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“Einstein said that if quantum mechanics were correct then the world would be crazy. Einstein was right — the world is crazy.”― Daniel M. Greenberger
The Einstein-Podolsky-Rosen (EPR) paradox is like a puzzle proposed by Albert Einstein, Boris Podolsky, and Nathan Rosen. They thought that quantum mechanics didn’t tell the whole story about how the world works. In 1935, in a paper called “Can Quantum-Mechanical Description of Physical Reality be Considered Complete?” they said there could be hidden things we don’t know about, and maybe we can come up with a theory that includes these hidden parts. Figuring out this puzzle is important for understanding quantum mechanics better.
In this thought experiment, there are two particles prepared in a special connected way known as an entangled state. Einstein, Podolsky, and Rosen noticed that in this state if you measure the position of the first particle, you can predict the result of measuring the position of the second particle, and the same goes for momentum. They argued that nothing you do to the first particle can instantly change the other one. This is becauseit would mean information travels faster than light, which goes against the theory of relativity.
Einstein, Podolsky, and Rosen suggested a rule that says if we can be certain about a physical thing without messing with it, that thing must be real.
They used this rule to say that the second particle should already have a definite position and momentum, even before we check them. However, in quantum mechanics, it’s believed that you can’t know both the position and momentum of a particle at the same time. So, this led them to argue that quantum theory is incomplete in describing how the world works.