STATE AND SCALE OF TIME

By Soumendra Nath Thakur | 21 June 2020

State of Time – A Binary Interpretation:

In this interpretation, time exists in a binary state system, where it can either be in the prevailing state (`t = 1`) or the singular state (`t = 0`). This binary framework mirrors Boolean logic, where a state is either True (1) or False (0). Thus, the state of time is not continuous by nature, but digital in its essence—either active or inactive, present or null.

Scale of Time – Decimal Representation of Measurable Events:

While the state of time is binary, the measurement of events within time operates on a continuous decimal scale, such as in the International System of Units (SI), where time is measured in seconds. Within its True state (`t = 1`), time can take on any positive value: `t = +n`, where `n` can be represented in decimals (e.g., 3.14 seconds). This scalar value, though expressed decimally, can be converted into binary digits for digital computation and system logic.

Note: The decimal system consists of ten digits: 0 through 9. A decimal number is a fractional quantity written in a positional notation, where the position of each digit determines its value.

Time as an Independent and Abstract Entity:

Time, in this formulation, is understood as an independent entity, not inherently relative to motion, mass, or spatial position. It exists in itself, not merely in relation to other things. This view departs from relativistic formulations, emphasizing instead a foundational ontology of time.

Moreover, time is an abstract construct—a conceptual framework that allows us to interpret the indefinite progression of existence and events. Like all mathematical abstraction, it arises by stripping away empirical specifics to reveal a deeper, underlying essence.

The interpretation of this idea:

"Time within the eventual universe is in the `t = 1` state" means:

• Time exists as an active dimension.

• It is functioning, measurable, and progressing—while the events, sequences, causality, and change occur.

• The universe we observe is within this prevailing (t = 1) temporal framework where time flows, or at least unfolds in a continuous, quantifiable manner.

• All physical events, motions, and processes occur only when time is in active state.

In contrast, the `t = 0` state, which it has  described as the singular or false state of time, would represent:

These statements express the idea that:

"Time in the eventual universe exists in the prevailing state `t = 1`, representing the active and measurable dimension in which all events, sequences, and changes occur. This contrasts with the singular state `t = 0`, wherein time is absent, suspended, or undefined. The binary framework thus provides a conceptual distinction between the presence (`t = 1`) and absence (`t = 0`) of time across different existential conditions."

Supplementary Notes:

• Timescale:

The span of time within which certain events occur or are scheduled to occur, considered in relation to a broader period of time.

• Time (general definition):

The indefinite continued progress of existence and events in the past, present, and future regarded as a whole.

• Mathematical Abstraction:

  The process of extracting the underlying essence of a mathematical concept by removing its dependence on real-world objects.

#Time #StateOfTime #ScaleOfTime #BinaryTime #AbstractTime #SoumendraNathThakur

Transformative Implications and Multidomain Applications of Extended Classical Mechanics (ECM): A Comprehensive Summary.

June 21, 2025

1. Practical Applications of ECM (Extended Classical Mechanics)

ECM introduces dynamic mass redistribution, effective mass (Mᵉᶠᶠ), and apparent mass (−Mᵃᵖᵖ) to enhance real-world systems:

• Transportation & Energy: Optimizes fuel consumption, propulsion systems, and vehicle dynamics.

• Aerospace & Defense: Improves missile systems, spacecraft efficiency, radar evasion, and maneuverability.

• Renewable Energy: Increases efficiency in solar, wind, and storage systems via optimized energy flow.

• Biomedical & Electronics: Enhances biosensors, tissue engineering, and power management in devices.

• Sustainability: Assists in waste reduction, recycling efficiency, and green tech innovations.

2. Challenges to Classical and Relativistic Mechanics

Though ECM is fundamentally based on the principles of Classical Mechanics, it challenges traditional physics in the following ways:

• Mass Redefined: Mass becomes dynamic (Mᵉᶠᶠ, −Mᵃᵖᵖ, ΔMᴍ), not static, invalidating key assumptions in classical and relativistic frameworks.

• Gravity Reinterpreted: ECM introduces a simpler model of gravitational force using effective mass, avoiding spacetime curvature.

• Energy Conservation Updated: Potential energy changes directly influence mass terms, especially in gravitational systems.

• Photon Dynamics: Photons carry −Mᵃᵖᵖ, and their energy is explained via ΔMᴍ = hf/c².

• Unified Model: ECM bridges classical, quantum, and cosmological scales with a single consistent formalism.

3. ECM in Aerospace & Missile Systems

• Fuel Efficiency: Real-time adjustment of Mᵉᶠᶠ improves fuel use and range.

• Radar Evasion: Mass redistribution reduces radar cross-section and enables complex evasion maneuvers.

