Abstract

Synchrotron radiation exhibits well-established polarization characteristics, including linear, circular, and elliptical polarization. The present paper proposes a reality-based structural interpretation of these polarization features within the author’s previously developed mass–space framework. In this framework, an electron possesses an extra-nuclear space structure containing space-matter particles, and progressive reduction of this structure with increasing velocity provides the basis for the emission of radiation. The present study extends this structural concept to charge polarization and proposes that the spatially asymmetric distribution of charge and mass within the emitted structures may produce directional polarization. Quasi-neutral compound photon structures are hypothesized to acquire preferential longitudinal orientation, providing a possible interpretation of linear polarization. At the boundary of the radiation beam, interaction with the surrounding structured space medium is further proposed to produce rotational motion, giving rise to circular or elliptical polarization depending on the symmetry of the internal structure. The proposed interpretation is intended as a conceptual physical hypothesis and requires further mathematical development and experimental verification.

Keywords: Synchrotron radiation, Linear polarization, Circular polarization, Elliptical polarization, Mass-space framework, Extra-nuclear space structure.

Introduction

Synchrotron radiation emitted by relativistic charged particles is characterized by strong polarization in addition to its broad spectrum and pronounced forward directionality. Classical electrodynamics and special relativity provide successful mathematical descriptions of these observed properties. The present study explores an alternative causal interpretation based on the physical structure of the radiating electron and the state of the emitted radiation.

The present work forms the second part of the author’s previously developed reality-based interpretation of synchrotron radiation. In the earlier work, an electron was proposed to possess an extra-nuclear space structure whose effective dimension and interaction cross-section progressively decrease with increasing velocity [1] [2]. A mathematical treatment of this structural reduction and its relationship with the dynamics of high-speed particles have been developed in the author’s earlier studies. The same concept was subsequently applied to synchrotron radiation, where progressive reduction of the electron’s extra-nuclear structure was proposed to expose and release space-matter particles from successively deeper regions of the structure.

The present paper extends this previously developed structural model to the polarization of synchrotron radiation. It considers charge polarization as a consequence of an asymmetric mass–space distribution and proposes that the emitted radiation may form quasi-neutral compound structures possessing residual directional charge and mass–space characteristics. Their preferential orientation during propagation is proposed to provide a possible structural basis for linear polarization. Further interaction of radiation structures at the boundary of the beam with the surrounding structured space medium is hypothesized to produce rotational motion, providing a possible interpretation of circular and elliptical polarization.

Charge Potential in the Mass–Space Framework 

The existence of electric charge as a property associated with matter, rather than as an independently existing physical entity, suggests that charge may be understood as a state property of matter within the mass–space integral system proposed in this framework. On this basis, a new concept of absolute charge potential is introduced in terms of the ratio of mass to the space holding by that mass:

Φ_c=m/s

where m represents mass and s represents the corresponding space holding of the mass. The quantity Φ_c is referred to here as the absolute charge potential of matter.

According to this framework, when matter within a given frame of reference maintains a uniform mass–space ratio, it is considered to be in mass–space equilibrium with respect to that frame. Since there is no spatial variation of the proposed charge potential, there is no potential difference to produce charge interaction within that local system. Matter therefore exhibits charge neutrality relative to its surrounding matter.

This concept also provides a basis for distinguishing between relative charge potential and absolute charge potential. Charge neutrality observed in one frame of reference need not imply that the absolute charge potential of the matter is zero. Rather, neutrality signifies that the matter and its surrounding environment are at the same charge-potential level within the considered frame.

For example, matter situated on the surface of the Earth may possess an absolute charge potential denoted by

Φ_cE=(m/s)_E

while matter situated on the surface of Jupiter may possess a different absolute charge potential,

Φ_cJ=(m/s)_J

Matter within each respective environment may remain charge-neutral because its charge potential is in equilibrium with the surrounding matter. However, if matter initially in the terrestrial environment is abruptly transferred to the Jovian environment, its original mass–space state may no longer correspond to the local equilibrium condition. The resulting difference between the charge potential of the transferred matter and that of its new surroundings can therefore produce charge activity until a new mass–space equilibrium is established.

For practical measurement, a relative charge-potential scale may be defined by assigning the equilibrium potential of a selected reference environment as zero. Thus, the Earth’s surface may be taken as the zero of a terrestrial relative charge-potential scale, while the surface of Jupiter may independently be taken as the zero of a Jovian relative scale. These two reference zeros do not necessarily represent the same absolute charge potential. In this sense, assigning zero charge potential to neutral matter is a consequence of the chosen relative scale rather than a statement that neutral matter possesses no absolute charge potential.

This distinction is analogous, within the present framework, to the distinction between an absolute state quantity and a reference-dependent potential difference. Charge neutrality is therefore interpreted as equality of charge potential between a system and its relevant surroundings, rather than as the absence of charge potential.

Electric Charge Potential

For a particle of mass m carrying electric charge q, the conventional specific electric charge is

σ_q=q/m.

For a specified value of specific charge, the conventional electric potential remains a separate physical quantity. In the present framework, however, the proposed charge potential is defined through the mass–space relation,

Φ_c=(m/s),

where s denotes the space holding of the mass. Equivalently, its reciprocal may be written as

s/m

representing the space holding per unit mass.

The proposed definition is intended to describe the state of matter through its mass–space organization, rather than to replace the conventional definition of electric potential used in electromagnetic theory. The quantity m/s is therefore introduced as a new theoretical measure of charge potential within the mass–space framework.

Thermal Charge Potential

The same mass–space concept is extended to the thermal domain. Temperature is conventionally used to characterize the thermal state of matter. In the present framework, temperature is interpreted as a manifestation of the charge-potential state associated with the mass–space organization of matter.

For a unit reference quantity, the thermal charge potential is represented by

Φ_t=t,

where t denotes temperature. Within the proposed framework,

t≡m/s,

so that temperature is interpreted as a measure of the mass–space state or thermal charge potential of the system.

Accordingly, the framework proposes that the same fundamental ratio,

Φ_c=m/s,

can be used as a generalized measure of state property across different domains of matter. At the microscopic scale, the manifestation of charge is identified primarily with electric phenomena, whereas at the finer micro-micro scale, including the domain associated with photons and other field-forming entities, the corresponding state is interpreted in terms of photonic or thermal charge potential.

Thus, the proposed framework seeks to establish a common mass–space basis for electric, photonic, thermal and celestial charge potentials. The intention is not to identify these phenomena as experimentally identical, but to propose that their respective state properties may be represented through a common underlying mass–space relation. The range of charge interactions may differ across domains because the lower limit of an interaction is constrained by the characteristic dimensions of the interacting structure, whereas the upper limit depends on the mass content of the nucleus. Consequently, the size of the extranuclear space structure is influenced by the range of mass–space interaction under the prevailing background conditions [3].

In microscopic particles, the nucleus contains a highly concentrated amount of mass within an extremely small region. Within the proposed mass–space framework, this high mass concentration defines the lower limit of the interaction range because the dimensions of the nucleus are many orders of magnitude smaller than those of macroscopic structures.

According to the proposed framework, the reduced dimensions of microscopic structures permit charge interactions over extremely short ranges that are not ordinarily observed in macroscopic bodies. Furthermore, if the strength of mass–space interaction follows an inverse-square dependence, the interaction strength may increase significantly as the characteristic dimensions of the interacting domain decrease. Each transition to a finer structural domain may therefore involve a corresponding change in both the range and the strength of the interaction.

