Wigners Theorem And Linerarity

[bhobba]

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

 

[dextercioby]

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.