Our external physical reality is a mathematical structure. That is, the physical universe is mathematics in a well-defined sense, and in those [worlds] complex enough to contain self-aware substructures SAS [they] will subjectively perceive themselves as existing in a physically 'real' world (- Max Tegmark's mathematical universe).
Programming mass space and time in a computer simulated virtual Universe
The simulation hypothesis proposes that all of reality, including the earth and the universe, is in fact an artificial simulation, most likely a computer simulation.
In this site I look at simulation hypothesis that uses a geometrical approach as the basis for a programmable virtual universe (the computer simulation model). The physical units are constructed as geometrical forms whereby the geometry of these forms encodes the dimensionality of the unit. These forms are embedded in a virtual electron which is based on a dimensionless black-hole electron model (the electron as a mathematical constant). This model suggests that the units of mass, space and time are not independent but rather overlap and within the virtual electron they cancel; units = 1. Thus we may create as much mass as we wish as long as we create the equivalent space and time to balance our units; M^9 = L^15/T^11 units = 1. As such, if we know the SI values for Planck length and Planck time then we may calculate the value for Planck mass.
Using the computer game as an analogy, the 2 principal problems that the 'virtual universe' programmer must resolve are;
1. To create self-aware substructures (see Max Tegmark's mathematical universe hypothesis definition). This requires that these substructures have a potential for learning, a self-awareness, and a (limited) freedom of action (at minimum the appearance of free-will). Thus the game will have the potential for divergent outcomes within a boundary condition, a limited non-determinism (see Swarm Intelligence).
2. To create a virtual space that these self-aware substructures would then perceive as being a physical reality within which they may function (to simulate a physical universe within a software environment).
This website is a discussion of problem #2; how to program an observable universe; 4 forces, the (Planck) units; mass, space, time, charge, temperature (SI units kg, m, s, A, K) and the physical constants (G, h, c, e, me, kB) in a virtual space. The model is divided into 5 parts;
a. The square root of Planck momentum is used to link the mass constants with the charge constants thereby reducing the number of required SI units to 3. By reversing a formula for a black-hole electron constructed from magnetic monopoles we can further reduce the SI units to 2 and define (G, h, c, e, me, kB) in terms of these 2 units.
b. The Planck units are constructed from a dimensionless geometrical component (via 2 mathematical constants; the fine structure constant alpha and an assumed constant Omega), a scalar component (2 scalars) and a single dimensioned unit 'u'. The geometry component determines (encodes) the function of the units (mass, space, time etc), as these geometries are dimensionless, they are unit independent. Two 2 scalars convert from these base geometries to their respective SI numerical values. From these Planck units we can then derive the physical constants (G, h, c, e, me, kB). Results are consistent with CODATA 2014. The SI units (kg, m, s, A, K) are defined in terms of a dimensioned unit u as exponents un. As this resembles a software array format we may conjecture that unit u is a mathematical rather than a physical construct. Thus we require 2 mathematical constants, 2 variable scalars and 1 dimensioned unit to generate with 10-digit precision the constants (G, h, c, e, me, kB).
c. The universe reduces to a constantly expanding region (defined as a virtual black-hole) that can be constructed from a loop (i.e.: FOR n=1 TO the_end: Do.... : Next). This loop sets the universe clock-rate. With each increment we add 1 each of the Planck units to form the scaffolding of the 'array'. Results for a 14.6 billion year old virtual black hole are consistent with the cosmic microwave background.
d. The 4-D space time of physics is translated onto a (black hole) virtual hyper-sphere. We thus have a Machian relativistic universe projected onto a Newton fixed background.
e. The forces as physical links of momentum (orbits are replaced by orbitals).
A Mathematical Universe
Mathematical realism holds that mathematical entities exist independently of the human mind. Thus humans do not invent mathematics, but rather discover it, and any other intelligent beings in the universe would presumably do the same. Platonism is a theory that numbers or other abstract objects are objective, timeless entities, independent of the physical world and of the symbols used to represent them. read more ...
The Physical Constants
The physical constants form the scaffolding around which the theories of physics are erected, and they define the fabric of our universe. And yet, no one has ever successfully predicted or explained any of the constants. Physicists have no idea why they take the special numerical values that they do. if many of them were even slightly different, living beings would not be possible. The desire to explain the constants is behind efforts to develop a complete unified description of nature, or "theory of everything". Physicists have hoped that such a theory would show that each of the constants of nature could have only one logically possible value. It would reveal an underlying order to the seeming arbitrariness of nature.' read more ...
Swarm intelligence (SI) is the collective behavior of decentralized, self organized systems. For example, a single ant is quite inept, ants are not smart but ant colonies are, by solving complex problems using swarm intelligence. No ant seems to be in charge, there are no generals, no managers, the queen just lays eggs; even a half million ant colony has no management that we can detect although tasks may be specialized, worker ants, army ants... Nature uses the simple actions of individuals, ants following basic rules, to create the complex behavior of a group. No single ant can see the big picture yet each ant contributes to the colony success. read more ...