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.