Can General Relativity and Quantum Physics Coexist at Low Energies?

In the realm of physics, one of the most intriguing and longstanding questions revolves around the compatibility of general relativity (GR) and quantum mechanics (QM). Specifically, scientists often wonder whether these two fundamental theories can coexist or be compatible at low energies. To address this issue, it is essential to understand the conditions under which these theories overlap and diverge.

Definition of Low Energies

The term 'low energies' is often used to describe scenarios where the gravitational constant (G), the speed of light (c), and the Planck constant (h) play specific roles in determining the physical phenomena. In such scenarios, G is small, allowing general relativity to reduce to special relativity at low energies. Similarly, h can be significant, meaning quantum mechanics does not behave as Galilean physics. The key observation here is that when c-1 is small, relativistic quantum mechanics reduces to ordinary quantum mechanics, and when G is very small, general relativity simplifies to special relativity.

Theoretical Consistency at Low Energies

At low energies, the compatibility of general relativity and quantum physics can be assessed by considering the reduced forms of both theories. When c-1 is small, relativistic quantum mechanics (RQM) reduces to ordinary quantum mechanics (OQM), and when G is very small, general relativity (GR) simplifies to special relativity (SR). Furthermore, when h is small, quantum mechanics becomes more classical, analogous to Galilean physics.

Thus, at low energies, there is no inherent incompatibility between general relativity and quantum physics. This is because the physical phenomena described by these theories at such energies fall within their respective domains. However, it is crucial to note that these lower energy approximations are not representative of the full range of phenomena each theory can describe.

Exploring the Compatibility Question

Despite the theoretical consistency at low energies, the question of whether ordinary quantum mechanics (OQM) and Newtonian gravitational physics can coexist remains open. Joy Christian has highlighted that, to date, there is no theory that unifies these two concepts. While we know that quantum mechanics experiments on Earth can account for the presence of gravity, our current theories of quantum mechanics exclude gravity entirely.

The search for a unified theory capable of describing both relativity and quantum mechanics at high energies continues, with attempts such as string theory and loop quantum gravity promising to bridge these gaps. However, these theories are primarily designed to explain phenomena at much higher energies, where general relativity and quantum mechanics would be expected to diverge more significantly.

Therefore, when we consider the domains of these theories, asking whether general relativity and quantum mechanics can coexist at low energies is somewhat redundant. It is like asking if cricket and baseball are compatible at some regime; they operate in different domains and do not need to coexist.

Conclusion

In summary, while general relativity and quantum mechanics can coexist at low energies due to their reduced forms and the conditions they describe, the question of their fundamental compatibility remains open, especially in the absence of a unified theory applicable at these energies. The prevailing theories in these domains operate in their respective regimes, making the direct compatibility a non-starter.

The ongoing quest for a theory that unifies these fundamental forces at high energies continues, but in the meantime, the low-energy approximations highlight the consistency and compatibility of these theories within their operational domains.