A quick introduction to the Wolfram Physics project.

1. Wolfram Physics Project
A Quick Introduction
A Computational Approach to Find a Fundamental Theory of Physics
- Vin Bhalerao

2. Let us first state some definitions, and then move on
to describing the Wolfram Physics project

3. Definition: Cellular Automata
A cellular automaton is a very simple
computation consisting of cells on a
grid, that evolve through a number of
discrete time steps, using rules
based on the states of neighboring
cells.
For example, here is “Rule 30”. The
first part of the picture describes the
rule. The second part shows its
results over a few successive runs.

4. Definition: Graph
A set of vertices, with connections between them. Represented as a set of pairs of
integers corresponding to the vertices.
Example: {{1, 2}, {3, 4}, {2, 4}, {2, 5}, {3, 5}, {4, 5}}

5. Definition: Graph Rules
Graph rules are analogous to
cellular automata rules, but
applied to graphs.
Example rule:
{{x, y, z}} → {{w, w, y}, {w, x,
z}}
Applying the rule over and
over leads to complex graphs
like:

6. Definition: Hypergraph
Generalization of a graph in which a “hyperedge” can join any number of vertices,
not just two, as in an ordinary graph.
Example: {{1, 2, 3}, {3, 4, 5}} (Hyperedge connecting {1, 2, 3} to {3, 4, 5})

7. Hypergraph Rules
Example Rule:
{{x, y, z}} → {{w, w, y}, {w, x,
z}}
Applying the rule over and
over leads to graphs like:

8. Hypergraph Intuition
Hypergraphs generated by some rules resemble physical / biological structures:

9. Wolfram’s Proposal
● The universe is a hypergraph consisting of (of the order of) 10500 vertices.
● The hypergraph started with a single seed vertex. A rule was applied over
and over until it got to the current level of complexity.
● Note that the actual rule itself still remains to be discovered.
● Space at any instant corresponds to a state of this graph at that instant.
● The graph continues to evolve using the rule, and all events in the universe
can be thought of as the rule being applied to various parts of the graph,
leading to new states of the graph.
● The passage of time corresponds to the evolution of the graph through a
sequence of states.
Now let’s look at some interesting details that emerge from this proposal.

10. Computational Reducibility and Irreducibility
● Computational Irreducibility: The answer to certain questions can only be
determined by performing or simulating the computation. There is no shortcut
“formula” or equation to find the answer.
● Computational Reducibility: Sometimes, a formula or equation does allow you
to “jump ahead” and predict the output of a computation before performing it.
● While most of the hypergraph suffers from computational irreducibility, it
contains parts that are reducible. This is what allows us to discover laws /
equations of Physics that work.
● The way we have made progress in physics so far is by following these
“veins” of computational reducibility in the hypergraph. But given irreducibility
in other parts of the graph, we will not be able do this with all of Physics.

11. Causal Invariance and Quantum Mechanics
● The hypergraph rule may get applied to various parts of the graph in various
different orders.
● But some rules have a property called “Causal Invariance”: No matter which
order the rule gets applied in, all such evolutionary paths periodically
converge into common final states.
● This may provide an intuitive way to understand quantum mechanics.
● The different paths through the graph could correspond to the different
quantum states that a particle may be in, and the final state could correspond
to the “classical” state that an observer observes.
● This explains why we experience definite things happening even though
multiple quantum states with different probabilities may exist underneath.

12. Other Insights
The Wolfram proposal provides valuable insights into the following types of
questions:
● Why does our universe appear to have 3 dimensions?
● How do the theory of relativity and curvature of space emerge?
● Where does quantum entanglement come from?
● Why does entropy appear to be increasing?
● Could the Physics discovered by aliens be quite different from our physics?
Interested in learning how Wolfram’s proposal addresses these and other
fascinating questions?

13. Further Learning
● Godel’s incompleteness theorems, Turing’s model of computation etc.:
Hilbert, Godel, and Turing
● Wolfram’s blog post describing his proposal in short: Finally We May Have a
Path to the Fundamental Theory of Physics…and It’s Beautiful
● Wolfram’s lecture describing the proposal: Computation and the Fundamental
Theory of Physics - with Stephen Wolfram
● A long interview with Wolfram including many more details: Lex Fridman
Podcast #124
● The main site of the project: Wolfram Physics