Distinguishing Negative Mass from Dynamical Mass Terms in Extended Classical Mechanics:

Soumendra Nath Thakur 

April 19, 2025

In response to a public comment by Dr. Valentyn Nastasenko, who stated, “Negative mass only exists in abstract mathematics. It does not exist in real physics,” I wish to offer a clarification grounded in the framework of Extended Classical Mechanics (ECM).

This assertion brings attention to an important conceptual distinction: ECM does not introduce or rely upon physically realisable “negative mass” as defined in speculative physics. Instead, it defines and consistently applies the concepts of negative apparent mass (−Mᵃᵖᵖ) and negative effective mass, which are dynamic constructs with observational support—not exotic or literal negative masses.

Specifically, ECM introduces:

Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ)

where:

• Mᴍ is the total matter mass, including both ordinary and dark matter, and  
• −Mᵃᵖᵖ is the negative apparent mass, dynamically emergent from gravitational and kinetic interactions.

The term −Mᵃᵖᵖ is assigned to radiation or kinetic energy contributions (e.g., in massless particles like photons) and is used to model antigravitational behaviour in gravitational fields. It is a mathematical and physical representation of how energy behaves dynamically—not a postulated exotic entity.

Moreover, this approach is not without precedent. As shown in:

Chernin, A. D. et al (2013). Dark energy and the structure of the Coma cluster of galaxies. Astronomy and Astrophysics, 553, A101.

the notion of negative effective mass is applied to describe the repulsive gravitational contribution of dark energy. ECM generalizes this insight to broader contexts and scales while remaining consistent with classical force laws and relativistic behaviour.

Thus, ECM carefully distinguishes:

• Intrinsic matter mass (Mᴍ),
• Dynamically emergent apparent mass (−Mᵃᵖᵖ), and
• The net gravitational mass (Mᵉᶠᶠ) observable in cosmic and quantum systems.

In summary, ECM does not propose negative mass in the literal or unphysical sense. Instead, it offers a structured, observationally motivated reinterpretation of inertial and gravitational effects, especially in systems where classical mechanics and cosmological phenomena intersect. I hope this letter helps dispel misconceptions and encourages further dialogue on reconciling mechanics with observed cosmic behaviour.

Sincerely,  

Soumendra Nath Thakur  

April 19, 2025

Clarifying the Misconception: ECM Does Not Invoke Physical Negative Mass but Dynamic Mass Equivalents.

April 19, 2025

Dear Dr. Valentyn Nastasenko,

Thank you for your comment. Your statement, “Negative mass only exists in abstract mathematics. It does not exist in real physics,” reflects a crucial concern in foundational physics—one that Extended Classical Mechanics (ECM) has carefully and deliberately addressed by making a distinction between physically real mass and dynamically emergent mass terms, such as negative apparent mass or negative effective mass, which are not "physical negative mass" in the conventional or literal sense.

To clarify:

In Extended Classical Mechanics (ECM), at no point is a physically realizable negative mass postulated. Rather, negative apparent mass (−Mᵃᵖᵖ) arises from the dynamic redistribution of kinetic energy under gravitational influence and motion. It does not signify an exotic substance or particle with negative inertial mass, which would indeed be speculative and lack empirical support.

Similarly, effective mass (Mᵉᶠᶠ) is a composite quantity defined in ECM as:

Mᵉᶠᶠ = Mᴍ + (−Mᵃᵖᵖ)

where:

• Mᴍ is the matter mass (including both ordinary and dark matter), and
• −Mᵃᵖᵖ is the dynamic negative apparent mass arising from the gravitational and kinematic configuration.

This formulation is strictly observational and phenomenological—it is constructed to match and explain cosmological and quantum mechanical behaviour, including light deflection, redshift, and repulsion effects attributed to dark energy.

In fact, negative effective mass is not an invention of ECM. It is empirically supported in observational cosmology, particularly in works such as:

• A.D. Chernin et al., "Dark energy and the structure of the Coma cluster of galaxies," Astronomy and Astrophysics, 553, A101 (2013).

Here, the gravitating effect of dark energy is explicitly modelled as a negative effective mass contribution, denoted as (Mᴅᴇ < 0), resulting from a uniform antigravitational density. This "negative mass" in the cosmological context is not a negative particle mass, but a gravitational term required to reconcile observations of galaxy clusters and cosmic acceleration.

ECM formulates and extends this line of thought by assigning: −Mᵃᵖᵖ to kinetic energy or radiation (e.g., photons), and Interpreting this as the source of antigravitational behaviour in massless particles, particularly under gravitational influence.

This does not violate classical or relativistic principles; rather, it refines them through well-defined, observation-based extensions that remain grounded in Newtonian force dynamics and energy equivalence. The gravitational repulsion observed in phenomena like dark energy becomes natural when modelled through this lens.

Therefore, I respectfully submit that ECM does not introduce or rely upon abstract or unphysical “negative mass,” but rather makes precise distinctions between:

• Intrinsic matter mass (Mᴍ),
• Dynamically derived negative apparent mass (−Mᵃᵖᵖ), and
• Net observable mass (Mᵉᶠᶠ) as it appears in gravitational and inertial contexts.

Your critique is therefore an opportunity to clarify a misidentification: ECM is not invoking exotic or non-physical negative mass, but instead reinterpreting known energetic phenomena (such as the momentum-energy of massless particles and repulsive cosmological expansion) through carefully defined dynamic mass equivalents.

I remain deeply appreciative of your engagement with the subject and welcome further discussion on how ECM models can complement our shared aim of reconciling classical mechanics with the modern observational universe.

Warm regards,

Soumendra Nath Thakur

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