Wigners Theorem And Linerarity

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This means that the evolution is linear, there is no deeper explanation for it. Leonard Susskind, a renowned physicist, discussed this in his lecture and is releasing the lectures as a series of books. The first one, on classical physics, is already available for purchase.
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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.
 

1. What is Wigner's Theorem?

Wigner's Theorem is a mathematical theorem that states that any symmetry present in a physical system will correspond to a symmetry in its wave function. In other words, if a system has a certain symmetry, its wave function will also exhibit that same symmetry.

2. What is linearity in the context of Wigner's Theorem?

In this context, linearity refers to the property that the wave function of a physical system must satisfy in order for Wigner's Theorem to hold. This means that the wave function must be able to be expressed as a linear combination of basis states, which allows for the system's symmetries to be properly accounted for.

3. How does Wigner's Theorem relate to quantum mechanics?

Wigner's Theorem is a foundational principle in quantum mechanics as it helps to explain the relationship between symmetries and the wave function of a physical system. It also has applications in the study of quantum measurements and the concept of observables in quantum mechanics.

4. Can Wigner's Theorem be applied to all physical systems?

Yes, Wigner's Theorem is a general principle that applies to all physical systems, regardless of their size or complexity. It is a fundamental aspect of quantum mechanics and is used in various fields of physics, including quantum chemistry and solid-state physics.

5. Are there any limitations to Wigner's Theorem?

While Wigner's Theorem is a powerful and general principle, it does have some limitations. For example, it does not account for certain types of symmetries, such as time-reversal symmetry. It also does not apply to systems with infinite degrees of freedom, such as continuous systems, without additional modifications.

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