Measurements in spacetime

Measurements of time and measurements of space combine to make a measurement in spacetime.

Just square it.

The first term is called the interval. If two observers agree that it is the same value - the two observers are in an equivalence class together because they agree about the interval - then one is dealing with Special Relativity (SR).

The next three terms do not have a name, so I made one up: space-times-time. If two observers agree about those three numbers do not change - the two observers are in a different equivalenc class which is about space-times-time - then that is my proposal for a new approach to gravity, Quaternion Gravity (QG).

Four observers of the events were looked at.

1. Walking toward the events (SR)
2. Walking away from the events (SR)
3. Watching from above the events (QG)
4. Watching from below the events (QG)

The walkers measured the same interval, but calculated different space-times-times.

The above and below observers agreed on the space-times-time, but differed on the interval.

The precise amounts of the differences - and they are exceedingly precise and tiny - depends on more math than shown in the graphics. One would need to read the essay for that.