objects on Earth. The more matter in space-time (such as stars, galaxies, and quasars), the greater its fabric bends and the more pronounced the effect.

This approach to Mach is compatible with Einstein’s standard theory but goes considerably further. In a mathematical sense it extends general relativity to complex numbers, opening the way to all sorts of wavelike phenomena that were formerly the purview of quantum mechanics. In a physical sense the idea that a particle is a wave—whose behavior depends on the rest of the matter in the universe—links the local to the remote. This result came as a surprise to both quantum and classical physicists familiar with the approach, since it shows a way of bridging the two topics. More work is under way to see if the bridge represents a broad boulevard or just a catwalk.

Ancient mariners used to steer by the stars—relying on those distant beacons to help them sail across uncharted seas. If Mach’s principle is true, the stars guided their vessels in subtler ways than they ever could have imagined.

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