# General relativity

• I
• LSMOG
Einstein showed that if you have a theory of gravity that is based on the geometry of invariant space-time intervals (GR), then that theory should be the same for all observers, regardless of their location and speed. That's the key idea behind GR: that the laws of physics should be the same for all observers, regardless of their locations and speeds.If you try to do this in terms of Euclidean geometry, you run into trouble. Consider the following scenario: two observers, A and B, are located at two different points in space. Observer A is moving towards observer B, while observer B is moving away from observer A. According to Euclidean geometry, the distance between the

#### LSMOG

LSMOG said:

In its most general context, I would summarise it as being about the relationship between events in spacetime, and how those relationships depend on sources of gravity. By extension, it is also about formulating the laws of physics in such a way that their form remains the same for all observers, regardless of where/when they are in spacetime, and how they move with respect to each other, and to sources of gravity.

But just out of curiosity, I would be interested to hear how others here would choose to summarise GR in simple terms.

LSMOG said:

Well, GR grew out of Einstein's attempts to incorporate gravity into special relativity in a manner that was compatible with experiment, and that's not a bad way of looking at it.

To understand it more fully, first you need to understand special relativity. I'm not sure where you're at at understanding special relativity, the level of understanding of SR that's most helpful for understanding GR is to understand SR as a kind of space-time geometry.

You can regard Euclidean geometry as being the geometry of distances. Straight lines segments are definable as the shortest distance between two points, circles are definable as a set of points a constant distance away from a center point, and angles are definable as the distnace (length) measured along a segment of a circle. So once you have the notion of distance, you have the fundamental motiation for Euclidean geometry, though there are many details yet to fill in.

For special relativity, the analogue to the Euclidian distance is the invariant space-time interval, called the Lorentz interval. You need other concepts as well, but they're all built on this same fundamental base, much as Euclidean geometry is based on distance.