Fundamental problems in Planck’s Quantum Theory and Newly Proposed Cosmological Model of symmetry-distribution and energy-distribution of the space quantum.

The Planck quantum theory is based on the concept of photons. However, the geometrical shapes of photons were not disclosed or discussed in the theory. Photons were described variously as: i) packets of energy, ii) electromagnetic waves (EM-waves), and iii) particles. The mathematical equation proposed for the energy of photons is: E = hν , where h is Planck’s constant and ν (nu) is the frequency of the photon. Frequency ν is functionally related to the speed of light ( C ) and the wavelength of light ( λ ) by the equation: λν = C , which resembles a "pressure (P)–volume (V)" constancy-type relation, such as Boyle’s law, PV = K = constant .While defining photons as energy packets, the typical electromagnetic wave profile was used to establish the relation λν = C . This raises a fundamental question: how can "energy" and "EM-wave" be considered the same physical variable? The energy of atoms and molecules remains confined to specific regions of space, whereas EM-waves propagate from one region of space to another. Thus, energy and EM-waves must be dimensionally different physical quantities. In this research article, an analytical approach has been adopted to propose a new cosmological-cum-topological and mathematical model of photons. This model is described as “auto-generated” in the sense that the logic and philosophies of physics, combined with the topological, cosmological, and mathematical coherence of the new concepts, naturally lead to the formulation.The proposed model first establishes that "energy" and "electromagnetic waves" are distinct physical variables. It argues that Planck’s prediction of energy being inversely proportional to wavelength is incorrect, as the mathematical relation λν = C is a thermodynamically invalid proposition in science. The true physical significance of the Spectral Power Distribution (SPD) of the Black Body Radiation (BBR) curve is evaluated through a new 3D cosmological model of Newton’s color wheel . Furthermore, it is shown that the mathematical equation developed by Max Planck for the distribution of energy in BBR curves—based on the inverse relationship between frequency/energy and wavelength—is unjustified.