Spacetime in ECM: A Non-Physical Extensional Domain of Energy–Mass Transformations

Soumendra Nath Thakur
September 23, 2025

Within the framework of Extended Classical Mechanics (ECM), energy and mass are treated as the fundamental physical essences of existence, undergoing continuous and cyclical transformations. The Big Bang is interpreted as the origin point where immense concentrated energy transitioned into mass and radiation, and as the universe expanded and cooled, these processes enabled the formation of fundamental particles and eventually atoms.

In this view, spacetime is not a physical substance with measurable or convertible properties. Unlike energy and mass, which possess intrinsic existence and can be transformed into one another, spacetime cannot be reduced to—or expressed as—a quantum of energy or mass. Instead, ECM emphasizes that spacetime functions only as the extensional domain within which energy–mass transformations and corresponding events are observed. It is a relational framework, not a material component of the universe.

Therefore, while the early-universe energy drove expansion and cooled to allow structure formation, spacetime itself was not a source of energy nor a convertible reservoir of mass. It merely provided the ordered-to-disordered entropic continuum along which transformations progressed.

From an ECM perspective, this distinction is critical:

• Energy and mass constitute existence itself.

• Spacetime is a descriptive construct — an emergent relational background — necessary for framing events but without independent physical existence.

Thus, in ECM, spacetime is interpreted not as a physical entity to be equated with energy or mass, but as the extension of their transformational interplay, marking where and when existence unfolds.

Analysis

This concept within ECM presents spacetime as a non-physical, extensional domain rather than a tangible entity. Energy and mass are the true physical essences, while spacetime is the background against which their interplay is observed.

Spacetime vs. Energy–Mass

• Energy and Mass: Physical substances of existence, interconvertible. The Big Bang marks their first large-scale transformation.

• Spacetime: Not a substance, not convertible into energy or mass. Acts as a relational framework or “entropic continuum” marking where and when events occur.

This distinction is central to ECM:

• Energy and mass are the “what” of the universe.

• Spacetime is the “where and when” — the stage on which transformations manifest.

Commentary

• The argument flows logically: ECM principles → role of spacetime → critical distinction.

• Language is precise and consistent, keeping key terms clear.

• The bullet-point summary strengthens readability.

• Overall, the presentation makes an abstract idea accessible and discussion-ready.

Discussion prompts

• Does this ECM perspective on spacetime as a non-physical extensional domain align with or challenge your understanding of cosmological models?

• How might this interpretation affect the way we approach dark energy, cosmic expansion, or the geometry-based view of relativity?

The scale at which anti-gravity becomes relevant:

The cosmic antigravity can be stronger than gravity not only globally, but also locally on scales of ~ 1–10 Mpc (Chernin et al. 2000, 2006; Chernin 2001; Byrd et al. 2007, 2012), as studied using the HST observations made by Karachentsev’s team (e.g., Chernin et al. 2010, 2012a).

The local weak-field dynamical effects of dark energy can be adequately described in terms of Newtonian mechanics (e.g., Chernin 2008). Such an approach borrows from general relativity the major result: the effective gravitating density of a uniform medium is given by the sum

ρₑ𝒻𝒻 = ρ + 3P,

where ρ and P are the fluid’s density and pressure (c = 1 hereafter). In this model, the dark energy equation of state is Pᴅᴇ = −ρᴅᴇ, and its effective gravitating density.

A Unified Framework in Extended Classical Mechanics (ECM):

September 18, 2025

Extended Classical Mechanics (ECM) establishes a unified framework linking entropy, time distortion, gravitational dynamics, and cyclic cosmology. It proposes that time is not absolute but a dynamic quantity shaped by energy and entropy transformations. This perspective reinterprets galactic dynamics as consequences of temporal gradients rather than dark matter and resolves cosmic singularities by describing the universe as passing through ordered, disordered, and reordering phases in an ongoing cycle without a definitive beginning or end.

Key Concepts

Extended Classical Mechanics (ECM):

A theoretical framework that incorporates effective mass (Mᵉᶠᶠ), apparent mass (Mᵃᵖᵖ), and their negative counterparts to reinterpret cosmological phenomena. ECM unites frequency-based relations such as Planck’s E = hf and de Broglie’s wave–momentum duality within a classical foundation, without relying solely on quantum mechanics or general relativity.

Temporal Dynamics:

Time is a variable quantity intrinsically linked to entropy. Its flow (+T) corresponds to increasing entropy, while a reverse direction (−T) corresponds to decreasing entropy, governed by transformations in mass-energy.

Cyclic Cosmology:

The universe progresses through repeating phases:

• Ordered Phase: latent, low-entropy state with minimal time distortion.

• Disordered Phase: expansion with maximal entropy and time distortion.

• Reordering Phase: contraction and entropy reduction, preparing for the next cycle.

This cyclic process avoids a single Big Bang singularity and instead presents a continuous, indefinitely repeating cosmological evolution.

Conceptual Connections

Entropy and Time:

Time’s arrow is determined by entropy transitions, directly connecting temporal directionality to energy redistribution.

