Electron Approach Theory. A Damped Oscillation Model Based on Relativistic Effects and Space-Time Feedback.

This study proposes a new theoretical model to describe the behavior of the electron in the atom, reinterpreting the classical problem of its collapse towards the nucleus through a damped oscillation governed by relativistic effects and a space-time feedback. The electron, in its approach to the nucleus, undergoes an increasing acceleration until a critical point where its velocity approaches that of light, leading to a temporal discontinuity and a subsequent reversal of motion. This process is formalized through the Lorentz factor with imaginary values, suggesting a transition between quantum states rather than a real superluminal velocity. The model is supported by a mathematical analysis based on the exponential decay of energy and the time constant RC, which shows a connection with the Heisenberg uncertainty principle and the time scales of quantum processes. The electron descent-ascent cycle introduces the concept of space-time memory, with a coordinate recalculation mechanism that ensures atomic stability.The results suggest that energy quantization can emerge as a macroscopic effect of an oscillating dynamical system and that absolute space-time plays a key role in maintaining temporal coherence. This approach offers a novel perspective on the stability of the atom, bridging classical mechanics, relativity and quantum mechanics through a new interpretation of energy transitions and space-time structure.