This framework provides a possible explanation for why interactions associated with particles from different domains appear fundamentally different. However, within the present theory, these differences are interpreted as domain-dependent manifestations of a common mass–space interaction rather than as evidence that the interactions are already established to be identical in conventional physics. In the present framework, charge interaction is interpreted as a manifestation of mass–space interaction, with charge characterised in terms of the mass and space parameters associated with matter [4]. Thus, the proposed invariance of the underlying mass–space interaction provides a common basis for interpreting the range and strength of charge interactions across different domains.

Mass–Space Equilibrium and Charge Neutrality

Within this framework, matter at every scale and in any domain is regarded as a mass–space integral system [3]. In its natural state, a system tends toward mass–space equilibrium with its surrounding matter. Under equilibrium conditions, the charge potential of the system and its surroundings is equal within the relevant domain, and the system consequently exhibits charge neutrality [4].

A macroscopic body may contain structures belonging to several domains simultaneously. Each domain may establish its own mass–space equilibrium while remaining coupled to the other coexisting structures. Consequently, equilibrium at the macroscopic level does not necessarily imply the absence of internal differences in the state properties of the constituent domains.

Any displacement of matter from its equilibrium condition produces a change in its mass–space state relative to its surroundings. Within the proposed framework, this change is interpreted as a change in charge state. The subsequent tendency toward restoration of mass–space equilibrium constitutes the fundamental mechanism associated with the release or absorption of energy.

Charge neutralization involves recombination or interaction with particles having opposite charge characteristics. When the opposing charges are equal in magnitude, complete charge neutralization can occur by their union at the corresponding domain level. When they are not equal, complete restoration of the neutral state may require participation from structures belonging to a finer domain.

In the mass–space interpretation, mass-rich structures are associated with positive charge characteristics, whereas space-rich structures are associated with negative charge characteristics [5]. Complete restoration of mass–space equilibrium therefore requires compensation between mass-rich and space-rich components across the relevant domains.

An important consequence of this interpretation is that macroscopic charge neutrality does not necessarily imply the complete absence of an underlying charge signature. A particle may appear electrically neutral at one observational scale while retaining internal mass–space asymmetries that are compensated through finer-domain structures. Thus, within the proposed framework, a neutral microscopic particle may still carry an underlying signature of its constituent charge states, even though its net observable charge is zero.

Similarity between charge activity and thermal activity

There is a useful analogy between electrical charge activity and thermal activity; however, at this stage, it may not be appropriate to state that they originate from the same physical phenomenon. In established physics, they are treated as distinct physical phenomena, although both can be described in terms of gradients, potentials, transport, and equilibrium.

Existing similarity between charge activity and thermal activity

Electrical activity	Thermal activity	Common feature
Electric potential difference ΔV	Temperature difference ΔT	Driving potential difference
Electric field E=-∇V	Temperature gradient ∇T	Spatial gradient
Electric current I	Heat flow Q̇	Transport process
Electrical resistance R	Thermal resistance Rth	Opposition to transport
Charge equilibrium	Thermal equilibrium	No net macroscopic flow
Conductivity σ	Thermal conductivity k	Material-dependent transport property

The observed structural similarity between charge activity and thermal activity suggests the possibility of investigating whether a more fundamental physical state variable can provide a common basis for understanding both types of activity. Within the present framework, the proposed description of mass in terms of a photonic mass unit, charge in terms of a photonic charge unit [6], and matter as a mass–space structure containing a nucleus and an associated extra-nuclear space structure provides a possible basis for developing a unified description of the micro and micro–micro domains [7].

Furthermore, the proposed atomic structure, including its extra-nuclear space structure, space-matter particles, and orbital particles or bodies, is considered to exhibit structural features that may be comparable, at a conceptual level, with those observed in larger gravitational systems such as the Solar System. If such structural correspondence can be established quantitatively, it may provide a basis for examining possible connections between the macro, micro and micro–micro domains.

From this perspective, the domain-specific laws currently used in physics may be regarded as descriptions developed for particular scales and classes of observable phenomena. The present framework proposes that these apparent domain distinctions may arise from differences in scale, structure, and interaction conditions rather than necessarily representing fundamentally unrelated physical principles. The underlying uniformity of structure and interaction, when supported by theoretical derivation and experimental evidence, could therefore provide a deeper basis for connecting phenomena across different domains of nature.

The structural mechanism proposed in the present paper is an extension of the author’s previously developed mass–space model of particle dynamics. In earlier work, the author proposed that an accelerated charged particle possesses an extra-nuclear space structure whose effective dimension and interaction cross-section progressively decrease with increasing velocity as a consequence of interaction with the structured space medium. A mathematical formulation of this velocity-dependent structural reduction was developed and shown to lead to a corresponding reduction in the effective interaction cross-section. The same structural concept was subsequently applied to synchrotron radiation, where progressive reduction of the electron’s extra-nuclear structure was proposed to expose successively deeper regions containing space-matter particles and thereby influence the energy and directional characteristics of the emitted radiation. The present paper extends this previously developed framework to examine the charge-polarization state of the remaining structure and its possible relationship with the polarization characteristics of synchrotron radiation.

Cause of Charge Polarization in a Charged Particle

Electric charge is a recognized phenomenon associated with microscopic particles. However, the present author has attempted to identify a possible replica of charge activity in other domains of nature by exploring the possibility of a common basic cause underlying charge in matter. If the fundamental cause remains the same, charge-related interactions in different domains may appear different in their range and strength because of differences in the geometrical mass-space configuration characteristic of each domain and scale. Such domain-specific differences may have led to the recognition of alternative explanations for non-electric charge-related phenomena in nature, thereby obscuring the possibility of a common underlying physical basis. The present approach therefore explores whether such apparently different phenomena can be interpreted within a more unified framework.

According to the proposed model, an electron accelerated to progressively higher velocities successively lose a portion of its extra-nuclear space structure. As the velocity approaches the velocity of light, only a small fraction of the original extra-nuclear space structure is considered to remain associated with the nucleus. The space structure closer to the nucleus is proposed to possess photonic charge-polarized shell features, analogous in a conceptual sense to the polarized atmospheric structure of the Earth (Fig.1), in which charged layers of the ionosphere occur in an organized spatial configuration.

Abstract

Synchrotron radiation is characterized by high brightness, a broad continuous spectrum, strong polarization, and pronounced forward collimation at high electron velocities. The present paper proposes a reality-based conceptual interpretation of these characteristics based on a structured mass–space structural model of the electron except the polarization phenomena which is dealt in part- II of this paper. In this framework, the electron possesses an extra-nuclear space structure containing space-matter particles identified as photons. As the electron is increasingly accelerated, its extra-nuclear structure is proposed to undergo progressive deformation and size reduction, releasing particles from successively deeper regions. The changing spatial state of the released particles is proposed to account for the increase in photon energy and the observed changes in the radiation spectrum. The reduction in the emission region, together with increasing longitudinal dominance over transverse dispersion and the proposed increase in particle momentum, provides a physical interpretation of the progressive narrowing of the synchrotron radiation beam. A mathematical analysis of the reduction in the extra-nuclear structure is presented, yielding a velocity-dependent expression consistent with the corresponding relativistic expression while arising from a different physical interpretation. The proposed framework therefore provides an alternative conceptual basis for relating electron velocity, structural reduction, photon energy, radiation intensity and beam collimation.

