Exploring Extended Classical Mechanics (ECM) as an Alternative Framework in Cosmology.

February 28, 2028

The exploration and analysis of "Extended Classical Mechanics" (ECM), a theoretical framework proposed to offer alternative explanations for various cosmic phenomena, particularly those currently attributed to dark matter and dark energy.

Here's a summary of the key points covered:

• ECM's Core Concepts:
  • We delved into the central concepts of ECM, including "effective mass" (Mᵉᶠᶠ) and "negative apparent mass" (-Mᵃᵖᵖ), and their role in explaining gravitational interactions.
  • We examined how ECM proposes to modify classical mechanics to account for observed cosmic phenomena.
• ECM vs. Standard Cosmology:
  • We contrasted ECM with the standard cosmological model (Lambda-CDM), highlighting the differences in their approaches to mass, gravity, and the universe's expansion.
  • We examined how ECM attempts to provide explanations without relying on dark matter and dark energy.
• ECM's Explanation of Cosmic Phenomena:
  • We discussed how ECM explains galaxy rotation curves, gravitational lensing, and the accelerated expansion of the universe.
  • We explored ECM's perspective on black holes, proposing that they possess anti-gravitational properties due to negative effective mass and contribute to galactic recession.
  • We examined ECM's explanation of gravitational collapse at the Planck scale.
  • We discussed ECM's ideas about photon dynamics, and the photon to dark energy transition.
• Mathematical Consistency and Observational Validation:
  • We emphasized the importance of mathematical rigor and observational evidence in validating ECM.
  • We discussed the importance of producing testable predictions.
• Emphasis on Planck Scale Physics:
  • Much of the discussion revolved around the Planck scale, and how ECM attempts to explain phenomenon at that scale.
• Negative Mass Concepts:
  • A large portion of the discussion was about the impacts, and mechanics of negative mass.

In essence, we explored a theoretical framework that challenges conventional understandings of cosmology and physics, and we examined the strengths, weaknesses, and potential implications of ECM.

Inconsistencies in Special Relativity’s Treatment of Time:

Soumendra Nath Thakur 

February 28, 2o25

Mr. Zoie Mezhevchuk posed an important question regarding anomalies or inconsistencies in Special Relativity (SR). In response, I present the following list of inconsistencies, particularly concerning SR's treatment of time:

List of Inconsistencies in Special Relativity

Failure to Invalidate Classical Abstract Time

Special Relativity (SR) introduced a new concept of time without first invalidating the classical notion of abstract time. Without a clear refutation, classical abstract time remains a valid interpretation. SR does not provide a direct answer to the question: Why is classical abstract time incorrect? This omission creates an unresolved ambiguity.

Inconsistent Adoption of Relativistic Time

While SR dismisses the independence of classical abstract time, it introduces an alternative "natural time" without logically resolving the conflict between the two. This leads to an inconsistent relativistic time framework that does not align with classical abstract time.

Imposition of a Dilatable Time Concept

Time, as perceived by humans, is an abstract, Hyperdimensional concept that emerges as a consequence of changes within universal existence. SR arbitrarily imposes a dilatable time, contradicting the fundamental perception that time is invoked by physical events rather than being an independent, modifiable entity. While physical changes can be measured, abstract time itself cannot. The SR framework, therefore, introduces an inconsistency by treating time as a physically modifiable quantity.

Expansion of the Time Scale to Justify Time Dilation

SR artificially enlarges the time scale to accommodate time dilation, yet a standard clock is not designed to reflect such an expansion. This raises the question of whether time dilation is a real effect or simply an imposed reinterpretation of clock errors.

Time Dilation as a Violation of Measurement Standards

Time dilation conflicts with established timekeeping standards set by measurement authorities. Since proper time is defined based on these standards, any modification of the time scale to accommodate relativistic effects becomes an inconsistent reinterpretation rather than an empirical necessity.

Piezoelectric Crystal Oscillator Experiments Reveal Force-Induced Errors

Experiments with piezoelectric crystal oscillators show that external forces can cause deformation in oscillations, leading to errors in timekeeping. SR, however, presents this error as genuine time dilation, ignoring the mechanical distortions affecting clock operation.

Phase Shift in Oscillator Frequency Misinterpreted as Time Dilation

A phase shift in oscillator frequency results in an error in the wavelength of clock oscillations, leading to deviations in measured time. Instead of recognizing this as a mechanical or electromagnetic effect, SR inconsistently classifies it as time dilation.

