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Almost everybody has seen the equation E = mc2 and most everybody have heard the phrase, "Matter tells Spacetime how to curve, and Spacetime tells matter how to move". This section is an attempt to show what this phrase by John Wheeler looks like.

Einstein's Field Equations are a Piece of Cake
He developed a Notation System where one letter can stand for a set of equations. The set of equations are then consistent with the Operations defined by an equation of larger scope. Each term is more than arbitrary variables like y = f(x), though y is constrained by the value of x and x itself is constrained by the operation of f(). These steps of Constraints form a path to Concepts. Now step along a path of Concepts guided by the considerations laid down thus far, existence, observation, length, time, relativity, and mass.

Einstein's Field Equations Solutions come in various forms based on the level of detail desired and the application. Here is a form that serves as a basic comparison to Newton's Law of Gravity which is a specific case of Einstein's Field Equations for General Relativity
    8πG
----
c4		  
G = T
     
where G measures curvature, G is the Newtonian gravitational Constant, c is the speed of light, and T measures matter content of the system.
The terms G and T are sets of equations imbedded in G = (8πG/c4)T which if expanded would obscure the concepts of curvature and matter content. "Matter tells Spacetime how to curve, and Spacetime tells matter how to move", said John Wheeler because he saw the link between G and T and knew what G and T are.

We will start with G and build Newton's stage out of Wooden Blocks, rows and columns to make a layer and then layer upon layer to fill a space. Every rigid block has its identical rigid neighbours. The edges of the blocks make up a rigid coordinate system identifying up-down, right-left, and forward-backward. No matter where you are Time "ticks" simultaneously and uniformly from past to future. If you are here and someone is over there, then something happens elsewhere. Everyone in Newtonian Space and Time agree when and where "it" happens. Observations revealed details that show Newton's Law of Gravity is a special case solution of the large scope description of gravity encapsulated by Einstein's Field Equations.

Replace the Wooden Blocks by soft stretchy spongy cubes. Each cube continues to "tick" Time from past to future. Each tick is the amount of Time it takes for light to traverse an edge from corner to corner. This "time scale" applied to Newton's Blocks by Einstein comes from Maxwell's Equations. There is much to be said about Maxwell's Equations, but for now all we need is the maximum "Speed of Light", c. The block can now be squished, stretched, twisted, dimpled, bumped, curved, concaved, convexed, and even flattened to resemble rigid Wooden Blocks. When a volume is compressed the lines of spacetime (space and time) get closer to each other, When stretched they diverge to increase the distance between events in space and time (spacetime).

In our everyday world we experience the lines of spacetime as parallel and evenly spaced. We each live on our own line of spacetime. If I agree to met you at Joe's Market a 3 o'clock and we both arrive on time our spacetime lines have converged. After picking up our Lottery Winnings we leave to go our separate ways, our spacetime lines have diverged. The distance of our spacetime paths we traveled to and from Joe's Market are determined by the soft stretchy spongy cubes of spacetime that envelope our Neighbourhood. The spacetime cubes are so close to the Newtonian Wooden Blocks that we get the same results we calculating the distances traveled and the time spent to pick up our Lottery Winnings. Truth be told, Newton's Wooden Blocks work for describing the orbit of the Moon and the Planets around the Sun. Except for a small detail about Mercury's Orbit.

The Wooden Blocks of Newton were somewhat squish and twisted. What's more, time played into the proper squish and twist of the Blocks so they could be dynamic enough to work at Joe's Market, the Moon and the orbit of the other Planets. The un-parallel-ness and un-evenly spaced lines of spacetime in the Neighbourhood of the Sun cause Mercury to fall in the observed orbit it has around the Sun.

So, "Spacetime tells matter how to move" is the G part of Einstein's Field Equation. "Lets have some Cake".

You come home one day and smell someone has been baking. A 9 by 13 inch White Cake is near. The aroma is intoxicating. Upon entering the kitchen a golden cake with just the hint of chocolate swirls on top meets your gaze. "No frosting, the deliciousness is in the Details", the Master-Baker slices a piece of Cake. A dense Brownie Mix had been swirled in to the lighter White Cake Batter. You can not fathom how they could have baked together. But, I digress. The textures delight your Taste. There is something else, robust and tantalisingly gooey. Yes, it's peanut butter but there is more. Small, sharp, hard, well defined. "My God, its full of heath toffee."

And that's what matter content T is, the ingredients keeping their distance one from another by their nature (mass and a few more) yet influencing the baking in the distance between (spacetime).
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