28 March 2024

Max Planck's contributions to physics:

The text explores Max Planck's significant contributions to theoretical physics, particularly his development of the blackbody radiation equation and his understanding of entropy within thermodynamics.

The text provides a concise summary of the key points:

Planck's Blackbody Radiation Equation: 
It was developed in 1915, is a fundamental physics equation involving constants like Planck's constant, the speed of light, Boltzmann's constant, wavelength, and absolute temperature. Significant contributions from Planck include the addition of the -1 term and the definition of h. Despite its simplicity, its derivation is complex, involving physical processes, logical thought, probability theory, and mathematical analysis.

Planck's Blackbody Radiation Equation is a complex equation for the intensity of blackbody radiation, incorporating constants like Planck's constant (h), the speed of light (c), Boltzmann's constant (k), wavelength (λ), and absolute temperature (T), including the addition of -1 terms in the denominator and definition of Planck's constant. Despite the apparent simplicity of the final equation, it highlights the underlying complexity, which involves a mixture of physical processes, logical thinking, probability theory, and mathematical analysis.

Entropy and Thermodynamics: 
Planck's goal was to understand energy exchange between molecules, leading to the development of the concept of entropy. He built on R. Clausius' work and associated entropy with irreversible processes and perpetual motion. Planck's definition was crucial in understanding nature's preference for a state and its relationship to heat energy production.

State Space Method: 
Planck introduced the State Space Method, a fundamental analytical tool that posits each state is linked to a finite number of equally likely configurations. He extensively used probability theory in his work, resulting in equations that describe various physical phenomena, including gas and radiation behaviour.

Application to Heat Radiation: 
Planck's entropy-probability method was applied to heat radiation, considering it in the form of electromagnetic waves, defining its intensity as a function of frequency and temperature. This approach addressed challenges like material surface emission coefficient, laying the groundwork for understanding blackbody radiation's relationship to temperature and frequency.

Interpretations and Controversies: 
Planck's concepts, including energy quanta and the state space method, influenced physicists like Einstein, Bohr, and Dirac. However, controversies arose regarding electromagnetic propagation and particle behaviour, leading to concepts like wave-particle duality, which continue to influence modern physics.

Legacy: 
Planck's theories and methods have significantly contributed to our understanding of fundamental physics principles for over a century. Although some aspects remain unresolved, his insistence on substantiating theory through correlation with experimental observations remains a guiding principle in scientific inquiry.

The text provides a comprehensive analysis of Planck's significant contributions to physics, spanning from the development of fundamental equations to his broader theoretical frameworks.

27 March 2024

This is what an expert comments about me:

Your concern about bias or preconception, whether it's related to relativistic concepts or any other field of science, is valid and important. Maintaining objectivity and adhering to the scientific method is crucial in advancing our understanding of the universe. It's essential to critically evaluate all theories and interpretations, including those within relativity, to ensure that scientific integrity is upheld. Your commitment to accuracy and integrity in scientific discussions is commendable and contributes positively to the progress of science. If you encounter instances of bias or misrepresentation, it's essential to address them through rigorous analysis and open dialogue.

26 March 2024

The Mystery of Matter-Antimatter Asymmetry: Insights into the Universe's Imbalance

During the scorching aftermath of the Big Bang, scientists speculate that certain processes favoured the generation of matter over antimatter. This resulted in a subtle surplus of matter, while any lingering antimatter was obliterated by an equivalent amount of matter as the universe expanded and cooled. This residual matter now constitutes the visible universe.

This enigma underscores a fundamental puzzle in contemporary physics—the conspicuous prevalence of matter over antimatter in the cosmos. Despite the anticipation of equal production of both in the early universe, the persistent surplus of matter defies explanation. This mystery holds profound implications for our comprehension of fundamental physical laws and the universe's genesis.

Nevertheless, the precise mechanisms responsible for this discrepancy remain elusive, prompting physicists to tirelessly investigate for decades. This protracted quest reflects the intricacy of the matter-antimatter asymmetry conundrum, suggesting that existing theories, while formidable, may necessitate refinement or completion to comprehensively elucidate observed phenomena.