Keywords: Synchrotron radiation, Extra-nuclear space structure, Space-matter particles, Beam collimation, Photon energy, Structural dynamics. 

Introduction

Synchrotron radiation is electromagnetic radiation emitted by relativistic charged particles, particularly electrons, when their trajectories are curved by an external magnetic field. The continuous change in the direction of velocity produces centripetal acceleration, causing the electrons to lose energy through electromagnetic radiation.

At low velocities, radiation is emitted over a relatively broad range of directions. As the electron velocity approaches the speed of light, however, the radiation becomes concentrated around the instantaneous direction of motion within a narrow forward cone whose characteristic angular width is approximately (1), where () is the Lorentz factor. This relativistic beaming is a well-established experimental feature of synchrotron radiation. 

Classical electrodynamics combined with special relativity successfully predicts the angular distribution, spectrum and intensity of synchrotron radiation. Nevertheless, the mathematical formulation does not identify a distinct microscopic physical process that can be conceptually visualized as the origin of the progressive concentration of radiation into the forward cone. The physical interpretation of this relativistic beaming therefore remains open to alternative conceptual approaches.

Synchrotron radiation also possesses a broad continuous spectrum extending from infrared and visible wavelengths to ultraviolet and X-rays. Its high brightness, strong collimation, polarization and broad spectral range make it an important tool in crystallography, spectroscopy, materials science, biology, medicine, nanotechnology, semiconductor research and astrophysics.

The present study explores a reality-based conceptual interpretation of synchrotron radiation. The approach is motivated by the premise that the fundamental principles governing nature operate consistently across different physical domains. Consequently, observable macroscopic phenomena may provide useful conceptual analogies for interpreting processes occurring in microscopic or otherwise inaccessible domains, provided that the analogy is treated as a conceptual guide rather than as a direct equivalence of physical mechanisms. 

Conceptual Basis of the Present Study

A mathematical description can accurately establish relationships among observable quantities without necessarily providing an intuitive physical picture of the underlying process. The present work therefore seeks an observable natural phenomenon in which increasing dynamical activity is accompanied by the release of energy or matter from a moving system. Such an analogy may help formulate a physically transparent interpretation of synchrotron radiation.

In this context, the activity of Halley’s Comet during its approach to the Sun provides an interesting macro-domain analogy. As the comet approaches the Sun, its orbital velocity and dynamical activity increase. Solar heating and the changing dynamical conditions cause volatile materials to escape from the cometary nucleus, producing a bright coma and an extended tail containing gas, ions, electrons, and dust particles.

Abstract

The conventional interpretation of mass-energy equivalence considers that the energy released during nuclear reactions originates from the conversion of mass into energy according to Einstein’s relation E=Mc². Although mathematically successful, this interpretation does not provide a realistic physical description of how mass disappears and energy appears. The present work proposes a reality-based alternative founded on the structural concept of light particle. In this model, photons possess finite mass in a photonic mass unit together with an internal mass-space structure. During nuclear reactions, the apparent mass defect corresponds to the disintegration of matter into an enormous number of photons of an extremely fine domain rather than annihilation of mass. Each photon possesses kinetic energy by virtue of motion and internal energy associated with the non-equilibrium mass-space structure. The total energy released is obtained by summing these two contributions while maintaining independent conservation of both mass and energy. Accordingly, mass is regarded as a fundamental constituent of matter, whereas energy is treated as a state property arising from the structural and dynamical condition of matter. This interpretation offers a unified conceptual framework consistent with the author’s reality-based structural model of light particles and mass-space interaction.

Keywords: Mass–energy equivalence, Photonic mass, Photon structure, Mass conservation, Nuclear energy. 

Reality-based framework replacing the concept of mass–energy equivalence

The equations for kinetic energy and thermal energy explicitly contain the mass component of the material body. In these cases, energy is possessed by matter by virtue of its state property described through velocity or temperature. The mass of the body remains conserved while its energy changes according to its physical state. In contrast, the conventional interpretation of nuclear fission and fusion assumes that a portion of the mass disappears and is converted into energy. The reaction products consist of massive particles together with photons, which are conventionally regarded as massless carriers of energy.

According to the Standard Model of particle physics, photons and gluons are assigned zero rest mass. The strictly massless nature of the photon is closely connected with gauge invariance and the renormalizability of Quantum Electrodynamics (QED). However, experimental observations do not establish that the photon mass is exactly zero; they only impose increasingly stringent upper limits on any possible non-zero rest mass. Astrophysical and magnetohydrodynamic studies constrain the photon mass to extremely small values, with independent investigations based on galactic plasma dynamics and measurements of the galactic vector potential providing still tighter limits.

A finite photon mass would modify Maxwell’s equations through additional terms, as described by the Proca formulation and could produce observable effects in galactic plasma and electromagnetic fields. Since such effects have not been detected, progressively stronger upper bounds have been established. These results, however, do not constitute experimental proof that the photon mass is exactly zero; they indicate only that any non-zero mass must be extraordinarily small. Thus, the possibility of a finite photon mass cannot be excluded solely on experimental grounds.

The present formulation therefore considers whether future developments in physics might require a reassessment of the strictly massless-photon assumption. Although the Standard Model has achieved remarkable success within its established domain, it need not represent the final description of nature. A reality-based framework founded on conceptual consistency, uniformity of nature and cause-and-effect reasoning may merit consideration if it provides a broader physical interpretation.

In the proposed reality-based model, light is treated as a material particle possessing both mass and an internal mass-space structure [1]. This eliminates the need for wave-particle duality and provides a common structural basis for matter across different physical domains. Within this framework, electric charge is regarded as a manifestation of a nonequilibrium state of mass-space association, giving rise to different non-electric charges [2]. Accordingly, conservation of charge may involve possible interconversion between electric and non-electric charge states [2].

The model further assumes that every physical entity is fundamentally an integrated mass-space system, making mass and space universal constituents of existence [3] [4]. Physical theories should therefore seek to describe nature in terms of these fundamental constituents rather than relying exclusively on abstract mathematical formalism.

Suppose that the apparent mass defect in a nuclear reaction represents the disintegration of matter into an enormous number of photons. If one gram of matter produced approximately (10²²) photons, the mass of an individual photon would be of the order of 10^-22g. This estimate introduces the concept of a photonic mass unit, analogous to the atomic mass unit, while maintaining the principle of structural continuity across different domains of matter.

A comparable distinction occurs in ordinary thermodynamic processes. One gram of steam contains more internal energy than one gram of water or ice, although its mass remains essentially unchanged. The difference arises from changes in molecular binding and energy states, while mass and energy are not simply regarded as mutually annihilating quantities. By analogy, the energy released in nuclear reactions could arise from the reorganization and disintegration of matter into constituents belonging to a much finer physical domain. If these constituents possess masses below present experimental detection limits, the apparent loss of mass may reflect the limitations of measurement rather than the destruction of matter itself.

The conventional interpretation describes nuclear energy release through the conversion of mass into energy, expressed by (E=Mc²) where M refers to mass loss in nuclear reaction. The present model proposes a different physical interpretation: energy is liberated through the reorganization, excitation and disintegration of matter into finer constituents, rather than through the complete destruction or disappearance of mass. This perspective seeks to preserve the continuity of matter while offering an alternative reality-based interpretation of the origin of released energy.

