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Why would'nt this work?
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Yes, the speed of sound in an object is how fast neighboring atoms can react to each other, and not only is that information (therefore limited to C already) but specifically it's the electric field caused by the electrons that keep atoms certain distances from each other and push each other around. And changes in the electric/magnetic fields are famously carried by photons (light) specifically - so even in bulk those changes move at the speed of light at most