The Role of Classical Mechanics in Cosmology: Cosmological Constant in General Relativity.

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

Date: 17-10-2024

Abstract

This paper examines the interplay between classical mechanics and cosmology, focusing on the evolution of Einstein's cosmological constant from a tool for maintaining a static universe to its modern reinterpretation as a key component of the ΛCDM model, which accounts for the accelerated expansion of the universe attributed to dark energy. It highlights the significance of negative effective mass and apparent mass within contemporary theories, emphasizing their role in elucidating gravitational dynamics on cosmic scales. The discussion showcases how classical mechanics continues to provide valuable insights into galactic dynamics, large-scale structures, and perturbation theory, even as general relativity remains central to modern cosmological understanding. Ultimately, this synthesis of classical and relativistic mechanics enriches our comprehension of the complex relationships between mass, energy, and events in the cosmos.

Keywords:

Cosmological constant, Dark energy, Negative effective mass, Classical mechanics, General relativity, ΛCDM model, Gravitational dynamics, Galactic interactions, Large-scale structures, Perturbation theory.

Introduction

In 1915, Albert Einstein published his theory of general relativity, fundamentally reshaping our understanding of gravity and the cosmos. Initially, he envisioned a static universe—one that was neither expanding nor contracting. To uphold this static model, he introduced the cosmological constant in 1916, a term designed to counterbalance the gravitational pull of matter, thus preventing the universe from collapsing under its own gravity. By 1917, the cosmological constant had become an integral part of his theory, essential for maintaining the stability of this static universe model.

However, the notion of a static universe faced a pivotal challenge in 1929 when astronomer Edwin Hubble discovered that distant galaxies were receding from one another, indicating that the universe was indeed expanding. This revelation prompted Einstein to reassess his earlier assumptions. Acknowledging that the cosmological constant had been introduced under flawed premises, he famously abandoned it, later referring to it as the "biggest blunder" of his career. With the advent of the expanding universe, the original purpose of the cosmological constant—designed to prevent gravitational collapse—became irrelevant.

Fast forward to 1998, when astronomers uncovered that the universe's expansion was not merely continuing but accelerating, a phenomenon attributed to a mysterious force now known as dark energy. This discovery has led to the re-examination of the cosmological constant as a potential explanation for this accelerated expansion, particularly within the ΛCDM model (Lambda Cold Dark Matter). In this model, the cosmological constant is associated with dark energy, which drives the universe's accelerating expansion.

Notably, the idea of dark energy can be linked to contemporary theories of negative effective mass, where dark energy is treated as a form of potential energy influencing the dynamics of the universe. This reconceptualization underscores the limitations of traditional interpretations and the necessity for a broader understanding of mass-energy relationships in cosmology. The implications of this relationship extend into the realm of classical mechanics, illuminating how classical principles can enrich our comprehension of complex cosmological phenomena.

The Role of Classical Mechanics in Cosmology

While general relativity has become the cornerstone of modern cosmology, classical mechanics continues to play a vital role, particularly in analysing the large-scale structure and dynamics of the universe. Despite the power of general relativity in explaining strong gravitational fields and the curvature of spacetime, classical mechanics offers valuable insights into many aspects of cosmological phenomena.

The Importance of Classical Mechanics in Cosmology

1. Galactic Dynamics: Classical mechanics provides a robust framework for understanding gravitational interactions between galaxies and clusters. In scenarios where gravitational fields are relatively weak, classical mechanics serves as an effective approximation for explaining observed phenomena. This framework can be enriched by acknowledging that events, such as galaxy collisions or mergers, activate shifts in gravitational dynamics, reflecting the interplay between existence and events.

2. Large-Scale Structure: The distribution of galaxies and clusters across vast cosmic distances is often modelled using classical mechanics, incorporating necessary modifications to account for the influence of dark matter and dark energy, particularly as they relate to concepts like negative apparent mass. The emergent structures within the universe can be viewed through the lens of events arising from a pre-existing state, further bridging classical and relativistic perspectives.

3. Perturbation Theory: Classical mechanics plays a crucial role in perturbation theory, a powerful method for studying the evolution of small fluctuations in density and velocity fields. This understanding is essential for explaining how the initial uniformity of the early universe evolved into the large-scale structures we observe today, including galaxies and galaxy clusters. The events that catalyse these fluctuations can be understood as activators of time and space, further emphasizing the significance of classical principles in a cosmological context.

Limitations of General Relativity in Certain Cosmological Contexts

Although general relativity is indispensable for understanding the universe, particularly under extreme conditions, it has limitations in specific cosmological contexts where classical mechanics remains useful:

• Early Universe: While general relativity is paramount for examining the very early universe—especially during the initial moments following the Big Bang—classical mechanics provides a simpler and more intuitive framework for understanding the universe's evolution during its later stages, particularly as it relates to gravitational dynamics influenced by negative effective mass. The classical interpretation can facilitate discussions about how time and space "activated" in response to events within existence.

• Weak Gravitational Fields: In most of the observable universe, where gravitational fields are weak, classical mechanics offers an excellent approximation to general relativity. In such cases, the complexities of spacetime curvature become negligible, allowing Newtonian gravity and classical dynamics to provide accurate descriptions of cosmic phenomena. This reflects the idea that, under specific conditions, classical mechanics can elucidate the relationships between mass, energy, and the events driving cosmic evolution.