• Adaptive Propulsion: ECM-based systems respond dynamically to flight conditions.

• High Maneuverability: Enables steep, unpredictable paths to avoid interception.

• Guidance & Control: Mass-aware navigation boosts accuracy and responsiveness.

4. Scientific & Technological Impacts

• Astrophysics: ECM provides alternative explanations for dark matter and dark energy through mass redistribution effects.

• Quantum Mechanics: Mass fluctuations relate to vacuum energy, possibly refining quantum field theories.

• Vibration Damping: ECM enables nonlinear energy sinks and broadband mitigation in engineering structures.

• Plasma Physics: ECM modes relate to coherent turbulence and heat transport in fusion research.

5. ECM in Industry & Energy Management

• Heat Recovery: ECM boosts energy extraction in power plants and electric vehicles.

• High-Efficiency Boilers: Heat pump integration and flue gas condensation achieve >100% efficiency.

• Smart Contracting (EMC Models): Enables funding mechanisms for energy-saving tech via shared savings.

6. Technical and Implementation Challenges

• Complexity: Real-time control of mass redistribution is technologically demanding.

• High Costs: Equipment, energy consumption, and skilled training present barriers.

• Material Limitations: Only conductive and chemically stable materials can be used in ECM-based machining.

• Environmental Issues: Electrolytes pose corrosion and waste risks.

• Slow Processing: Setup and machining speeds are slower than conventional methods.

7. ECM vs Traditional Machining

ECM machining (not to be confused with Extended Classical Mechanics) in automotive and aerospace sectors offers:

• No tool wear or thermal damage

• Precision with difficult materials

* Complex geometries with no mechanical stress

• High-volume consistency and better surface finish

8. Effective Mass (Mᵉᶠᶠ) – ECM's Core Concept

• Definition: Mᵉᶠᶠ = Mᴍ − Mᵃᵖᵖ; it varies dynamically based on energy states.

• Negative Mass Effects: Explains increased acceleration, photon dynamics, and dark energy behavior.

• Applications: From photon motion to cosmic acceleration via Mᴅᴇ < 0 analogies.

9. Repercussions on Relativistic Physics

If ECM gains acceptance:

• Time Dilation Recast: Attributed to phase deformation, not spacetime curvature.

• Cosmic Expansion: Driven by massless particle dynamics and −Mᵃᵖᵖ -induced anti-gravity.

• Hubble Radius Redefined: Allows superluminal phenomena in certain energy contexts.

• Unification with Quantum Theory: Offers consistent scaling across all domains.

10. Scientific & Philosophical Implications

• Holistic Physics: ECM merges space, time, and mass as interdependent, not orthogonal entities.

• Experimental Evidence: Grounded in studies on piezoelectric effects, rotational mechanics, and photon emission.

• Broader Applications: Includes materials science, biology (drug delivery), and quantum-cosmic bridges.

Conclusion

Extended Classical Mechanics (ECM) represents a paradigm shift by introducing dynamic mass properties and energy redistribution, offering unified explanations for gravitational interaction, quantum behavior, and cosmic evolution. While promising in theory and application, ECM's full acceptance depends on independent validation, further research, and technological readiness for large-scale implementation.

Re-examining the Foundations: Critical Scrutiny of Relativistic Time Dilation and Spacetime Curvature:

Soumendra Nath Thakur | June 19, 2025

The theory of relativity has long stood as one of the cornerstones of modern physics. However, it is essential to distinguish between the original theoretical propositions presented in Einstein’s foundational papers and the numerous experiments and observations that have later been cited in support of the theory. Notably, none of the widely referenced experimental validations — such as those involving time dilation or gravitational lensing — were included in Einstein’s original formulations. These subsequent tests, though often used to reinforce the theory, are external in origin and do not constitute direct validations from within the foundational texts themselves. As such, they should not be automatically conflated with the internal consistency or completeness of the original theory.

Many of these post-hoc validations also suffer from philosophical and methodological concerns. For instance, gravitational lensing — frequently cited as evidence of spacetime curvature — may be more accurately interpreted as a classical interaction between photons and gravitational fields, rather than an effect of geometric curvature in spacetime itself. Similarly, what is commonly referred to as "relativistic time dilation" could be more precisely described as wavelength dilation, especially when framed through alternative gravitational or field-based interpretations. These reinterpretations merit serious consideration rather than being dismissed as contrarian or unorthodox.

Furthermore, scientific understanding should be driven by critical thinking and personal evaluation, rather than uncritical reliance on textbooks or majority consensus. While students understandably depend on structured educational resources, the scientific enterprise itself must remain open to reinterpretation, refinement, and — when necessary — revision. Science, unlike politics, is not a matter of popular vote; it is a discipline governed by principles of logic, reproducibility, and theoretical coherence. Confining scientific inquiry within the bounds of academic orthodoxy risks stalling its progress and marginalizing alternative yet potentially valid interpretations.