External Energy Loss Induces Infinitesimal Time Distortion

External influences, such as radiation or thermal effects, cause an infinitesimal loss of wave energy, resulting in small distortions in time measurement. SR, however, presents this phenomenon as a fundamental dilation of time rather than an external perturbation.

Proper Time Cannot Accommodate Dilated Time

The time scale designed for proper time measurement cannot logically accommodate dilated time. Yet, SR interprets time dilation as a real effect rather than an observational or instrumental discrepancy.

Entropy Suggests a Constant Change in Time, Contradicting Time Dilation

The principle of entropy suggests that the progression of time is uniform in any closed system. SR, however, introduces variations in time scales that contradict this fundamental concept, leading to inconsistencies in thermodynamic interpretations of time.

Mathematical Inconsistency in Modifying Abstract Time with Physical Forces

Time, as a mathematical abstraction, should not be subject to physical influences. Yet, SR modifies proper time as a function of velocity-dependent physical forces. In mathematics, abstract quantities should not be altered by external forces, making this a fundamentally inconsistent operation.

Limitations of Lorentz Transformations in Accounting for Acceleration and Material Stiffness

Relativistic Lorentz transformations do not inherently incorporate acceleration and material stiffness in their formulation. This presents a significant limitation, as velocity is not a fundamental quantity but rather a derivative of acceleration. Any relativistic transformation based solely on velocity inherently neglects the cumulative effects of acceleration across different reference frames. Consequently, this omission leads to an incomplete representation of physical reality, especially in scenarios where continuous acceleration and material properties play a crucial role in dynamics.

Conclusion

This list represents just a fraction of the inconsistencies in the relativistic concept of time. A thorough examination of SR’s time dilation framework reveals that many of its assumptions rely on arbitrary modifications of measurement standards rather than empirical necessity. Addressing these inconsistencies is crucial for refining our understanding of time and its role in physical theories.

The Role of Dark Energy in Galactic Recession:

Dark Energy’s Influence on Galaxy Clusters and the Accelerated Recession of Galaxies:

The Extended Classical Mechanics (ECM) expands upon traditional classical mechanics by incorporating additional complexities to analyse intricate systems while remaining grounded in Newtonian principles. Unlike the standard framework, ECM considers factors such as the internal structure of objects (beyond point masses) and aspects of continuum mechanics to study deformable bodies.

This approach aligns with the findings of the intercontinental observational study titled "Dark Energy and the Structure of the Coma Cluster of Galaxies" (2013), conducted by A. D. Chernin, G. S. Bisnovatyi-Kogan, P. Teerikorpi, M. J. Valtonen, G. G. Byrd, and M. Merafina. The research was carried out across multiple institutions, including Tuorla Observatory (University of Turku, Finland), Sternberg Astronomical Institute (Moscow University, Russia), Space Research Institute (Russian Academy of Sciences, Russia), University of Alabama (USA), and the Department of Physics (University of Rome "La Sapienza", Italy). Their study confirmed the universally accelerated recession of galaxies within the Coma Cluster (Abell 1656), a massive galaxy cluster in the constellation Coma Berenices.

Key Finding: The Role of Dark Energy in Galactic Recession

The presence of dark energy significantly influences the structure and dynamics of galaxy clusters, as evidenced by the Coma Cluster. Modelled as a uniform vacuum-like fluid with a negative effective gravitating density, dark energy induces a repulsive force that counteracts gravitational attraction. The key determinant of this effect is the zero-gravity radius (Rᴢɢ), beyond which dark energy’s repulsion dominates over the cluster’s gravitational pull. Observations and theoretical models indicate that at distances beyond Rᴢɢ ≈ 20 Mpc, the mass contribution of dark energy surpasses that of the cluster’s gravitating mass, leading to effective outward acceleration. This localized manifestation of cosmic antigravity aligns with the broader accelerated expansion of the universe, demonstrating how dark energy drives the recession of galaxies by overcoming gravitational binding at large scales.

RG Discussion Link

Dear Mr. Dmitriy Tipikin,

Thank you for your response and for sharing your perspective on the interpretation of Type Ia supernovae data and the recent findings from the James Webb Space Telescope (JWST) and the Dark Energy Spectroscopic Instrument (DESI). Your argument challenges the premise of cosmic acceleration by suggesting that observational discrepancies in supernova brightness could be attributed to light scattering rather than an expanding universe driven by dark energy.

