Abstract
Microscopic speed limits that constrain the motion of matter, energy, and information abound in physics, from the “ultimate” speed limit set by light to Lieb-Robinson speed limits in quantum spin systems. In addition to these state-independent speed limits, systems can also be governed by emergent state-dependent speed limits indicating slow dynamics arising, for example, from slow low-energy quasiparticles. Here we describe a different kind of speed limit: a situation where complex information/entanglement spreads rapidly, in a fashion inconsistent with any speed limit, but where simple signals continue to obey an approximate speed limit. If we take the point of view that the motion of simple signals defines the local spacetime geometry of the universe, then the effects we describe show that spacetime locality can be compatible with a high degree of non-local interactions provided these are sufficiently chaotic. With this perspective, we sharpen a puzzle about black holes recently raised by Shor and propose a schematic resolution.
Highlights
Cuts, wormholes of a sort, through which, say, photons can propagate
If the local structure of spacetime were defined in terms of the propagation of simple signals, it might be the case that non-local connections would be ineffective at propagating such signals in a detectable form
We argue that the physical effects described here provide a skeleton for a resolution of that puzzle by showing that rapid non-local entanglement growth can coexist with speed limits for simple signals
Summary
A toy model of the effect is shown in figure 1. With the help of the LC model, we show the entanglement growth rate is proportional to the number of degrees of freedom, indicating a much faster scrambling ability for non-local signals. There is a physical setup where simple signals in L obey the ordinary rules of local causality, up to a small attenuation induced by C Such signals do have a small amplitude to propagate non-locally, but this is hard to distinguish from the thermal noise being emitted by C into L. We will argue that this sort of non-locality at the stretched horizon is necessary, at least for black holes similar to those in Anti de Sitter spacetime, connecting to a recent discussion due to Shor It has long been known in simple models of quantum gravity that non-locally interacting “matrix” degrees of freedom somehow generate local dynamics, but the precise mechanisms remain mysterious. Our calculations complete the survey of the entanglement dynamics property of the semi-holographic Fermi liquid
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