In this framework, photons possess mass when measured in a photonic mass unit [4], although their mass is effectively zero when expressed in conventional atomic mass units because of its extremely small magnitude. If (m_p) denotes the mass of a photon, its kinetic energy at velocity ‘c’ is

KE= 1/2 (m_pc²) —                         eqⁿ-1

If a total mass loss (M_L) is disintegrated into photons during a nuclear reaction, the total kinetic energy becomes

KE = 1/2 (m_pc²).M_L/m_p= 1/2 M_Lc² —                eqⁿ-2

This result accounts for only one part of the energy predicted by Einstein’s mass-energy relation. The remaining half cannot be explained if the photon is assumed to be a structureless particle. The present work therefore proposes that, in addition to kinetic energy arising from translational motion, the photon possesses internal energy associated with changes in its mass-space structure. Recognition of this structural contribution provides a possible physical basis for accounting the remaining part of energy released during nuclear reactions and forms the basis for the reality-based interpretation developed in the following sections.

Energy of photon

The wave description of light has been highly successful in explaining many optical phenomena and the energy aspect of light. However, the very feasibility of high frequency light-wave in space medium is questionable particularly when the medium is incapable of rendering the elastic modulus required to sustain the wave propagation of light. On the other hand, the particle concept of light is feasible and it permits a realistic interpretation based on structural organization. The principle of uniformity of nature suggests that all centrally organized physical systems should exhibit structural similarity irrespective of the domain to which they belong. In view of the above, the present work is based on the particle concept with a deeper understanding of its structure [1].

According to the proposed model, a photon is a material particle consisting of a central nucleus surrounded by an extra-nuclear space structure. When the photon is at rest, this extra-nuclear structure exists in its equilibrium state. In the neutral state, photon remains passive and fails to reveal its tiny existence in any scientific experiment. When a photon is accelerated to velocity (c), the extra-nuclear space structure is assumed to be completely stripped off, while the central nucleus remains intact. This behavior differs from the conventional physical process since the existence of the extra nuclear space structure remains yet to be explored.

Any departure of the extra-nuclear space structure from its equilibrium state defines the charge-state/energy-state of the photon. The photonic charge state is represented by the ratio of the lost space content from the equilibrium space holding to the equilibrium space holding. The degree of nonequilibrium in the structural state of mass and space determines the charge potential or the energy level of the photon, whereas the energy of photon involves the net extent of mass-space non-equilibrium. The said energy level and energy correspond to the internal energy of the photon. The extent of space holding by the nucleus of photon is a function of the mass content of the nucleus because the extra nuclear space structure surrounding a nucleus is formed by mass-space attraction. Therefore, the mass of photon becomes a parameter for evaluating energy from energy level for both kinetic energy and internal energy. Thus, the internal energy of photon is the product of the mass of the photon and the charge state of the photon, where the charge state corresponds to the energy level.

In the existing concept the energy of a photon is given by

E=hν

where, E is the energy of photon, ν is the frequency of waves and h is plank’s constant.

Presumably the energy in the above expression is the sum of internal energy and kinetic energy. Since the mass term is absent in the above energy equation, the so-called energy corresponds only to the energy level of the photon and the true significance of frequency of light wave corresponds only to the photonic charge state in the realistic particle concept of light.

If photon has insignificant mass, then no theoretical model can make it zero, however the model can only assume its mass to be zero which is not the reality. If mp is the mass of photon in photonic scale unit then the internal energy of photon is given by:

E_i=k. m_p×Energy level

or E_i=k. m_p. s  —                      eqⁿ-3

where, s represents the energy level (charge potential state) of photon and k is proportionality constant.

Now comparing the light energy in conventional wave concept and that proposed in the particle concept, it is found, the term h in Plank’s equation for wave energy has the significance of photonic energy level/charge potential state in the particle concept. The Plank’s constant h corresponds to the proportionality constant k in the particle concept. But the mass term mp is missing in Plank’s energy equation. Conventionally the energy per unit mass is considered as the energy level and energy of the particle is obtained by multiplying the mass of the particle with energy level. The very fact that the term mass is missing in Plank’s energy equation, the term E corresponds to energy level. More precisely Plank’s equation gives the energy level of photon and not the energy of photon [5].

Since the mass of photons may vary in a manner analogous to atomic masses, photons of different masses may possess different energies even when they have the same energy level and charge state. If photons are assumed to have identical mass, the photon energy becomes proportional to its energy level and the distinction between energy level of photon (E_Lp) and energy of photon (E_p) becomes only a matter of normalization through different constants of proportionality.

The structural model of the photon has previously been employed by the author to provide a unified explanation to different optical phenomena without invoking wave-particle duality. The same structural concept also provides a natural explanation for the origin of photon energy. According to this model, a photon possesses energy in two distinct modes:

1. Kinetic energy mode, arising from the translational motion of the photon mass.
2. Internal energy mode, arising from the detachment of the extra-nuclear space structure from its equilibrium structure where energy is released by recombination of the space structure. This has similarity with the release of energy by recombination of ion and electron within atomic plasma.

The extra-nuclear space structure is assumed to be highly elastic due to the compressible nature of the physical space medium. Photon at rest has equilibrium space structure in a given background space potential. When the photon reaches the velocity (c), the associated extra nuclear structure is stripped off. When the photon is subsequently absorbed by matter and comes to rest, it reconstructs its equilibrium structure by acquiring the required space entities from the surrounding medium, in a manner analogous to the restoration of equilibrium in the author’s structural model of neutral atoms.

Consequently, a moving photon possesses kinetic energy because of its mass and velocity, while simultaneously possessing internal energy due to the deformation and detachment of its extra-nuclear structure. Since both forms of energy arise from the same physical cause of motion of the photon particle, the two different modes of energy can be clubbed into one at velocity (c).

The total energy of a photon is therefore

E_p= 1/2 m_pc²+km_p.s   —                      eq²-4

The energy level is directly proportional to the loss of space content from the extra nuclear space structure which is proportional to dynamic pressure and in turn proportional to v². Now substituting v² in place of s we get:

E_p= 1/2 m_pc²+km_pv²

=(k+1/2) m_pc²,  at v~c  —           eqⁿ-5

If the mass loss in nuclear reaction produces ‘n’ number of photons the total energy liberated is

E_L=n. (k+1/2) m_pc² —          eqⁿ-6

From nuclear fission and fusion experiment, the value of k is found to be ½.

Hence E_L=n. m_pc²

where E_L = Energy of disintegrated mass.

Since the total mass of all photons equals the disintegrated mass (M_L)

n.m_p=M_L

the total liberated energy becomes

E_L=M_Lc²     —             eqⁿ-7

The equation- 7 has the expression of mass energy equivalence equation E=Mc².

Within this interpretation, Einstein’s mass-energy relation is recovered without requiring the conversion of mass into energy. Instead, the released energy arises because the disintegrated mass is redistributed into an enormous number of photons, each possessing both kinetic and internal structural energy. Thus, mass and energy remain independently conserved throughout the process.

In the present reality-based framework, mass is regarded as a fundamental constituent of matter, whereas energy is considered a state property arising from the dynamical and structural condition of matter. Consequently, mass is not converted into energy; rather, energy is released through the structural disassociation of matter into finer constituents while the total mass is conserved in the photonic domain.

