Relativity

Gravity is not a force, but is a consequence of the fact that spacetime is not flat— it is curved (or warped) by the distribution of mass and energy in it.

Light cone

The visualization offered by light cones helps us to understand both the events that can affect an event $P$ (past), and the events that can be effected by $P$ (future). Anything that lies outside the cone at any given time is unable to be affected by the event $P$, since nothing can travel faster than the speed of light. Things that are unable to be affected are said to be in the elsewhere of the event.

• ex. at the moment a distant (but still visible from Earth) star explodes, we are in the elsewhere of the event, since the light of that explosion event has yet to reach us. We will remain in the elsewhere until such time has passed that the light from this event reaches us, and then we will be in the future light cone of the event.

Any object that exists within a light cone can have an impact on (past cone) or can be impacted by (future cone) an event

For any event existing in space-time, we may construct a light cone. And since the speed of light is the same at every light and in every direction, every light cone will look identical and will all point in the same direction.

Imagine living in a 2D world, and someone turns on a light (an event, $P$). That light would emanate out in all directions (x and y) in a disk and grow gradually over time. Now that we've introduced time, we plot it on the z-axis. The result is an upside-down cone.

• any object that is within this cone is subject to being influenced by the event

  • naturally, whether or not an object is within the cone is a function of time; An object may not be within the cone one minute, but may enter it in the next.
  • ex. the death of our sun will not be known to us until 8 minutes after the event has taken place. At this initial moment, the Earth is outside the cone. After 8 minutes, Earth enters the sun's future cone, and we observe the event of the sun dying:

• Likewise, there is also the concept of a past cone. Events that are able to affect event $p$ are said to exist in the past cone.