Math of General Relativity - Part 19
If you want to look at the equation relating the matrix G with the mass, energy and motion (or Stress-Energy Tensor) of the gravitating matter, see the below link.
So now we know how to assign a Matrix of 16 numbers to each point P in space inside MSG at each point in time. On Earth, these numbers won't change with time, to a huge degree of accuracy. Now we want to translate this point P inside MSG to a point P4 on a Riemann surface in Riemann Space.
Relating a space-time point P (x ,y, z, t) in real space-time to the surface, or Riemann Space R4, can be done using the simple "mapping" equations x = u1, y = u2, z = u3 and u4 = ct, where c is the speed of light , and the U are the coordinate axes on the surface of R4.
This gives us a point P4 = (u1, u2, u3, u4) in R4, or on the surface R4, whichever way you want to look at it.
Theory: This point P4 was mapped from MSG to R4, and the value of the gravitational field G at the point P4 is the value of the Metric Tensor at P4.
In other words, the theory is that real space-time and gravity in real space-time can be translated into a purely GEOMETRIC mathematical scenario. Gravity in 3D space-time produces a 4D surface in an alternate 4D mathematical Universe. How this is not the "real" Universe will be shown next.
At this scale, it is easier to see that the trees are not under the influence of "artificial" gravity. It is real.
🌎🌐
The gravitational field around each blade of grass and tree is the same as the field around each blade of grass and tree on the surface of Earth.
Notice that if you drive on a road perpendicular to the cylinder axis, you will increase gravity driving one way and decrease it driving the other. If you drive opposite to the spin and at the radial speed, your gravitational field turns Minkowskian, and you are in a "free fall" or inertial coordinate system. That is, you and the car become "weightless."
That means this: The value of a gravity field can go from a surface-of-a-planet value to a free-fall value by a coordinate transformation among systems that are moving at a constant velocity with respect to each other.
At any instant of time, a car moving at the radial speed is in a Minkowski field, and a system at rest on the cylinder is in a planet-surface field. A ...
"Aja" is the title track of Steely Dan's 1977 album, and its meaning has been a subject of interpretation rather than a straightforward explanation from the band themselves, Walter Becker and Donald Fagen, who were known for their cryptic and layered lyrics. The song doesn’t tell a linear story but evokes a mood and imagery that fans and critics have analyzed over the years.
The word "Aja" is often speculated to refer to a person, place, or concept. One popular theory ties it to the name "Aja," which Becker and Fagen reportedly chose after learning of a Korean woman named Aja who married a friend of theirs. This fits Steely Dan’s tendency to draw inspiration from real-life fragments and transform them into something abstract. The lyrics—"Up on the hill / People never stare / They just don’t care / Chinese music under banyan trees"—suggest an exotic, serene escape, possibly a romanticized or imagined refuge from the complexities of modern life.
Musically and lyrically, "Aja" ...
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The title "Deacon Blues" itself is intriguing. It’s been suggested that it references football—the "Deacon" could nod to Wake Forest University’s Demon Deacons, a team whose colors are black and gold, though Fagen and Becker have said it’s more about vibe than a literal connection. "Blues" ties it to the musical genre, evoking a sense of soulful melancholy. In a 2003 interview, Fagen described the song as being about "a broken dream of a broken man living a broken life," but delivered with a sardonic twist typical of Steely Dan’s ...
