The Duck Pond Splash Down

1. A Framework:

• Spacetime is a four-dimensional continuum.
• This integrates the three dimensions of space with the dimension of time.
• It IS THE MEDIUM through which all matter and energy exist and interact.

2. With Curvature:

• What we understand as the “gravitational field” is the curvature of spacetime CAUSED by MASS AND ENERGY.
• This curvature dictates how objects move through spacetime and how they experience the force of gravity.

3. Described by Field Equations:

• Field equations describe how MASS AND ENERGY DICTATE the curvature of spacetime.
• These equations essentially ‘say’ that the presence of mass or energy “tells” spacetime how to curve, and the curvature of spacetime “tells” objects how to move.
• In this sense, the gravitational field is represented not by a separate entity permeating space but by the geometry of spacetime itself.

Unpacking the Equality

Gravity = Curvature of Spacetime: 

Gravitational phenomena are a result of the geometry of spacetime, not a traditional force acting at a distance.

Spacetime ≠ Mass and Energy: 

While spacetime is influenced by mass and energy, they are not equivalent. Spacetime is the “arena” in which fields and particles (including mass and energy) exist and interact. Mass and energy are sources that influence the curvature of this arena.

Mass and Energy Influence Spacetime: 

The presence of mass and energy alters how spacetime is shaped, and thus, how it behaves, affecting the paths that objects take through it.