Wolfram Physics Summer School report

[Philip Thrift]

Stephen Wolfram @stephen_wolfram

https://twitter.com/stephen_wolfram/status/1289381082165633026

So exciting to see how quickly things are moving with #WolframPhysics...  Makes me think of quantum mechanics circa 1925.  It's taken me 2 weeks just to summarize part of what got done at our Summer School ...

tech ref: https://www.wolframphysics.org/technical-introduction/

https://writings.stephenwolfram.com/2020/07/a-burst-of-physics-progress-at-the-2020-wolfram-summer-school/

[excerpt]

... 

The starting point for any discussion of quantum mechanics in our models is the notion of multiway systems, and the concept that there can be many possible paths of evolution, represented by a multiway graph. The nodes in the multiway graph represent quantum (eigen)states. Common ancestry among these states defines entanglements between them. The branchial graph then in effect gives a map of the entanglements of quantum states—and in the large-scale limit one can think of this as corresponding to a “branchial space” ...

The full picture of multiway systems for transformations between hypergraphs is quite complicated. But a key point that has become increasingly clear is that many of the core phenomena of quantum mechanics are actually quite generic to multiway systems, independent of the details of the underlying rules for transitions between states. And as a result, it’s possible to study quantum formalism just by looking at string substitution systems, without the full complexity of hypergraph transformations.

A quantum state corresponds to a collection of nodes in the multiway graph. Transitions between states through time can be studied by looking at the paths of bundles of geodesics through the multiway graph from the nodes of one state to another.

In traditional quantum formalism different states are assigned quantum amplitudes that are specified by complex numbers. One of our realizations has been that this “packaging” of amplitudes into complex numbers is quite misleading. In our models it’s much better to think about the magnitude and phase of the amplitude separately. The magnitude is obtained by looking at path weights associated with multiplicity of possible paths that reach a given state. The phase is associated with location in branchial space.

One of the most elegant results of our models so far is that geodesic paths in branchial space are deflected by the presence of relativistic energy density represented by the multiway causal graph—and therefore that the path integral of quantum mechanics is just the analog in branchial space of the Einstein equations in physical space.

To connect with the traditional formalism of quantum mechanics we must discuss how measurement works. The basic point is that to obtain a definite “measured result” we must somehow get something that no longer shows “quantum branches”. Assuming that our underlying system is causal invariant, this will eventually always “happen naturally”. But it’s also something that can be achieved by the way an observer (who is inevitably themselves embedded in the multiway system) samples the multiway graph. And as emphasized by Jonathan Gorard this is conveniently parametrized by thinking of the observer as effectively adding certain “completions” to the transition rules used to construct the multiway system.

It looks as if it’s then straightforward to understand things like the Born rule for quantum probabilities. (To project one state onto another involves a “rectangle” of transformations that have path weights corresponding to the product of those for the sides.) It also seems possible to understand things like destructive interference—essentially as the result of geodesics for different cases landing up at sufficiently distant points in branchial space that any “spanning completion” must pull in a large number of “randomly canceling” path weights.

... 

@philipthrift

[Lawrence Crowell]

I probably need to look at Wolfram’s ideas here a bit. He is making references to these graphs as entanglements. I am a bit unclear on what is meant here. An bipartite entanglement is represented as *-----------* and a tripartite entanglement is a three-way thing, a bit like the bolos the Argentine gauchos throw, where each node is entangled with the other two, but not all three individually. To talk about geodesics is where things get a bit strange. A general relativity = quantum mechanics perspective, which has been something I have worked on since 1988, where spacetime is constructed from large N-tangles, may reference some sort of such correspondence. There are topological obstructions between a bipartite and tripartite entanglement transforming into each other  Yet if quantum entanglements and spacetime topological connection in ER bridges or wormholes are fungible with each other it is then possible to think of an N-tangle or constructed tensor network of entanglements as equivalent to N entangled black holes that contain a common interior.

LC

[Philip Thrift]

To get up to speed on his "summer school" requires first reading the 

    tech ref: https://www.wolframphysics.org/technical-introduction/

to learn the "Wolfram" hypergraph rewriting vocabulary.

Graph/Hypergraph rewriting has been around a long time, now migrating from computer science to physics. Remains to be seen whether Wofram's project gets traction.

The algebras of graph rewriting

https://www.researchgate.net/publication/311737035_The_algebras_of_graph_rewriting

Graph rewriting is Turing-complete, hence sufficiently expressive to encode any other model of computation. It is applied with considerable success in modeling of biological systems (especially protein interaction networks, see [13]). In fact, many models in statistical physics, theoretical chemistry and combinatorics can be seen as particular cases of graph rewriting systems. Most notably, the Heisenberg-Weyl algebra, the combinatorial algebra underlying chemical reaction systems and the theory of the harmonic oscillator, is a particularly simple case of a graph rewriting algebra.

...

More abstractly, the physical concept of worldlines of particles is reflected to a certain extent in the syntax of the rule diagrams through causality constraints bearing on vertices and edges. A given rule diagram represents the “time evolution” of vertices and edges through the course of sequential applications of rewriting steps. In this way, one might indeed interpret rule diagrams as some form of analogues of Feynman diagrams for modeling interactions in particle physics.

@philipthrift