Dear Christi,
Regarding "change," - you say "change is governed by Einstein's equations or, if emphasis is on time evolution, by the ADM equations."
By the phrase "prefer emphasis on time evolution," there seems to be the clear implication that there are other possible preferences that can be emphasized on. The idea looks like it is in accordance with Einstein's "arbitratry transformations of space and time"...
Is the idea of a "preferred emphasis on space evolution" also correct? And is "space evolution" what you mainly describe by the following?
- metric defines distance
- metric can be represented by a matrix
- matrix depends on the position in space and on time
- matrix has a determinant
- determinant also depends on the position in space and time
- matrix determines (curvature) gravity
- gravity in turn is determined by the fields of matter (particles)
- determinant cannot be prevented from becoming 0
- determinant becomes 0 because it changes
- matter (particles) determines (curvature) metric
- metric evolves into a black hole if matter is dense enough
If it is not "space evolution" that you mean, then what do you mean? Does the word "metric" describe "motion" that defines distance covered per unit time?
Do the words "change," "evolution," and "transformation" convey the same meaning?
You seem to be unclear regarding "matter." You say "if matter is dense enough", implying that matter can be of various densities. Do you also mean there can be the preferred emphasis on the evolution of matter (particles)?
Oddly, Einstein made no mention of the transformations of matter in conjunction with the arbitrary transformations of space and time. But he gave us the famous formula that really looks like the definition of mass-energy (matter) transformations. It would be somewhat novel if there is the proposition of the arbitrary transformations of space, time and matter.
The maths are always impressive. But the beauty of the maths depends on the good sense in the interpretation.
It really looks like matter (mass, energy) appears to be the most discrete phenomena in nature. So, I prefer the idea of the evolution of matter, the transformations of mass-energy - which at the fundamental level is, for me, the motion transformations defined on the ethereal substance within the space dimension. Gravity, electromagnetism, fields, mass, energy, etc., are all motions to me, albeit of varying forms according to the transformations of motion.
My view is unconventional. But this allows me the idea that there is this much motion confined as particulate mass in this much unit of volumetric space and I can say this much kinetic energy can be release via a nuclear explosion of this much particulate mass from this much unit of space. Quantized motions! These have clear meanings to me...
My rather novel ideas have been very difficult to get through to the reigning counter-intuition establishment. So, it would be nothing new if you don't get my drift...
I hope you will rate my essay, too - so that I may also get the chance to be read by the establishment.
Castel