Part 6/11:
A key question here is the invariance of the Planck length, akin to how special relativity demands that the laws of physics remain constant. As velocities approach light speed, the notion of length contraction raises concerns. Under conventional relativity, the Planck length might shrink with increased velocity, suggesting a strange directional dependence of quantum spacetime properties.
To explore this conundrum and the implications of Planck length's invariance, we find Giovanni Amelino-Camelia's concept—doubly special relativity (DSR)—emerging prominently within the discourse. By ensuring both Planck length and Planck energy remain invariant regardless of velocity, DSR attempts to offer a coherent framework where gravity and quantum mechanics could potentially be reconciled.