:

The pre-universe is imagined as a foundational state, providing the necessary existence from which events could unfold, enabling the evolution of the universe. According to The Emergence and Evolution of the Universe, events such as particle collisions, galaxy formation, and quantum interactions are the driving forces behind the universe's ongoing development. This highlights how the progression of cosmic structure, from the primordial universe to the vast expanse we observe today, is shaped by a sequence of events occurring within existence.

Equation 3, which posits that time and space emerge when events occur in existence, directly aligns with this view. Just as events define the development of the universe, this equation supports the idea that spacetime itself is contingent on the activity within existence, particularly during significant events like the Big Bang or galaxy mergers. These occurrences give rise to the evolving structure of the universe.

Pre-Existence and Quantum Fluctuations:

The concept of pre-existence probability discussed in The Emergence and Evolution of the Universe aligns with the speculative nature of the pre-universe vision. Before the familiar events of the Big Bang, the pre-universe might have housed the potential for quantum fluctuations, as suggested in some theoretical models. These quantum fluctuations, related to Zero-Point Energy (ZPE), are believed to have seeded the density variations that led to the formation of galaxies and other cosmic structures. This idea seamlessly integrates with the notion that events in the pre-universe initiated the processes that led to the Big Bang and subsequent cosmic inflation, which smoothed out early irregularities and provided the initial conditions for the observable universe.

In the pre-universe model, these early quantum events would serve as the "activators" of time and space, echoing the principle that time only becomes relevant when events occur within existence. As The Emergence and Evolution of the Universe suggests, the primordial universe represented a period of infinite density and energy, where pre-existing conditions paved the way for the unfolding of the Big Bang.

Key Events in the Evolution of the Universe:

The major events following the Big Bang—cosmic inflation, nucleosynthesis, and recombination—are milestones in the universe's evolution, and they are essential in shaping its current structure. These key events highlight the critical role that events play in driving the progression of time and space, as discussed in both the pre-universe model and The Emergence and Evolution of the Universe.

Inflation, the rapid expansion of the universe shortly after the Big Bang, corresponds to the initial expansion of space.

Nucleosynthesis, where atomic nuclei formed, and recombination, when electrons and protons combined to form neutral atoms, demonstrate how events directly contribute to the structure of matter and energy in the universe.

These events mark the transitions that allowed for the formation of galaxies and the eventual large-scale structures of the cosmos, reaffirming that both time and space are shaped by the succession of events within existence.

Cosmic Structure and Physical Laws:

The universe's ongoing development is governed by physical laws and the interplay of space, time, matter, and energy. The Emergence and Evolution of the Universe underscores that these components are intertwined within spacetime, shaped by the events that occur in the cosmos. The vision of the pre-universe posits that this complex relationship between events and spacetime can be traced back to a singular moment, where the first event—the Big Bang—initiated the continuous evolution of cosmic structure.

By viewing the universe as an interconnected system where existence, events, time, and space are dynamically related, this vision enhances the understanding of how the universe emerged from a state of infinite energy density and evolved into its current state. This perspective, while rooted in the principles of conservation of energy, also ventures into deeper inquiries about the nature of the pre-universe and the conditions that led to the formation of spacetime.

Conclusion:

The vision of the pre-universe, as articulated through the relationship between existence, events, time, and space, finds strong support in the principles outlined in The Emergence and Evolution of the Universe. Both views emphasize that time and space emerge as a result of events, and that existence serves as the foundation for cosmic development. The events that shape the universe—from quantum fluctuations in the pre-universe to galaxy formation in the observable universe—are essential in understanding how spacetime unfolds and evolves. This alignment not only reinforces the scientific coherence of the pre-universe model but also extends its conceptual reach into the theoretical foundations of cosmology.

#Existence, #Events, #BigBang, #CosmicStructure, #QuantumFluctuations,

Nuanced Interpretation of Potential Energy, Mass, and Kinetic Energy in Classical Mechanics:

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

04-10-2024

Abstract

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 proportionality between force and acceleration (a ∝ F) and the inverse relationship between acceleration and mass (a ∝ 1/m) illustrate that increasing acceleration necessitates a decrease in effective mass, emphasizing the dynamic interplay of these variables. Furthermore, the generation of kinetic energy stems from changes in potential energy, underscoring that KE is not a "free lunch," but rather a consequence of energy transformations. The paper suggests that without accounting for these changes, the classical mechanics framework remains incomplete. By recognizing the interconnectedness of PE, mass, and KE, this interpretation provides deeper insights into the principles governing motion and energy transformations within physical systems.

