On 6/21/2015 5:11 PM, Warren D Smith wrote:
Suppose you are God. You want to design a universe. (You may not believe in God, intelligent design, etc. I'm ignoring that debate here as much as I can. I'm just trying to investigate the problems you would face if you were such a God.)
Well, almost all the known physics formulas out there, are of the form SomethingImportant = PRODUCT_j (FundamentalConstant_j)^(R_j)
where the R_j are known rational numbers, and the FundamentalConstants are things like "electron mass" or "pi." In the rare cases where formula is not of this form, it is usually because it is a sum of two such formulas, in which case you usually can either (a) neglect one of the two terms, or (b) optimize some design parameter which trades off one term versus the other. Either way, the formula then becomes of our kind.
Now, if you are a God with certain Goals (such as, creating humans) then you need to choose the FundamentalConstants in such a way that various inequalities are obeyed that enable those goals. Such as, the lifetime of a star capable of incubating life, needs to exceed the time it takes for humans to evolve. The mass of such a star, needs to exceed the minimum possible star-mass but be below the maximum possible star-mass. Etc.
The observation I want to make is: this is a LINEAR PROGRAMMING PROBLEM. I.e. the logs of the fundamental constants are the variables, and the inequalities are constraints.
If you now want to assess "how likely" our life-friendly universe was, or how likely other observed properties of universe are, so you can compute how much of a "miracle" it all is, then you can do so by computing polytope volume ratios. One volume being, say, the parameter-vectors yielding a life-friendly universe,
But what do you do for the volume in the denominator? What range of values is possible?...natural?...canonical? Brent Meeker
To try to do that, I made this collection of physics formulas: https://dl.dropboxusercontent.com/u/3507527/WDSphysicsFormulas.html