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 MUH).
Programming a Virtual Universe
In this site we look at a geometrical solution for a virtual universe as a programmed series of algorithms (the computer simulation approach). Using the computer game as an analogy, the 2 principal problems that a 'universe' programmer must solve 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 #2; how to program the measurable 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 mode. The model is divided into 5 parts;
1. 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.
2. The Planck units are then separated into a dimensionless geometrical component (via 2 mathematical constants) a scalar component and a dimensioned unit. The geometry determines (encodes) the function of the constants (mass, space, time etc), as the geometries are dimensionless, they are unit independent. Two 2 scalars convert from these base geometries to the SI numerical values. Results for (G, h, c, e, me, kB) 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.
As both the scalars and the unit u collapse within the electron yet are also encoded within the electron, then the (black-hole) electron is a mathematical constant, i.e.: a virtual particle independent of the system of units yet also the origin of the units. Thus no 'physical' artifacts are required.
3. The universe reduces to a constantly expanding space (defined as a virtual black-hole) that can be stored within an array structure. 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 black hole are consistent with the cosmic microwave background.
4. The 4-D space time of physics is translated onto a 4-axis (black hole) virtual array. We thus have a Machian relativistic universe projected onto a Newton fixed background.
5. 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 ...