It is thus both reasonable and necessary to place foundational concepts such as relativistic time dilation and spacetime curvature under rigorous re-examination. Doing so does not imply dismissiveness toward historical scientific achievements, but rather affirms a commitment to ongoing inquiry — a hallmark of genuine scientific progress. The vitality of science lies in its openness to scrutiny, its freedom from institutional or ideological entanglements, and its fidelity to truth over tradition.

Appendix 12: Effective Acceleration and Gravitational Mediation in Reversible Mass-Energy Dynamics in ECM.

 June 17, 2025

🚀📘 New ECM Appendix Published!

We're excited to announce the release of:

🔹 Appendix 12: Effective Acceleration and Gravitational Mediation in Reversible Mass-Energy Dynamics in ECM

📖 DOI: https://doi.org/10.13140/RG.2.2.19018.48320

This latest instalment in the Extended Classical Mechanics (ECM) series explores how internal energy restructuring—guided by effective acceleration and gravitational interaction—sustains the speed of light and drives mass-energy balance across scales.

This appendix presents a comprehensive analysis of effective acceleration (aᵉᶠᶠ) and gravitational mediation in the context of reversible mass-energy dynamics under the Extended Classical Mechanics (ECM) framework. Through a detailed examination of photon escape processes, mass-energy redistribution, and gravitational redshift, we establish the role of apparent mass (−Mᵃᵖᵖ) and energy exchange in sustaining the invariant photon speed v = c. The formulation of aᵉᶠᶠ = 6 × 10⁸ m/s² is shown to uphold the velocity of light even under extreme conditions through mass-compensated energy restructuring. This work connects kinematic behaviour to energetic reconfiguration, reinforcing ECM's explanatory power in describing dynamic equilibrium. In the Extended Classical Mechanics (ECM) framework, motion and gravitational acceleration are not merely kinematic-they are primary drivers of mass-energy transformation. At subatomic scales, exchanges between potential energy (−ΔPEᴇᴄᴍ) and kinetic energy (KEᴇᴄᴍ = ½Mᵉᶠᶠv²) govern how matter mass (Mᴍ) is redistributed or replaced by −ΔMᴍ and −ΔMᵃᵖᵖ. Emissions such as photons and gamma rays extract energetic mass from electrons and nuclei respectively, reflecting reversible transformations between Mᴍ and energy. Gravitational acceleration (gᵉᶠᶠ) and ECM-specific force (Fᴇᴄᴍ = Mᵉᶠᶠgᵉᶠᶠ) mediate this exchange, allowing internal energy restructuring. Thus, acceleration and deceleration-both inertial and gravitational-emerge as the central pathways by which pure energy (½Mᵉᶠᶠc²) is transformed into observable matter (Mᴍ), giving rise to the material universe.

Key insights include:

⚛️ How photons maintain v = c even while losing energy

🌀 The role of apparent mass (−Mᵃᵖᵖ) and effective acceleration (aᵉᶠᶠ)

🌌 Gravitational redshift as a mediator of energy transformation

🔄 Reversible dynamics in both subatomic and cosmic systems

📚 Part of the ECM Series by Soumendra Nath Thakur

Tagore's Electronic Lab, India

#Physics #Gravitation #PhotonDynamics #MassEnergy #ECM #Research #EnergyTransformation #GravitationalRedshift #ClassicalMechanics #OpenScience

Appendix 13: Proportionality Consistency and Inertial Balance in ECM Framework

🔬📘 New ECM Release: Appendix 13 is Now Live!

Title: Proportionality Consistency and Inertial Balance in ECM Framework

By: Soumendra Nath Thakur

📅 Published: June 17, 2025

📎 DOI: 10.13140/RG.2.2.25046.56648

🧠 What It’s About:

This newly published appendix explores how acceleration, force, and mass are interconnected in the Extended Classical Mechanics (ECM) framework—an upgrade to traditional Newtonian physics.

In simple terms, it reveals how even "massless" or light-speed particles like photons behave under force and acceleration when energy transformations are taken into account. ECM refines Newton's old equation (F = ma) by including hidden or "apparent" mass arising from energy. It shows that what we call "effective acceleration" depends not just on how heavy something is—but also on how energy inside it transforms.

💡 Why It Matters:

This work provides a deeper understanding of motion, inertia, and energy, especially in extreme conditions where classical physics starts to break down. Whether for massive objects or light-speed particles, ECM offers a unified picture of how nature balances force, motion, and mass.

📘 For the Curious:

Dive into this appendix to learn how energy shifts inside particles affect how they accelerate or respond to gravity—one more step toward a more complete physics.