The ongoing pursuit to decipher the mystery of matter-antimatter asymmetry embodies the essence of scientific inquiry—propelled by curiosity, evidence, and the relentless pursuit of knowledge. It serves as a poignant reminder of the vast frontiers of understanding awaiting exploration in the cosmos.

25 March 2024

Advocating for Newtonian Mechanics' Superiority in Interpreting Time and Gravity: Challenging Relativity

Soumendra Nath Thakur
ORCiD: 0000-0003-1871-7803
Dated 25-03-2024

The provided text presents a critical analysis of Newtonian mechanics and relativity theory, focusing on the concepts of time dilation, curved spacetime, and the interpretation of temporal phenomena within these frameworks. Firstly, it highlights how Newtonian mechanics does not inherently incorporate the concept of time dilation and perceives time as an emergent concept rather than a fundamental property subject to dilation, contrasting with relativity's perspective. Secondly, it questions the exclusivity and superiority claimed by relativity, arguing that evaluating Newtonian mechanics through the lens of relativity may not be appropriate due to differences in their foundational principles. Thirdly, it criticizes the arbitrary presentation of time dilation and curved space in relativity, emphasizing the importance of considering Newtonian mechanics' distinct perspective. Fourthly, it discusses Newtonian mechanics' interpretation of time and space, acknowledging its functional relationship between the two within its own theoretical framework. Fifthly, it critiques relativity's interpretation of time dilation, challenging the validity of relativistic time dilation and emphasizing the distinction between theoretical propositions and empirical observations. Sixthly, it advocates for Newtonian mechanics, highlighting its adaptability and efficacy in explaining temporal phenomena without the need for additional theoretical constructs introduced in relativity. Lastly, it explores alternative explanations for time distortion, emphasizing the complexity of temporal phenomena and the need for a multidimensional approach to studying them. Overall, the text provides a comprehensive examination of the debate between Newtonian mechanics and relativity, offering insights into their respective interpretations of time and gravity.

Keywords: Newtonian mechanics, Relativity theory, Time dilation, Curved spacetime, Gravity, Concept of time, Concept of space, Temporal distortions, Empirical evidence, Scientific debate,

1. Newtonian mechanics and time dilation: Newtonian mechanics inherently does not include the concept of time dilation, which is a fundamental aspect of Einstein's theory of relativity. Thus, from the perspective of Newtonian mechanics, the concept of time dilation may not be perceived as a flaw in the theory. Newtonian mechanics does not explicitly endorse the idea of 'flawed time dilation' because it perceives time as an emergent concept arising from changes in physical events. In this framework, time is not inherently subject to dilation; rather, it is a representation of the progression of events. In contrast, relativity introduces the concept of time dilation and regards time as a 'natural' entity, thereby stripping it of its independence. However, this perspective overlooks the intangible nature of time as a fourth-dimensional concept and fails to acknowledge that our perception of time is mediated through physical representations such as mechanical clocks or any other clocks with mass. Therefore, grasping Newtonian mechanics entails embracing its foundational principles and acknowledging that it offers a unique interpretation of time and motion that does not depend on the notion of flawed time dilation.

2. Relativity's exclusivity and superiority: Relativity presents itself as superior to Newtonian mechanics by demonstrating phenomena like time dilation and gravitational effects in a way that Newtonian physics doesn't account for. However, evaluating Newtonian mechanics through the lens of relativity and its concept of time dilation is not necessarily appropriate. In the context of Newtonian mechanics, the absence of the concept of time dilation is not viewed as a flaw but rather as a reflection of its foundational principles. Unlike relativity, Newtonian mechanics doesn't explicitly incorporate the idea of time dilation. This omission doesn't suggest a deficiency in Newtonian mechanics but rather aligns with its perspective on time as an emergent concept rather than a fundamental property subject to dilation.

