Wigners Theorem And Linerarity

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The discussion centers on Wigner's Theorem and its implications for the linearity of quantum mechanics (QM) evolution. Leonard Susskind's lecture suggests that the linear evolution is an axiom of QM, but participants clarify that it is a consequence of Wigner's Theorem combined with Stone's theorem. These theorems rely on specific axioms, including the preservation of probability distributions during time evolution and the requirement that the state space is a linear topological space. The conversation highlights the foundational aspects of quantum mechanics and the significance of these theorems in understanding its linearity.

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  • Understanding of Wigner's Theorem
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With reference to the following lecture by Leonard Susskind :
http://www.newpackettech.com/Resources/Susskind/PHY30/LectureRv9_Video_Lec7.htm

Someone asked why evolution is linear - I was waiting for him to say - Wigner's Theorem implied it. But no - he said there is no deeper explanation - its simply an axiom of QM.

Anyone got any idea what he was getting at? Or am I mistaken and it really is a separate axiom?

BTW - superb lecture.

I believe he is releasing the lectures as a series of books. Already ordered the classical physics one and can hardly wait for the others.

Thanks
Bill
 
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The evolution is a consequence of Wigner's theorem + Stone's theorem, which do indeed depend on some hypotheses (axioms as you may call them): preservation of probability distributions under time evolution and the state space being a linear topological space.
 

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