User:GreatContributor1/Digital Physics

Category:Digital media Category:Theoretical physics Category:Theory of computation

Proposed Theories
Many scientists have expressed or develop ideas surrounding digital physics. Edward Fredkin and Konread Zuse pioneered the idea of a computable universe based on cellular automation. This is similar to the ideas described by Stephen Wolfram in his book A New Kind of Science argues that the computable universe is based on a rewriting network as cellular automation cannot account for relativistic features such as no absolute time frame. However these theories were merely speculative and the lack mathematical formulation.

Gerard ’t Hooft developed has developed an interpretation of quantum mechanics that is deterministic and follows the paradigms of digital physics. Similarly to Fredkin’s and Muse’s model his theory relies on cellular automation but it also has a mathematical formulation. The theory relies on the concept of an optimal basis on the Hilbert space which he calls the "Ontological basis". In this basis, the the evolution of the universe proceeds in discrete intervals by permuting the basis vectors hence the cellular automata analogy. This theory explains superposition as a result of us starting the experiment from an incorrect state, which is not the ontological basis but is spanned by it. There is inherent inability to determine the ontological basis in this theory which means that the basis serves as a hidden-variable.

A mathematical theory was put forth by Seth Lloyd in 2005. His theory tries to establish a formalism where fundamental processes are described as pairwise interaction between quantum degrees of freedom. More specifically, the theory describes each quantum computation as a directed, acyclic graph. The vertices of the graph correspond to input states while the edges correspond to quantum wires that move information from place to place. The internal vertices represent quantum logic gates the theory postulates that the structure of spacetime is derived from the the behavior of quantum bits as they move through the computation. The final vertices of the graph correspond to output states. This formulation can generate the results of Regge calculus which can describe a simplified form of general relativity. This formalism has many consequences both theoretical and observational. Theoretically it predicts that there cannot be any length less than the Planck length. Observationally, it predicts that microscopic black holes should evaporate unitary and that quantum fluctuations in the positions and momenta of two stars in a pulsar can give rise to potentially detectable gravitational waves.

Another theory by Paola Zizzi presents the universe as a the result of a quantum mechanical computer. This theory mimics in some aspects and mathematical approaches quantum loop gravity. It is largely based on two postulates: firstly it assumes that space-time is discrete and quantized in plank units. The second postulate is that each quanta of the plank area encodes one qubit calling the universe “qubitsed.” In this way the theory creates a formalism where quantum Boolean functions can describe physical laws. To do that the theory utilizes results and frameworks largely used in quantum loop gravity such as spin networks.

Limitations

Most digital physics theories are by definition deterministic. This is incompatible with the current interpretation of quantum mechanics that includes inherent randomness. To overcome that issue most digital physics theories use a hidden-variables approach. However, most such theories are incompatible with the results of Bell’s theorem. However, theories such as Hooft's cellular automata interpretation that are based around superdeterminism do not necessarily have this limitation. Theories of digital physics that rely on periodic graphs such as Loyd’s are believed to be unfeasible with their current formulation. Such formulation relies on periodic graphs on a Euclidean metric, a requirement that is never satisfied in large scale geometries.