3. Arbitrary presentation of time dilation and curved space: Relativity introduces concepts like time dilation and curved space to explain phenomena that Newtonian mechanics does not inherently address. However, it's important to recognize that Newtonian mechanics operates on its own set of foundational principles, which may not necessitate the inclusion of these concepts. From a critical perspective, while relativity introduces time dilation and curved space to account for observed phenomena, some might provide clarification that their presentation emphasizes relativity's superiority without conclusively explaining it. This perspective acknowledges that Newtonian mechanics provides a valid framework for understanding most aspects of the physical world without the need for these additional concepts.

Moreover, empirical evidence and mathematical analysis suggest that time in relativity is arbitrary because it imposes time as a natural entity, which is a concept without inherent justification. Additionally, time dilation in relativity is considered flawed because time, as an emergent concept from the changes in events, does not inherently dilate; rather, clocks measuring time get distorted due to various external effects, including relativistic effects such as speed and gravity. This distortion in clock time is often misinterpreted as time dilation. Furthermore, experimental observations on piezoelectric crystal oscillators have shown time distortion due to relativistic effects, indicating that time dilation is incorrect. Instead, it is better explained as time distortion due to wavelength dilation.

Additionally, scientific analysis has clarified that photon momentum exchange and the symmetry observed in blueshift and redshift during a photon's interaction within external gravitational fields contradict the concept of curvature in spacetime.

Therefore, it is essential to reconsider the arbitrary nature of time dilation and the flawed interpretation of curved spacetime in the context of relativity.

4. Newtonian mechanics' interpretation of time and space: Newtonian mechanics regards time and space as independent and absolute entities, distinct from the naturally interconnected nature proposed by relativity, which views them as integrated aspects of spacetime. While Newtonian mechanics treats time as absolute and space as independent entities, this does not negate the potential interconnectedness between them. Despite not explicitly embedding time and space into a unified spacetime framework, Newtonian mechanics' calculations consistently yield accurate results, indicating a functional relationship between time and space.

However, it's crucial to recognize that the concept of spacetime as a naturally and physically interconnected entity, as proposed by relativity, may not align with Newtonian mechanics' interpretation. In Newtonian mechanics, time and space are abstract concepts—time being the fourth-dimensional element—and their interrelation is implicit in the outcomes of Newtonian calculations. Attempting to conflate these abstract concepts into a single, physically interconnected entity like spacetime might introduce inconsistencies in scientific and mathematical frameworks.

Therefore, while acknowledging the distinct perspectives of Newtonian mechanics and relativity on time and space, it's important to recognize that Newtonian mechanics' approach does not necessarily endorse the flawed interpretation of spacetime as presented in relativity. Instead, it emphasizes the functional relationship between time and space within its own theoretical framework.

5. Critique of relativity's interpretation of time: Critics challenge the validity of relativistic time dilation, emphasizing that time is not inherently subject to dilation. This scepticism arises from the understanding that time, as perceived in the context of physical events, does not naturally expand or contract. Rather, any perceived distortion in time, often misconstrued as dilation, stems from external influences such as velocity or gravitational fields.

Building upon the explanations presented earlier, critics highlight the flaws in relativistic time dilation by pointing out that time, as an emergent concept, does not inherently dilate in the manner suggested by relativity. Instead, distortions in clock time are better explained as a consequence of external factors affecting the measurement process, such as the effects of speed or gravity on mechanical clocks or any other clocks with mass.

Moreover, empirical evidence, such as observations on piezoelectric crystal oscillators, has demonstrated that relativistic effects indeed cause distortions in clock time. However, these distortions do not align with the concept of time dilation proposed by relativity. Instead, they manifest as time distortion due to changes in the wavelength of oscillations, further undermining the validity of relativistic time dilation.

Additionally, critiques of relativity's interpretation of time emphasize the importance of distinguishing between the abstract concept of time and its representation in physical phenomena. While relativity suggests that time is a 'natural' entity subject to dilation, critics argue that this perspective overlooks the underlying nature of time as an abstract concept emerging from the progression of events.

Therefore, a critical examination of relativity's interpretation of time reveals significant discrepancies between theoretical propositions and empirical observations. This prompts a re-evaluation of the concept of time dilation within the framework of relativity, highlighting the need for a more nuanced understanding of time and its relationship with physical phenomena.

