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 -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/63a030bc-fc5d-4fa0-98f7-95e174416025n%40googlegroups.com.
