On What Is Sustained by Force:

Toward a Dual-Pillar Framework in Physics

By Keying Guan with ChatGPT

Abstract

This work examines foundational questions concerning the relation between force, energy, and power in physical systems. Motivated by issues arising in the interpretation of radiation pressure and static force, it explores a complementary perspective in which sustained interaction is associated with an underlying energetic structure.

A relation of the form                                             

is considered as a conceptual extension linking force and power under conditions where displacement-based formulations may be insufficient.

From this viewpoint, classical distinctions—such as static and dynamical force, equilibrium and nonequilibrium, and closed and open systems—are reexamined in terms of energy exchange and power flow. It is suggested that equilibrium may correspond to dynamically maintained balances of underlying processes rather than complete inactivity.

The discussion further indicates that features such as wave–particle duality and the coexistence of deterministic and probabilistic descriptions may reflect different structures of interaction and energy transfer.

The work proposes a structural viewpoint and highlights the importance of experimental investigation—particularly using controlled, high-intensity, and localized energy transfer—in clarifying the relation between force and power.

Introduction

The concept of force lies at the foundation of physical theory, yet its interpretation continues to evolve across different domains of physics. While classical mechanics provides a precise description of force in relation to motion, and modern physics has established deep connections between mass and energy, the broader structure linking force, energy, and power remains open to further examination.

This work is motivated by questions arising from the interpretation of radiation pressure and the role of static force in physical systems. In particular, it explores whether sustained interaction—especially in equilibrium configurations—may involve an underlying energetic structure that is not fully captured by displacement-based formulations of work.

To address these questions, a complementary viewpoint is proposed in which the relation between force and power is considered alongside mass–energy equivalence. Rather than introducing a new theoretical framework, the aim is to identify structural features that may help clarify how physical interactions are organized in terms of energy exchange and power flow.

The discussion proceeds by examining a sequence of related topics, including static force and dissipation, equilibrium and nonequilibrium, system boundaries, and the structure of causality. A brief outlook on broader physical implications is also provided.

The purpose of this paper is not to offer definitive conclusions, but to present a coherent line of inquiry and to suggest possible directions for further theoretical and experimental investigation.

Chapter 1. The Two Pillars

The concept of force is among the oldest in human thought. Long before it acquired a precise mathematical definition, it appeared in language as an experiential notion, referring not only to pushing and pulling, but also to supporting, resisting, sustaining, and producing effects. In this broader pre-scientific sense, force implicitly contained both static and dynamic aspects, although these were not yet distinguished in a formal framework.

With the development of modern physics^[1], the concept of force has taken on multiple roles across different domains, often appearing in distinct theoretical contexts. This raises a natural question: whether a more unified and structurally consistent description of force may be possible.

At the same time, modern physics rests on a small number of foundational equivalence principles that unify distinct physical quantities into coherent conceptual structures. Among these, Einstein’s mass–energy equivalence^[9],

,

stands as one of the most profound insights, revealing that mass itself is a form of energy.

Motivated by questions arising in the study of radiation pressure^{[4], [5], [6], [8]} and the interpretation of static force, the author has explored the possibility that an analogous structural relation may exist for force^[14,15,16]. A proposed formulation is given by the force–power relation

In parallel, it is natural to ask whether an analogous relation may exist for force. A possible formulation is given by the force–power equivalence,

,

where denotes a sustained or intrinsic force, and  represents the unit velocity that establishes an energetic scale..

This relation is not intended to replace the standard expression^[2] , but rather to provide a complementary viewpoint that may be relevant in situations involving sustained interaction, particularly in equilibrium configurations where conventional interpretations may require further clarification.

From this perspective, the mass–energy equivalence and the proposed force–power relation may be viewed as two complementary principles:

·     ,  describing what a physical system is in energetic terms;

• :  characterizing what is required for a system to sustain      interaction.

While the former concerns the content of existence, the latter emphasizes the cost of maintaining physical processes. Even in situations traditionally regarded as static—such as a body held in equilibrium by a constant force, there may exist an underlying energetic structure not fully captured by classical formulations.