🔗 Read it here: https://doi.org/10.13140/RG.2.2.25046.56648

#ECM #ExtendedClassicalMechanics #Physics #Inertia #Mass #Force #Acceleration #Gravitation #PhotonDynamics #ResearchUpdate #SoumendraThakur #TagoresElectronicLab

Appendix 11 of the Extended Classical Mechanics (ECM) Series is Now Available!

 🔬📘 New Release: Appendix 11 of the Extended Classical Mechanics (ECM) Series is Now Available!

Title: Mass Redistribution and the Fourfold Structure of Mass in ECM

📄 DOI: https://doi.org/10.13140/RG.2.2.26068.92805

🧑‍🔬 Author: Soumendra Nath Thakur | Tagore’s Electronic Lab

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🌌 What’s it about?

This new appendix offers a ground-breaking view of mass—not as a single, unchanging quantity, but as something that can be split, repurposed, and transformed within physical systems.

ECM (Extended Classical Mechanics) introduces four types of mass:

1. Matter Mass – The total content of a system, including dark matter.

2. Displaced Mass – The part of matter that becomes energy in motion or radiation.

3. Effective Mass – What’s left to create gravity and resistance to motion.

4. Apparent Mass – A unique, field-related counterpart to energy, especially in the case of photons.

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💡 Why it matters:

This new approach helps explain how light exists without rest mass, how gravity can be attractive or repulsive, and how mass-energy conversions happen deep within cosmic and atomic structures. It also clarifies the role of dark matter in shaping galaxies.

Whether you're a physicist or just someone curious about the universe’s inner mechanics, this paper brings powerful ideas into focus—with equations and concepts that bridge matter, energy, and gravity in an elegant structure.

---

📚 Explore related entries:

• Appendix 8: Energetic Structures Beyond Planck Threshold

• Appendix 9: ECM’s Cosmic Genesis and Gravitational Descriptions

• Appendix 10: Pre-Universal Gravitational and Energetic Conditions

📥 Download the new Appendix now and see how mass behaves when energy is on the move.

The Four Faces of Mass in Extended Classical Mechanics (ECM):

Extended Classical Mechanics (ECM) redefines mass into distinct, interconnected concepts to explain its mass-re-configurative model of energy. This section breaks down each definition. Understanding these is key to grasping the entire framework.

Matter Mass (Mᴍ)

The total, original mass of a system before any energetic transformations. It's the complete material content from which all other mass components are derived or redistributed.

Displaced Mass (ΔMᴍ)

The portion of matter mass that is physically displaced to manifest as kinetic energy. It is the mass-equivalent of motion itself.

Effective Mass (Mᵉᶠᶠ)

The residual mass that remains after displacement. It's responsible for gravitational potential energy. Calculated as Mᴍ − ΔMᴍ.

Apparent Mass (Mᵃᵖᵖ)

A conceptual mass defined as the negative of displaced mass (ΔMᴍ). It's primarily used to describe the dynamics of light-speed particles like photons.

The Foundational Equations

The relationships between the different mass concepts are formalized in a set of core equations. These equations provide the mathematical backbone for ECM, ensuring dimensional consistency while describing total energy as a function of mass redistribution.

Total Energy as Mass Redistribution

The conceptual heart of ECM, showing that total mass is conserved by partitioning it into potential (effective) and kinetic (displaced) components.

        Eₜₒₜₐₗ ⇒ (Mᴍ − ΔMᴍ) + ΔMᴍ

Full Energy Equation

The practical formula for calculating total energy, using effective mass for both potential and kinetic terms.

        Eₜₒₜₐₗ = Mᵉᶠᶠgᵉᶠᶠh + ½Mᵉᶠᶠv²

Photon Energy (Light-Speed Dynamics)

ECM derives the energy of a photon non-relativistically, defining it as being equivalent to its displaced mass.

        hf = ΔMᴍc²

Public Announcement Appendix 10: Pre-Universal Gravitational and Energetic Conditions in ECM

🌌 Public Announcement | ECM Update

📅 June 15, 2025
📍 Tagore's Electronic Lab
🧠 Research by: Soumendra Nath Thakur

🔬 New Appendix Published:
Appendix 10: Pre-Universal Gravitational and Energetic Conditions in ECM
📄 Read Now

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🔍 What Is It About? 

Where did the universe come from before the Big Bang?

This new research paper explores that very question—not through assumptions about singularities, but by tracing the energy dynamics and mass patterns that existed even before stable particles formed.

According to the Extended Classical Mechanics (ECM) framework, the early universe was filled with potential energy, which began to flow and redistribute in very specific ways. As energy transitioned, it gave rise to something unexpected: negative mass effects, or what we experience today as dark energy.

