Substates don't evolve according to Schroedinger equation?

[rodsika]

In the thread "Does Schrödinger's Cat Paradox Suck?" in message #116:

Ken G stated:

"But that's what I'm saying isn't true-- even if we start with pure states for each component of the system, when we couple them, the only pure state is now a combined system. The cat is now a substate of that system, and substates don't evolve according to the Shroedinger equation, so they don't evolve unitarily and they don't become superposition states. There is really no such thing as the state of a part of a system, but we as physicists can make correct predictions by using the concept of a mixed state to treat such substates, or in some special circumstances, we have enough information to treat a substate as a pure or superposition state. That ability is quickly lost for the cat in the box, even if it starts out in an impossible-to-know pure state."

Let's take a simpler example of a group of of electrons and photons. Ken said that if we start with pure states for each component of the system (of say electrons and photons), when we couple them, the only pure state is now a combined system. The electrons are now a substate of that system, and substates don't evolve according to the Shroedinger equation. Is this true?? Since they are all pure state. How can the substate be no longer in pure state? Hope someone else beside Ken G can confirm or refute this. Thanks.

 

[Physics Monkey]

Here is a simple example.

Consider two spins, 1 and 2, in a triplet state of the form $$a_1 |+ + \rangle + a_0 \left(\frac{|+ - \rangle + | - + \rangle}{\sqrt{2}} \right) + a_{-1} | - - \rangle$$. Let the Hamiltonian be a simple magnetic field in the x direction $$H = - g B (S_1^x + S_2^x)$$

Under the action of this Hamiltonian the initially unentangled state $$|+ + \rangle$$ will evolve into a general entangled state like I wrote above. In other words, the spin will precess around the x axis.

From the point of view of spin 1, it begins life in a pure state but later evolves into a mixed state (and later still becomes a pure state again). Thus the evolution of spin 1 cannot be described by unitary evolution. This is true even though the whole system continues to evolve unitarily.

Hope this helps.

 

[rodsika]

Here is a simple example.

Consider two spins, 1 and 2, in a triplet state of the form $$a_1 |+ + \rangle + a_0 \left(\frac{|+ - \rangle + | - + \rangle}{\sqrt{2}} \right) + a_{-1} | - - \rangle$$. Let the Hamiltonian be a simple magnetic field in the x direction $$H = - g B (S_1^x + S_2^x)$$

Under the action of this Hamiltonian the initially unentangled state $$|+ + \rangle$$ will evolve into a general entangled state like I wrote above. In other words, the spin will precess around the x axis.

From the point of view of spin 1, it begins life in a pure state but later evolves into a mixed state (and later still becomes a pure state again). Thus the evolution of spin 1 cannot be described by unitary evolution. This is true even though the whole system continues to evolve unitarily.

Hope this helps.

Thanks. Is this related to decoherence?