Assuming that the particles interact with the object, but not with one another, the accuracy of such measurements grows in proportion to the number of particles in the beams, N. By allowing such particle interactions, scientists have now demonstrated a way to break this so-called Heisenberg limit. They used a beam of photons to measure the small magnetic field produced by a gas made up of 1m ultra-cold rubidium atoms. Normally, the spin of each photon would rotate by a certain amount, thanks to its interactions with the magnetic field of the atoms. But the frequency of the photons was chosen so that the photons also interacted with each other when they were in the gas, so that the presence of one photon altered the way a second behaved. These interactions led to a measurement accuracy that grew in proportion to N3/2 – greater than Heisenberg’s limit

i wish i understood this better, but how is that possible?

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