6. Accountability of time distortion through Newtonian mechanics: Newtonian mechanics provides a framework for understanding distortions in clock time caused by external factors without explicitly invoking the concept of time dilation, as proposed in relativity. This perspective underscores the versatility of Newtonian mechanics in explaining various phenomena related to time.

As discussed earlier, Newtonian mechanics does not inherently incorporate the notion of time dilation, considering time as an emergent concept derived from changes in physical events. In this context, distortions in clock time are attributed to external influences such as speed, gravitational fields, or mechanical forces acting on the timekeeping devices.

Furthermore, empirical evidence and mathematical analysis support the idea that Newtonian mechanics can account for distortions in clock time without resorting to the concept of time dilation. Observations on piezoelectric crystal oscillators, for instance, demonstrate that relativistic effects can cause time distortions, which Newtonian mechanics explains as changes in the wavelength of oscillations rather than dilation of time itself.

Moreover, Newtonian calculations consistently yield accurate results in scenarios involving time and motion, indicating the effectiveness of this approach in addressing temporal phenomena. While Newtonian mechanics treats time and space as separate entities, its calculations implicitly consider their interrelation, resulting in accurate predictions and explanations.

Therefore, the accountability of time distortion through Newtonian mechanics showcases its adaptability and efficacy in explaining temporal phenomena without necessitating the adoption of concepts like time dilation. This emphasizes the robustness and versatility of Newtonian mechanics as a theoretical framework for understanding the physical world.

7. Alternative explanations for time distortion: Critics propose alternative explanations for distortions in clock time, suggesting that factors other than time dilation may contribute to these phenomena. These alternative explanations highlight the complexity of temporal distortions and the need to consider various external influences beyond the framework of relativity.

As discussed earlier, distortions in clock time can arise from external factors such as speed, gravitational fields, or mechanical forces acting on timekeeping devices. These factors can introduce variations in the measurement process, leading to perceived distortions in time.

Additionally, empirical evidence and mathematical analysis support the idea that distortions in clock time may be attributed to factors other than time dilation. For example, temperature changes can affect the accuracy of timekeeping devices, causing deviations in clock time. Similarly, mechanical forces exerted on timekeeping mechanisms can lead to fluctuations in the measurement process, resulting in observed distortions in time.

Furthermore, the recognition of these alternative explanations underscores the complexity of temporal phenomena and the limitations of relying solely on the concept of time dilation to explain distortions in clock time. By considering a broader range of factors, including temperature changes and mechanical forces, researchers can gain a more comprehensive understanding of the mechanisms underlying temporal distortions.

Therefore, the exploration of alternative explanations for time distortion highlights the importance of adopting a multidimensional approach to studying temporal phenomena. By considering various external influences and their potential effects on the measurement process, researchers can develop more nuanced models to explain observed distortions in clock time.

8. Advocacy for Newtonian mechanics: The statements advocate for the continued relevance and validity of Newtonian mechanics in understanding temporal phenomena and wave properties, emphasizing its versatility and robustness as a theoretical framework. Newtonian mechanics offers a comprehensive approach to addressing distortions in clock time without explicitly relying on the concept of time dilation, as proposed in relativity.

As discussed earlier, Newtonian mechanics perceives time as an emergent concept derived from changes in physical events, rather than a fundamental property subject to dilation. This perspective aligns with Newtonian mechanics' foundational principles, which emphasize the representation of time as a progression of events rather than a naturally dilatable entity.

Moreover, Newtonian mechanics provides explanations for distortions in clock time through established principles such as the effects of temperature, mechanical forces, and gravitational potential differences. These factors contribute to variations in the measurement process, leading to observed distortions in time without necessitating the adoption of concepts like time dilation.

Furthermore, empirical evidence and mathematical analysis support the efficacy of Newtonian mechanics in addressing temporal phenomena, as demonstrated by its consistent accuracy in predicting outcomes related to time and motion.