The purpose of the present work is not to establish a completely new theory, but to explore a set of logically connected questions that arise from this dual perspective. These include the nature of static force, the role of dissipation ^[13], the interpretation of equilibrium^[3], and the structure of energy exchange in physical systems.

Chapter 2. Static Force and Dissipation

In classical mechanics, work provides the fundamental link between force and energy. A force is said to perform work only when it acts through a displacement. Consequently, a static force—one that maintains a system in equilibrium without motion—is typically regarded as doing no work and thus having no direct energetic consequence.

This interpretation, while consistent within the formal framework of mechanics, relies on an idealized description of physical systems.

Consider a simple example: a body held at rest against gravity. In the standard formulation, no work is performed if the body does not move. However, in any realistic physical implementation, the maintenance of such a state involves ongoing processes. Muscles consume metabolic energy, mechanical supports undergo internal stress redistribution, and electromagnetic systems require sustained currents.

This observation suggests a distinction between two levels of description:

• an idealized      mechanical description, in which static forces are treated as      energetically neutral;

• a physical      realization, in which sustained forces are associated with continuous      energy exchange.

This distinction leads naturally to a central question:

Can a truly static force exist without any associated energetic process?

In classical theory, the answer is implicitly affirmative, since the definition of work depends solely on displacement. However, once dissipative^[13] effects are considered, the situation becomes more subtle.

In the study of dissipative systems, forces are explicitly linked to energy loss and power consumption. Friction, viscosity, and other forms of resistance provide familiar examples. Yet such forces are typically introduced as corrections to otherwise conservative systems, rather than as indications of a more general principle.

From a broader perspective, it is therefore reasonable to consider whether the distinction between “static” and “dissipative” forces is fundamental, or whether it reflects a limitation of the descriptive framework. What appears as a static force at the macroscopic level may correspond, at a more detailed level, to a balance of underlying processes that continuously transform or redistribute energy.

This viewpoint suggests a reinterpretation of equilibrium itself. Rather than representing the absence of physical activity, an equilibrium state may correspond to a condition in which multiple processes are dynamically balanced.

It is also important to note that force, as an experimentally measurable quantity, is typically determined through equilibrium configurations, for example, by means of elastic balances or spring-based instruments^[8]. In this sense, static force is not merely a limiting case of dynamics, but the very condition under which force becomes operationally defined.

Within the framework introduced in Chapter 1, one may tentatively associate a sustained force with a corresponding minimal power requirement, even in the absence of observable motion. This does not contradict the classical definition of work, but suggests that the energetic structure of physical systems may not be fully characterized by displacement-based formulations alone.

The purpose of this chapter is not to replace the standard framework of mechanics, but to highlight a conceptual gap between idealized descriptions and physical realizations. By drawing attention to this gap, we establish a basis for reexamining equilibrium, dissipation, and the structure of interaction in subsequent chapters.

Chapter 3. Equilibrium and Nonequilibrium

The considerations developed in the previous chapter suggest that equilibrium should not be interpreted merely as the absence of motion. Instead, it may be understood as a special condition within a broader class of physical processes.

In classical mechanics, an equilibrium state is defined by the vanishing of net force. A system is said to be in equilibrium when all forces balance and no acceleration occurs. This definition, while precise, describes only the macroscopic outcome and does not necessarily account for the underlying processes that sustain this state.

From a broader perspective, it is natural to ask whether equilibrium corresponds not to the absence of activity, but to a balance of ongoing processes.

This reinterpretation becomes particularly relevant when dissipative effects are considered. In many real systems, equilibrium is maintained through continuous interactions with internal degrees of freedom or with the surrounding environment. Energy may be absorbed, transformed, and redistributed, even though no macroscopic change is observed.

In this context, the notion of dissipation may be understood in a generalized sense. Beyond familiar forms such as friction or viscous resistance, dissipation may also include processes involving radiation, energy transfer across fields, and structural reconfiguration at different scales. From this viewpoint, dissipation is not restricted to specific mechanisms but reflects a broader class of irreversible or energy-redistributing processes.