Instead of a violent explosion from nothing, this view suggests a structured emergence—a phase where energy borrowed from itself, set things into motion, and gradually unfolded the cosmos into matter, motion, and gravity.

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🧠 Key Highlights in Simple Terms:

• The universe began not with a bang, but with flowing energy and no matter.

• Dark energy may come from negative apparent mass—a kind of gravitational ghost.

• Early expansion happened with superluminal speed (faster than light), but in a structured, lawful way.

• Stable atoms and real mass emerged gradually from these early energy structures.

---

🔗 Explore the ECM Series:

1. Appendix 7: Photon Emission in ECM

2. Appendix 8: Beyond Planck Thresholds

3. Appendix 9: Cosmic Genesis & Gravitation

4. Appendix 10: Pre-Universal Energetics

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✉️ For Collaboration & Inquiries

📧 postmasterenator@gmail.com
🏛️ Tagore's Electronic Lab, West Bengal, India

Release Announcement | ECM Appendix 9: Cosmic Genesis and Gravitational Descriptions.

🌌 Release Announcement | ECM Appendix 9

Soumendra Nath Thakur | Tagore's Electronic Lab, India
📘 ECM's Cosmic Genesis and Gravitational Descriptions
🆕 DOI: 10.13140/RG.2.2.13289.40801
📅 June 15, 2025

🔭 What if the Universe didn’t begin with a bang... but with a vibration?
Appendix 9 of the Extended Classical Mechanics (ECM) series introduces a bold new idea: the Universe may have started not from a singular explosion, but from a calm and timeless field of potential energy—a kind of cosmic “hum.”

This pre-universe didn’t contain matter or particles. It was a state of pure potential, gently vibrating. Then, something shifted: a portion of that potential energy redistributed itself, setting the stage for motion, structure, and the expansion of space itself.

This model proposes:

• The Big Bang as a transformation of pure energy—not a creation from nothing

• Gravity emerging from energy gradients—not just from mass

• Dark energy as a real consequence of this early energetic displacement

• And matter as a product of deeper energy restructuring

ECM provides a new language to describe how the universe evolved—from vibration to motion, from energy to matter.

This is not just a new theory—it’s a rethinking of where everything begins.
🌐 Read the full appendix: https://doi.org/10.13140/RG.2.2.13289.40801

#ECM #CosmicGenesis #Physics #VibrationalUniverse #DarkEnergy #SoumendraNathThakur #ScientificFramework

Gravitational Collapse, Quantum Boundaries, and the Planck Threshold: A Clarification from ECM

Soumendra Nath Thakur | June 14, 2025

In response to a thoughtful question by Carmen Wrede on whether the Planck scale functions as a universal resolution limit, even in low-gravity or flat regions of spacetime, I wish to clarify the ECM position:

📌 In Extended Classical Mechanics (ECM), the Planck scale is not viewed as a fixed “pixel size” of space. Rather, it is a latent energetic threshold—one that only becomes physically relevant when energy, frequency, or gravitational force approach extreme, near-infinite conditions.

🌀 It is not operative in regions of minimal curvature or low energy. Space remains continuous and force-defined until the Planck frequency

fᴘlank≈2.999×10⁴² Hz

is approached. Only then does spacetime collapse into pure kinetic oscillation—beyond which classical and quantum constructs dissolve.

🔁 In ECM, the Planck domain is a transformative boundary, not a constitutive one. It signals a point where all known forces unify, mass ceases, and energy becomes the sole physical currency, vibrating in a zero-dimensional state beyond structure.

🧠 This perspective aligns in spirit with Roger Penrose’s proposal that wavefunction collapse is gravitational, but goes further: in ECM, wavefunctions no longer apply beyond this threshold—only persistent energetic logic remains.

Further Reading:

📄 Appendix 8: Energetic Structures Beyond Planck Threshold and the Breakdown of Classical Action
🔗 http://dx.doi.org/10.13140/RG.2.2.35283.28960

🧾 Supplement A to Appendix 8: Gravitational Collapse of Quantum States and the Planck Threshold as a Classicalizing Boundary
🔗 https://www.researchgate.net/publication/392666360_Supplement_A_to_Appendix_8_Gravitational_Collapse_of_Quantum_States_and_the_Planck_Threshold_as_a_Classicalizing_Boundary

📘 Supplement B to Appendix 8: Interpretive Boundaries of the Planck Scale in Low-Energy and Flat-Space Regimes
🔗 https://www.researchgate.net/publication/392666477_Supplement_B_to_Appendix_8_Interpretive_Boundaries_of_the_Planck_Scale_in_Low-Energy_and_Flat-Space_Regimes

#ECM #QuantumGravity #PlanckScale #PenroseCollapse #GravitationalThreshold #SoumendraNathThakur #ExtendedClassicalMechanics #PhysicsFrontiers

Appendix 8: Energetic Structures Beyond Planck Threshold and the Breakdown of Classical Action.