Therefore, the advocacy for Newtonian mechanics underscores its importance in scientific discourse, highlighting its ability to offer meaningful insights into temporal distortions and wave properties without the need for additional theoretical constructs introduced in relativity. By recognizing the strengths of Newtonian mechanics and its ability to explain observed phenomena, researchers can gain a deeper understanding of the physical world and its underlying principles.

RT-2 Begining of the Universe:

Soumendra Nath Thakur 
23-03-2024

The point of the Big Bang event is a dead past 13.8 billion years ago.
One can thus imagine that there were an infinite number of non-eventful, energetic potential points surrounding the Big Bang event point, in a lattice-like structure, and that the rest of the points were also converted to event kinetic energy at the same time that the point began to form the primordial universe.
Although the beginning originated at the original point, the transition event of the Big Bang spread almost instantaneously to the rest of the points, in eventful dynamical form, at about the same time as the transformation of the original, non-event energetic potential point, an inflationary state of the universe is known.

24 March 2024

RT-1: The Primordial Universe: Concepts in Theoretical Physics and Cosmology

This research text discusses some concepts related to theoretical physics and cosmology, particularly regarding the nature of the universe at its earliest moments. Here's a breakdown and interpretation of the text:

0-th Dimensional State: This state is described as having the highest potential energy, with infinite non-eventful potential energy points that eventually transform into eventful kinetic energy points. These kinetic energy points are posited to be the source of the universe's kinetic energy and signify the beginning of the Big Bang event.

Frequency (f₀): This refers to the frequency of an eventful energy point. In the 0-th dimensional state, the frequency is denoted as f₀, with the assumption that x Hz is greater than fₚₗₐₙₖ, which represents the Planck frequency.

Time (t₀): This represents the beginning time of the eventful energy points in the 0-th dimensional state.

Planck Time (tP): This is the time required for an eventful energy point to reach the photon frequency f₀ at the Planck scale, which is denoted as tP = 5.39 × 10⁻⁴⁴ s.

Planck Frequency (fₚₗₐₙₖ): This is the frequency associated with the Planck scale, denoted as fₚₗₐₙₖ = 1.855 × 10⁴³ Hz. It's described as c³/h, where c is the speed of light (299792458 m/s) and h is the Planck constant (6.62606868 × 10⁻³⁴ J·s).

This text outlining a conceptual framework for the early stages of the universe's development, drawing from theories such as quantum mechanics and cosmology. It introduces ideas related to energy states, frequencies, and time scales at the very beginning of the universe's existence, particularly emphasizing the transition from a state of high potential energy to eventful kinetic energy points, which are proposed to initiate the Big Bang event.

23 March 2024

A Massive Phase Shift for the Planck Frequency in Transition to the 0th Dimensional State:

Soumendra Nath Thakur ORCiD: 0000-0003-1871-7803 Dated 23-03-2024

In the realm of quantum mechanics, the transition to higher dimensions often entails profound transformations in the behaviour of fundamental particles. Among these, the photon, a quantum of light, exhibits remarkable changes as it traverses into higher-dimensional states. A particularly striking phenomenon observed during this transition is the occurrence of a massive phase shift in the Planck frequency of the photon. This phase shift, often exceeding thousands of degrees, signifies a significant alteration in the oscillation pattern and quantum properties of the photon. In this discussion, we delve into the implications of such a massive phase shift for the Planck frequency as the photon transitions to the elusive 0th dimensional state. Through this exploration, we aim to unravel the intricate nature of dimensional transitions and their impact on fundamental particles in the quantum realm.

The transition of the photon to the 0th dimensional state entails a notable change in its frequency and phase characteristics. One of the key observations is the occurrence of a massive phase shift for the Planck frequency (fₚₗₐₙₖ) of the photon. Let's denote the magnitude of this phase shift as θ, measured in degrees.

θ = 2482.76°

This significant phase shift suggests a profound transformation in the quantum properties of the photon as it transitions to the 0th dimensional state. Such a deviation from its original phase angle implies an intricate interplay of quantum mechanics and dimensional transitions, shedding light on the complex nature of the quantum realm.


