To raise the question whether we could be living in Simulated Reality is largely equivalent to asking whether there could be Reality with non-computable physics, equivalent to physics in a continuum. We would dispose of the question simply by pointing out that the Zeno paradoxes demonstrate the fundamental untenability of considering transformation in a continuum of space and time.
Physics is the study of states and transformations of energy. Transformation, as the Zeno paradoxes indicate, is impossible in a hypothetical continuum of space and time. That is, physics and physical processes, defined with reference to the key word "transformation," are not implementable in a continuum. Consequently, the concept of non-computable physics, implying the implementation of physics in a continuum, is oxymoron. Rather than speak of non-computable physics, we would do better to speak of non-computable states understood as non-physical, "transphysical" or "metaphysical," only in the sense that computable or mathematically representable states and transformations are the key defining properties of our concept of "physicality."
The implication of the foregoing is the hypothesis that all physical systems or universes have computable states and processes, a description of which constitute the physics of the system or universe. If ever we encounter a universe of space and time continuum its "world" would qualify for definition as "transphysical" or "metaphysical" in the sense that its state would be found to be non-computable (i.e. not yielding to description in mathematical terms) and its "world" would be found wholly exclusive of mathematically definable tranformations which characterize physical systems. Such universe would be one in which all laws of physics described in the language of mathematics break down and new properties unpredictable in the context of our experience of physical universes emerge.
Do we have any theoretical proposal of a metaphysical or transphysical state?
Yes, we have one, in the postulation of a singularity in Einstein's General Relativity. Einstein's General Relativity (GR) postulates the possibility of collapse of a massive body to a Black Hole with a singularity at the center. The idea of a Black Hole dates back to John Michell who did a thought experiment sometime in 1783. He knew that a body had to attain to a minimum velocity to escape the gravitational attraction of our planet. He knew also that light has a finite speed (the astronomer Roemer had demonstrated that in 1675). He knew also that the gravitational force that a body exerted on another increased with the mass of the body. He reasoned, therefore, that if a massive body could have its entire mass concentrated in a sufficiently small volume of space, the gravitational force it exerts could become so powerful that an escape velocity greater than the velocity of light would be required for any body to escape its gravitational field. Nothing, not even light, would be able to escape the gravitational field of such a body. If no light can escape from a body then it would be invisible in space.
The American physicist John Wheeler first coined the term Black Hole for such bodies. The region about the body where escape velocity equals the speed of light is termed the Event Horizon, and it is the boundary of a Black Hole within which all events are permanently hidden from an outside observer. What happens inside a Black Hole has remained a mystery to astrophysicists who have contemplated what a trip into a Black Hole would be like.
Near the Event Horizon of a Black Hole, the strong gravitational field makes a clock run slowly, from the perspective of an outside observer. Captain Kirk and his crew of the Enterprise approaching the Black Hole would be unaware of the changes you observe from your position away from the Black Hole. As Enterprise approaches the Event Horizon, its time slows to a stop and signals from Enterprise become red-shifted to infinite wavelength. All matter falling into a Black Hole would appear to an outside observer to stop and fade at the Event Horizon, taking an infinite time to fall through it. Black Holes are, therefore, sometimes called Frozen Stars because the matter of the star collapsing into the Black Hole appears frozen in place.
The crew of Enterprise, however, will have a different experience. In theory, they will notice nothing unusual. In principle, a Black Hole could be massive enough to have an Event Horizon so large that tidal forces which should rip Enterprise apart will be so mild that an astronaut would survive a trip into it. But there could never be a question of escape or return to our world. Physicists speculate that an astronaut who falls into a Black Hole will proceed irreversibly to its center–a point of zero volume and infinite density. Mathematical physicists call this point a singularity–a point at which the laws of physics break down.