Soumendra Nath Thakur

Tagore's Electronic Lab, WB, India

postmasterenator@gmail.com | postmasterenator@telitnetwork.in | June 13, 2025

Abstract

In classical physics, the relationship $W=F\cdot s$ defines work as force acting through space, and quantum theory introduces the Planck constant $h$ as the fundamental quantum of action. However, both frameworks become inadequate at frequencies approaching the Planck limit fᴘₗₐₙₖ​ ≈ 1.855 × 10⁴³ Hz. Extended Classical Mechanics (ECM) introduces a refined energetic domain where spacetime, mass, and classical action cease to function as defining constructs. This appendix presents a critical re-examination of action, frequency, and energy interactions beyond the Planck threshold. It describes the transition into a regime of super-Planckian energetic oscillations, where particle identity is lost, potential energy is instantly rendered kinetic, and only energetic wave behaviour remains. Importantly, this framework preserves energy conservation, albeit through abstract, non-quantized means, proposing a new proportionality constant k where h fails. Connections to published ECM materials and quantum-gravitational unification are included to support this conceptual and mathematical extension of physical theory.

1. Classical and Quantum Action Breakdown

In standard mechanics, physical work is defined as:

$$$$W = F⋅s

And in quantum mechanics, action is characterized by:

$$$$h ∼ E⋅t or h ∼ p⋅x

However, these frameworks both fail to accurately describe energy interaction at or beyond the Planck frequency threshold. At this scale, ECM shows that space and time are no longer stable constructs and classical action loses physical applicability. Instead, energy transforms instantly into a purely kinetic vibrational field, and conventional particulate carriers of momentum or mass cease to exist.

2. Energetic Environment Beyond Planck Scale

At the Planck boundary:

• Rest mass collapses; no material particle structure persists.

• Spacetime decomposes into non-local vibratory states.

• Potential energy cannot remain latent; it converts directly into immediate kinetic manifestation.

• Conservation of energy persists but not via classical measurable action.

This corresponds to a regime defined by:

$$$$Δf = f₀− fᴘₗₐₙₖ during t₀− tᴘₗₐₙₖ

Here, Planck's constant $h$ can no longer serve as a useful quantum of action. Instead, ECM postulates a separate constant $k$, governing super-Planckian transitions, which are described by pure oscillatory existence.

3. Unified Gravitational Field and Pre-Spacetime Oscillation

In this state:

• Energetic density approaches infinity.

• Gravitational influence becomes unbounded and self-unified.

• No classical force or rest mass structure exists.

• All known physical laws break down—except the principle of energy persistence.

ECM redefines this realm as a zero-dimensional oscillatory continuum, where:

• Time exists only as cyclical recurrence.

• Frequency becomes the sole parameter of physical distinction.

• Propagation trends toward superluminal oscillation—not via signal transmission, but via pure geometric vibration.

4. Physical Meaning of Super-Planckian Frequencies

Planck frequency fᴘₗₐₙₖ = 1/tᴘₗₐₙₖ does not mark the upper bound of energetic phenomena but rather signifies a dimensional transition zone. Observable high-frequency radiation such as:

• Ultra-high-energy gamma rays (e.g., 
  $Hz$lies far below this threshold.

• Beyond this, hyper frequencies may exist within a non-local, pre-physical substratum—functionally invisible under classical spacetime observation.

5. ECM Position: Beyond h, Beyond Mass, Beyond Force

ECM maintains:

• Conservation of energy continues beyond Planck boundaries.

• New constants must replace h in describing such energetic domains.

• Planck’s constant is a threshold, not a finality.

ECM thereby unifies gravitational, quantum, and energetic phenomena through oscillatory logic, not particulate behaviour.

List of ECM Appendices and Annexures

• Appendix A – Standard Mass Definitions in ECM

• Appendix 3 – Fundamental Total Energy in ECM

• Appendix 4 – Negative Apparent Mass and Mass Continuity in ECM

• Appendix 5 – Temporal Modulation vs Temporal Scale Variation in ECM

• Appendix 6 – Angular-Time Correspondence in ECM

• Supplement A – Interpretive Basis and Conclusion to Appendix 6

• Supplement A2 – External Commentary on Supplement A

• Appendix 7 – ECM-Specific Framework for Photon Sourcing and Emission Pathways

• Appendix 8 – Energetic Structures Beyond Planck Threshold and the Breakdown of Classical Action

Primary References (from Appendix 8 content)