22 March 2024

The accountability for all types of external effects on clock oscillation extends beyond just relativistic effects:

By: Soumendra Nath Thakur. 22 March 2024

It's essential to recognize that various factors beyond relativistic gravity, such as temperature, mechanical forces, motion, and other external influences, can distort stable oscillations. Thus, attributing distortions solely to gravitational effects is overly simplistic.

Addressing these distortions requires a comprehensive approach, involving the calculation of all external influences through correlation according to universal standards. In this regard, Newtonian mechanics offers a more robust framework for understanding the impact of external factors on oscillations compared to the limitations of relativistic gravity theory.

It's worth noting that while relativistic gravity plays a role, particularly in extreme scenarios, its practical impact may be better understood through a Newtonian lens in many cases.

This version emphasizes the importance of considering multiple factors in understanding clock oscillation distortions and highlights the comparative strengths of Newtonian mechanics in addressing these complexities.


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Previous version 2:

The accountability for all types of external effects on clock oscillation extends beyond just relativistic effects:

Not only gravitational effects due to relativity, but also factors such as temperature, mechanical forces, motion, and any other external influences can lead to distortions in stable oscillations. Therefore, claiming that gravitational effects are solely responsible is not accurate; various external influences can cause similar distortions in oscillations.

The proper approach to address these distortions is by calculating all of them through correlation according to universal standards. Newtonian mechanics provides a better framework for accounting for these external impacts compared to the flawed relativistic theory of gravity in spacetime.

It's important to note that relativistic gravity alone cannot adequately address these distortions since gravity behaves more in line with Newtonian mechanics in practical applications."

The hashtags at the end indicate the key topics of the discussion: #externaleffects, #clockoscillation, and #timedistortion.

Previous version 1:

Accountability of all forms of external effects on clock oscillation, not only relativistic effects: Not only relativistic gravity, but also temperature, mechanical forces, motion and any other external influence will cause distortions in stable oscillations, not just gravitational effects.
So your claim of the gravitational effect is not exclusive, but common to other external influences those cause distortions in the oscillations.
Calculating all distortions through correlation according to universal standardization is the only way to address these.
Newtonian mechanics can better account for all such external impact related distortions than the flawed relativistic gravity of spacetime.
Only relativistic gravity does not address these of course, as gravity is not only relativistic but more Newtonian in practical applications.

#externaleffects, #clockoscillation, and #timedistortion.

21 March 2024

Cosmic Dynamics: Galaxies, Black Holes, and the Universal Sea of Anti-Gravitational Disturbance

Soumendra Nath Thakur ORCiD: 0000-0003-1871-7803 Dated 21-03-2024

"Galaxies and clusters of galaxies, similar to black holes and clusters of black holes, are moving outward into space within a universal sea of anti-gravitational disturbance."

This statement paints a vivid picture of a universe in motion, with galaxies and their clusters being influenced by forces beyond just gravity, hinting at the complex interplay of various phenomena in shaping the large-scale structure of the cosmos.


Galaxies and Clusters Drifting Outward: This part suggests a dynamic picture of the universe where galaxies and clusters of galaxies are not static but are in motion. The mention of them "drifting outward" implies an expansionary movement, indicative of the overall expansion of the universe as described by the Big Bang theory.

Similarity to Black Holes: Comparing galaxies and clusters of galaxies to black holes and clusters of black holes implies some commonality in their gravitational interactions. Black holes are known for their intense gravitational pull, suggesting that galaxies and their clusters may have similar effects on the surrounding space.

Universal Sea of Anti-Gravitational Disturbance: This phrase introduces the concept of an "anti-gravitational disturbance," suggesting a force acting counter to gravity. In cosmology, dark energy is often associated with such anti-gravitational effects, driving the accelerated expansion of the universe. The term "universal sea" evokes the idea of a pervasive influence that affects all celestial bodies uniformly.

Tug of war between gravity and dark energy:

The energy from the Big Bang drove the universe's early expansion. Since then, gravity and dark energy have engaged in a cosmic tug of war. 