Presentation

In classical mechanics, the relationships among potential energy (PE), mass, and kinetic energy (KE) are often interpreted too simplistically. A more nuanced understanding reveals that changes in potential energy inevitably influence mass and the generation of kinetic energy.

While force (F) and acceleration (a) are directly proportional (a ∝ F), mass (m) is inversely proportional to acceleration (a ∝ 1/m). This means that as acceleration increases due to an applied force, the effective mass may decrease to maintain equilibrium in this relationship. This inverse relationship underscores that alterations in potential energy significantly impact mass.

Moreover, the generation of kinetic energy cannot be considered a "free lunch." Kinetic energy is fundamentally derived from the change in potential energy, represented by the equation KE = ΔPE = (PE in motion) − (PE at rest). This indicates that the kinetic energy produced during motion is a direct consequence of changes in potential energy. Thus, the mass of the object cannot remain constant; it must adapt to reflect these energy transformations.

Importantly, when considering only the relationship between force and acceleration (a ∝ F), without accounting for changes in potential energy, the overall understanding remains incomplete. The mass (m), which in classical mechanics can represent potential energy, must also change when potential energy varies. Therefore, ΔPE should be viewed as influencing a mass that differs from the invariant mass, effectively representing an effective mass.

Conclusion

Recognizing the interconnectedness of potential energy, mass, and kinetic energy provides a more comprehensive view of classical mechanics. This nuanced interpretation enriches our understanding of how energy transformations influence the properties of mass and motion within physical systems. Acknowledging these relationships not only clarifies existing theories but also opens avenues for future research and practical applications in the field of physics.

References:

[1] Thakur, S. N. (2024). Extended Classical Mechanics: Vol-1 - Equivalence Principle, Mass and Gravitational Dynamics. Preprints.org (MDPI). https://doi.org/10.20944/preprints202409.1190.v2

Significance of Planck's constant (h):

Planck's constant is fundamental to quantum mechanics, which describes the behaviour of particles and waves on the atomic scale. It's also essential for understanding how atoms and subatomic particles move, and how quantum mechanics and modern electronics operate.

German physicist Max Planck discovered Planck's constant, represented by the symbol h, in 1900 while studying blackbody radiation. 

Planck was trying to develop a formula to describe how objects emit radiant energy based on their heat. He observed that existing formulas didn't accurately describe the results for all temperatures. To keep his formula accurate, he defined that energy could only be emitted in whole increments of a value. He calculated this increment value from observational data, which became known as Planck's constant.

The value of Planck's constant is 6.626 × 10⁻³⁴ Js.

Time Dilation: A Misguided Notion

​Soumendra Nath Thakur
03-10-2024

Time dilation is, in my view, a fabricated concept. No scientist can sit before me and convincingly prove that time dilates or that time travel is possible. I refuse to accept such claims, and I would scientifically maintain that any scientist attempting to establish the idea of time dilation is not only intellectually dishonest but also driven by preconceived notions promoting this flawed concept.

Time, in reality, progresses constantly, independent of the varying events that occur within it. The idea that time dilation, where t' > t (proper time), could occur within the proper time scale is impossible—making time dilation inherently immeasurable. If a clock appears to run more slowly compared to a standard clock, this suggests an error in the faulty clock, not evidence of time dilation. The notion of time dilation is nothing more than a "cock and bull story" designed to deceive the average mind.

Those who invoke the name of Albert Einstein to support the concept of time dilation are themselves biased and misguided. I challenge anyone—or anything—to face me in a scientific contest on this matter. I stand ready to expose the flaws in any contest promoting time dilation and welcome any challengers willing to dispute this position.

#FlawedTimeDilation

The Significance of the Planck Length in Quantum Gravity.

 

03-10-2024

To whom it may concern,

The Planck length is highly relevant in the context of quantum gravity, as it represents a fundamental length scale crucial for understanding quantum gravitational effects.

The Planck length, one of the Planck units introduced by Max Planck, plays a pivotal role in theoretical physics. For instance, the speed of light is one Planck length per Planck time.

At this scale, the Planck length serves as a lower bound for the smallest possible length in spacetime. It is theoretically impossible to construct a device capable of measuring lengths smaller than this scale. Moreover, at the Planck scale, gravity's strength is expected to become comparable to other fundamental forces, potentially leading to a unification of all forces.

