Gravitational Effects on a Hydrogen Atom: Length Contraction and Time Redefinition

This paper investigates the behavior of a hydrogen atom in Schwarzschild spacetime using Quantum Field Theory in Curved Spacetime (QFT-CS), employing a novel global Cartesian-like coordinate system and the vierbein formalism. Our primary contribution is the discovery of a gravitational length contraction effect encoded in the modification of electron’s probability density, quantified as $B_0^2 = e^3_z$, which emerges from solving the Dirac equation and reveals a spatial compression subtle near Earth ($\Delta B_0^2 \sim 10^{-26}$ across the bohr radius) but significant in stronger fields. We further reinterpret gravitational redshift and time dilation as local quantum phenomena driven by atomic energy-level modulation via $e^t_0$, challenging their classical depictions and proposing time as a process-specific parameter rather than a universal dimension. These findings advance the quantum-gravitational synthesis, offering new insights into spacetime’s interaction with quantum systems and suggesting testable signatures in extreme gravitational environments.