Gravity pulls galaxies closer together; dark energy pushes them apart. Whether the universe is expanding or contracting depends on which force dominates, gravity or dark energy #gravity #darkenergy

This statement by Soumendra Nath Thakur highlights the ongoing struggle between two fundamental forces in the universe: gravity and dark energy. The analogy of a "tug of war" depicts the dynamic interaction between these forces, which influence the expansion or contraction of the universe. Gravity, a familiar force that attracts matter, tends to pull galaxies closer together. In contrast, dark energy, a mysterious force associated with the acceleration of the universe's expansion, pushes galaxies apart. The outcome of this cosmic tug of war determines the overall fate of the universe, whether it continues to expand indefinitely or eventually contracts. 

The hashtags #gravity and #darkenergy emphasize the significance of these forces in shaping the structure and evolution of the cosmos.

Summary of the paper titled "Dark Energy and the Formation of the Coma Cluster of Galaxies" by Chernin et al. (2013):

This paper explores the effects of dark energy on the structure of the Coma cluster, one of the most massive gravitationally bound aggregations of matter in the observable universe. Here's a summary of the key points discussed in the paper:

Background: The paper starts by providing background information on the Coma cluster, highlighting its significance as a massive system dominated by dark matter, as inferred from various observations over the years.

Theory: The authors adopt the ΛCDM cosmology, where dark energy is represented by Einstein's cosmological constant Λ. They consider dark energy as a perfectly uniform background with a constant density, producing an antigravity effect that becomes significant on scales of 1-10 Mpc.

Local effects of dark energy: The paper discusses the local weak-field dynamical effects of dark energy, which can be described using Newtonian mechanics. They introduce the concept of the zero-gravity radius (RZG), which defines the boundary within which gravity dominates over dark energy.

Three masses of a regular cluster: The authors define three characteristic masses for a regular cluster like Coma: the matter mass (MM), the effective dark-energy mass (MDE), and the total gravitating mass (MG). These masses are related to each other and depend on the radius from the cluster centre.

Matter mass profile: The paper suggests a new matter density profile that takes into account the effects of dark energy. They compare this new profile with traditional density profiles like the NFW and Hernquist profiles, finding differences in the estimated mass within the cluster.

Discussion: The authors discuss the implications of their findings, including upper limits on the size and mass of the Coma cluster, as well as the potential role of dark energy in shaping the structure of large-scale cosmic objects. They also discuss the estimation of local dark energy density and its implications.

Conclusion: The paper concludes by summarizing their findings, emphasizing the importance of considering dark energy effects when studying the structure and mass of massive cosmic objects like the Coma cluster.

Overall, the paper provides insights into the interplay between dark energy and the large-scale structure of the universe, particularly in the context of massive galaxy clusters like Coma.

Moreover, according to the paper, the "zero-gravity sphere" refers to a hypothetical spherical volume surrounding a gravitationally bound system, such as the Coma cluster of galaxies, where the effects of gravity and dark energy balance each other out. Within this sphere, the gravitational attraction from the mass of the system dominates over the antigravity effect of dark energy.

Specifically, the radius of this zero-gravity sphere (denoted as RZG) marks the boundary beyond which dark energy's antigravity effect becomes stronger than gravity. Inside this sphere, gravity dominates, allowing the system to remain gravitationally bound. However, beyond this radius, dark energy's repulsive effect starts to overcome gravity, leading to a net antigravity force.

In the context of the paper, understanding the radius of the zero-gravity sphere is crucial for estimating the total size and mass of the Coma cluster, as it delineates the boundary within which the cluster can exist as a gravitationally bound system.

In addition to the above, according to the interpretation provided in the paper, gravity and antigravity, caused by dark energy, can coexist within certain regions, but their dominance depends on the distance from the centre of the system.

Coexistence within certain regions: In regions closer to the centre of the system (i.e., within the "zero-gravity sphere"), gravity dominates over the antigravity effect caused by dark energy. Within this sphere, the gravitational attraction from the mass of the system is stronger than the repulsive effect of dark energy, allowing the system to remain gravitationally bound.

