Gravity: Do Objects Bend Space or Directly Affect Others?

Understanding how gravity works is one of the most critical questions in physics. For a long time, it was believed that gravity acts as a mysterious force that pulls objects together, but with the advent of general relativity (GR), our understanding has evolved significantly. In this article, we'll explore the idea that instead of a force acting through space, gravity bends and warps space itself, influencing the paths of objects.

General Relativity and the Stress-Energy-Momentum Tensor

General relativity, formulated by Albert Einstein, provides a more accurate and comprehensive description of gravity. The theory is based on the Einstein field equations (G8πT), which relate the geometry of spacetime (described by the metric tensor) to the distribution of mass, energy, and momentum (described by the stress-energy-momentum tensor T). The presence of T on the right-hand side of the equations accounts for the sources of gravitational fields.

These equations tell us that the geometry of spacetime is not static but can be dynamically influenced by the presence of matter and energy. The metric tensor, which describes the geometry of spacetime, is not the same as in Newtonian physics. This change in the metric tensor significantly alters our understanding of motion and force.

Geodesics and Photon Paths

In Newtonian physics, we imagine that objects travel in straight lines, or geodesics, in a flat spacetime. However, in GR, the paths of objects, including photons, are described by the geodesics of the curved spacetime. For example, massless photons travel along the shortest path in curved spacetime, which can be a curved line, not a straight one as in Newtonian physics. This curvature is not a bending of space in the traditional sense but a change in the geometry of spacetime.

The concept of geodesics helps us understand phenomena like gravitational lensing. During a solar eclipse, light from distant stars is deflected around the sun, causing a double deflection compared to Newton's predictions. This effect, accurately predicted by Einstein, is a clear indication of the warping of spacetime by mass.

The Photonic Perspective

To further illustrate the concept, imagine a smooth, two-dimensional sheet (representing spacetime), where a massive object creates a dent or a depression. Smaller objects, like photons, follow the shortest path (geodesic) through this curved sheet, which might not be straight. This is a simple but effective way to visualize how gravity affects the paths of objects in spacetime.

Another way to think about it is that spacetime itself is curved by the presence of massive objects. This curvature affects the paths of all objects—be they photons or massive particles—causing them to follow trajectories that deviate from those predicted by Newtonian physics.

Motions and Accelerations in Spacetime

The change in the metric tensor due to the presence of mass and energy not only affects the path of objects but also changes our understanding of position, velocity, and acceleration. In GR, these vectors are defined in a non-Euclidean space, which is different from the flat space assumed in Newtonian mechanics.

For instance, consider the perihelion precession of Mercury. This precession, which is the gradual shift in the elliptical orbit of a planet, cannot be fully explained by Newtonian physics but is accurately predicted by GR. The curvature of spacetime by the sun's mass is responsible for this effect.

Electromagnetic and Gravitational Fields

A similar effect can be observed in electromagnetism. Electric and magnetic fields cause charged particles to deviate from a straight line, but the degree of deviation depends on the charge-to-mass ratio. This deviation in the path of charged particles is different for electrons and protons, yet not for neutrons. In GR, the stress-energy tensor T0 (which represents the energy-momentum distribution) causes the same change in geometry for all massive particles.

Final Thoughts

The key takeaway is that rather than acting on objects from a distance, gravity affects objects by warping spacetime. Massive objects create "dents" in spacetime, and other objects follow the shortest paths through these curved areas. This is a fundamental revolution in our understanding of the universe, one that has been confirmed by numerous experiments and observations.

For a more detailed and nuanced explanation, readers can refer to Sean Carroll's recent book, which dedicates an entire chapter to this topic. Understanding GR not only deepens our grasp of gravity but also paves the way for a more accurate modeling of the cosmos.