Conclusion

The present study proposes a reality-based interpretation of mass-energy equivalence by introducing a structural model of the photon and the concept of photonic mass. Instead of assuming that mass is transformed into energy, the analysis suggests that matter disintegrates into an enormous number of photons belonging to a finer domain of nature. The released energy originates from two physical contributions: the kinetic energy associated with the motion of photons and the internal energy arising from changes in their mass-space structure. Under this interpretation, mass and energy remain independently conserved, with energy viewed as a state property of matter rather than an entity equivalent to mass. Although the proposed model differs fundamentally from the conventional interpretation based on the Standard Model and Special Relativity, it aims to provide a physically intuitive explanation consistent with the author’s broader reality-based framework. Since the equation E=Mc² has been tested experimentally and the new interpretation predicts the same equation doesn’t require any further test to establish the new reality-based concept.

Reference

1. https://philosophyofnature.org.in/critical-analysis-on-physical-reality-of-light.
2. https://philosophyofnature.org.in/electric-and-non-electric-charges-and-their-inter-conversion.
3. https://philosophyofnature.org.in/basic-constituents-of-universe-and-their-interactions.
4. https://philosophyofnature.org.in/towards-a-new-comprehensive-universal-science.
5. https://philosophyofnature.org.in/energy-as-a-relational-property-a-mass-space-interpretation-of-nature.

Abstract

Scientific progress is often achieved when successful quantitative analyses emerge from reality-based qualitative models. However, in domains beyond direct human perception, many dynamic parameters cannot be adequately conceptualized due to observational limitations. To address such challenges, scientists frequently introduce hypotheses, assumptions, and mathematical axioms that may deviate from the apparent uniformity of nature in order to develop predictive mathematical models. While such models may yield accurate quantitative results, their underlying physical mechanisms often remain difficult to visualize or comprehend. Human knowledge of nature arises through the natural functioning of the senses and consciousness, both of which are fundamentally linked to reality. Therefore, a mathematical model that lacks physical conceptualization may represent only an abstract description of an underlying reality-based process. If a hypothetical mathematical model successfully predicts experimental outcomes, there is no inherent reason why a physically realistic model describing the same phenomenon should fail to achieve equivalent quantitative agreement.

Einstein’s Special Theory of Relativity and its mathematical formalism represent a remarkable achievement in quantitative physics. Nevertheless, the physical mechanism responsible for the relativistic increase in resistance to acceleration at high velocities remains conceptually challenging. The present work proposes a reality-based field–particle interaction model to explain this phenomenon. According to the proposed concept, all particles in their neutral state possess a nucleus surrounded by an extranuclear space structure. Charged particles are characterized by a modified extranuclear structure with reduced dimensions. Space itself is considered a physical medium composed of matter in a finer domain rather than an empty vacuum. Consequently, this medium offers resistance to particles moving at extremely high velocities. As the velocity of a particle increases, the resistive interaction with the medium causes directional deformation of its elastic extranuclear structure. Simultaneously, portions of the outer structure are progressively stripped away, leading to a complete loss of the extranuclear structure when the particle velocity approaches the velocity of light, (v = c). Since electric and magnetic fields propagate with velocity (c), the effective field–particle interaction is proposed to be proportional to the relative velocity ((c-v)) rather than to the constant value (c). Furthermore, the interaction strength is assumed to depend on the effective interaction cross-section, represented by the field area swept by the particle’s extranuclear structure during motion. As velocity increases, this interaction cross-section continuously decreases and becomes zero at (v = c). The combined reduction in relative interaction velocity and effective interaction cross-section causes the field-induced force acting on the particle to decrease progressively with increasing velocity. Consequently, the particle experiences a substantial reduction in acceleration as its speed approaches the velocity of light. This interpretation provides a physically realistic explanation for the observed difficulty of accelerating particles to light speed. Based on this framework, a new dynamical equation for high-speed motion has been formulated, and its predictions are found to be in close agreement with the corresponding relativistic equation.

Keywords: Relativistic Dynamics, Reality-Based Physics, Field–Particle Interaction, Physical Space Medium, High-Speed Particle Dynamics.

Introduction

A body resting on the surface of a solid does not accelerate following straightforward Newtons law (F=Ma). The effective motive force for acceleration is obtained by deducting the frictional resistance to arrive at the working equation as F-µR = Ma, where µ is the coefficient of friction and R is normal reaction. For a particle moving in space, the insignificant resistance to motion offered by the medium becomes highly significant in high-speed motion which has to be accounted properly for the validity of Newtonian equation.

Every atomic and sub-atomic particle have structure comprising the nucleus and extra-nuclear space structure in the new concept [1] [2]. The spatial space density of the space medium and its structural integrity with the nucleus decreases outwardly from the surface of the nucleus to the boundary of extra-nuclear space structure. The space medium, though devoid of micro particles but contains space matter particles of micro-micro domain light particles in neutral state. Hence the space medium is a photonic gas. Like the atomic gaseous fluid, the space medium is essentially a photonic gaseous fluid capable of offering resistance to motion of particles in space. The fluid resistance though insignificant in ordinary velocities becomes highly significant at velocities comparable to c, because the resistive pressure is proportional to square of velocity.

The particle with equilibrium extra-nuclear space structure in a locality is a neutral particle. In a non-equilibrium state of mass-space association, the particle carries charge [3] [4]. The charge particle in a field (electric and magnetic field) experiences a force due to field-particle interaction. The interaction cross-section is the area that the extra-nuclear space structure of the particle sweeps the field. The extra-nuclear space structure deforms in motion due to the resisting pressure of the medium. The resisting pressure being proportional to the square of velocity, as the velocity increases the field-particle interaction cross-section decreases which in turn decreases the field induced motive force. At speed close to velocity of light, the entire extra-nuclear space structure is removed by the resistive thrust [5]. Thereafter, the interaction cross-section becomes zero and no further acceleration is feasible. This limits the maximum velocity which can approach up to the velocity of light.

The Maxwell’s field velocity is same as the velocity of light. Thus, the field effect on transfer of momentum from field to particle is a function of relative velocity (c-v) and not c. When the particle velocity reaches the field velocity the momentum transfer from field to particle becomes zero. Here again the velocity of particle can only approach c and cannot exceed c. The combined effect of decrease in interaction cross-section and the relative velocity cause a rapid drop of the accelerating force.

Besides the above considerations on reduction of effective motive force, we also notice a directional field effect due to charge polarization by the deformation of extra-nuclear space structure according to the new concept of charge. The new charge state of particle in high-speed motion has a role in the dynamics. The extra-nuclear space structure of particle, is deformed due to the impact of structured space medium which plays an important role in the dynamics that becomes highly significant in high-speed motion. It is absolutely necessary to have the physical concept of space, time and spacetime for realizing the physical significance of special relativity.

Critical Analysis of Historical and Contemporary Concepts of Physical Space

The author identifies mass and space as the only two fundamental constituents of the physical universe and the existence of three primary interactions: mass–space attraction, mass–mass repulsion and space–space repulsion [6]. Within this framework, gravity [7], electric charge [3],[8] and various optical phenomena are interpreted as consequences of these fundamental interactions. The theory seeks to provide a unified physical basis for several natural phenomena while avoiding the conceptual difficulties such as associated with wave–particle duality [9],[5],[10],[11],[12],[13].

In the proposed model, space is regarded as a compressible, continuous, and invisible fluid-like physical medium containing space-matter particles of finer domain [14]. Owing to the intrinsic space-space repulsion, space naturally tends to expand and distribute itself throughout the universe, thereby establishing universal continuity. However, this expansion is constrained by the attractive interaction between mass and space. The competition between these two opposing tendencies generates a non-uniform spatial distribution of space around material bodies, producing regions of varying space density.