However, the assertion that "there may be no additional accelerated expansion of the universe" contradicts multiple independent lines of observational evidence that have consistently supported cosmic acceleration. While it is valuable to reassess Type Ia supernovae as standard candles and consider alternative explanations for their apparent dimming, the broader confirmation of accelerated expansion does not rely solely on supernovae data.

Multiple Lines of Evidence Supporting Cosmic Acceleration

Baryon Acoustic Oscillations (BAO):

Large-scale surveys such as the Sloan Digital Sky Survey (SDSS) and DESI have mapped BAO features in the distribution of galaxies, providing independent confirmation of an accelerating universe. BAO measurements are not susceptible to the same potential systematic uncertainties as supernovae brightness and offer a robust, geometrical probe of cosmic expansion.

Cosmic Microwave Background (CMB) Observations:

The Planck satellite and WMAP have measured the CMB power spectrum, which reveals indirect but strong constraints on the presence of dark energy through the integrated Sachs-Wolfe effect. These measurements align with a ΛCDM cosmology where a cosmological constant (or an equivalent dark energy component) drives late-time acceleration.

Galaxy Cluster Dynamics and Mass Distribution:

Observational studies, such as those by Chernin et al. (2013), have directly analysed the dynamics of galaxy clusters like the Coma Cluster. These studies indicate an outward acceleration that cannot be explained purely by gravitational interactions among visible and dark matter components. This provides a direct, large-scale confirmation of cosmic acceleration independent of supernovae data.

Weak Lensing and Large-Scale Structure Growth:

The large-scale distribution of galaxies and the weak lensing of background light due to mass distribution in the universe further support an accelerating expansion. These gravitational lensing measurements align with models requiring a dark energy component.

Re-evaluating the Role of Type Ia Supernovae

Your reference to JWST’s higher-redshift supernovae images suggesting greater-than-expected light scattering is an intriguing possibility that warrants further examination. However, even if alternative mechanisms contribute to Type Ia supernovae dimming, they do not negate the entirety of the independent observational framework supporting cosmic acceleration.

Therefore, the claim that "there may be no additional accelerated expansion of the universe" does not hold when considering the full spectrum of astrophysical data. The conclusions drawn from a single observational effect—light scattering in supernovae—must be weighed against a comprehensive suite of cosmological measurements that have independently verified cosmic acceleration.

Below, I include further supporting discussion on dark energy’s role in galaxy clusters and the broader cosmic expansion.

Dark Energy’s Influence on Galaxy Clusters and the Accelerated Recession of Galaxies:

The Extended Classical Mechanics (ECM) expands upon traditional classical mechanics by incorporating additional complexities to analyse intricate systems while remaining grounded in Newtonian principles. Unlike the standard framework, ECM considers factors such as the internal structure of objects (beyond point masses) and aspects of continuum mechanics to study deformable bodies.

This approach aligns with the findings of the intercontinental observational study titled "Dark Energy and the Structure of the Coma Cluster of Galaxies" (2013), conducted by A. D. Chernin, G. S. Bisnovatyi-Kogan, P. Teerikorpi, M. J. Valtonen, G. G. Byrd, and M. Merafina. The research was carried out across multiple institutions, including Tuorla Observatory (University of Turku, Finland), Sternberg Astronomical Institute (Moscow University, Russia), Space Research Institute (Russian Academy of Sciences, Russia), University of Alabama (USA), and the Department of Physics (University of Rome "La Sapienza", Italy). Their study confirmed the universally accelerated recession of galaxies within the Coma Cluster (Abell 1656), a massive galaxy cluster in the constellation Coma Berenices.

Key Finding: The Role of Dark Energy in Galactic Recession

The presence of dark energy significantly influences the structure and dynamics of galaxy clusters, as evidenced by the Coma Cluster. Modelled as a uniform vacuum-like fluid with a negative effective gravitating density, dark energy induces a repulsive force that counteracts gravitational attraction. The key determinant of this effect is the zero-gravity radius (Rᴢɢ), beyond which dark energy’s repulsion dominates over the cluster’s gravitational pull. Observations and theoretical models indicate that at distances beyond Rᴢɢ ≈ 20 Mpc, the mass contribution of dark energy surpasses that of the cluster’s gravitating mass, leading to effective outward acceleration. This localized manifestation of cosmic antigravity aligns with the broader accelerated expansion of the universe, demonstrating how dark energy drives the recession of galaxies by overcoming gravitational binding at large scales.