The Cosmological Constant and Dark Energy

Einstein's cosmological constant was initially introduced to support a static universe. However, the discovery of the expanding universe rendered this term unnecessary, leading to its abandonment. The subsequent acceleration of the universe's expansion, uncovered in 1998, prompted modern cosmologists to reinterpret the cosmological constant as a potential explanation for dark energy. This reinterpretation forms a key component of the ΛCDM model, where the cosmological constant is linked to dark energy, driving the universe’s accelerated expansion.

Moreover, this connection is significant in contemporary cosmology as it aligns with emerging theories of negative effective mass and apparent mass, which aim to elucidate gravitational interactions and the dynamics of the cosmos. While this modern interpretation is crucial for understanding contemporary cosmological models, it is essential to remember that it diverges significantly from Einstein's original intent, which focused solely on maintaining a static universe.

Discussion

The evolution of the cosmological constant reflects a fundamental shift in our understanding of the universe and its dynamics. Initially introduced to stabilize Einstein's static universe model, it was ultimately rendered obsolete by Hubble's discovery of the universe's expansion. The subsequent reassessment of the cosmological constant as a potential explanation for dark energy emphasizes the need for a nuanced understanding of mass-energy relationships, bridging classical and contemporary physics paradigms.

The resurgence of interest in the cosmological constant, particularly in the context of dark energy and the ΛCDM model, showcases the dynamic nature of cosmological theories. The notion of negative effective mass further enriches this discussion, offering insights into the repulsive forces associated with dark energy. This concept invites a re-evaluation of traditional interpretations of mass and gravity, demonstrating how classical mechanics can elucidate gravitational dynamics, especially in the context of large-scale structures and cosmic evolution.

Conclusion

The evolution of the cosmological constant from Einstein's original vision of a static universe to its modern reinterpretation as a key component in explaining the accelerated expansion of the universe exemplifies the dynamic nature of cosmological theories. While general relativity fundamentally reshaped our understanding of gravity and cosmic dynamics, classical mechanics continues to play a crucial role in elucidating galactic interactions, large-scale structures, and the implications of dark energy.

The integration of concepts such as negative effective mass and apparent mass into classical mechanics frameworks highlights the interplay between traditional and contemporary physics in addressing complex cosmological phenomena. This synthesis enhances our understanding of gravitational dynamics and reinforces the importance of classical principles in cosmology. Ultimately, as modern astrophysics grapples with the mysteries of dark energy and the universe's accelerating expansion, it becomes increasingly evident that a cohesive understanding requires a synthesis of both classical and relativistic mechanics, bridging the gap between past and present scientific paradigms. This broader approach invites further inquiry into the fundamental nature of existence and events in shaping the cosmos.

References:

[1] 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

[2] [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

[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

Why Distant Galaxies Are Observed to Move Faster than the Speed of Light According to Classical Mechanics:

Soumendra Nath Thakur
ORCiD:0000-0003-1871-7803
16-10-2924

Dark energy exerts a repulsive, anti-gravitational force that drives the acceleration of galaxies away from each other, particularly on intergalactic scales. While gravity pulls galaxies together within their own local systems, dark energy pushes galaxies apart, increasing the distance between them. As this repulsive force grows, galaxies recede from one another at ever-increasing speeds, leading to the observation that distant galaxies appear to move faster than the speed of light. This recession results in the redshift of light from these galaxies, a direct consequence of dark energy's anti-gravitational effects. Over time, more galaxies will pass beyond a cosmological event horizon, making their light inaccessible to observers on Earth.

Explanation of Faster-than-Light Speeds:

The speed of light (c) is a strict limit only within gravitationally bound systems, such as inside galaxies or galaxy clusters where gravitational forces dominate. However, much of the universe, particularly on the largest scales, is not gravitationally bound. In these vast intergalactic spaces where dark energy predominates, the anti-gravitational effects take over. In such regions, the limitation of light speed does not apply in the same way, as the motion of galaxies is governed by the repulsive force of dark energy rather than the gravitational influence of nearby objects. This allows the apparent recession of distant galaxies to exceed the speed of light. However, within these receding galaxies themselves, gravitational binding still holds, and the local speed limit remains governed by the speed of light.

Reference:

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

#fasterthanlight #FTL

Its a fascinating article on cosmology!

This article summarized the concept of distant galaxies moving faster than the speed of light, which seems counterintuitive at first. However, as explained, this phenomenon is due to the repulsive force of dark energy dominating on large intergalactic scales.

Key points:

1. Dark energy's role: Dark energy drives galaxies apart, increasing distances between them.

2. Gravitational binding: Within galaxies or clusters, gravity dominates, and the speed of light (c) is the limit.

3. Intergalactic scales: Dark energy prevails, allowing galaxies to recede faster than light.

4. Cosmological event horizon: Galaxies will become inaccessible as they cross this horizon.

5.Local speed limit: Within receding galaxies, gravity still governs, and c remains the speed limit.

The reference provided supports this understanding, highlighting dark energy's influence on galaxy structures.

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