空间元理论假说

Abstract This work assumes that space is continuous in the mathematical sense. The spatial element is a relative unit defined to describe the metric; it possesses in itself no mass, energy, or inertia and is a kind of non-inertial ether. In vacuum there is always a sustained pressure acting on the surfaces of elementary particles, whose reaction constitutes the origin of gravitation and is also the source of dark energy and the vacuum energy. A photon is defined as the propagation of momentum through spatial elements; momentum is conserved, locally exclusive, and mutually incompatible. A spatial element occupied by momentum and separated by a complete closed surface becomes an elementary fermion. The instantaneous velocity of a photon within one period is described by the tangent function, and its period average equals the speed of light in the local space. The spatial membrane retains a never-vanishing opening in the direction of velocity; this opening takes the geometric form of a spherical cap, whose half-angle corresponds strictly to the phase angle of the tangent function. On the basis of the area relation for a spherical cap, this work shows that the fraction covered by the spatial membrane is the cosine of the phase angle and the open fraction is its sine, the instantaneous velocity being the ratio of the two multiplied by the dimensionless spatial scaling factor, which yields the tangent function naturally. By discretizing a half-period into n equal subdivisions and calibrating each subdivision with the Planck length as its average length, this work inverts the given scaling factor to solve for n, and then, using the angular gap determined by the non-divergent extrapolation at the high end together with the symmetric condition of equal durations at the two ends, rigorously derives the truncation angle beta of the extremal opening. Beta equals two thirds of the single-subdivision angular width epsilon, and the end interval is therefore two thirds of the Planck time rather than the Planck time itself. From this one obtains the non-divergent minimum and maximum velocities and proves that their product is exactly the square of the scaling factor. This work further derives the photon dynamic mass formula from the conservation of momentum and energy, giving its instantaneous form, its period-equivalent mean, and its bounded extrema, and on this basis reconstructs the complete system of electromagnetic equations, including the Maxwell equations, constitutive relations, the wave equation, potentials and gauge, the Poynting theorem, the energy-momentum tensor, the complex refractive index, and the effective Euler-Heisenberg Lagrangian. In the collision part, taking the Lorentz invariant s as the unifying thread, this work systematically derives the center-of-momentum energies of the three classes of collisions: photon-photon, photon-fermion, and fermion-fermion. Complete chains of formulas are given for the complex cases of head-on collisions and arbitrary angles, symmetric and extremely asymmetric configurations, stationary and moving targets, multi-photon processes, and in-medium threshold corrections. These are linked to the Breit-Wheeler cross-section, the differential scattering angular distribution, the perturbative order, and the half-period phase selection condition, thereby bringing the various collision processes treated separately in the standard model under one and the same spatial membrane opening and phase mechanism. 摘要 本文假定空间在数学意义上连续,空间元是为刻画度规而定义的相对单元,其本身不具有质量、能量与惯性,是一种非惯性以太。真空中始终存在作用于基本粒子表面的持续压强力,其反作用力构成万有引力的起源,亦是暗能量与真空能的来源。光子被定义为动量在空间元中的传播,动量不灭、局域独占且不相容;空间元被动量占据并形成完整闭合面而独立,即成为基本费米子。光子在一个周期内的瞬时速度由正切函数描述,其周期平均等于所在空间的光速;空间膜在速度方向上保留永不消失的开口,该开口以球面极冠的几何形式存在,其半角与正切函数的相位角严格对应。 本文以球面极冠面积关系为基础,证明空间膜覆盖占比为相位角的余弦函数,开口占比为正弦函数,瞬时速度为二者之比并乘以无量纲空间缩放因子,从而自然给出正切函数。通过把半周期离散为 n 个等份、并以普朗克长度作为每份平均长度的标定,本文由给定缩放因子反解出等份数 n,再以离散高端不发散外推所确定的角隙,结合两端等时长的对称条件,严格导出开孔极值的截断夹角 β。β 等于单份角宽 ε 的三分之二,端部时段因此等于普朗克时间的三分之二而非普朗克时间本身;由此得到不发散的速度最小值与最大值,并证明二者乘积恰为缩放因子的平方。本文进而由动量守恒与能量守恒导出光子动质量公式,给出其瞬时形式、周期等效均值与有界极值,并据此重构包括麦克斯韦方程、本构关系、波动方程、势与规范、坡印廷定理、能量动量张量、复折射率与欧拉—海森堡有效拉格朗日在内的完整电磁学方程组。 在碰撞部分,本文以洛伦兹不变量 s 为统一线索,系统推导双光子、光子与费米子、费米子与费米子三类碰撞的质心系能量,对头碰撞与任意夹角、对称与极端不对称、静止与运动靶、多光子以及介质中的阈值修正等复杂情形给出完整公式链,并与 Breit—Wheeler 截面、微分散射角分布、微扰阶数及半周期相位筛选条件相衔接,从而把标准模型中分散处理的多种碰撞过程,纳入同一空间膜开孔与相位机制之下。