Causal invariance versus confluence with Jonathan Gorard

Causal invariance is one of the most important concepts in the Wolfram model... and one of the most difficult to capture.
So I really wanted to hear Jonathan Gorard’s take on it.
In this excerpt from our conversation, Jonathan addresses the differences between causal invariance and confluence.
Causal invariance means that regardless of the order in which a rule is applied to the hypergraph, the same events occur, with the same causal relationships between them.
Confluence, on the other hand, is the coming-together of different branches of the multiway graph.
Jonathan explores different ways we might determine whether two nodes, two edges or two hypergraphs are the same, and explains that if we identify nodes and edges according to their causal histories, then causal invariance and confluence become the same idea.
I’ve found myself listening to Jonathan’s explanation of causal invariance over and over to make sense of it, but it’s one of the areas where I’m convinced Jonathan has a unique contribution to make.
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Jonathan Gorard
• Jonathan Gorard at The Wolfram Physics Project www.wolframphysics.org/people...
• Jonathan Gorard at Cardiff University www.cardiff.ac.uk/people/view...
• Jonathan Gorard on Twitter / getjonwithit
• The Centre for Applied Compositionality www.appliedcompositionality.com/
• The Wolfram Physics Project www.wolframphysics.org/
Concepts mentioned by Jonathan
• Causal invariance mathworld.wolfram.com/CausalI...
• Multiway system mathworld.wolfram.com/Multiwa...
• Causal structure en.wikipedia.org/wiki/Causal_...
• Causal Set Theory en.wikipedia.org/wiki/Causal_...
• Directed acyclic graph mathworld.wolfram.com/Acyclic...
• Isomorphic mathworld.wolfram.com/Isomorp...
• Space-like separation phys.libretexts.org/Bookshelv...
• Simultaneity and simultaneity surfaces in relativity en.wikipedia.org/wiki/Relativ...
• Lorentz invariance en.wikipedia.org/wiki/Lorentz...
• Poincaré invariance en.wikipedia.org/wiki/Poincar...
• Conformal invariance en.wikipedia.org/wiki/Conform...
• Diffeomorphism invariance en.wikipedia.org/wiki/Diffeom...
• General covariance en.wikipedia.org/wiki/General...
• Confluence mathworld.wolfram.com/Conflue...
• Church-Rosser Property mathworld.wolfram.com/Church-...
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Prefer to listen to the audio? Search for The Last Theory in your podcast player, or listen at lasttheory.com/podcast/035-ca...
Kootenay Village Ventures Inc.

[@NightmareCourtPictures]

Thank you! This stuff is so important...and interesting it just has me hooked. It's funny cause it was this particular notion of graph isomorphism way back that I knew that when I stumbled on the Wolfram model, that it had to be right because graph isomorphism ensures Lorentz Symmetry (and also a bunch of other symmetries). There is a scientist that had a similiar approach to this made many years ago, named Fotini Markopoulou. (video: Fotini Markopoulou on QUANTIZATION) Her theory was like a precursory kind of idea to Wolfram's (lead me, like a trail of bread crumbs) She's worth looking into, for people that want to dive into this particular idea about networks and graphs, and how they ensure this notion of symmetry that Relativity is built on. Little bit of history, she was pressured out of physics community and they wrote her off... did her pretty dirty, and she just left the field to do her own thing. I even got banned for bringing up one of her lectures on a physics forum too, to try to learn more about networks.

[@lasttheory]

Interesting, thanks for the pointer, I'll take a look at that video. I really want to dig into these other/precursor approaches. And yes, every time I listen to Jonathan I get pulled in deeper and deeper, and get a dozen ideas for further investigation and videos.

[@paulfoss5385]

The reason I give people is "it sometimes makes me sob uncontrollably" which is true, but my main reason is what research says about the health effects, but that would sound judgmental.

[@kostoglotov2000]

Again a brilliant discussion and it makes complete sense. Thanks Mark.

[@lasttheory]

Yes, Jonathan has a habit of talking about these pretty difficult ideas in a way that makes complete sense. Thanks!

