[b]Lee Smolin
Einstein was not the best mathematician around, and others, undeterred by neither the difficulty of the equations nor the war that was ravaging Europe (this was 1916), were able to find solutions. Some of the most important solutions ever found—those that describe the gravitational fields of stars and black holes—were written down by a German officer named Karl Schwarzchild as he lay dying in a field hospital of a skin disease he had picked up in the trenches.[/b]
Actually, I didn’t know that.
Einstein’s theory of gravity is a theory of causal structure. It tells us that the essence of spacetime is causal structure and that the motion of matter is a consequence of alterations in the network of causal relations. What is left out from the notion of causal structure is any measure of quantity or scale.
Sounds plausible to me.
[b]Before Einstein, geometry was thought to be part of the laws. Einstein revealed that the geometry of space is evolving in time, according to other, deeper laws.
It is important to absorb this point completely. The geometry of space is not part of the laws of nature. There is therefore nothing in those laws that specifies what the geometry of space is. Thus, before solving the equations of Einstein’s general theory of relativity, you don’t have any idea what the geometry of space is. You find out only after you solve the equations.[/b]
Next up: Before Newton.
Science is not about what’s true. It’s about what people with originally diverse viewpoints can be forced to believe by way of public evidence.
And then there’s the stuff that, say, the engineers believe.
The geometry of a universe is very much like the grammatical structure of a sentence. Just as a sentence has no structure and no existence apart from the relationships between the words, space has no existence apart from the relationships that hold between the things in the universe. If you change a sentence by taking some words out, or change their order, its grammatical structure changes. Similarly, the geometry of space changes when the things in the universe change their relationships to one another.
You know, as a general description.
For simple black holes, which do not rotate and have no electric charge, the values of the temperature and entropy can be expressed very simply. The area of the horizon of a simple black hole is proportional to the square of its mass, in Planck units. The entropy S is proportional to this quantity. In terms of Planck units, we have the simple formula S = .25 A / h G. Where A is the area of the horizon, and G is the gravitational constant.
Not to be confused with the considerably more complex black holes.