1. Thakur, S. N. (2025). Appendix 3: Fundamental Total Energy in ECM. https://doi.org/10.13140/RG.2.2.21532.19841

2. Thakur, S. N. (2025). Mass-Energy Transformations in ECM. https://doi.org/10.13140/RG.2.2.24863.27040

3. Thakur, S. N. (2025). Periodicity and Phase Shift Dynamics between the Big Bang and Planck Time. https://doi.org/10.13140/RG.2.2.29274.25285

4. Thakur, S. N. (2024). Description of Planck Equation and Energy-Frequency Relationship. https://www.researchgate.net/publication/375416343

5. Thakur, S. N. (2024). Unified Quantum Cosmology: Exploring Beyond the Planck Limit with Universal Gravitational Constants. https://doi.org/10.32388/26u31c

6. Thakur, S. N. (2024). Why is 1° time interval (T) the smallest meaningful mathematical expression of the Planck frequency? https://doi.org/10.13140/RG.2.2.32358.40001

7. Thakur, S. N. (2023). Quantum Scale Oscillations and Zero-Dimensional Energy Dynamics. https://doi.org/10.13140/RG.2.2.36320.05124

8. Thakur, S. N. (2023). Energy Persistence Beyond Planck Scale. https://www.researchgate.net/publication/375488896

Additional References

• Thakur, S. N. (2025). Appendix A – Standard Mass Definitions in Extended Classical Mechanics (ECM). https://doi.org/10.13140/RG.2.2.31762.36800

• Thakur, S. N. (2025). Appendix 4 – Negative Apparent Mass and Mass Continuity in ECM. https://doi.org/10.13140/RG.2.2.10264.92165

• Thakur, S. N. (2025). Annexure 5 – Temporal Modulation vs Temporal Scale Variation in ECM. https://doi.org/10.13140/RG.2.2.35784.64009

• Thakur, S. N. (2025). Appendix 6 – Angular-Time Correspondence in ECM. https://doi.org/10.13140/RG.2.2.33048.51200

• Thakur, S. N. (2025). Supplement A to Appendix 6 – Interpretive Basis and Conclusion.

https://www.researchgate.net/publication/392591776_Supplementary_A_to_Appendix_6_On_the_Physical_Recasting_of_Angular_and_Temporal_Units_in_ECM

• Thakur, S. N. (2025). Supplement A2 – Commentary on Supplement A.

https://www.researchgate.net/publication/392591986_Supplement_A2_-_Commentary_on_Supplement_Apdf

• Additional references to standard photon physics, emission spectra, and synchrotron mechanisms as discussed in astrophysics literature (NASA, CERN reports, etc.)

Appendix 8 introduces a new frontier in theoretical physics through the Extended Classical Mechanics (ECM) framework

June 13, 2025

It addresses energetic structures that may exist beyond the Planck scale, where spacetime, mass, and the familiar concept of action no longer apply.

This technical report reconsiders the boundary defined by Planck’s constant $h$, proposing that in super-Planckian domains, a new proportionality constant $k$ may govern energy transformations. It describes a regime where all rest mass collapses, gravitational fields unify, and energy manifests purely through oscillatory motion, possibly at superluminal rates. Despite the collapse of classical physics, the law of energy conservation persists, ensuring continuity even beyond observable structures.

This work contributes to ECM’s ongoing development of a unified theory for energy, frequency, and gravitational embedding at the most fundamental levels of existence.

🧾 Full paper: http://dx.doi.org/10.13140/RG.2.2.35283.28960
📚 Related works: Appendices A–7 on ECM, photon dynamics, gravitational embedding, and time-energy correlation.

Appendix 7: ECM-Specific Framework for Photon Sourcing and Emission Pathways

🔔 New ECM Update Published!

📘 Appendix 7: ECM-Specific Framework for Photon Sourcing and Emission Pathways

📅 Date: June 13, 2025

🔗 DOI: https://doi.org/10.13140/RG.2.2.13715.39205

We’re excited to share a brand-new addition to the Extended Classical Mechanics (ECM) series!

What’s it about?

Appendix 7 explores how photons—the basic particles of light and electromagnetic radiation—are created in nature and technology. It explains how photons come from things like:

• Electrons jumping between energy levels in atoms

• Radioactive nuclear decays (alpha, beta, and gamma emissions)

• Hot stars and blackbody radiation

• High-speed particles in space and magnetic fields

• Lasers, lightning, and even X-ray machines

But in ECM, these aren't just random energy events. Instead, each photon is part of a bigger picture of mass and energy shifting, like a kind of mechanical stress and release in the fabric of nature. ECM also introduces the idea that some photons may behave as if they have negative apparent mass (−Mᵃᵖᵖ), which flips how they interact with gravity and energy systems.

Why does it matter?

