Math of General Relativity Part 14
Albert Einsten, with the stealth help of Berhard Riemann, showed how to construct a 4D Space with a one-to-one correspondence with real Space-Time. To keep it real and specific:
Consider a certain volume of space, like the inside of Madison Square Garden (MSG), but only during a certain interval of time, from midnight tonight to the midnight the night after that. That's 24 hours, which contains 86,400 seconds. At midnight tonight, we set a "Seconds" Clock at zero. So the Space-Time (call it S4) that we are visualizing is the inside of MSG from time zero to time 86,400. This is S4.
Net, we will create a Riemann 4D "space" R4 that is given a one-to-one correspondence with S4. To keep it real, you can completely think of R4 as a surface. It is a 4D surface, whereas you can really only "picture" 2D surface, but when I talk about R4, just think of a surface R2 and then push your mind out from there.
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.