Additionally, the Planck length may represent the approximate lower limit for the formation of black holes. It is at this scale where quantum gravitational effects become significant, allowing for the measurement of the geometry of space and time.

In conclusion, the Planck length may represent a minimal, fundamental length, thereby completing the set of fundamental scales in nature.

#PlancklScale #PlanckLength #PlanckTime

Piezoelectric and Inverse Piezoelectric Effects on Piezoelectric Crystals: Applications across Diverse Conditions

 ResearchGate.net Publication

Soumendra Nath Thakur
03-10-2024

Abstract

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 is highlighted as the mechanism that enables crystals to generate electric charge in response to mechanical stress, which is essential for devices such as sensors and energy harvesters. The inverse piezoelectric effect is also examined, where electric fields induce mechanical deformation, applicable in actuators and sound-generating devices. Additionally, the influence of gravitational forces on enhancing the piezoelectric effect is analysed, particularly in innovative applications such as raindrop harvesting and energy conversion from vibrations. Findings from recent studies illustrate the potential for developing advanced and eco-friendly piezoelectric devices, paving the way for sustainable technologies in diverse fields.

Keywords: Piezoelectric Effect, Inverse Piezoelectric Effect, Accelerometers, Gravitational Force, Energy Harvesting,

Soumendra Nath Thakur
ORCiD: 0000-0003-1871-7803
Tagore’s Electronic Lab, WB, India
Correspondence: postmasterenator@gmail.com
postmasterenator@telitnetwork.in

Newton's Second Law and Piezoelectric Accelerometers:

A piezoelectric crystal, like any physical object, adheres to Newton's second law of motion, expressed mathematically as:

F = ma

Where:

F is the applied force,
m is the mass, and
a is the acceleration.

In piezoelectric accelerometers, this principle is utilized by attaching a seismic mass to the piezoelectric crystal. When the accelerometer experiences vibrations, the mass remains stationary due to inertia, resulting in the deformation of the piezoelectric crystal—either compressing or stretching. The mechanical stress exerted on the crystal is directly proportional to the input acceleration, as the force acting on the crystal derives from the mass and acceleration influencing it.

Piezoelectric Effect in Accelerometers:

As the crystal deforms due to mechanical stress, it generates an electric charge—a phenomenon known as the piezoelectric effect. The amount of charge generated is proportional to the applied force, which is itself determined by the product of the seismic mass and the input acceleration. Consequently, an increase in either mass or acceleration results in a greater force acting on the crystal, leading to an enhanced electrical output. This unique property makes piezoelectric materials vital in vibration sensors and accelerometers, where they convert mechanical vibrations into electrical signals for accurate measurement and analysis.

Hooke's Law and Elastic Deformation in Piezoelectric Crystals:

Piezoelectric crystals exhibit deformation when subjected to mechanical stress, and within the linear elastic range, this deformation follows Hooke's Law:

F=−kx

Where:

F is the applied force,

k is the stiffness (spring constant) of the material, and

x is the displacement from the equilibrium position.

This linear response, where the force is directly proportional to displacement, is fundamental to the behaviour of piezoelectric materials. For small mechanical stresses, the crystal’s behaviour remains predictable, and the relationship between stress and deformation is linear. This property is crucial in applications like sensors, actuators, and energy harvesters, where precise coupling between mechanical and electrical phenomena is essential.

Working Principle of Piezoelectric Crystals:

The operation of a piezoelectric crystal relies on its capacity to convert mechanical energy into electrical energy. When a mechanical force, such as pressure or vibration, is applied to the crystal, it undergoes deformation, leading to an internal displacement of ions. This displacement generates an electric charge measurable as voltage (electromotive force, or EMF) across the crystal's surfaces. The voltage's magnitude is directly proportional to the applied pressure, allowing the piezoelectric material to efficiently convert mechanical stress into electrical energy. Typically, this electrical output manifests as an alternating current (AC) signal, applicable in various sensing and transducer applications.

Piezoelectric Effect:

The piezoelectric effect refers to the ability of certain dielectric materials to generate surface charges in response to mechanical deformation. In their neutral state, piezoelectric crystals maintain a balance between positive and negative charges. However, when subjected to external forces, this balance is disrupted, causing net charges to emerge on opposite faces of the crystal. This ion displacement results from internal polarization, rendering piezoelectric materials highly effective in converting mechanical stress into electrical output. This characteristic is exploited in numerous applications, including vibration sensors, pressure transducers, and energy harvesters.

