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Quantum foam suggests spacetime is not smooth from "summary" of The Fabric of the Cosmos by Brian Greene

Quantum foam is a concept that arises from the marriage of quantum mechanics and general relativity. It suggests that at extremely small scales, smaller even than the subatomic realm, spacetime is not the smooth, continuous fabric that we typically imagine. Instead, it is a seething cauldron of quantum fluctuations, a bubbling brew of energy fluctuations that pop in and out of existence on timescales so short that they cannot be observed directly. In this frothy concoction, the very structure of spacetime itself is in a state of constant flux and turmoil. Virtual particles, particles and antiparticles, continuously materialize and annihilate, creating a frenetic dance of creation and destruction. This frenzied activity gives rise to a fundamentally uncertain and dynamic nature of spacetime at the smallest of scales. The implications of quantum foam are profound. If spacetime is not smooth and continuous, as it appears on large scales, but rather is a turbulent sea of quantu...
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    The Fabric of the Cosmos

    Brian Greene

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