Best regards,

Soumendra Nath Thakur

Dark Energy’s Influence on Galaxy Clusters and the Accelerated Recession of Galaxies

The Extended Classical Mechanics (ECM) expands upon traditional classical mechanics by incorporating additional complexities to analyse intricate systems while remaining grounded in Newtonian principles. Unlike the standard framework, ECM considers factors such as the internal structure of objects (beyond point masses) and aspects of continuum mechanics to study deformable bodies.

This approach aligns with the findings of the intercontinental observational study titled "Dark Energy and the Structure of the Coma Cluster of Galaxies" (2013), conducted by A. D. Chernin, G. S. Bisnovatyi-Kogan, P. Teerikorpi, M. J. Valtonen, G. G. Byrd, and M. Merafina. The research was carried out across multiple institutions, including Tuorla Observatory (University of Turku, Finland), Sternberg Astronomical Institute (Moscow University, Russia), Space Research Institute (Russian Academy of Sciences, Russia), University of Alabama (USA), and the Department of Physics (University of Rome "La Sapienza", Italy). Their study confirmed the universally accelerated recession of galaxies within the Coma Cluster (Abell 1656), a massive galaxy cluster in the constellation Coma Berenices.

Key Finding: The Role of Dark Energy in Galactic Recession

"The presence of dark energy significantly influences the structure and dynamics of galaxy clusters, as evidenced by the Coma Cluster. Modelled as a uniform vacuum-like fluid with a negative effective gravitating density, dark energy induces a repulsive force that counteracts gravitational attraction. The key determinant of this effect is the zero-gravity radius (Rᴢɢ), beyond which dark energy’s repulsion dominates over the cluster’s gravitational pull. Observations and theoretical models indicate that at distances beyond Rᴢɢ ≈ 20 Mpc, the mass contribution of dark energy surpasses that of the cluster’s gravitating mass, leading to effective outward acceleration. This localized manifestation of cosmic antigravity aligns with the broader accelerated expansion of the universe, demonstrating how dark energy drives the recession of galaxies by overcoming gravitational binding at large scales.

An Extended Classical Mechanics (ECM) Perspective: Limitations of Lorentz Transformations in Addressing Acceleration.

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

February 28, 2025

Lorentz transformations, which describe coordinate changes in Minkowski space while preserving the invariance of the speed of light, fundamentally assume inertial frames. However, they do not inherently accommodate acceleration as a factor in their formulation. This presents a significant limitation, as velocity is not a primary quantity but rather a derivative of acceleration. Any relativistic transformation based purely on velocity inherently omits the cumulative effects of acceleration between separating frames.

1. Acceleration Embedded in Velocity – The Lorentz Factor’s Incompleteness

The Lorentz factor:

γ = 1/√(1 - v²/c²)

illustrates the relationship between velocity and relativistic effects, yet standard relativistic formulations introduce acceleration separately through Rindler coordinates or within general relativity. This creates a conceptual gap, as special relativity does not naturally accommodate time-dependent acceleration effects between separating frames. While general relativity can describe acceleration in curved space-time, the absence of acceleration in Lorentz transformations leads to an incomplete representation of motion.

At t₀ = 0, if the initial velocity V₀ = 0, the conditions are:

a₀ᵉᶠᶠ = 0, γ = 1.

As the moving frame attains velocity v₁ at t₁ > t₀, where (v₁ − v₀) < c, acceleration is given by:

a₁ᵉᶠᶠ = (v₁ − v₀)/(t₁ − t₀)

Since negative apparent mass (-Mᵃᵖᵖ) modifies inertial resistance, acceleration is sustained dynamically, even under relativistic conditions. This challenges the assumption that velocity alone dictates time dilation and length contraction, reinforcing the necessity of incorporating acceleration into transformations.

2. Measurement Dependencies and Deformation Mechanics

Relativistic time dilation is traditionally viewed as a fundamental transformation of time itself. However, within Extended Classical Mechanics (ECM), time distortions are interpreted as measurement dependencies. The clock frequency alteration:

f₁ = (f₀ - x°) / (T𝑑𝑒𝑔 × 360)

demonstrates that relativistic effects on time can be attributed to phase shifts and mechanical deformations rather than an intrinsic warping of time.