This appendix builds a bridge between classical physics, quantum behaviour, and gravitational effects, all under a single framework. It’s the first ECM document to outline photon sources from electrons to galaxies in one unified model.

For researchers and enthusiasts alike, Appendix 7 offers new insight into how energy becomes light—and how even light may carry traces of mechanical stress and deeper mass-energy behaviour than previously understood.

Stay tuned—next, we’ll explore how electrons and photons interact in even more detail, and how this ties into gravitational and electromagnetic coupling in ECM!

Appendix 6: Angular-Time Correspondence in Extended Classical Mechanics — ∏ᵈᵉᵍ as a Physical Angular Object and Phase-Time Displacement Δt.

Soumendra Nath Thakur

Tagore’s Electronic Lab, WB, India

Email: postmasterenator@gmail.com| postmasterenator@telitnetwork.in

Date: June 11, 2025

Quantized Angular Objects and Time Displacement: Formalization of ∏ᵈᵉᵍ and T(θ°) = Tₓ° in Extended Classical Mechanics

Abstract:

Extended Classical Mechanics (ECM) requires all mathematical entities to correspond to real, measurable, physical structures. The abstract constant ∏, commonly regarded as a dimensionless scalar, is instead formalized here as an angular object ∏ᵈᵉᵍ, representing the measurable degree-equivalent of one radian. Simultaneously, the derived relation:

                   T(θ°) = Tₓ° = θ°/360f = Δt

Interprets angular phase shifts in real systems as measurable temporal displacements. These formulations extend ECM's core principle: every mathematical transformation reflects a physical redistribution—whether of mass, energy, or time—and all quantities must preserve dimensional identity.

1. Formalization of ∏ᵈᵉᵍ as a Physical Angular Object

In ECM, circular and rotational motion must reflect real physical angular displacements, not abstract ratios. Traditionally, ∏ represents the ratio of a circle’s circumference to its diameter, used across trigonometric and rotational contexts. However, ECM interprets this ratio in terms of real, countable angular units, resulting in the definition:

∏ᵈᵉᵍ = 180°/∏ ≈ 57.2948°

This value corresponds to the physical angular span subtended by one radian in a circle when expressed in degrees. Rather than treating ∏ as dimensionless, ECM treats ∏ᵈᵉᵍ as an angular object with measurable identity. The number of such angular units required to span a half-circle becomes:

180°/∏ᵈᵉᵍ ≈ 3.14158

So we express:

180° = 3.14158 × ∏ᵈᵉᵍ 

This formulation matches ECM’s unit consistency protocol and parallels ECM's other physicalised constructs, such as phase-time shifts and energy-based deformation.

2. Angular Phase Shift as Temporal Displacement in ECM

Just as angular constants are converted into physical angular displacements, ECM requires phase shifts to represent real temporal displacement. When a system oscillates at a frequency f, and undergoes an angular shift θ° or ₓ°, the corresponding time shift Δt is given by:

T(θ°) = Tₓ° = θ°/360f  = Δt

Where:

• θ° or ₓ°: Angular shift in degrees

• f: Oscillatory frequency (Hz)

• Δt: Actual physical time delay due to angular offset

This is consistent with earlier ECM derivations of time modulation due to angular displacement in rotating or oscillating systems. It physically represents the temporal redistribution required to generate a phase delay in systems such as waveforms, rotating fields, or piezoelectric deformations.

Illustrative Example:

For a 90° phase shift at 50 Hz:

T(90°) = 90/(360 × 50) = 1/(4 × 50) = 0.005 sec

This quantifies how an angular rotation of 90° corresponds to a real delay of 0.005 seconds in the waveform or rotating field, causing time distortion in the waveform.

3. Physical Implications in ECM Modelling

The dual application of ∏ᵈᵉᵍ and T(θ°) or Tₓ° supports ECM’s unified treatment of geometry and time:

• In circular or rotational geometry, ∏ is no longer abstract but counts as ∏ᵈᵉᵍ units of angular displacement.

• In periodic systems, angular displacements translate into real temporal redistributions, measurable as Δt.

These relations find application in:

• Rotor and gyroscopic dynamics

• Phase-shifted electrical signals

• Electromechanical resonance

• Polarized wave front modulation

• Photon delay or advancement due to angular phase in ECM field theory

Conclusion:

The reinterpretation of ∏ as ∏ᵈᵉᵍ and the derivation of:

T(θ°) or Tₓ° = θ°/360f or ₓ°/360f  

Collectively advance ECM’s central thesis: all observable effects—geometric, temporal, or energetic—must be grounded in real, quantifiable displacements. These constructs replace dimensionless scalars with physically representative units, aligning ECM’s language with observable structure and enforcing continuity across mass, space, and time.