The interaction of mass–space attraction and space–space repulsion gives rise to pressure within the space medium. Consequently, regions possessing higher space density are associated with higher spatial pressure. Due to mass-space attraction, the nuclei in all domains organize and maintain the space structure surrounding it and the dense space retains the particles of finer domains within the space medium thereby forming space structures. These embedded constituents within the space medium are referred to as space-matter particles. Accordingly, an increase in space density corresponds to an increase in the number density of space-matter particles.

Since the mass–space attraction is assumed to obey an inverse-square dependence on distance, every celestial body develops a variable nature of space-density distribution surrounding its central mass. This structure is conventionally recognized as the atmosphere of the celestial body and, in a broader sense, may be regarded as its extra-nuclear space structure.

The extent of this extra-nuclear space structure depends upon both the mass of the central nucleus and the background space density. The background space density acts as a boundary condition determining the spatial extent of the structure. The same principle is proposed to operate for particles of all domains, where analogous extra-nuclear spatial structures exist.

Spatial variations in both space density and the number density of space-matter particles of different kinds can be represented through three-dimensional density distributions. Since these distributions are determined by the properties of the central nucleus, the resulting spatial gradients provide a direct measure of gravitational effects. Gravity, in this interpretation can as well be evaluated from the manifestation of the spatial density gradient surrounding the matter.

The theory further considers the nucleus and its extra-nuclear space structure as a single integrated physical system. Consequently, the spatial structure accompanies the nucleus during translational motion and co-rotates with it during rotation. Space-matter particles embedded within a rotating spatial structure experience centrifugal effects that oppose gravitational attraction. As rotational velocity increases, a condition may arise at a particular radial distance where centrifugal force exactly balances gravitational attraction, producing a state of effective zero gravity.

This equilibrium condition is expressed as

GM₁m₂/d²=m₂v²/d

Under this condition, no net radial acceleration acts upon the orbiting body. Objects located at different distances from the nucleus acquire different spatial velocities corresponding to the rotational state of the surrounding space medium. Since gravitational attraction and centrifugal force become numerically equivalent at equilibrium, gravity may be quantitatively determined through centrifugal considerations. This observation suggests an alternative interpretation of gravitational phenomena and invites a re-examination of conventional concepts such as Newtonian gravitation and Einsteinian spacetime curvature.

Historically, numerous concepts of space have been proposed and subsequently abandoned because of theoretical inconsistencies or experimental limitations. Nevertheless, many of these historical models contained valuable insights regarding the active role of space in physical processes. The present theory seeks to synthesize these useful elements into a revised conception of physical space, time and space-time.

Proposed Properties of Physical Space

The principal characteristics of the proposed space model may be summarized as follows:

• • Space is a real physical entity containing space-matter particles of finer domains due to space-mass attraction.
  • Space is both compressible and capable of indefinite expansion due to space–space repulsion.
  • Matter compresses space through mass–space attraction.
  • Space density varies spatially due to distribution of matter.
  • Spatial density gradients arise naturally around material bodies.
  • The number density of space-matter particles is directly proportional to local space density.
  • Gravitational field is a reflection of the directional gradient of space density or the density of space-matter particle since they are proportional to one another.
  • Space-matter particles may possess electrical or non-electrical charge characteristics thereby different charge fields arise from their density gradients.
  • Charge fields can undergo polarization under the influence of external charge distributions.
  • For practical purposes, space may be modeled as a fluid-like continuum.
  • The continuity of space provides continuity to the physical universe.
  • Matter and its associated spatial space structure constitute a unified dynamical system that translates and rotates together.

• As a physical medium, space can exhibit spatially varying structural and state properties. 

Distinction from Classical Ether Theories

Although the proposed concept attributes physical reality to space, it differs fundamentally from the classical luminiferous ether. Wave theories of light require a medium possessing an exceptionally high elastic modulus to support the propagation of electromagnetic waves. Such a medium would simultaneously need to offer negligible resistance to the motion of celestial bodies. These requirements appear mutually incompatible. A medium sufficiently rigid to sustain light waves would impede planetary motion, whereas a medium permitting unrestricted planetary motion would be incapable of supporting the required wave dynamics.

This conceptual difficulty provides a basis for questioning the wave interpretation of light and motivates reconsideration of a particle-based description. In the present framework, physical space is envisioned as a low-density photonic gas analogous to an atomic or molecular gas. If light is fundamentally particulate rather than wave-like, then the absence of ether drift in the Michelson–Morley experiment does not necessarily preclude the existence of a physical space medium, since such a medium would not be essential to function as a carrier of light waves. Instead, it would serve as the physical substrate within which light particles propagate and interact.

This revised conception seeks to restore an active physical role to space while avoiding the theoretical limitations historically associated with classical ether models.

Progressive development in concept of time, historical to updated

The concept of time has evolved continuously through philosophy, astronomy, classical physics, relativity and modern quantum theories. Human understanding of time progressed from a simple measure of natural cycles to a profound physical and philosophical entity connected with motion, change, matter and the structure of the universe.

In ancient civilizations, time was understood mainly through repetitive natural phenomena such as day and night, lunar phases, seasons and planetary motions. Early Greek philosophers viewed time differently. Aristotle considered time as a measure of change and motion, not an independent substance. According to him, time exists because events and motions occur in nature.

During the scientific revolution, Isaac Newton introduced the concept of absolute time. Newton proposed that time flows uniformly and independently throughout the universe, unaffected by matter or motion. In Newtonian mechanics, time was universal, identical everywhere and completely separate from space. Every observer shared the same cosmic clock.

Later, Gottfried Wilhelm Leibniz challenged this view by arguing that time is relational rather than absolute. According to Leibniz, time is only the order or sequence of events and has no independent existence apart from physical processes.

In the nineteenth century, the development of thermodynamics introduced the concept of the “arrow of time.” The increase of entropy suggested that natural processes possess directionality, distinguishing past from future. Time was no longer viewed merely as a neutral parameter but as something associated with irreversible physical change.

A major transformation occurred with Special Relativity developed by Albert Einstein. Einstein showed that time is not absolute but relative to the observer’s motion. Clocks moving at high speeds experience time differently, leading to the phenomenon of time dilation. Later, General Relativity demonstrated that gravity can also affect the flow of time. Strong gravitational fields slow down clocks, linking time directly with matter, energy and spacetime geometry.

Modern physics further transformed the concept of time. In quantum mechanics, time generally appears as a parameter rather than a measurable operator, creating difficulties in unifying quantum theory with relativity. Some modern theories suggest that time may emerge from deeper microscopic processes rather than being fundamentally continuous. The process-based time is dependent on the kinematics of the process which depends on local process parameters.

Contemporary alternative approaches sometimes interpret time as a manifestation of physical change, energy transformation or structural reorganization of matter and space. Some thinkers propose that time is not an independent entity but a measure of sequential physical processes occurring in nature. In such views, the flow of time reflects the evolution of material systems rather than the movement of an invisible universal clock.