[@pipeorgan21]

Thank you for another wonderful and informative talk. Like you I will need to listen to it a number of times for it all to fully sink in. Thanks also for all the Hyperlink references attached which will be very helpful to clarify and better understand the subject. Well done to you and Johnathan.

[@lasttheory]

Thanks, I really appreciate it. Much more to come from my conversation with Jonathan!

[@fabienleguen]

Striking similarities with hashgraph distributed ledger technology. Wolfram hypergraph could maybe borrow some hashgraph tools to label nodes based on their causal history using hash function like sha256. It it very computer efficient and you are garranted to have a unique string of bits identifying your node.

[@lasttheory]

Yes. I wish I knew more about this, but I know Jonathan's well aware of the similarities here. Causality is a strangely relevant topic with wide theoretical and practical import. Thanks for the comment!

[@tommysullivan]

Yes! When I understood git and its blockchainy notion it seemed like a possible implementation for guaranteeing “consistent histories” for scientists who presumably exist as copies across many worlds And also how to explain “spooky action at a distance” - it’s not an instant distant action; it’s entangled particles where people forget that it’s not until later, when scientists compare results of the measurements of remote entangled particles that they find the correlations of up vs down - the comparison after normal evolution of the separated systems within the speed of light - brings together many copies of scientist measurement pairs under normal relativity limits and then lo and behold, when two scientists come together somehow their results always match in the expected way one up one down… how can the universe know how to give those results at that moment in many worlds without some git like history or pointer within each system or node

[@tommysullivan]

I’d have to spend time to say this much better.. I’m really enjoying these videos! You guys are awesome

[@tommysullivan]

In other words, assuming many worlds, we have created two entangled qubits and spatially separate them, when we act locally by measuring, it might not be at that moment that the remote qubit “collapses” but rather when the remote system, or information about a measurement of it travels relativistically back to the other qubit, it could be at that moment that the separated qubits first come back into causal contact that the universe “connects” worldlines of the superpositions of states for system a with compatible “consistent history” worldlines of the superpositions of states of system b. If each state in system a and system b had a git commit history for its branch / identity, then the universe could lazily hook those together in a way where the history within any recombined branch is the same, potentially leading the experimentalist scientists within them to believe they are special and unique and that a spooky collapse occurred

[@tommysullivan]

I dunno how related that is to the causal graph but your comment on the blockchain or version control like identity structure in a multi way system def reminded me of my own theories on explaining apparent collapse and spooky distant action

[@lasttheory]

Thanks Tommy! Yes, action at a distance in general, and quantum entanglement in particular, starts to look a whole lot less "spooky" when you model a universe with a hypergraph that has mostly local edges (i.e. edges connecting nodes that are close in physical space) but can also have non-local edges (i.e. edges connecting nodes that are distant in physical space).

[@tommysullivan]

@@lasttheory ok so a node or neighborhood of nodes in the hypergraph may be close to some other set of nodes by way of small number of arrows to follow between them, but whose physical spaces those sets of nodes represent are far away from each other in spite of the closeness of the arrows in the underlying hypergraph? And is this mechanism the sole channel by which spooky distant actions seem to occur? Or is there some other explanation

[@harriehausenman8623]

Wow! Thanks for the insight. What a neat idea 😃

[@lasttheory]

Thanks Harrie!

[@harriehausenman8623]

@@lasttheory BTW, I really admire your style and intellect. Mr. Wolfram often gets interviewed by people who dont understand the topic and he just starts talking. This is the exact contrary 😉

[@gavinlangley8411]

A simple example of when something can be causally invariant and not exactly equivalent would be good! I can't see how that could possibly be true if each node/edge encodes it's own 'path' and so identity. Maybe if the order is not important in the path/identity such that nodes can eventually become coincide over different evolutions. I guess what I'm asking is invariance-in-respect-to what? Order of the application of rules?

[@lasttheory]

Yes, this is difficult to visualize, and I have a video planned that'll demonstrate casual invariance with actual hypergraphs. But you're right, causal invariance is where the evolution of the hypergraph is the same even if the application of the rule is applied to different places in the hypergraph in a different order. Thanks for the question, Gavin: better (and more visual) answer coming soon!

