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I've been reading up on quantum entaglement, and I'm still trying to understand exactly how they entangle particles in the lab, and I was wondering if anyone knows if it happens in nature or what natural circumstances would entangle quantum particles

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The word entanglement was first used by Schrödinger to describe states of two or more particles; it is very much a figure of speech. It is just used to indicate a coherent state involving more than one thing, which is such that there are correlations between outcomes of measurement performed on each of them.

 

I'm still trying to understand exactly how they entangle particles in the lab
One common instance is a pair of particles in a so-called singlet state, meaning their intrinsic angular momenta (spins) total zero. IOW they are equal and opposite.

 

I was wondering if anyone knows if it happens in nature or what natural circumstances would entangle quantum particles
Certain atomic orbital states and certain transitions. Indeed the term singlet traces back to spectroscopic data, where the term triplet had also been used. Spectroscopists had noticed associations between some single lines and corresponding groups of three. The triplet state is now interpreted as when the spins are equal (instead of opposite).

 

An important early analysis of entanglement was the EPR paradox, with a pair of particles being emitted so that their momenta must total zero. Einstein came up with it as a way to break the Heisenberg principle for each of the two particles but actually it shows that the system being examined is composed of both. My way of seeing it is that, in order for Einstein's argument to apply, he would need the exact knowledge of position and momentum of the centre of mass of the pair.

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