The Simulation theory ( Simulation hypothesis) in physics and cosmology is a limited mathematical universe theory which posits that what is perceived as physical reality is actually an artificial simulation, most probably a form of computer simulation. One variant is the simulated reality, the premise being a proposed technology in the future that would seem realistic enough to convince its inhabitants that the simulation was real, such as may be anticipated if the development of computer games continues at the present rapid pace. The other extreme is the full simulation in which the entire universe down to the quantum level and/or to the Planck level is an artificial simulation, we and our physical environment are essentially data forms inside a celestial computer.
The mathematical universe refers to universe models whose underlying premise is that the physical universe has a mathematical origin, the physical (particle) universe is a construct of the mathematical universe, and as such physical reality is a perceived reality.
The mathematical universe can be considered a form of Pythagoreanism or Platonism in that it proposes the existence of mathematical objects; and a form of mathematical monism in that it denies that anything exists except these mathematical objects.
Physicist Max Tegmark in his book "Our Mathematical Universe: My Quest for the Ultimate Nature of Reality" proposed that Our external physical reality is a mathematical structure. That is, the physical universe is not merely described by mathematics, but is mathematics (specifically, a mathematical structure). Mathematical existence equals physical existence, and all structures that exist mathematically exist physically as well. Any "self-aware substructures will subjectively perceive themselves as existing in a physically 'real' world".
In 2003, philosopher Nick Bostrom proposed a trilemma that he called "the simulation argument". Despite the name, Bostrom's "simulation argument" does not directly argue that we live in a simulation; instead, Bostrom's trilemma argues that one of three unlikely-seeming propositions is almost certainly true:
- "The fraction of human-level civilizations that reach a posthuman stage (that is, one capable of running high-fidelity ancestor simulations) is very close to zero", or
- "The fraction of posthuman civilizations that are interested in running simulations of their evolutionary history, or variations thereof, is very close to zero", or
- "The fraction of all people with our kind of experiences that are living in a simulation is very close to one"
The trilemma points out that a technologically mature "posthuman" civilization would have enormous computing power; if even a tiny percentage of them were to run "ancestor simulations" (that is, "high-fidelity" simulations of ancestral life that would be indistinguishable from reality to the simulated ancestor), the total number of simulated ancestors, or "Sims", in the universe (or multiverse, if it exists) would greatly exceed the total number of actual ancestors.
Bostrom goes on to use a type of anthropic reasoning to claim that, if the third proposition is the one of those three that is true, and almost all people with our kind of experiences live in simulations, then we are almost certainly living in a simulation.
|“||Many works of science fiction as well as some forecasts by serious technologists and futurologists predict that enormous amounts of computing power will be available in the future. Let us suppose for a moment that these predictions are correct. One thing that later generations might do with their super-powerful computers is run detailed simulations of their forebears or of people like their forebears. Because their computers would be so powerful, they could run a great many such simulations. Suppose that these simulated people are conscious (as they would be if the simulations were sufficiently fine-grained and if a certain quite widely accepted position in the philosophy of mind is correct). Then it could be the case that the vast majority of minds like ours do not belong to the original race but rather to people simulated by the advanced descendants of an original race.
Therefore, if we don't think that we are currently living in a computer simulation, we are not entitled to believe that we will have descendants who will run lots of such simulations of their forebears.
In an interview with MIT researcher Lex Fridman, Tesla and SpaceX CEO Elon Musk stated that it is his belief that we are all living inside a simulation. When asked what question he would pose the first artificial general intelligence system, he replied: “What’s outside the simulation?” Musk has previously asserted the possibility that we’re all living in a “Matrix” style simulation, claiming there’s only “a one in billions chance we’re in base reality.” His argument is premised on the evolution of video games from “Pong” ( Pong is one of the earliest arcade video games, a 1972 table tennis sports game featuring simple two-dimensional graphics) to “photo-realistic 3-D simulations with millions of people playing simultaneously.” Given enough time, those games would become “indistinguishable from reality.” 
Full Simulation HypothesisEdit
God the ProgrammerEdit
The full simulation argument posits that the universe in its entirety, including all life forms, is a simulation, analogous to a computer simulation, that is programmed by an intelligence external to the simulated universe.