Inverse Piezoelectric Effect:

Beyond generating electricity in response to mechanical stress, piezoelectric materials also demonstrate the inverse piezoelectric effect. In this process, applying an external electric field induces mechanical deformation in the crystal. The crystal’s structure alternates between expansion and contraction in response to the electric field, thus converting electrical energy into mechanical motion. This effect is particularly advantageous in applications such as actuators, where electrical signals are harnessed to create precise mechanical movements.

When the frequency of this expansion and contraction falls within the audible range (20 Hz to 20,000 Hz), the resultant mechanical vibrations generate sound waves. This property is utilized in devices such as speakers and ultrasonic transducers, where piezoelectric materials convert electrical energy into sound or ultrasonic waves.

Piezoelectric Effect through Gravitational Force:

The piezoelectric effect is a remarkable phenomenon wherein specific materials generate electricity when subjected to mechanical stress, such as being squeezed, pressed, or bent. Gravitational force, such as the pull of Earth’s gravity, can significantly trigger or enhance this effect across various applications. For example, in piezoelectric accelerometers, when the device moves, gravity acts on a piezoelectric material within, creating an electric charge that indicates the device's acceleration. Similarly, piezoelectric rotational energy harvesters utilize gravitational forces as they spin, resulting in minor deformations in a specially designed component coated with piezoelectric material, thereby generating electrical energy.^[1]

An innovative application involves raindrop harvesting, where the impact force of falling raindrops on a piezoelectric surface generates a small amount of electricity, influenced by the design of the surface itself. Moreover, gravity plays a crucial role in shaping and compressing piezoelectric materials into curved or compact forms during heating, enhancing their efficiency for use in sensors, actuators, and energy harvesters. Notably, the piezoelectric effect is reversible; these materials can generate electricity from motion and change shape when an electric current is applied, underscoring their versatility and value in everyday technologies.^[2]

A pertinent study titled "Gravity-Induced Structural Deformation for Enhanced Ferroelectric Performance in Lead-Free Piezoelectric Ceramics" by Kim, S. et al., further elucidates this relationship. The researchers discovered that integrating gravity into the heating and shaping processes of specialized ceramic materials significantly enhances their ability to generate electricity when mechanically stressed. This enhancement stems from gravity-induced structural changes that tighten the material's atomic bonds, resulting in improved electricity generation. These findings pave the way for developing better and more eco-friendly piezoelectric devices, including sensors and energy harvesters, thereby promoting sustainable technologies across various fields. ^[3]

References:

[1] AZoSensors, (2019, August 22). Applications and the working principle of piezoelectric accelerometers, https://www.azosensors.com/article.aspx?ArticleID=309
[2]Galassi, C., Dinescu, M., Uchino, K., & Sayer, M. (2000), Piezoelectric Materials: Advances in science, technology and applications. In Springer eBooks. https://doi.org/10.1007/978-94-011-4094-2
[3] Kim, S., Nam, H., Rahman, J. U., & Sapkota, P. (2024). Gravity-induced structural deformation for enhanced ferroelectric performance in lead-free piezoelectric ceramics, Scripta Materialia, 244, 116021, https://doi.org/10.1016/j.scriptamat.2024.116021

#PiezoelectricEffect, #InversePiezoelectricEffect, #Accelerometers, #GravitationalForce, #EnergyHarvesting,

Unified Study on Gravitational Dynamics: Extended Classical Mechanics - Vol-2. [ECM-2]

ResearchGate.net Publication

Soumendra Nath Thakur
01-10-2024

Abstract

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 mechanical and relativistic kinetic energy. It posits that classical mechanics is enriched by integrating these components, thus enhancing our understanding of gravitational dynamics across both macroscopic and microscopic scales.

The study redefines gravitational mass, moving beyond its traditional equivalence with matter mass to encompass contributions from dark matter and negative apparent mass. By examining the relationships between these components, it establishes a comprehensive model for gravitational interactions that includes both positive and negative mass contributions. Furthermore, the paper explores the influence of dark matter on gravitationally bound systems, highlighting its critical role in modifying effective mass and apparent mass dynamics.

In the context of cosmic dynamics, this study elucidates the transition from gravitationally bound systems to intergalactic space, where dark energy and negative mass dominate. The findings suggest that in these vast regions, negative apparent mass exerts a significant influence, leading to a repulsive force that drives the accelerated expansion of the universe.

