Do we live in a [quantum] simulation? Constraints, observations, and experiments on the simulation hypothesis (2212.04921v2)

Abstract: The question "What is real?" can be traced back to the shadows in Plato's cave. Two thousand years later, Rene Descartes lacked knowledge about arguing against an evil deceiver feeding us the illusion of sensation. Descartes' epistemological concept later led to various theories of sensory experiences. The concept of "illusionism", proposing that even the very conscious experience we have is an illusion, is not only a red-pill scenario found in the 1999 science fiction movie "The Matrix" but is also a philosophical concept promoted by modern tinkers, most prominently by Daniel Dennett. Reflection upon a possible simulation and our perceived reality was beautifully visualized in "The Matrix", bringing the old ideas of Descartes to coffee houses around the world. Irish philosopher Bishop Berkeley was the father of what was later coined as "subjective idealism", basically stating that "what you perceive is real". With the advent of quantum technologies based on the control of individual fundamental particles, the question of whether our universe is a simulation isn't just intriguing. Our ever-advancing understanding of fundamental physical processes will likely lead us to build quantum computers utilizing quantum effects for simulating nature quantum-mechanically in all complexity, as famously envisioned by Richard Feynman. In this article, we outline constraints on the limits of computability and predictability in/of the universe, which we then use to design experiments allowing for first conclusions as to whether we participate in a simulation chain. Eventually, in a simulation in which the computer simulating a universe is governed by the same physical laws as the simulation, the exhaustion of computational resources will halt all simulations down the simulation chain unless an external programmer intervenes, which we may be able to observe.

• The paper outlines major constraints, such as computational predictability and recursive simulation limitations, that challenge the feasibility of universe simulation.
• It employs quantum mechanics as a central framework, emphasizing inherent uncertainties and limitations in simulating fundamental physical phenomena.
• The study proposes experimental approaches to test the simulation hypothesis, urging advancements in quantum computing and theory integration.

Evaluation of the Simulation Hypothesis: Constraints and Considerations

The paper in question scrutinizes the simulation hypothesis, a philosophical postulate that posits the possibility of our universe existing within a broader series or hierarchy of simulations. The authors, Florian Neukart et al., interrogate a pantheon of theoretical and computational constraints that challenge the feasibility of simulating the universe as we know it or any universe in general. They approach the hypothesis with a view toward providing a rigorous framework that outlines the boundaries and constraints necessary for conducting experiments aimed at validating or refuting our potential existence in a simulation.

Central to the paper is the understanding and application of quantum mechanics as the most fundamental layer of natural law that could underpin any simulation of the universe. The authors invoke Richard Feynman's insights to emphasize that any accurate simulation must reflect the quantum nature of our universe, considering that current quantum theories offer the most granular explanation of natural phenomena. However, the paper also acknowledges the limitations of quantum theory, particularly its current inability to integrate fully with general relativity—a gap that underscores the formidable complexity of simulating a universe.

A significant thrust of the document is the enumeration of key constraints that inform or inhibit the simulation of a universe, which include computational predictability, physical predictability, and computability constraints. Each is predicated on the realities of quantum mechanics and classical physics, as well as the limitations inherent in modern computational systems:

1. Computational Predictability Constraint: The authors discuss the challenge of predicting future states based on current data, given the quantum mechanical nature of particles that necessitate probabilistic rather than deterministic outcomes.
2. Physical Predictability Constraint: The paper asserts that true prediction and simulation cannot be achieved under quantum mechanics due to inherent uncertainties and entanglement issues.
3. First Computability Constraint: This constraint arises within a recursive loop in which every computational simulation of a universe must also simulate the computational tools it employs for that simulation, leading to untenable computational complexity.
4. Second Computability Constraint: Realistically, the number of particles required to simulate a universe with the same complexity would inevitably require a system as complex as the universe itself, which is computationally infeasible.
5. Third Computability Constraint: As entropy increases over time resulting in greater complexity, a simulation would need ever-increasing computational resources, which further challenges the feasibility of simulating a universe consistently over time.
6. Combined Predictability Constraint: Here, quantum fluctuations and vacuum states introduce uncertainties that even the most complex computational systems could not accommodate accurately or predictably.

Practical and theoretical implications emerge distinctly from these discussions. Practically, the paper suggests methods by which experiments could test whether we exist within a simulation. For instance, by attempting to simulate universes ourselves and observing emergent properties (or lack thereof), judgments may be made regarding our own universe's nature. Theoretically, the findings underscore the need for enhanced computational methodologies in quantum systems, alongside a better integration with general relativity, to handle the complexities discussed.

The authors also touch upon speculative consequences, should humanity discover itself within a simulation—contingencies that call into question the fabric of reality and life itself, redefining both ontology and epistemology within computational and physical confines.

This comprehensive treatment of the simulation hypothesis is intricate and contemplative. It is but a cornerstone of the debate within contemporary physics and philosophy regarding the nature of existence and reality. Future research, supported by advancements in quantum computing and maybe an ultimate unified physical theory, may provide pathways to more tangible investigations or potentially pivot discussions surrounding the theory away from abstraction and closer to resolution.