The mathematical electron model ("Plato's Cave; the Source Code of the Gods") looks at the mathematics of a Full Simulation Hypothesis model that operates at the Planck level. The model assigns dimensionless geometrical objects to particles and the Planck units (mass, space, time and charge), the complexity of the universe deriving from combinations of these objects. The model itself is divided into 4 parts, each part constructed upon a quantum space and time as measured in Planck units;
- From a mathematical electron fe  can be constructed Planck unit equivalents as geometrical objects in terms of 2 dimensionless physical constants (α, Ω). To translate from these dimensionless geometrical objects to numerical based unit systems such as the SI Planck units requires 2 numerical scalars and a rule set that determines the relationships between the geometries of mass, space, time and charge. The characteristic feature being that the geometrical objects are indistinguishable from their corresponding physical structures.
- The universe is an expanding hyper-sphere array that increments in Planck micro black-holes in Planck-time steps (a Planck unit model). Thus for any chosen universe age defined in units of Planck time we may calculate the mass and radiation density of the Planck black-hole universe.
- All motion derives from the constant expansion of the hyper-sphere, in hyper-sphere co-ordinates all particles and objects travel at the speed of light (the velocity of expansion), time and velocity are therefore constants, however particle 3-D space has no means to measure this motion and so self-aware structures are restricted to relative motion, relativity as the mathematics of perspective. 
- Gravitational orbits are replaced by discrete (quantum gravity) gravitational orbitals or gravitons as units of orbital momentum (hbar c) whereby the orbital angular momentum of a planetary orbit becomes the sum of these orbitals. Gravitational interactions at the Planck level reduce to momentum interactions between discrete units of Planck mass.
Could we be living in a computer simulation?. The present level of technology uses digital computers, consequently computer simulations use digital (incremental) time instead of analog (continuous) time. It may be that future technologies and/or Gods use analog computers, however evidence that our universe time is digital rather than analog could strongly suggest a simulation. Quantum spacetime and Quantum gravity models refer to Planck time as the smallest discrete unit of time. A digital time simulation universe argument would then be as follows;
FOR age = 1 TO the_end 'in units of Planck time, big bang = 1 FOR n = 1 TO all_particles 'all the particles in the simulation IF particle(n) = ... ........ NEXT n NEXT age
The variable age is the simulation clock-rate (the universe age) as measured in units of Planck time. For each age the n-loop calculations are performed, only when they are finished does age increment. As such, age is a (discrete) incremental variable and not a real (analog) time dimension, for there is no interval between increments. Although the n-loop calculations may be extensive, self-aware structures from within the simulation would have no means to determine this, they would perceive themselves as being in a real-time. Information is exchanged by photons which are limited by the speed of light, therefore information apparently exchanged in real time irrespective of distance could be construed as evidence of an 'n-loop'. The common example is the thought experiment; if the sun were to magically disappear, we would see this only 8 minutes later (the time taken for photons to reach the earth), but would we continue to orbit the sun for those 8 minutes or would we immediately drift into space. Do the effects of gravity (as distinct from gravitational waves) update throughout the universe in real-time?
- Tegmark, Max (November 1998). "Is "the Theory of Everything" Merely the Ultimate Ensemble Theory?". Annals of Physics 270 (1): 1–51. doi:10.1006/aphy.1998.5855.
- M. Tegmark 2014, "Our Mathematical Universe", Knopf
- Tegmark, Max (February 2008). "The Mathematical Universe". Foundations of Physics 38 (2): 101–150. doi:10.1007/s10701-007-9186-9.
- Tegmark (1998), p. 1.
- Bostrom, Nick (2003). "Are You Living in a Computer Simulation?". Philosophical Quarterly 53 (211): 243–255. http://www.simulation-argument.com/simulation.html.
- Macleod, Malcolm J. "Programming Planck units from a virtual electron; a Simulation Hypothesis". Eur. Phys. J. Plus 113: 278. 22 March 2018. doi:10.1140/epjp/i2018-12094-x.
- Macleod, Malcolm J.; "Method for programming a Planck black-hole universe, a simulation hypothesis model". SSRN. 21 June 2018. doi:10.2139/ssrn.3333513.
- Macleod, Malcolm J.; "Method for programming Relativity as the mathematics of perspective in a Planck Simulation Hypothesis Universe". RG. Feb 2011. doi:10.13140/RG.2.2.18574.00326/1.
- Macleod, Malcolm J.; "Programming gravitational orbits via units of momentum for use in Planck unit Simulation Hypothesis models". RG. April 2018. doi:10.13140/RG.2.2.11496.93445.