Captions provided by CCTubes – Captioning the Internet! If you have perfect knowledge of every single particle in the universe, can you use the laws of physics to rewind all the way back to the Big Bang? Is the entire history of the universe perfectly knowable? Or has information somehow lost along the way?
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Noether’s Theorem and The Symmetries of Reality
The laws of physics are equations of motion. They are mathematical rules that dictate how systems evolve in time. Newton’s equations for classical mechanics, Maxwell’s equations for electromagnetism, and the Schrodinger equation for quantum mechanics. These laws can be used to predict how the universe will evolve into the future. They are deterministic; perfect knowledge of a system in the present perfectly predicts how the system will change in the next instant, and the instant after that, ad infinitum. But determinism in the forward-time direction does NOT guarantee that the same laws can perfectly predict the past. And yet this sort of deterministic symmetry – time-reversal symmetry – is essential for information itself to be conserved. Today we learn why conservation of information is such a fundamental requirement of quantum mechanics. In a future episode we’ll see how this law might be broken by black holes.
Here’s that fun proof that independent quantum states can’t evolve into the same quantum state while preserving unitarity! Apologies for the unavoidable technical notation, but a quick college course in introductory quantum mechanics will get you up to speed in no time 😛
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Written by Graeme Gossel and Matt O’Dowd
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