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
On Sunday, August 2, 2020 at 3:09:09 PM UTC-5 Lawrence Crowell wrote:
> 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
>
> On Sunday, August 2, 2020 at 6:27:06 AM UTC-5 [email protected] wrote:
>
>> 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
>>
>
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