[@pollywops9242]

I couldnt understand until the blockchain comparance , its fantastic no? We don't have to argue or google or research anymore, reality is in the universal ledger node 😊 (not actually i know but I'm excited that i couldn't understand this video and then it clicked it's my favorite rush thanks)

[@christian6340]

Is the project still active? I can't find any updates on KZbin any longer, nor on any of the websites.

[@lasttheory]

Good question. The Wolfram Physics Project still live on the web, though you're right, it does seem to be less active in terms of putting out new content. Jonathan Gorard is certainly keeping these ideas alive and well at the universities of Cardiff and Cambridge, and expanding the ideas to fields other than physics. He's also continuing to put out really important original research on the Wolfram model. This paper arxiv.org/abs/2303.07282 was published on 10 Mar 2023 and has some truly important results in it. Bottom line is that Stephen Wolfram has a _lot_ going on, but others are focused on moving this forward, for sure.

[@diracflux]

@@lasttheory Thanks, I too was wondering about the state of the project given the lack of updates.

[@christian6340]

It's certainly somewhat worrying that activity has dwindled this past year. I've heard Stephen mention his enthusiasm for the model and the ideas here and there, so I've assumed things are being done quietly. I for one very much miss the live working sessions where one really felt being part of something monumental. I hope they get back to that kind of transparency soon. Thank you for your great content! 🙏

[@lasttheory]

@@christian6340 Yes, I hear you! I think we really need - and Stephen Wolfram, with all his commitments, really needs - others to take this further. Hoping Jonathan Gorard will help inspire people to do so!

[@rayagoldendropofsun397]

What is Quantum Entanglement ?

[@lasttheory]

Good question. It's a difficult thing to explain, since it's at the heart of the weirdness of quantum mechanics. I'll try to give as brief an explanation as I can. Suppose you have two particles in two different states moving in opposite directions from the same starting point to distant places in the universe. And suppose you know from particle physics that one must have, say, spin up and the other spin down, but you don't know which one's spin up and which one's spin down. According to quantum mechanics, it's not that one of the particles has spin up and the other spin down, it's that both particles are in a superposition of the two states. However, when you _observe_ one of the particles, and discover that, say, it has spin up, then you collapse the wavefunction, not only of the spin up particle, but also of the other particle, which is no longer in a superposition of the two states, but now has spin down. So we say that the two particles are _entangled._ Even if, when we observe the spin up particle, the two particles are at opposite ends of the universe, our observation causes the particle at the other end of the universe to instantly collapse into a spin down state. At least, that's the conventional interpretation of quantum mechanics. At the very least, it does seem like there's something non-local going on, i.e. our act of observation at one end of the universe is having an instant effect at the other end of the universe. Hope that helps!

[@rayagoldendropofsun397]

Very helpful, thanks ! The reason for that question is that Entanglement seems more fitting for Bonding Gase's creating solid objects. Is it about ELECTRONS Superposition ?

[@ImNotHereAnymore09876]

Listening to the lecture and spacing out. (Dozing off.) Idfk: Metaphorical FUBAR: (Sounds nifty, but it makes me dizzy to think about.) Sounds similar to planetary rotation through space as the solar system travels through space in a graph, but as wave patterns. Similar to a braided steel cable. Then spun around in a toroidal motion to run it back to itself. Synchronous motion causing the pieces to form an alignment and reassimilate. I'm tired, if this doesn't make sense don't be shocked. Ultimately causing an endless output of... ???? -Random things my brain comes up with.....-

[@ktrethewey]

Sadly, the introduction of Jonathan into your videos detracts from the excellent teaching level you yourself have adopted. Mark, you should stick to doing these explanations yourself.

[@lasttheory]

Right, thanks for the feedback, Ken. Jonathan can be hard to follow, I know! My plan is to do my own videos on all these topics, e.g. causal invariance, which I hope will explain them from first principles. It's going to take a while, but I'll get there!

[@gaving7127]

I’ve been really enjoying hearing Jonathan’s explanations, I think having both Mark and Jonathan has been great. I’d love to see Mark do an interview format with Jonathan and get some back and forth.