Deformation mechanics further support this perspective. The classical deformation equation:

ΔL = FL/AY

undergoes modifications in ECM, where effective acceleration dynamically affects mass. This introduces non-trivial corrections beyond Hookean elasticity, indicating that relativistic length contraction should consider mechanical resistance rather than purely kinematic effects.

3. The Persistence of This Issue Across Space-Time Formalisms

The argument that "acceleration is handled within Rindler space-time or general relativity" does not resolve the fundamental issue; it merely shifts the mathematical treatment to different coordinate descriptions. Whether in Minkowski space, Rindler coordinates, or curved space-time, acceleration between separating frames remains a physical phenomenon that cannot be dismissed as a mere mathematical reformulation. Its absence from Lorentz transformations represents a fundamental limitation requiring an extended framework such as ECM.

Conclusion: The Need for an Extended Framework

Lorentz transformations provide a mathematically consistent approach to preserving light-speed invariance in inertial frames but fail to incorporate acceleration effects explicitly. While general relativity and Rindler coordinates introduce acceleration through alternative formulations, the fundamental issue remains: velocity is derived from acceleration, and its omission in primary transformations leads to inconsistencies in time dilation, length contraction, and inertial effects.

The statement that "Lorentz transformations fail to account for acceleration between separating frames" remains scientifically valid across different space-time formalisms and highlights the necessity of a broader framework for a complete physical description of motion.

Mathematical Presentation

Comparison of Results

1. Relativistic Derivation of Length Contraction with Lorentz Factor

Lorentz Factor (γ) Derivation:

The Lorentz factor is defined as:

γ = 1/√(1-v²/c²)

For an object moving at 1% of the speed of light:

v = 0.01c

Plugging into the Lorentz factor equation:

γ = 1/√(1-(0.01c/c)²) = 1/√(1-0.0001) ≈ 1.00005

Length Contraction Calculation:

The formula for length contraction is:

L = L₀√(1-v²/c²)

Given:

v = 0.01c, L₀ = 1 metre

Substituting the values:

L = 1 × √(1−(0.01)²) ≈ 0.99995 meters

The contracted length:

ΔL = (1 − 0.99995) m = 0.05 millimetres

Summary of Relativistic Contraction:

At 1% of the speed of light, length contraction is minimal.

The contraction factor is approximately 0.99995, leading to a length change of 0.05 mm for a 1-meter object.

2. Classical Derivation of Length Change with Hooke's Law

Hooke's Law:

The law states:

F = kΔL

Where:

F is the applied force.
k is the spring constant.
ΔL is the displacement or change in length.

Given:

m = 10 grams = 0.01 kg
v = 2997924.58 m/s = 0.01c
t = 10000 seconds

Calculate Acceleration:

Using the formula for acceleration:

a = v/t = (2997924.58 m/s) / (10000 s) = 299.792458 m/s²

Force Calculation:

Using Newton's second law:

F = ma = 0.01 kg × 299.792458 m/s² = 2.99792458 N

Determine Spring Constant (k):

Assuming a known displacement ΔL = 0.0001m

k = F/ΔL = 2.99792458 N / 0.0001 m = 29979.2458 N/m

Calculate Length Change:

Using Hooke's Law:

ΔL = F/k = (2.99792458 N) / (29979.2458 N/m) = 0.1 millimetres

Summary of Classical

For a force of 2.9979 N applied to a 10-gram object, the length change is 0.1 mm. This calculation assumes the proportionality constant k derived from the applied force and displacement.

Acceleration and Length Changes between Rest Frames and Separation

In Classical Mechanics:

Acceleration is accounted for directly using F = ma

The force required to maintain and change velocity is considered, incorporating acceleration.

In Relativistic Mechanics:

Acceleration is less straightforward due to the dependence of mass on velocity.

The Lorentz factor γ is used, which only considers the object once it is in motion, not accounting for the force and acceleration required to reach that velocity.

Conclusion

This comparison highlights the differences between classical and relativistic mechanics in handling length changes and acceleration. While classical mechanics directly incorporates acceleration and force, relativistic mechanics focuses on the effects of velocity on length and time, often omitting the detailed dynamics of reaching those velocities.