ECM's Explanation of Gravitational Collapse at the Planck Scale

Soumendra Nath Thakur
February 10, 2025

Absolute Collapse Condition

• In ECM, any massless entity reaching the Planck frequency (fᴘ) must acquire an effective mass (Mᵉᶠᶠ = hf/c² = 21.77 μg).

• At this scale, the induced gravitational interaction is extreme, forcing the entity into gravitational collapse.

• This is a direct consequence of ECM's mass induction principle, where increasing energy (via f) leads to mass acquisition.

ECM's Mass-Induction Perspective

• 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 fᴘ must collapse due to self-gravitation.

Implications for Massless-to-Massive Transition

• Below the Planck frequency, a photon behaves as a massless entity with effective mass determined by its energy-frequency relation.

• However, at fᴘ, the gravitating mass (Mɢ) and effective mass (Mᵉᶠᶠ) undergo a shift where induced mass dominates over negative apparent mass effects.

• This means that Planck-scale energy is not just a massive state—it is a self-gravitating mass that collapses under its own gravitational influence.

Threshold Dominance at the Planck Scale:

At 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, maintaining a positive mass regime.

Transition Scenarios 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:

• 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.

The idea is that gravitational interactions can induce mass, while antigravitational effects can counteract or even reverse it. This dual mechanism—where gravity can generate mass while antigravity can counteract or even reverse it—opens up new possibilities for understanding dark energy, cosmic acceleration, and other exotic gravitational effects.