The Math of GR (and SR)
Part 2
In Physics, in order to have a person/observer set up to make measurements on where an object is located and what time it is, he (or she) needs two things. One is a clock. That is the easy part. The second is: he needs to set up a Coordinate System. The method you all know is where you set up lines of latitude, longitude and altitude on the surface Earth. Then you have to give me these three numbers to know where something is.
If you are doing laboratory measurements, where the experiment is in a relatively small area, that would not be practical. The easiest method is to set up three perpendicular and straight rods that all meet at one point called the ORIGIN. See the picture.
This will represent "you," as an observer. When someone asks you where something is, you will use this to answer. How? First, you set up these three rods in the room. Then you hang an small ball in the room. WHERE the ball is can be answered using this procedure. (Next)
Proving the Relativistic Energy-Momentum relation, the hard way and the easier way.
This adds the proof for the relativistic mass effects from motion, proving that gravity causes it.