Quantization of Space

This paper assumes that space consists of elementary constituents possessing a finite intrinsic volume, here termed spacions. Each spacion is assumed to have an intrinsic mass m, an intrinsic volume v equal to the Planck volume, and an intrinsic negative pressure p_s. We postulate the equation of state p_s = −mc²/v. When one spacion is amplified into two, the effective initial energy of the splitting process is taken to be 2mc² by including the energy contribution associated with negative pressure. Both the total energy and total volume consequently double, while the energy density remains constant. Assuming further that each spacion splits at a constant amplification rate, we describe the time evolution of the number of spacions and the spatial volume. The amplification rate is estimated from the present volume of the observable universe and the age of the universe. For a quantum-theoretical description, we consider a scalar field with continuous mass modes and a cubic interaction. However, the microscopic mechanism supplying energy associated with intrinsic negative pressure remains undetermined; a rigorous derivation of the amplification rate from the interaction is left for future work. We also consider time dependence of the amplification rate as a possible explanation for the numerical discrepancy with the present cosmic expansion rate, without claiming that this discrepancy has been resolved.