Gravitational Dynamics:

Galactic rotation curves, lensing, and large-scale gravitational phenomena emerge from temporal gradients and mass-energy transformations, replacing the need for hypothetical dark matter.

Anti-Gravitational Effects:

Negative apparent mass (−Mᵃᵖᵖ) within ECM provides a natural mechanism for repulsive gravitational behavior, aligning with observations typically attributed to dark energy.

Experimental Analogy: Piezoelectric Oscillators

ECM draws support from laboratory systems such as rotating piezoelectric crystals, where motion induces phase shifts and frequency variation, illustrating how temporal distortions emerge from dynamic mass-energy interactions.

Implications and Applications

Singularity Resolution:

The framework avoids the Big Bang singularity by describing transitions between contraction and expansion phases, governed by entropy cycles.

Dark Matter Alternative:

Gravitational anomalies are explained through temporal effects and negative mass states, eliminating reliance on unobserved dark matter.

Unified Framework:

ECM extends classical mechanics into a comprehensive structure that integrates entropy, time, and energy. It provides consistent interpretations for cosmology, gravitational repulsion, black holes, and potentially superluminal astrophysical jets.

Time Distortion and Proper Time in Piezoelectric Crystal Oscillators

Building on this experimental analogy, the distinction between motion-induced time distortion and bias-driven proper time in piezoelectric oscillators provides a concrete demonstration of how temporal dynamics emerge within ECM.

• Self-Generated Phase Shifts (No Bias Voltage):

 When a piezoelectric crystal is set into motion without any applied bias voltage, it can spontaneously generate a measurable electrical signal. This signal manifests as a phase shift accompanied by frequency variation, representing a distortion of time that arises directly from dynamic mass–energy interactions.

• Bias Voltage and Proper Time:

 In contrast, when a piezoelectric crystal is driven by an external bias voltage at rest, it oscillates stably at its resonant frequency. This stable oscillation corresponds to the emergence of proper time, free of additional distortions.

• Combined Effect Under Motion:

 When a biased crystal oscillator is set into motion—such as rotation at a prescribed frequency (e.g., 50 cycles/second)—its stable, bias-driven oscillation (proper time) becomes modulated by motion-induced phase shifts. This results in additional time distortion superimposed upon proper time.

Conclusion

Together, these observations show that proper time arises from stable, bias-driven oscillations, while motion introduces phase-dependent distortions. In a moving oscillator, time distortion is thus modulated upon proper time, providing a concrete laboratory analogy for ECM’s treatment of temporal dynamics as emergent from the interplay of energy, motion, and entropy.

Variable Matter Mass in Extended Classical Mechanics (ECM)

Soumendra Nath Thakur

September 10, 2025

Abstract: 

This paper explores the concept of variable matter mass within the framework of Extended Classical Mechanics (ECM), where mass is defined as a frequency-dependent, energy-related property that evolves through interactions, oscillations, and energy exchange processes. Unlike traditional physics, which treats mass as an invariant quantity, ECM proposes that matter mass (Mᴍ) is dynamically shaped by frequency–time distortions, energy density structures (ρᴇ), and the interplay of apparent and effective mass components. The transformative nature of matter mass allows primordial energy to turn into mass and, conversely, mass back into energy—a process deeply influenced by dark energy’s negative effective mass. As dark energy’s role grows, it causes fluctuations in Mᴍ, reducing or even inverting mass, and enabling energy to redistribute across cosmic scales. Observational studies on dark energy’s effects in galaxy clusters, alongside ECM’s theoretical framework, support this view of mass as an emergent, adaptable property rather than a rigid constant[1]. By focusing on how frequency governs these distortions, ECM offers a coherent explanation for how oscillatory energy processes drive the evolution of the universe—stretching its energy density and guiding the constant transformation between mass and energy.

Keywords

Variable Matter Mass; Frequency–Time Distortions; Negative Apparent Mass; Dark Energy; Energy Density Structures; Extended Classical Mechanics (ECM); Emergent Mass; Cyclic Cosmology,

ORCiD: 0000-0003-1871-7803 | Tagore's Electronic Lab, India | postmasterenator@gmail.com

Gamma ray transformation explained in Extended Classical Mechanics (ECM)

 A thought on the ECM principle:

Soumendra Nath Thakur | ORCiD: 0000-0003-1871-7803 | September 02, 2025

In a non-excessive gravitational environment, such as the periphery of a star like the Sun, gamma rays cannot persist for long durations. Their sustained existence appears to demand extreme gravitational conditions approaching the Planck scale, where only the highest-energy gamma rays remain viable. Near or beyond the Planck scale, however, the stabilization of energy appears possible only in plasma-like or collective energy-density structures, as isolated radiation modes become unsustainable.

Within ordinary stellar environments, gamma rays undergo interaction through a ΔMᴍ transformation: their excess mass–energy component (ΔMᴍ) energizes local electrons, which then re-radiate the energy as lower-frequency photons. In this sense, gamma rays effectively convert into photonic energy, reflecting ECM’s broader principle that ΔMᴍ transitions regulate the frequency-governed transformation of energy across different scales. This transition may be expressed compactly as:

KEᴇᴄᴍ = ΔMᴍc² = hf