This research ultimately provides a refined framework for understanding the complexities of gravitational dynamics and kinetic energy, laying the groundwork for future investigations into the unification of mass and energy in the cosmos.

Keywords: Dark energy, Dark matter, Effective mass, Gravitational dynamics, Gravitational mass, Matter mass, Negative apparent mass, Relativistic kinetic energy, Total effective mass,

Soumendra Nath Thakur
ORCiD: 0000-0003-1871-7803
Tagore’s Electronic Lab, WB, India
Correspondence: postmasterenator@gmail.com
postmasterenator@telitnetwork.in
Declaration: No competing interest to declare, and No funding has been received for this research.

Introduction:

This unified study explores the integration of gravitational mass, matter mass, and dark matter dynamics within extended classical mechanics, alongside a comprehensive examination of kinetic energy domains. By addressing the roles of dark matter mass (Mᴅᴍ) and negative apparent mass (Mᵃᵖᵖ) in gravitational forces and effective mass (Mᵉᶠᶠ), while distinguishing mechanical and relativistic kinetic energy, this study provides a refined framework for understanding gravitational dynamics on macroscopic and microscopic scales. Classical mechanics is enhanced by incorporating dark matter and negative mass, distinguishing mechanical energy from relativistic mass-energy equivalence.

Gravitational Mass and Matter Mass in Extended Classical Mechanics:

Gravitational mass (Mɢ) is redefined beyond its classical equivalence with matter mass (Mᴍ), incorporating dark matter and negative apparent mass contributions ^[1]. Traditionally, gravitational mass (Mɢ) was considered equivalent to ordinary matter mass (Mᴏʀᴅ), but modern physics extends this view with dark matter and dark energy ^{[2] [3].}

The relationship between these components is captured by the equation:

Mᴍ = Mᴏʀᴅ + Mᴅᴍ + (-Mᵃᵖᵖ)

Here, Mᴏʀᴅ represents baryonic matter, Mᴅᴍ represents dark matter mass, and (-Mᵃᵖᵖ) accounts for negative apparent mass derived from effective acceleration. The total effective mass (Mᵉᶠᶠ) includes both dark matter and apparent mass, expressed as:

Mɢ = Mᵉᶠᶠ = Mᴍ + (-Mᵃᵖᵖ) = Mᴏʀᴅ + Mᴅᴍ + (-Mᵃᵖᵖ)

Gravitating mass (Mɢ), which governs gravitational dynamics, is the sum of matter mass (Mᴍ) and negative apparent mass (-Mᵃᵖᵖ), showing that gravitational interactions depend on both positive and negative mass contributions ^[1].

Dark Matter Mass and Its Role in Gravitational Dynamics:

Dark matter mass (Mᴅᴍ) significantly influences gravitationally bound systems, adding positively to the total matter mass (Mᴍ). Its contribution strengthens gravitational forces, altering the effective mass (Mᵉᶠᶠ) and apparent mass (Mᵃᵖᵖ) ^[1]. In gravitationally bound systems, the relationship is:

Mᵉᶠᶠ = Mᴍ + (-Mᵃᵖᵖ)

Dark matter dominates in galactic dynamics, while apparent mass reduces the overall effective mass in gravitational systems.

Modified Newtonian Laws with Dark Matter and Negative Mass:

The study modifies Newton's Laws to integrate dark matter and negative apparent mass ^[1]. The gravitational force equation becomes:

Fɢ = G·(Mᵉᶠᶠ·m₂)/r²

Where Mᵉᶠᶠ encompasses the contributions from matter mass (Mᴍ) and apparent mass (Mᵃᵖᵖ), both of which influence the gravitational force. Additionally, m₂ is defined as the sum of matter mass and apparent mass for the second mass in the interaction ^[1]. Similarly, the modified force equation:

F = Mᵉᶠᶠ·aᵉᶠᶠ

incorporates these components, demonstrating their effect on system dynamics.

Distinct Domains of Kinetic Energy:

Mechanical kinetic energy governs large-scale motion, while relativistic kinetic energy applies to high-energy, nuclear reactions. The equation:

Mɢ = Mᴍ + (-Mᵃᵖᵖ)

shows how mechanical kinetic energy, including the influence of dark matter, impacts macroscopic systems, while relativistic kinetic energy remains important in microscopic scales.

