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We have analyzed the distribution of early-type galaxies (ETGs) in the effective surface intensity vs. effective radius ( I e − R e ) plane and in the total luminosity vs. central stellar velocity dispersion ( L − σ ) diagram, with the aim of studying the physical variables that allow the transformation of one space-parameter into the other. We find that the classical Faber–Jackson relation L = L 0 σ α , in which the parameters L 0 and α are confined in a small range of possible values, is incompatible with the distribution observed in the I e − R e plane. The two distributions become mutually consistent only if luminosity is not considered a pure proxy of mass but a variable tightly dependent on the past history of mass assembling and star formation and on the present evolutionary state of the stellar content of a galaxy. The solution comes by considering the L = L 0 ′ σ β law proposed by D'Onofrio et al. in 2020, in which both L 0 ′ and β can vary considerably from galaxy to galaxy. We will also show that the data of the Illustris numerical simulation prove the physical foundation of the L = L 0 ′ σ β law and confirm the prediction of the Zone of Exclusion (ZoE) originating from the intersection of the virial law with the L = L 0 ′ σ β relation. The ZoE is the region in the I e − R e and R e − M s diagrams avoided by real galaxies, and the border of which marks the condition of 'full' virial equilibrium with no recent significant merger events and no undergoing star formation. [ABSTRACT FROM AUTHOR]