ECM's Explanation of Gravitational Collapse at the Planck Scale: v-2

 

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

February 10, 2025

 

Absolute Collapse Condition

 

Mass Acquisition at Planck Frequency:

 

In Extended Classical Mechanics (ECM), any massless entity reaching the Planck frequency (fp) must acquire an effective mass (Mᵉᶠᶠ = hf/c² = 21.77 μg). This acquisition of mass is a direct consequence of ECM's mass induction principle, where increasing energy (via f) leads to mass acquisition.

 

Gravitational Collapse:

 

At the Planck scale, the induced gravitational interaction is extreme, forcing the entity into gravitational collapse. This is a direct consequence of the mass acquisition at the Planck frequency, where the gravitational effects become significant.

 

ECM's Mass-Induction Perspective

 

Apparent Mass and Effective Mass:

 

The apparent mass (−Mᵃᵖᵖ) of a massless entity contributes negatively to its effective mass. However, at the Planck threshold, the magnitude of the induced effective mass (|Mᵉᶠᶠ|) surpasses |−Mᵃᵖᵖ|, ensuring that the total mass is positive:

 

|Mᵉᶠᶠ| > |−Mᵃᵖᵖ|

 

This irreversible transition confirms that any entity at fp must collapse due to self-gravitation.

 

Implications for Massless-to-Massive Transition

 

Behaviour Below Planck Frequency:

 

Below the Planck frequency, a photon behaves as a massless entity with effective mass determined by its energy-frequency relation. However, at fp​, the gravitating mass (Mɢ​) and effective mass (Mᵉᶠᶠ) undergo a shift where induced mass dominates over negative apparent mass effects.

 

Planck-Scale Energy:

 

Planck-scale energy is not just a massive state—it is a self-gravitating mass that collapses under its own gravitational influence. This suggests that at Planck conditions, the gravitationally induced mass dominates over any negative mass contributions, maintaining a positive mass regime.

 

Threshold Dominance at the Planck Scale

 

Gravitational Mass Dominance:

 

At the Planck scale, gravitational mass (Mɢ​) is immense due to the fundamental gravitational interaction. Since |+Mɢ​| ≫|−Mᵃᵖᵖ|, the net effective mass remains positive:

 

Mᵉᶠᶠ = Mɢ = (−Mᵃᵖᵖ) ≈ +Mᵉᶠᶠ 

 

This suggests that at Planck conditions, the gravitationally induced mass dominates over any negative mass contributions.

 

Transition Scenarios for Negative Effective Mass

 

Conditions for Negative Effective Mass:

 

The condition −Mᵃᵖᵖ > Mɢ could, in principle, lead to a transition where the effective mass becomes negative. This might occur under strong antigravitational influences, possibly linked to:

 

• Dark energy effects in cosmic expansion.

 

• Exotic negative energy states in high-energy physics.

 

• Unstable quantum fluctuations near high-energy limits.

 

Linking Effective Mass to Matter Mass at Planck Scale

 

Matter Mass Emergence:

 

Since Mᵉᶠᶠ ≈ Mᴍ, under these extreme conditions, it implies that matter mass emerges predominantly as a consequence of gravitational effects. This aligns with ECM’s perspective that mass is not an intrinsic property but rather a dynamic response to gravitational interactions.

 

Conclusion

This work on ECM provides a detailed and nuanced understanding of how gravitational interactions can induce mass in initially massless particles, leading to gravitational collapse at the Planck scale. This perspective not only aligns with fundamental principles but also offers potential explanations for cosmic-scale phenomena involving dark matter, dark energy, and exotic gravitational effects. The detailed mathematical foundations and the implications of apparent mass and effective mass in ECM further clarify how mass can dynamically shift between positive, zero, and negative values based on gravitational and antigravitational influences.