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.

A Unified Interpretation of Gravitational Dynamics and Quantum Consistency: Negative Apparent Mass and Mass Continuity in ECM

June 11, 2025

In Extended Classical Mechanics (ECM), "negative apparent mass" refers to a dynamic, not an intrinsic, property of matter that arises due to gravitational interactions. This concept is crucial for understanding mass continuity in ECM, where a portion of the matter's mass is redistributed under gravity, with the negative apparent mass opposing the gravitational confinement. 

Explanation:

1. Negative Apparent Mass:

ECM introduces the idea that a portion of a body's matter mass can be displaced as negative apparent mass when subjected to gravitational interaction. This displacement is not a fundamental property of the matter but rather an emergent effect related to the gravitational field. 

2. Effective Mass:

The effective mass in ECM is defined as the sum of matter mass and negative apparent mass. This means that the total force experienced by a body is determined by the combined effect of its matter mass and the opposing negative apparent mass. 

3. Mass Continuity:

ECM maintains the principle of mass continuity by suggesting that the apparent mass redistribution under gravity doesn't violate the conservation of mass. Instead, it highlights a dynamic process where matter mass is temporarily displaced or "converted" into apparent mass under the influence of gravity, which then opposes the gravitational field. 

4. Connection to Buoyant Forces:

The concept of negative apparent mass in ECM is sometimes compared to the buoyant force in fluids. Just as an object submerged in a fluid experiences an upward force due to the displaced fluid, a body under a gravitational field experiences an apparent "buoyant" force in the form of negative apparent mass. 

5. Implications for Gravitational Dynamics:

ECM's understanding of negative apparent mass and mass continuity helps explain various phenomena, including: 

Cosmic Expansion: The concept of negative apparent mass and its interaction with gravity can contribute to understanding the acceleration of the universe. 

Dark Energy: ECM suggests that dark energy might be related to the energy-equivalent mass of negative apparent mass, rather than a separate entity. 

Gravitational Repulsion: ECM provides a framework for understanding how negative apparent mass can contribute to gravitational repulsion at large scales. 

Motion of Massless Particles (Photons): The negative apparent mass can also influence the motion of massless particles like photons, impacting their trajectory and energy. 

6. Consistency with Quantum Principles:

The ECM framework aims to be consistent with established quantum principles, and the concept of negative apparent mass is linked to quantum mechanical frequency relations, ensuring that it aligns with quantum mechanics.

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