Gravity Part 3
The apple is still hanging on the tree because of the stem, but gravity is acting on it to make it want to do ... what? Gravity is exerting a force on the apple to make it want to pick up speed in the vertical (up-down) direction. The apple is in the GRIP of gravity's power. The apple wants to pick up a speed of 32 feet per second DOWNWARDS for every second that it hangs there, but the stem stops it.
Note what you also might forget: The force of gravity doesn't also want the apple to change its speed horizontally. Gravity wants it to keep its speed of 0 in the horizontal directions; it only wants it to fall straight down, picking up a speed of an additional 32 feet per second for every second it falls.
In shorthand, we say that gravity acts to accelerate the apple down at a rate of 32, and accelerate at a rate of 0 horizontally. (That is the motion predicted by both Newton and Einstein's equations from the mathematics of their theories of gravity).
The Dirac Equation is Relativistically Invariant.
Proof attached.
Proving the Relativistic Energy-Momentum relation, the hard way and the easier way.