The reconciliation of general relativity (GR) and quantum mechanics (QM) remains an open and challenging problem in modern physics. Currently, there is no widely accepted theory that successfully unifies GR and QM into a single framework.
Gravitational time dilation, described by the formula you mentioned, arises from the effects of gravity on the flow of time. It is a prediction of general relativity and has been experimentally confirmed in various scenarios, such as gravitational time dilation near massive objects or the gravitational redshift observed in astronomical observations.
Lorentz's factor, on the other hand, is a concept from special relativity (SR) that describes the time dilation and length contraction effects due to relative motion between observers.
While both effects—gravitational time dilation and Lorentz's factor—describe time dilation phenomena, they arise from different theoretical frameworks (GR and SR) and have different underlying physical mechanisms. They are not typically considered to be "lost siblings" waiting for a reunion.
The challenge of reconciling GR and QM, often referred to as the problem of quantum gravity, arises because the two theories have different mathematical formalisms and conceptual frameworks. GR describes gravity in terms of the curvature of spacetime, while QM deals with the behavior of particles and fields on a microscopic scale.
Many physicists and researchers are actively working on developing theories that attempt to reconcile GR and QM. Some notable approaches include string theory, loop quantum gravity, and other quantum gravity proposals. However, these theories are still under development, and there is no consensus yet on which, if any, of these approaches will ultimately provide a successful unification.
It's important to note that the unification of GR and QM is a highly complex and active area of research. While there is optimism that a future theory may reconcile these frameworks, it remains an ongoing challenge, and it is difficult to predict when or how a successful unification might be achieved.