A singularity, from the perspective of the laws of physics, is inconceivable. A singularity as non-computable state is "transphysical" or "metaphysical" in the sense that its state does not yield to mathematical description or analysis. Current trend in development of theoretical physics is moving away from the implication of the Penrose-Hawking Singularity Theorem which seemed to suggest that singularities exist at the centre of Black Holes and at the Big Bang origin of the universe. Hawking, himself, now currently believes that quantum gravity ensures that general relativity breaks down at less than Planck unit of time, so that singularities do not form. While the final answer to the problem of existence of singularities await a complete theory of quantum gravity, proof that singularities really exist will amount to a demonstration of non-computable states and suggest, at least, the contiguity of our world with whatever may be theoretically considered Reality. But according to Stephen Hawking, we cannot approach the "world" of a singularity with the mathematical tools of physics neither can we interact directly with one. We, also, may never reproduce its state in any simulation of reality we will ever construct.
How Multiverse Theories converge with Simulated Reality scenarios
We may propose a definition of "physicality" in terms of physics-is-computation hypothesis. That is, a physical system as any with computable states and processes. Computability implies that the structure of any physical reality is replicable or reproducable in the language of mathematics. Physical systems are implementable only in fragmented space and time structures because computation which defines their states and transformations are implemented in discrete byte units of information.
The concept of Simulated Reality is best re-conceived in terms of replicability or reproducibility of the structure of a physical world system. The criterion for Simulated Reality as one indistinguishable from Reality it simulates lends to the insight that Simulated Reality is best conceptualized with the analogy of reproduction in biological systems or otherwise replication as it occurs in DNA information carrying molecules. We would be augmenting our insight into the problem of Simulated Reality scenarios and how these scenarios converge with Multiverse Theory by discussing the reproducibility of physical systems in place of what we have been referring to as simulation.
In the context of insight afforded by the physics-as-computation hypothesis, which asserts that the universe is output of program execution, any Simulated Reality system is, effectively, a reproduction or replication of the Reality it "simulates." Insight from biological sciences lends to understanding of how Multiverse Theory converges with Simulated Reality scenarios. All copies of a given universe in a Multiverse set are reproductions or replications of the same, standing on equal grounds with each other as alternative Realities, in accordance with Bin-Guang Ma's "Relativity of Reality" hypothesis.
Any Unified Theory of a physical system which describes a finite set of alternative universes (M-Theory, for instance) is a partial theory describing a species of worlds. A Theory of Everything (TOE) describes the set of all possible physical systems or universes. Physicists propose Multiverse Theories because, in computational terms, to define a species of alternative computable worlds or universes is more economical, in information content terms, than defining a single or particular example of the species. Thus, we may imagine that a worlds programmer setting out to build worlds on his computer machine would ultimately be looking to designing a Universal Reality Generator (URG), whose repertoire (David Deutsch) includes all physically possible environments. The program for a Universal Reality Generator would, presumably, be equivalent to an Ultimate Multiverse Ensemble which embraces all universes that can be described in the language of mathematics.
What would a Universal Reality Generator (URG) Program be like?
First, a URG must set out to specify only the features common to an Ultimate Ensemble and state the relationship between the features. This, in effect, is a Theory of Everything(TOE), ordinarily assumed to be a set-theoretic model definition of all possible physical universes.The program may, if the designer desires, include an algorithm which biases it in favor of particular preferred solutions of the theoretic model defined. Alternatively, as physicists prefer in their desire to avoid postulating a god who sets the initial configurations, the program may run by massive parallel processing, churning out randomly, an infinite set of possible alternative universes of which only a subset are viable universes to sustain living beings like us with aesthetic tastes which make us rather fussy or choosy about the type of world we live in.
In the scenario in which particular solutions to the Ultimate Ensemble program are generated randomly, we would expect, in the long-run, our Universal Reality Generator (URG) to produce several copies of a particular solution. In this context of understanding, it becomes easier to appreciate why copies of the same solution of a Multiverse program would stand on equal grounds as alternative "realities." However, in the event that intelligent beings with special aesthetic tastes evolve in one of these universes, they may decide to implement a program for a version of their universe more pleasing to their aesthetic sensibilities. When, or if they develop a Reality Program capable of implementing a Simulated Reality indistinguishable from their world, it would be more accurate to speak of their self-made world as a reproduction of the original rather than a simulation, for the word simulation comes with the implication of something not "real," or "authentic," a qualification which we have shown is meaningless in the context of definition of a physical universe as any with "computable states and processes."
This article is second in a series by JohnThomas Didymus published in Perpectives and Symbolism. You may read the entire illustrated series here.