Within such a framework, equilibrium may be regarded as a condition in which these processes are dynamically balanced. Rather than representing a static endpoint, it corresponds to a state in which multiple forms of energy exchange occur in a coordinated manner, resulting in no net macroscopic evolution.

This perspective naturally leads to a distinction between two forms of equilibrium:

• ideal equilibrium, in which no      internal or external energy exchange is considered;

• physical equilibrium, in which      underlying processes persist but remain dynamically balanced.

The latter description more closely reflects realistic physical systems.

Conversely, nonequilibrium states arise when such processes are no longer balanced. In these situations, energy flows are not mutually compensated, leading to observable changes in motion, structure, or energy distribution.

From this viewpoint, the transition between equilibrium and nonequilibrium is determined not simply by the presence or absence of motion, but by the degree to which underlying processes are balanced or unbalanced.

Further clarification may be obtained by comparing this perspective with the role of force in classical mechanics. In Newtonian theory, force is defined through the rate of change of momentum,

,

and is therefore directly associated with dynamical evolution. When a system is in equilibrium and no acceleration occurs, the net force in this sense vanishes.

However, this does not imply the absence of interaction. In many equilibrium configurations—such as a body supported against gravity—forces remain present and experimentally measurable, even though no motion is observed.

This suggests that the force defined by Newton’s second law captures primarily the dynamical aspect of interaction, namely its role in producing changes of motion. In contrast, the notion of intrinsic force introduced here is intended to describe the sustained aspect of interaction, which may persist even in the absence of observable acceleration.

From this perspective, equilibrium may be regarded as a condition in which the dynamical force vanishes at the macroscopic level, while the intrinsic force remains nonzero and is maintained through a balance of underlying processes.

In this sense, equilibrium is not a state of inactivity, but a dynamically sustained configuration.

This interpretation also provides a bridge to the analysis of system boundaries. Whether a system is considered closed or open, and how energy exchange is structured across its boundaries, becomes essential for understanding how equilibrium is realized in practice.

The purpose of this chapter is not to redefine equilibrium in formal terms, but to suggest that its physical realization may involve a deeper structure of interaction than is captured by purely kinematic descriptions. This viewpoint prepares the ground for the subsequent discussion of system openness and energy exchange.

Chapter 4. Closed and Open Systems

The analysis developed in the preceding chapters suggests that sustained forces and equilibrium configurations are associated with underlying processes involving continuous energy exchange. This observation naturally leads to a reconsideration of how such processes are accommodated within the standard distinction between closed and open systems.

In classical physics, a closed system is defined as one that does not exchange matter or energy with its surroundings. Within such a system, energy is conserved, and equilibrium is often interpreted as a final state in which all macroscopic processes cease. By contrast, an open system allows for exchanges of energy or matter with its environment and may maintain steady states through ongoing flows.

While this distinction is conceptually clear, its physical realization is often less straightforward.

In practice, systems that are treated as closed are typically only approximately so. Even in carefully controlled experimental conditions, interactions with external fields, thermal environments, or measurement apparatus cannot be eliminated. As a result, the notion of a perfectly closed system is best understood as an idealization rather than a physically realized condition.

From the perspective developed in the previous sections, this observation acquires additional significance. If sustained forces are associated with minimal power requirements, then their maintenance must, in general, involve some form of energy exchange—whether internal or external.

This leads to a more nuanced view. A system may appear macroscopically closed, in the sense that no net energy flow is observed across its boundary, while still supporting internal processes that redistribute or transform energy among its degrees of freedom. In such cases, equilibrium may be maintained even though the system remains dynamically active at a deeper level.

Conversely, in explicitly open systems, sustained forces and equilibrium states can often be directly related to continuous energy input from the environment. Examples include driven mechanical systems, electromagnetic devices, and biological organisms, all of which maintain stable configurations through ongoing energy consumption and dissipation.

These considerations suggest that the distinction between closed and open systems may be better understood not as a sharp dichotomy, but as a continuum characterized by the structure and scale of energy exchange.

