| Description: |
We present a geometric framework for spacetime quantization in which eachelementary particle occupies a single spherical Planck-scale membrane capable ofstoring a maximum rest mass equal to the Planck mass. The observable mass isinversely proportional to a discrete index N, which simultaneously sets the spatialextent R = N ℓP and intrinsic clock period τ = N tP . Acceleration reduces N,compressing the membrane and yielding relativistic time dilation, length contraction,and the increase of relativistic mass as direct geometric consequences. By substitutingthe quantized mass–velocity relation into the wave–momentum identity, we derive ageometric expression for the de Broglie wavelength that matches experimental valuesacross energy scales. The framework further predicts maximum attainable velocitiesfor massive particles and yields cosmological energy fractions consistent with Planck2018 results. These features suggest that the proposed quantized–membrane pictureoffers a unified and testable geometric foundation for relativistic and quantumphenomena. |