On the Synthesis of Planck Energy and Special Relativity

For massive particles with the speed of light in vacuum as their speed limit, their relativistic energy and momentum can theoretically tend toward infinity owing to the Lorentz expansion factor, but whether this divergence limit is still necessary as a physical actual state under the quantum gravity scenario when the particle speed is sufficiently close to the speed of light in vacuum remains crucial in current theoretical research. In this work, we studied an egalitarian Lorentz transformation system of special relativity by supplementing the postulate of the Planck energy upper bound: we adopted the correspondence principle to integrate Planck energy as the upper limit of particle energy with special relativity while maintaining the constancy of the speed of light in vacuum and the principle of relativity. Under the new Lorentz transformations, the divergence of the particle energy (momentum) upper limit is naturally eliminated. Here, we establish a practical upper bound on the experimentally measured mass of monochromatic photons from radiation sources; reveal that length contraction manifests significantly in any direction (including perpendicular to the motion direction) when the particle energy approaches the Planck energy scale; and propose a method to estimate the three neutrino mass eigenvalues under the normal ordering scheme, yielding specific values. These predictions also provide clear verifiable benchmarks for future measurement experiments.