Within this framework, the concept of power flow provides a unifying description. A strictly closed system would require that all power contributions be cancelled internally, resulting in no net exchange across its boundary. However, even in such idealized conditions, internal processes may persist if they remain dynamically balanced.

This perspective also clarifies the interpretation of equilibrium. In open systems, equilibrium may correspond to a steady state maintained by continuous input and dissipation of energy. In effectively closed systems, equilibrium may instead reflect a balance among internal processes. In both cases, the defining feature is not the absence of activity, but the balance of underlying power flows.

From this viewpoint, the realization of force and equilibrium depends sensitively on how energy exchange is structured within and across system boundaries. The classical definitions of closed and open systems remain valid as limiting cases, but their physical interpretation may be enriched by considering the role of sustained interaction and power flow.

The purpose of this chapter is not to revise established definitions, but to highlight the importance of system boundaries and energy exchange in understanding how physical states are realized. This provides a natural transition to the subsequent discussion of causality and the structure of interaction in time.

Chapter 5. Causality and Wave–Particle Duality

The preceding discussion has emphasized the role of sustained interaction, energy exchange, and power flow in the description of physical systems. This perspective naturally leads to a broader question: how are physical processes structured in time, and what underlies the causal relations observed in nature?

In classical mechanics, causality is typically expressed in terms of force and motion. A force acts on a system and produces a change in its state of motion, providing a clear operational notion of cause and effect. However, as discussed in earlier chapters, force may be understood as having both a dynamical aspect and a sustained aspect, the latter being associated with continuous interaction rather than observable acceleration.

From this viewpoint, it is natural to consider whether causality itself may be interpreted in terms of the structure of energy transfer. Rather than viewing cause and effect as isolated events, one may regard them as manifestations of underlying processes in which energy is continuously transmitted, transformed, and balanced.

This perspective does not alter the classical formulation of causality, but suggests that its physical realization may involve more than instantaneous interactions. In particular, sustained forces and equilibrium configurations indicate that causal relations may be embedded in ongoing processes that persist over time.

Such considerations bear a suggestive relation to the longstanding problem of wave–particle duality in quantum physics^{[7], [9], [10], [13]}. In conventional formulations, particle-like behavior is associated with localized and discrete interactions, while wave-like behavior corresponds to extended and distributed propagation. The coexistence of these two descriptions has been a central feature of quantum theory.

Without attempting to reformulate quantum mechanics, one may ask whether these different modes of behavior could reflect distinct structures of energy transfer. A particle-like description may correspond to localized transfer processes, while a wave-like description may be associated with distributed and continuous propagation.

From the standpoint developed in this work, the observable behavior of physical systems may depend not only on the entities involved but also on how interaction and energy exchange are organized in space and time.

It should be emphasized that the present discussion is exploratory in nature. No attempt is made here to derive new quantum laws or to replace established theoretical frameworks. Rather, the aim is to suggest that the concepts of sustained interaction, power flow, and energy exchange may provide a complementary structural viewpoint from which certain foundational questions can be reconsidered.

In this sense, causality and wave–particle duality may be viewed not as isolated problems, but as aspects of a broader structure of physical interaction. Further development of this perspective, both theoretically and experimentally, remains an open direction for future investigation.

Chapter 6. A Brief Cosmological Outlook

The framework developed in the preceding chapters has focused on the structure of physical interaction in terms of sustained force, energy exchange, and power flow. It is natural to ask whether these considerations may also be relevant at larger scales, including those encountered in astrophysical and cosmological contexts.

In many large-scale systems, equilibrium does not correspond to the absence of activity, but to a dynamically maintained balance of processes. Stars, for example, sustain their structure through a balance between gravitational compression and radiative energy output^[12]. More generally, a wide range of astrophysical systems exhibit long-lived configurations that are supported by continuous transformation and transfer of energy.

From the perspective of sustained interaction and power flow, such systems may be viewed as extended realizations of the principles discussed in earlier chapters. In this sense, equilibrium reflects not a static condition, but a stable organization of ongoing processes across different scales.

