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There’s a fairly obvious connection: Braiding is equivalent to circuits, as shown by Microsoft’s idea for a topological quantum computer. If you start a syste
by zmgsabst 3y ago
There’s a fairly obvious connection:
Braiding is equivalent to circuits, as shown by Microsoft’s idea for a topological quantum computer.
If you start a system braiding, it will build complexity because braiding appears to be non-local — and so the tangle becomes an increasingly complex circuit. The cusp of a black hole is a regime we’d expect such topological effects to accumulate.
AdS/CFT suggests that maybe there’s something deeper to the relationship between braiding in spacetime and quantum systems. Indeed, braiding is one of the few ways we know to generate quantized properties within a continuous geometric setting.
- EddieEngineers 3y agoThis feels like what GPT-4 would say on the Rogan podcast after mushrooms
- aaroninsf 3y agoIf I could give HN comments reddit awards, I'd start with this one.
- jiggawatts 3y agoI asked GPT-4 to pretend it's on shrooms and talking about these topics: https://chat.openai.com/share/b76b8139-4224-4de7-87ce-0e2a3aaa17b6 https://chat.openai.com/share/b76b8139-4224-4de7-87ce-0e2a3a...
- EddieEngineers 3y ago> Let's talk about braid theory. In the quantum world, particles can be thought of as strands, and their interactions as braids. The braids weave and loop around each other, creating intricate patterns, a dance of existence. Each unique pattern, or braid, represents a different state of the particle. The magic is that the braids can't get tangled. That is not too far off hahahaha
- zmgsabst 3y agoChatGPT is wrong in that they do get tangled: https://en.wikipedia.org/wiki/Anyon https://en.wikipedia.org/wiki/Anyon
- didgeoridoo 3y agoObviously!
- uoaei 3y ago> If you start a system braiding, it will build complexity because braiding appears to be non-local — and so the tangle becomes an increasingly complex circuit. The cusp of a black hole is a regime we’d expect such topological effects to accumulate. Would you please expand on the connections between the first and second sentence here? What does braiding 'look' like in topological spacetime?
- zmgsabst 3y agoBraiding is easier in a restricted topology. That’s why research on anyons uses restricted topologies which cross world lines rather than trying to construct 2-knots in a 3+1D spacetime. As you approach a singularity, “around” becomes much shorter than “across”, effectively restricting the space you’re in. Around being shorter than across is why black holes form Einstein rings: the light is taking the shortest path! So if paths cross while going around the singularity, they can’t untangle by moving across the singularity. Hence you have an easier time building topological modes, akin to the restricted topologies for anyons. (Or so my conjecture goes.)
- ChatGTP 3y agoBlackholes and Microsoft...
- sdfghswe 3y agoMeaningless word salad.
- SanderNL 3y agoYour comment raises important points. The non-local nature of braiding in topological quantum computing contrasts with the inherent locality of the AdS/CFT correspondence, prompting us to wonder how these paradigms might coexist. Could braiding and entanglement entropy, both non-local quantum properties, hint at new understandings in the AdS/CFT framework? Additionally, might these braided structures help illuminate the microstate structure of black holes as theorized by string theory? Finally, your insight into quantized properties emerging from continuous geometry recalls how quantum field theory has been linked to knot theory. Can we use these ideas to further probe the quantization of spacetime? Your reflections beautifully intertwine quantum computing, holography, and quantum gravity, encouraging us to weave together these disparate strands in the tapestry of theoretical physics.
- zmgsabst 3y agoMy understanding is that the non-locality is a feature of AdS/CFT: The map from the interior to exterior sends information that may be “local” on the interior across the surface (eg, crossing of a knot). That information isn’t lost… but it can get smeared across the surface. You can even imagine a situation where the surface as a whole contains the crossing information, but the projected shadow is locally a pseudoknot which doesn’t contain that locally for any “interaction”. Hence a local theory on the surface would need to not only be quantized (eg, a theory of crossing numbers), but statistically so (eg, a distribution of pseudoknot resolutions).
- SanderNL 3y agoYou've captured a fascinating aspect of AdS/CFT: how information in the interior, while local, can manifest non-locally on the surface, akin to a tug on a knot rippling through its structure. The pseudoknot example underscores the need for a statistical approach in our understanding of quantum gravity. It brings to mind the question: could there be dynamics in quantum gravity analogous to decoherence in quantum mechanics that can account for this statistical nature?
- CaptainNegative 3y agoI don't understand how this is obvious -- non-locality does not inherently imply that iteration increases complexity. For a concrete not-entirely-trivial counterexample, von Neumann's middle-square method also appears "non-local" (in that every output bit is a function of a majority of the input bits including well-separated ones) but famously tends to converge to short orbits if not a single constant value.
- dustingetz 3y ago“system braiding” - what is the wikipedia or googleable term for this?
- zmgsabst 3y agoI’m not sure there’s a good reference, but a few related topics: https://en.wikipedia.org/wiki/Anyon https://en.wikipedia.org/wiki/Anyon https://en.wikipedia.org/wiki/Topological_quantum_computer https://en.wikipedia.org/wiki/Topological_quantum_computer https://en.wikipedia.org/wiki/Tangle_(mathematics) https://en.wikipedia.org/wiki/Tangle_(mathematics)