Complex Numbers Physics - (Abdullah Baran 2026)

The number √-1 = i, represents the imaginary unit and is used here to denote stored or latent (hidden) components. Force DefinitionForce is divided into two components: i² = -1, F = J + i.B J (Active Force): The part of the force that produces acceleration. It is the consumed or expended force.B (Passive Force): The part of the force that is blocked or resisted. It represents stored stress and does not produce acceleration.Transition from Force to EnergyEnergy is defined as the integral of force with respect to displacement: E = ∫ F dx = ∫ (J + i.B) dx This is split into two parts: E = E_r + i.E_iE_r = ∫ J dx → Consumed (active) energyE_i = ∫ B dx → Stored (passive) energy In this model, energy is considered primary, while force is derived from it.Energy FormulaThe general energy expression is written as: E = pc + i m c² γ_general Where:pc represents the momentum-related energy term.i m c² γ_general represents the stored energy component, scaled by the general gamma factor.Modified Energy Formula (Proposed)To isolate only the additional energy (excluding the base rest energy), the following form is used: ΔE = pc + i m c² (γ_general - 1) For a stationary object (p = 0):ΔE = i.m c² (γ_general - 1) This formula aims to capture only the extra energy added to the system (due to motion, gravity, pressure, heat, electrical charging, etc.), rather than including the full rest energy.Definition of γ_generalThe general gamma factor is defined in terms of the increase in mass or energy: γ_general := 1 + Δm / (i m) γ_general := 1 + ΔE / (i m c²) This definition links the gamma factor directly to the relative increase in imaginary mass or imaginary energy caused by additional stored effects (compression, heat, electrical energy, etc.).SummaryThe model separates force into active (J) and passive (B) components.Energy is obtained by integrating force.The formula E = pc + i m c² γ_general is the general energy expression.The modified form ΔE = pc + i m c² (γ_general - 1) is intended to represent only the additional stored energy.For stationary objects, this reduces to ΔE = i m c² (γ_general - 1). γ_general is proposed as a generalized factor that can, in principle, account for various physical effects (motion, gravity, pressure, heat, electricity), provided it can be properly defined for each case. If power is taken as energy divided by time: P = E / t Since your energy is complex: E = ξ + i.U Then power also becomes complex: P = (ξ + i.U) / t This can be written as: P = P_r + i.P_i Where: P_r = ξ / t → Average consumed (active) power P_i = U / t → Average stored (passive) power Acceleration is derived directly from force: a = F / m Since force is defined as F = J + i.B, acceleration becomes: a = J/m + i.B/m =a_r + i.a_i The real part (J/m) represents the classical acceleration that produces actual motion. The imaginary part (B/m) represents the potential acceleration that would occur if the blocking forces (constraints) were removed. In short, acceleration also has both an active and a passive component in this model. The definition of Complex Mass in your model is: m = E / c² = ξ/c² + i.U/c² = m_r + i.m_i m_r → Real mass (active / motion-related part) m_i → Imaginary mass (stored / blocked part) ----- This work presents an original conceptual framework developed by Abdullah Baran. The core ideas, physical interpretation, and overall vision of the model belong solely to the author. While large language models were used to assist with mathematical formalization and typesetting, the fundamental concepts, structure, and physical reasoning presented in this work are the result of the author’s independent thinking and development. ### Original Framework and Definitions This work introduces an original conceptual framework based on the separation of active and passive components in both force and energy. The following core definitions and notations were developed as part of this framework: F = J + i.B a = F/m = J/m + i.B/m = a_r + a_i E = ∫ F dx = ∫ (J + i B) dx = ξ + i.U P = ξ/t + i.U/t = P_r + i.P_i m = E / c² = ξ/c² + i.U/c² = m_r + i.m_i General Gamma Factor (Original Definition): γ_general = 1 + ΔE / (i.mc²) This definition of γ_general is proposed to represent additional stored energy arising from various physical effects (such as pressure, heat, electrical energy, and mechanical compression) beyond the conventional rest energy.