At the same time, the attempt to describe physical systems across increasingly large or small scales reveals an inherent limitation. While physical processes may extend over a wide range of scales and levels of complexity, any theoretical formulation is necessarily expressed in finite terms. Mathematical models, measurement procedures, and observational data all rely on finite structures.

This contrast—between potentially infinite physical processes and finite modes of representation—may well constitute the underlying source of several enduring characteristics within modern physics. For instance, deterministic descriptions at the classical level coexist with probabilistic formulations in quantum theory; similarly, localized particle-like behaviors are described within the very same framework as extended, wave-like propagation.

Rather than viewing these features as contradictions, it may be more appropriate to interpret them as reflecting different ways in which finite descriptive frameworks approximate complex physical reality.

Within this broader context, the concepts of sustained interaction, power flow, and energy exchange may provide a structural viewpoint that complements existing formulations. While the present work does not attempt to establish a comprehensive cosmological theory, it suggests that similar principles of balance, interaction, and energy organization may operate across a wide range of physical scales.

It is also important to recognize that the development of physical theory is inseparable from the evolution of the systems that formulate it. Human observers, their instruments, and their mathematical languages are themselves finite structures. As these structures evolve through technological progress, computational capability, and conceptual refinement, the modes of describing and understanding physical phenomena may also change.

In this sense, the progress of physics may be understood not only as the discovery of new laws, but also as the refinement of the relationship between finite representation and the complexity of the physical world.

The considerations presented in this chapter are intended as a preliminary outlook rather than a definitive statement. The further development of these ideas, particularly in relation to cosmology and fundamental physics, remains an open direction for future investigation.

Chapter 7. Conclusion: A Program for Future Inquiry

The present work has examined a set of interconnected questions arising from a dual perspective in physics, namely the relation between mass and energy, and the proposed relation between force and power. Rather than introducing a complete theoretical system, the aim has been to identify structural features that may warrant further investigation.

A central theme throughout this work has been the distinction between dynamical and sustained aspects of interaction. While classical formulations of force provide an effective description of changes in motion, the analysis suggests that sustained interactions—particularly those associated with equilibrium configurations—may involve underlying energetic processes not fully captured by displacement-based definitions of work.

This viewpoint has led to a reinterpretation of several foundational concepts, including static force, equilibrium, and the distinction between closed and open systems. In each case, emphasis has been placed on the role of energy exchange and power flow as organizing principles of physical interaction.

At a broader level, the discussion has suggested that certain persistent features of modern physics—such as the coexistence of deterministic and probabilistic descriptions, and the dual characterization of wave-like and particle-like behavior—may be understood as reflecting different aspects of how physical interactions are structured and represented.

Within this context, the proposed force–power relation may be viewed as a conceptual tool for examining sustained interaction across a range of physical situations. Its role is not to replace established formulations, but to provide a complementary viewpoint that may help clarify the energetic structure of physical processes.

An important direction for future work concerns experimental investigation. While radiation pressure has been studied for over a century, its interpretation may depend sensitively on the experimental framework. Advances in high-intensity, highly collimated light sources may enable more precise studies in which the relative roles of momentum transfer and energy absorption can be examined under controlled conditions.

Such experiments may help to clarify the physical basis of sustained interaction and contribute to a more refined understanding of the relation between force and power.

More generally, the development of physical theory may be viewed as an ongoing process shaped by both conceptual and practical constraints. Theoretical descriptions are necessarily finite, while the systems they describe may exhibit levels of complexity that extend beyond any single representation. Progress, therefore, may depend not only on the discovery of new laws, but also on the refinement of the frameworks through which physical phenomena are interpreted.

The present work is intended as a contribution to this continuing process. It outlines a set of questions, proposes a structural perspective, and identifies possible directions for further study, while leaving open the deeper theoretical and experimental developments that may be required in the future.

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[14] Keying Guan with ChatGPT,  (2025), <White Paper on Equivalent Relationships of Physical Quantities>, Published by BookBaby.com, ISBN: 979-8-3780-602-6, eISBN: 979-8-3178082-8-0.

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