Stephen Wolfram, inventor of the Wolfram computational language and the Mathematica software, announced that he may have found a path to the holy grail of physics: A fundamental theory of everything. Even with the subjunctive, this is certainly a powerful statement that should be met with some skepticism.

What is considered a fundamental theory of physics? In our current understanding, there are four fundamental forces in nature: the electromagnetic force, the weak force, the strong force, and gravity. Currently, the description of these forces is divided into two parts: General Relativity (GR), describing the nature of gravity that dominates physics on astronomical scales. Quantum Field Theory (QFT) describes the other three forces and explains all of particle physics.

An overview of particle physics by Headbomb [CC-BY-SA 3.0]Up to now, it has not been possible to unify both General Relativity and Quantum Field Theory since they are formulated within different mathematical frameworks. In particular, treating gravity within the formalism of QFT leads to infinite terms that cannot be canceled out within the generally accepted framework of renormalization. The two most popular attempts to deliver a quantum mechanical description of gravity are String Theory and the lesser know Quantum Loop Gravity. The former would be considered a fundamental theory that describes all forces in nature while the latter limits itself to the description of gravity.

Apart from the incompatibility of QFT and GR there are still several unsolved problems in particle physics like the nature of dark matter and dark energy or the origin of neutrino masses. While these phenomena tell us that the current Standard Model of particle physics is incomplete they might still be explainable within the current frameworks of QFT and GR. Of course, a fundamental theory also has to come up with a natural explanation for these outstanding issues.

Stephen Wolfram is best known for his work in computer science but he actually started his career in physics. He received his PhD in theoretical particle physics at the age of 20 and was the youngest person in history to receive the prestigious McArthur grant. However, he soon left physics to pursue his research into cellular automata which lead to the development of the Wolfram code. After founding his company Wolfram Research he continued to develop the Wolfram computational language which is the basis for the Wolfram Mathematica software. On the one hand, it becomes obvious that Wolfram is a very gifted man, on the other hand, people have sometimes criticized him for being an egomaniac as his brand naming convention subtly suggests.

In 2002, Stephen Wolfram published his 1200-page mammoth book A New Kind of Sciencewhere he applied his research on cellular automata to physics. The main thesis of the book is that simple programs, in particular the Rule 110 cellular automaton, can generate very complex systems through repetitive application of a simple rule. It further claims that these systems can describe all of the physical world and that the Universe itself is computational. The book got controversial reviews, while some found that it contains a cornucopia of ideas others criticized it as arrogant and overstated. Among the most famous critics were Ray Kurzweil and Nobel laureate Steven Weinberg. It was the latter who wrote that:

Wolfram [] cant resist trying to apply his experience with digital computer programs to the laws of nature. [] he concludes that the universe itself would then be an automaton, like a giant computer. Its possible, but I cant see any motivation for these speculations, except that this is the sort of system that Wolfram and others have become used to in their work on computers. So might a carpenter, looking at the moon, suppose that it is made of wood.

The Wolfram Physics Project is a continuation of the ideas formulated in A New Kind of Science and was born out of a collaboration with two young physicists who attended Wolframs summer school. The main idea has not changed, i.e. that the Universe in all its complexity can be described through a computer algorithm that works by iteratively applying a simple rule. Wolfram recognizes that cellular automata may have been too simple to produce this kind of complexity instead he now focuses on hypergraphs.

In mathematics, a graph consists of a set of elements that are related in pairs. When the order of the elements is taken into account this is called a directed graph. The most simple example of a (directed) graph can be represented as a diagram and one can then apply a rule to this graph as follows:

The rule states that wherever a relation that matches {x,y} appears, it should be replaced by {{x ,y},{y,z}}, wherez is a new element. Applying this rule to the graph yields:

By applying this rule iteratively one ends up with more and more complicated graphs as shown in the example here. One can also add complexity by allowing self-loops, rules involving copies of the same relation, or rules depending on multiple relations. When allowing relations between more than two elements, this moves from graphs to hypergraphs.

How is this related to physics? Wolfram surmises that the Universe can be represented by an evolving hypergraph where a position in space is defined by a node and time basically corresponds to the progressive updates. This introduces new physical concepts, e.g. that space and time are discrete, rather than continuous. In this model, the quest for a fundamental theory corresponds to finding the right initial condition and underlying rule. Wolfram and his colleagues think they have already identified the right class of rules and constructed models that reproduce some basic principles of general relativity and quantum mechanics.

A fundamental problem of the model is what Wolfram calls computational irreducibility, meaning that to calculate any state of the hypergraph one has to go through all iterations starting from the initial condition. This would make it virtually impossible to run the computation long enough in order to test a model by comparing it to our current physical Universe.

Wolfram thinks that some basic principles, e.g. the dimensionality of space, can be deduced from the rules itself. Wolfram also points out that although the generated model universes can be tested against observations the framework itself is not amenable to experimental falsification. It is generally true that fundamental physics has long decoupled from the scientific method of postulating hypotheses based on experimental observations. String theory has also been criticized for not making any testable predictions. However, String theory historically developed from nuclear physics while Wolfram does not give any motivation for choosing evolving hypergraphs for his framework. However, some physicists are thinking in similar directions like Nobel laureate Gerard tHooft who has recently published a cellular automaton interpretation of quantum mechanics. In addition, Wolframs colleague, Jonathan Gorard, points out that their approach is a generalization of spin networks used in Loop Quantum Gravity.

On his website, Wolfram invites other people to participate in the project although it is somehow vague how this will work. In general, they need people to work out the potential observable predictions of their model and the relation to other fundamental theories. If you want to dive into the topic in depth there is a 448-page technical introduction on the website and they have also recently started a series of livestreams where they plan to release 400 hours of video material.

Wolframs model certainly contains many valuable ideas and cannot be simply disregarded as crackpottery. Still, most mainstream physicists will probably be skeptical about the general idea of a discrete computational Universe. The fact that Wolfram tends to overstate his findings and publishes through his own media channels instead of going through peer-reviewed physics journals does not earn him any extra credibility.

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Wolfram Physics Project Seeks Theory Of Everything; Is It Revelation Or Overstatement? - Hackaday