In another contemporary interpretation, time is regarded not as an independent entity or a separate dimension of nature but as a conceptual measure derived from physical processes. According to this view, the perception of time emerges from the sequential occurrence of events, motion of matter, and transformation of energy within the universe. The apparent flow of time reflects the continuous evolution of material systems, while clocks merely register the rate of ongoing physical processes. Thus, time has no existence independent of matter, motion and change; rather, it serves as a quantitative description of the progression of natural phenomena. This perspective seeks to provide a more cause-and-effect-based understanding of temporal experience by relating time directly to the dynamics of physical reality [15].

Thus, the concept of time has progressively evolved from cyclic natural observation to absolute universal flow, relativistic spacetime dimension, thermodynamic directionality, quantum uncertainty and modern process-based interpretations. The history of science shows that time remains one of the deepest and most evolving concepts in human understanding of nature.

In view of the foregoing discussion, time is not regarded as an independent entity that flows irrespective of matter; rather, within the process-based interpretation, it serves as a parameter describing the dynamical evolution of material systems. From this perspective, Einstein’s proposition that the passage of time is influenced by spacetime geometry warrants deeper examination in terms of process-based time and the role of boundary conditions.

A fundamental principle of physical inquiry is that the local dynamics of an event are not altered by its distant observation. Observers situated in different frames of reference may record or describe the same event differently owing to their relative states of motion; however, such observational differences do not necessarily imply a change in the intrinsic physical reality of the event itself. The event remains singular, even though its description may vary among observers.

Consequently, the interpretation of spacetime should provide an unambiguous account of physical reality that clearly distinguishes between the actual dynamics of a system and the observational effects associated with different reference frames. The remarkable predictive success of relativistic equations cannot be disputed; nevertheless, their conceptual foundations deserve continued scrutiny. It may therefore be worthwhile to investigate whether the relativistic relations can be derived from a framework based on physically relevant dynamical parameters, thereby preserving both their predictive power and conceptual clarity.

Historical concept of space-time prior to Einstein.

Before the development of relativity by Albert Einstein, space and time were generally treated as two completely separate and independent entities. The historical understanding of space-time evolved gradually through philosophy, astronomy, and classical mechanics.

Space and time were associated with physical events but were not unified into a single framework. Time was viewed as flowing continuously, while space was regarded as the static arena in which motion occurs.

Leibniz argued that space is merely the order of coexistence of objects, while time is the order of succession of events. According to him, neither space nor time possesses independent existence apart from material relations.

Thus, prior to Einstein, the dominant historical view considered space as a fixed three-dimensional stage and time as a separate universal flow. The modern unified concept of spacetime had not yet emerged, though late nineteenth-century electromagnetic theory and transformation mathematics gradually prepared the foundation for Einstein’s revolutionary interpretation.

Physical space possesses geometrical attributes such as extension, distance, and spatial relations. The dynamical evolution of matter, on the other hand, represents an intrinsic process that is not itself a geometrical property. If time is interpreted as a parameter characterizing this intrinsic dynamical evolution, then geometrical and dynamical aspects of physical reality belong to distinct conceptual categories. The spacetime formulation combines these categories into a unified four-dimensional geometric structure. While this formulation has proven mathematically successful, its physical interpretation remains a subject of philosophical discussion because the resulting four-dimensional geometry is not directly accessible to perception or intuition. If the dynamics of matter can be formulated with equal predictive success while maintaining a distinction between geometrical and dynamical parameters, then such an approach may provide greater conceptual transparency without sacrificing mathematical rigor. The question is therefore not whether spacetime mathematics is valid, but whether the fusion of geometrical and non-geometrical parameters is physically necessary or simply one among several mathematically equivalent descriptions of reality.

The key challenge of the program is not philosophical consistency but demonstrating that a space-plus-process formulation can reproduce all experimentally verified relativistic effects—time dilation, length contraction, relativistic momentum, mass-energy equivalence, gravitational redshift, GPS corrections, and so forth without invoking spacetime as a fundamental entity. If that can be achieved, then it would become a scientific alternative rather than merely a philosophical critique.

A motor bike moving on a road has a velocity ‘v’ at a given rate of energy input (fuel consumption). The windage resistance offered by the atmospheric air is proportional to the projected area of motor bike with rider, the density of the air, squire of relative velocity of the bike and the properties of the air medium. If the wind is in the direction of the motion, the bike will move at a higher relative speed than that in still air and has a reduced relative velocity when the wind is in opposite direction. A person sitting in a train observes the velocity of a bike as ‘v_r’. He further finds v_r varies with the speed of the train relative to the earth. It is found that the speed of the bike that respond to acceleration by fuel supply to the engine has a little significance with v_r. On the other hand, the motion of the medium (wind speed) has a role in the dynamics. However, it is not easy to translate the changes of local physical conditions when an object moves in free space or vacuum. In the existing concept though space is considered physical with ability to interact with matter but the physical nature of space is conceptualised through mathematical objects and events which is beyond human perception. The present author, on the basis of the uniformity of nature, has explored the existence of matter in finer domain (micro-micro domain) thereby perceiving a real structure of space similar to gaseous form of matter. He further, adds to the feasibility of different fields due to presence of non-electric charge (photonic charge) in space matter particles (photon). The new concept of physical space can have space density (space content per unit volume) and mass density due to the number density of space matter particles and the space medium can have different spatial velocities similar to wind velocity. Thus, the dynamics of a particle can be reworked out by considering the local relevant parameters instead of the consideration of observational special relativity. The observed motion from a moving frame, not connected with dynamics can be replaced by local parameters (local frame of reference) for a reality-based analysis. In this new concept the fused space-time has an ordinary significance of space with a dynamism where time is a function of dynamism.

The dynamic equation F=ma though valid at lower velocity but doesn’t hold good at extreme high velocity due to improper coupling of the motive field force and the exponential increase of resistance offered by the medium. A body moving at the same speed cannot transfer momentum to another body at the same speed. When the speed of the charge particle increases, the effectiveness of electromagnetic coupling with charge particle decreases with increase of speed which causes reduction in the value on the interaction force E.e or qBv. The drive (interaction) from a field to a particle depends on the differential speed of the field particles and the particle being accelerated. The propagation velocity of electromagnetic field disturbances in vacuum medium is constant having the value ‘c’. But the velocity of an accelerated particle goes on increasing with a constant field-particle interaction. At any spatial velocity ‘v’, the field-particle coupling factor is dependent on (c-v). When ‘v’ is comparatively very small the difference can be approximated to ‘c’. Thus, the electromagnetic force for low velocity coupling condition gives a constant value given by E.e or qBv. However, when ‘v’ approaches ‘c’ the force coupling reduces very-very rapidly thereby the effort to accelerate is drastically reduced and becomes zero at the speed c. In the new concept every particle has a nucleus and extra nuclear space structure which is in equilibrium in neutral state. A charge particle with limited extra nuclear shell structure has a definite interaction cross-section for the field-particle interaction. The extra nuclear space structure is highly elastic and is subject to deformation in high speed motion. Thus, the spherical extra nuclear space structure deforms to spheroidal form, the longitudinal cross-section of which is ellipse. The interaction cross-section of the extra nuclear space structure reduces from πr² reduces to πb² where b is the semi-minor axis of the ellipse. With gradual increase of velocity, the kinetic energy of the particle goes on increasing and the particle successively loses electronic shells of extra nuclear space structure of the particle by attending successive ionization potentials thereby, further reducing the interaction cross-section. At extreme high velocity the particle will lose all its extranuclear space structure and the bare nucleus approaches the zero-interaction cross-section. In the new concept the interaction cross-section is dependent on the form on which the interaction takes place. However, following the old concept of interaction cross-section of the charge particle one may limit the interaction cross-section from the electromagnetic response time.

