The Fundamental Mechanism of Mass and Spacetime Curvature in General Relativity

General Relativity (GR), proposed by Albert Einstein, introduces a profound and challenging understanding of the relationship between mass and spacetime curvature. Unlike classical Newtonian physics, which posits a force of gravity, GR elucidates that it is not the mass itself causing spacetime deflections directly, but rather the exchange of energy and the probabilistic nature of particle interactions that underpin these phenomena.

Quantum Mechanics and Particles

Massed objects, consisting of subatomic particles, do not directly cause spacetime geometry deflections. Instead, these objects are involved in a complex interplay of energy exchanges. Massed particles exchange energy with other particles and spacetime geometry in quantized amounts. These exchanges occur in a probabilistic manner, leading to the observed spacetime curvature. Thus, it is the aggregate effect of these exchanges—rather than the individual masses themselves—that fundamentally causes spacetime geometry deflections.

Principles of General Relativity

Central to Einstein's theory is the Principle of Equivalence, where the effects of gravity are indistinguishable from acceleration. This leads to the famous expression that "space tells matter how to move, and matter tells space how to curve" (John Archibald Wheeler). This principle encapsulates the essence of GR, where matter influences the curvature of spacetime, and this curvature in turn affects the motion of matter.

The principles of physics, particularly the Principle of Least Action, dictate that a free particle moves along the shortest path in spacetime. This path, known as a geodesic line, is analogous to the shortest line on a curved surface, such as a sphere. Planets, for instance, move along elliptical orbits due to the curvature of spacetime caused by the sun. Similarly, objects on Earth appear to fall down because of the Earth's gravitational field, which curves the spacetime around it.

Mass and Spacetime Tension

Mass, in a sense, can be thought of as radiating extra space. The total tension in this space, rather than the mass itself, is what causes gravity. This perspective suggests that mass does not merely occupy a space but actively contributes to the fabric of spacetime. This concept is a simplified metaphor, but it helps illustrate the dynamic relationship between mass and spacetime.

Quantum Field Theory and General Relativity

General Relativity, being a classical theory, operates at scales much larger than those explored by Quantum Field Theory (QFT). However, when considering all other known physical phenomena, one might conjecture that gravity must be consistent with the principles of QFT. Yet, the existence of GR raises questions about the completeness of QFT. There is a suspicion that GR may reveal aspects of spacetime that QFT does not account for, suggesting that a more unified theory may be necessary.

Theorists are currently working on integrating these disparate theories to create a more comprehensive and unified framework. This effort could potentially lead to significant progress in the next few years. As John Archibald Wheeler's quote succinctly captures: 'Space tells matter how to move, and matter tells space how to curve.' This mutual influence continues to be a cornerstone of our understanding of the universe.