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Forever Entangled

About the most beautiful equation

She said “tell me something beautiful”
And he said “(i∂̸ – m) ψ = 0”

Maybe you already ran into this short romantic story, about “the most beautiful equation of physics”, which would states that “if two systems interact with each other for a certain period of time and then are separated, they can no longer be described as two separate systems but, somehow, they become a single system. In other words, what happens to one of them continues to influence the other, even if miles or light-years away from each other”…

The story is really moving and fascinating, even if it seems to refer to a fatalist side of a relationship. It is not a fake, if that’s what you’re wondering. If anything, it’s just a little simplified version of a moment in history of physics, when it came out that a vacuum is unrecognizable in quantum mechanics: it is not empty. A blow to the physicists who, besides randomness, also had to accept “non locality”, or that a system can affect a distant system despite the fact that they are not communicating. If two systems get entangled in a wave, they will remain so forever, even if they move to the opposite sides of the universe, at a distance at which a signal cannot travel in time to tell one what the other one is doing.

The equation by the British physicist Paul Dirac was proposed in 1928, in an attempt to weld together ideas of Einstein’s relativity with quantum mechanics. In essence, Dirac managed to explain how electrons behave when they travel close to the speed of light. This work went on to explain and predict the existence of antimatter, the idea that every particle has a mirror-image antiparticle. The equation — chose by a group of mathematicians and physicists, and then by the public, through an online poll, as the most beautiful one — is loved both for its elegance and as a symbol of 20th century physics.

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