B Time Crystals & Spin: Engineering a New Reality?

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Were the time crystals developed in the 2010s looping in their quantum spin, or their linear momentum?
In 2016, https://en.wikipedia.org/w/index.php?title=Norman_Yao&action=edit&redlink=1 et al. proposed a different way to create discrete time crystals in spin systems. From there, Christopher Monroe and Mikhail Lukin independently confirmed this in their labs. Both experiments were published in Nature in 2017. In 2019 it was theoretically proven that a quantum time crystal can be realized in isolated systems with long-range multi-particle interactions (Wikipedia)

In these experiments, was it the quantum spin that underwent the looping time crystal phenomenon, or was it the actual linear motion which underwent this mechanism where it would repeat in time? If not, could we engineer a time crystal which loops over time not in linear motion, but with regards to its spin?
 
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It is the quantum spin that undergoes the looping time crystal phenomenon. It is not possible to engineer a time crystal which loops over time with regard to its spin, as this would violate the laws of quantum mechanics. Instead, the experiments used long-range multi-particle interactions to create a system where the spins display a periodic behavior over a long period of time.
 
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Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated... Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/ by @RUTA
Is it possible, and fruitful, to use certain conceptual and technical tools from effective field theory (coarse-graining/integrating-out, power-counting, matching, RG) to think about the relationship between the fundamental (quantum) and the emergent (classical), both to account for the quasi-autonomy of the classical level and to quantify residual quantum corrections? By “emergent,” I mean the following: after integrating out fast/irrelevant quantum degrees of freedom (high-energy modes...

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