Re-Examination of Blackbody Radiation Theory and Elimination of the Ultraviolet Catastrophe Based on a Revised Classical Electrodynamics Framework

The high-frequency divergence problem (ultraviolet catastrophe) encountered when the traditional Rayleigh-Jeans formula explains blackbody radiation originates from three fundamental errors in its theoretical derivation: first, the erroneous assumption that all electromagnetic standing wave modes satisfy the equipartition theorem; second, the failure to distinguish between "stationary modes" and "radiation modes" in electron motion; third, the misapplication of the equipartition theorem—suited for continuous quadratic systems—to the electromagnetic radiation process that is essentially a continuous energy transfer. This paper is based on our proposed modified classical electrodynamics theory, which posits that electrons radiate or absorb energy only when their frequency changes (during accelerated or decelerated motion), and that this process is continuous in terms of energy. We introduce a minimum energy measurement unit ε, whose numerical value is equal to Planck's constant h, to measure the continuous energy flow corresponding to each unit change in electron frequency. Based on this, through the statistical calculation of the average power of radiation modes, we have re-derived the radiation energy density formula. This formula is consistent with the Rayleigh-Jeans formula in the low-frequency region and naturally exhibits exponential decay behavior in the high-frequency region, thereby successfully eliminating the ultraviolet catastrophe and fully aligning with experimental observations. A comparison with Planck's quantization hypothesis shows that the "quantized" characteristics of the blackbody radiation spectrum can be explained entirely within a purely classical physics framework, without the need to introduce discrete energy packets or quantum hypotheses.