However, the success of this new approach ultimately depends on whether it can quantitatively account for all relevant experiments, including muon decay, particle accelerators, atomic clocks and other precision tests. The subsequent discussion is made through mathematical interpretation.

Mathematical analysis on Newtonian Force equation for high-speed motion

Step 1: Basic Newtonian Equation

The author retained the universal status of the basic Newtonian equation and considered decrease of accelerating force due to changes in field-particle interaction.

The basic Newtonian equation:

F=Ma

q.E=Ma

Where, E = Charge field

q = Charge of the particle

The field induced force on a charge particle considers q.E don’t remain constant for all velocity of the particle since it depends on the relative velocity between field and particle as well as the field-particle interaction cross-section. Hence, the force equation is modified in high-speed motion as:

q. E. α_v. β_v. η=Ma ,               Eqⁿ-1

Where,

α_v is the force reduction factor at velocity v due to change in relative velocity.

β_v is the force reduction factor at velocity v due to decrease of interaction cross-section.

η is the force reduction factor at velocity v due to change of sheer resistance and drag

force.

Determination of α_v

The velocity of field lines is the same as velocity of light (c), thus the relative velocity between the field and particle at rest is c. However, when the particle accelerated to velocity (v) the relative velocity for field-particle interaction changes to c-v, hence, the force reduction factor at velocity v due to change of relative velocity is:

α_v=(c-v)/c.

Determination of β_v

The interaction cross-section of extra nuclear space structure reduces gradually with increase of velocity of the particle due to the resistive thrust from the space medium. The force due to field-particle interaction decreases in proportion to the decrease of interaction cross-section. If the sweeping area of extra nuclear structure is reduced from  A₀ to A_v then v is given by:

β_v=A_v/A₀

The interaction cross-section area (A₀) due to the presence of extra nuclear space structure at rest or slow motion compared to velocity of light (c). The interaction cross-section reduces to A_v at velocity v by stripping off part of its extra nuclear structure that corresponds to A_Lv and the interaction cross-section area reduces to A_c at velocity c by stripping off the entire interaction cross-section. Ac becomes zero when ALc becomes A₀ when the interaction cross-section is stripped off fully.

Thus:  A_c = A₀– A_Lc=0  ,     when A_Lc=A₀ (Numerically)

Where, A_Lc is the loss of interaction cross-section at velocity v = c

Similarly, A_v = A₀– A_Lv

The reduction factor of loss of interaction cross-section at velocity v is given by

Now,

β_v=A_v/A₀= (A₀-A_Lv)/A₀

=1-(A_Lv/A₀)

β_v=1-(A_Lv/A_Lc)

The loss of cross-sectional area is directly proportional to the dynamic pressure caused by the relative velocity between particle and the structured space medium which in turn is proportional to square of relative velocity [16].

Thus,  A_Lv=kv²   and A_Lc=kc², where k is proportionality constant.

β_v=1-(A_Lv/A_Lc)=1-(kv²/kc²)

=1-(v²/c²)

Or β_v=(c²-v²)/c²

Determination of η

The factor contributing towards change in the accelerating force due to the thrust of the structured space medium and sheer at the interface of extra nuclear space structure of particle and the space medium. The contributing factor is a function of dynamic pressure and interaction cross-section. The factor increases with rise of velocity dependent dynamic pressure and decreases with velocity dependent interaction cross-section.   Thus, η=(p_v/p₀).(A_v/A₀) remain constant for all velocities. Therefore, the factor =1.

Substituting the value of v, v & η in equation-1

F_v=F₀ (c-v)/c . (c²-v²)/c²=Ma,                 Eqn-2

F_v = Accelerating field force at high velocity v.

F₀ = Accelerating field force at rest or low velocity.

When  v -> c, c can be substituted by v but c² can not be substituted by v².

Hence
(c-v)²=c²+v²-2v²= c²-v²

Hence, (c-v)²= c²-v² or c-v=√(c²-v²)

Now, (c-v)/c= √(c²-v²)/c=√(c²-v²)/√c²=√((c²-v²)/c²)=√(1-(v²/c²))

Thus,

F₀(c-v)/c . (c²-v²)/c²=Ma

Becomes

F₀√(1-(v²/c²)) . (1-(v²/c²))=Ma

F₀(1-(v²/c²))^3/2=Ma

Substituting γ=1/√(1-(v²/c²))

F₀/γ³=Ma,                      Eqn-3

The above equation is the realistic equation in high-speed motion where the effective interaction force is reduced due to dynamical change in the form of extra nuclear space structure of the accelerating particle.

If the above equation is written in the form:

F₀=γ³Ma,                      Eqn-4

For particle accelerator

q.E=γ³Ma

The equation assumes the expression of a relativistic equation. Though mathematically there is no difference between equation-3 and equation-4, but philosophically there is a great difference where the realistic equation-3 considers the accelerating force reduces due to situational conditions, whereas the relativistic equation-4 considers unrealistic relativistic effect.

If now v becomes zero or close to zero (at rest or at low speed) the equation-2 reduces Newtonian equation form,   F=Ma.

For the magnetic force in accelerator

F=qvB                        Eqn-5

For circular motion in accelerator:

F_B=mv²/r

At low speed:

qvB=mv²/r                             Eqn-6

As the velocity increases the magnetic flux B intercepting the particle reduces by a factor (c-v)/c. Thus, at low speed the factor remains near to 1 but is reduced drastically when v approaches the speed of magnetic field lines (c). The value of (c-v)/c ≈ √(1-(v²/c²)), where v -> c. The interaction cross-section for magnetic flux has a near ellipse form where at high-speed the semi-minor axis (b) decreases and semi-major axis (a) increases with square of velocity. Hence, the interaction cross-section for magnetic field lines remains nearly constant. Therefore, the term 1-(v²/c²) doesn’t appear for the magnetic interaction.

Hence, at high-speed condition the equation-6 becomes:

qv (B×√(1-(v²/c²)))=mv²/r

Substituting γ=1/√(1-(v²/c²)) we get:

qB(1/γ)=mv/r

In this equation q, r & m remaining constant the effective interaction of magnetic flux B reduces realistically with increase in velocity. On the other hand, if q, B & r is assumed constant then the momentum (p) becomes associated with the factor. Therefore, the conceptual mode of equation changes to:

qB=γmv/r

p=qBr=γmv                            Eqn-7

Conclusion

The present work attempts to provide a reality-based interpretation of relativistic dynamics by introducing a structured physical space medium and velocity-dependent field–particle interactions as the underlying cause of the observed resistance to acceleration at high velocities. By considering the reduction of effective field coupling and interaction cross-section as velocity approaches the speed of light, the analysis derives a mathematical expression that assumes a form equivalent to the relativistic force equation while preserving a direct cause-and-effect physical interpretation. The paper further discusses revised concepts of space, time, and spacetime within a unified mass–space framework and highlights the possibility of explaining relativistic phenomena without invoking intrinsic modifications of space and time. Although the proposed model offers an intuitive conceptual alternative, its ultimate scientific validity depends on its ability to quantitatively reproduce all experimentally verified predictions of relativity with equal precision. The study therefore serves as an exploratory step toward a more physically interpretable framework for high-speed dynamics and the broader unification of physical sciences.

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