Negative Apparent Mass and Cosmic Dynamics:

In intergalactic space, beyond the gravitational influence of bound systems, gravitating mass (Mɢ) governs dynamics as the sum of matter mass (Mᴍ) and negative effective mass of dark energy (Mᴅᴇ), as per Chernin et al. ^[2]:

Mɢ = Mᴍ + Mᴅᴇ

In Vol-1, matter mass dominates, while in Vol-2, negative apparent mass (−Mᵃᵖᵖ) drives cosmic expansion. The modified equation becomes:

Mɢ = Mᴍ + Mᵉᶠᶠ

Transition from Gravitationally Bound Systems to Intergalactic Space:

In gravitationally bound systems, such as galaxies or galaxy clusters, gravitational dynamics are primarily governed by the combined influence of matter mass (Mᴍ) and negative apparent mass (−Mᵃᵖᵖ) ^[1]. In these systems, the matter mass is the dominant factor, while the negative apparent mass plays a secondary role (Mᴍ>−Mᵃᵖᵖ). As a result, the gravitational mass is mostly influenced by the ordinary and dark matter, with a small reduction due to negative apparent mass.

However, in intergalactic space, beyond the reach of these gravitationally bound systems, the situation changes significantly. Dark energy and negative apparent mass become the dominant forces, with negative apparent mass contributing more heavily to the gravitational mass. This shift means that in these vast, cosmic regions, negative apparent mass exerts a much stronger influence, resulting in a repulsive force that drives the accelerated expansion of the universe. The effective mass in intergalactic space incorporates this dominant negative mass, while the matter mass plays a lesser role  (Mᴍ<−Mᵃᵖᵖ).

Thus, while gravitationally bound systems are dominated by attractive forces driven by matter mass, in intergalactic space, the negative mass associated with dark energy reshapes the dynamics, leading to the expansion and evolution of cosmic structures.

Conclusion:

This study emphasizes the distinction between mechanical and relativistic kinetic energies while integrating dark matter and negative apparent mass into gravitational models. Extended Classical Mechanics provides a comprehensive framework for understanding gravitational dynamics, laying the groundwork for future exploration into mass-energy unification.

List of Mathematical Denotations:

• Mᵃᵖᵖ - Apparent mass
• Mᴅᴍ - Dark matter mass
• Mᵉᶠᶠ - Effective mass,
• Mɢ - Gravitational mass
• Mᴍ - Matter mass
• Mᴏʀᴅ - Ordinary (baryonic) matter
• −Mᵉᶠᶠ - Negative effective mass
• −Mᵃᵖᵖ - Negative apparent mass

References:

[1] Thakur, S. N. (2024). Extended Classical Mechanics: Vol-1 - Equivalence Principle, Mass and Gravitational Dynamics, Preprints.org (MDPI) 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] Sanders, R. H., & McGaugh, S. S. (2002). Modified Newtonian dynamics as an alternative to dark matter, Annual Review of Astronomy and Astrophysics, 40(1), 263–317, https://doi.org/10.1146/annurev.astro.40.060401.093923
[4] Thakur, S. N., & Bhattacharjee, D. (2023). Phase shift and infinitesimal wave energy loss equations. ResearchGate, https://doi.org/10.13140/RG.2.2.28013.97763
[5] Thakur, S. N., Samal, P., & Bhattacharjee, D. (2023). Relativistic effects on phaseshift in frequencies invalidate time dilation II. TechRxiv. https://doi.org/10.36227/techrxiv.22492066.v2
[6] Thakur, S. N. (2024). Direct Influence of Gravitational Field on Object Motion invalidates Spacetime Distortion. Qeios (ResearchGate). https://doi.org/10.32388/bfmiau
[7] Thakur, S. N. (2023). Photon paths bend due to momentum exchange, not intrinsic spacetime curvature. Definitions, https://doi.org/10.32388/81iiae
[8]Thakur, S. N. [Soumendra Nath Thakur]. (2024). Effective Mass of the Energetic Pre- Universe: Total Mass Dynamics from Effective and Rest Mass. ResearchGate (378298896), https://www.researchgate.net/publication/378298896. https://doi.org/10.13140/RG.2.2.18182.18241

#Darkenergy, #Darkmatter, #Effectivemass, #Gravitationaldynamics, #Gravitationalmass, #Mattermass, #Negativeapparentmass, #Relativistickineticenergy, #Totaleffectivemass,