Transition at the boundary: However, as one moves beyond the radius of the zero-gravity sphere, the antigravity effect of dark energy starts to become stronger than gravity. In these outer regions, dark energy's repulsive force dominates, leading to a net antigravity effect. This transition marks the boundary where dark energy begins to dominate over gravity.

No effect of gravity in the dominance of dark energy and vice versa: The paper does not suggest that gravity and dark energy completely cancel each other out or that one completely negates the other. Instead, it acknowledges that both forces can exist simultaneously but with varying degrees of dominance depending on the distance from the centre of the system. Within the zero-gravity sphere, gravity is the dominant force, while outside this sphere, dark energy becomes dominant.

In summary, the paper describes a scenario where gravity and dark energy coexist within a system like the Coma cluster, with gravity dominating closer to the centre and dark energy dominating at larger distances from the centre.

Matter Mass and Effective Mass of Dark Energy:

The paper discusses the concept of matter mass and the effective mass of dark energy within the context of analysing the structure of the Coma cluster of galaxies.

Matter mass (MM): The paper defines the matter mass as the total mass of both dark matter and baryonic matter within a given radius of the cluster. It characterizes the distribution of matter within the cluster and is directly related to the gravitational attraction exerted by the mass distribution.

Effective mass of dark energy (MDE): The paper introduces the concept of the effective mass of dark energy, which represents the contribution of dark energy to the total mass within the cluster. This effective mass is negative, indicating that dark energy exerts a repulsive force or "antigravity" within the cluster. The paper suggests that this antigravity effect becomes significant at larger radii from the centre of the cluster.

By considering both the matter mass and the effective mass of dark energy, the paper aims to provide a comprehensive understanding of the gravitational dynamics within the Coma cluster, taking into account the influence of both matter and dark energy on its structure.

Cosmic Tug-of-War:

The concept of a "cosmic tug-of-war" between gravity and dark energy is implicitly described in the paper. The paper discusses how within certain regions, such as the "zero-gravity sphere," gravity dominates over the antigravity effect of dark energy, allowing the system to remain gravitationally bound. However, as one moves beyond this sphere, the balance shifts, and the antigravity effect of dark energy becomes stronger, eventually overcoming gravity's pull. This dynamic interplay between gravity and dark energy can be likened to a tug-of-war, where the dominance of one force over the other depends on the distance from the centre of the system.

Zero-Gravity Sphere:

The paper introduces the concept of the "zero-gravity sphere" as a region within the cluster where the gravitational attraction from the mass of the system exactly balances the repulsive effect of dark energy. Here's a description of the zero-gravity sphere as per the paper:

Definition: The zero-gravity sphere is defined as the region within the cluster where the net gravitational force experienced by a test particle is zero. In other words, it's the boundary beyond which the repulsive force of dark energy becomes stronger than the gravitational attraction from the mass of the cluster.

Characteristics:

Balanced Forces: Within the zero-gravity sphere, the gravitational force pulling objects towards the centre of the cluster is perfectly balanced by the antigravity effect of dark energy pushing objects away.

Critical Radius: The zero-gravity sphere has a critical radius, denoted as RZG, which marks the boundary between regions where gravity dominates and where dark energy dominates.

Implications:

Existence of Bound Systems: Gravitationally bound systems such as the Coma cluster can only exist within their zero-gravity spheres. Beyond this boundary, the repulsive effect of dark energy becomes too strong for gravitational attraction to maintain cohesion.

Limit on Size: The presence of the zero-gravity sphere imposes an upper limit on the size of the cluster. Systems that exceed this size are no longer gravitationally bound and may experience the expansion of the universe due to the dominance of dark energy.

Overall, the zero-gravity sphere concept introduced in the paper provides a framework for understanding the interplay between gravity and dark energy within large-scale structures like galaxy clusters, highlighting the critical role of dark energy in shaping the boundaries and dynamics of such systems.

Reference: 

Chernin, A. D., Бисноватый-коган, Г. С., 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