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Trying to wrap my brain around entanglement-superposition

  1. May 20, 2013 #1
    Could entangled superposition be something like the state of a mutiple choice question where 1)there are two or more options for answers (...the nature of a multiple choice question:approve:) before an answer is chosen by the observer-test taker and 2) the state of the question once the observer/test-taker answers the question. Before the question is answered the answers are in a kind of superposition - possibilities with accompanying probability. Once answered, the results take on a their differentiated "entangled" state... the one answer "chosen" determines the state of the other options - "not chosen". In binary quantum terms, "chosen" =1 , "not chosen" =0.

    In this way the test taker (observer) defines the identity of the answers rather than the designer of the question...i.e. the focus of the answer is on which answer is chosen, not the content of the answer or even if it is right or wrong.

    What think thee?
     
  2. jcsd
  3. May 20, 2013 #2

    bhobba

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    What you are describing is classical probability theory. The possible outcomes are the answers to questions and are called pure states. When the outcome could be a randomly selected pure state that is called a mixed state - that is the questions before an answer is selected. QM is different - the pure states themselves can give different pure states as outcomes if observed (this is called a superposition) - classical probability theory cant do this. If you have a pure state - then that's it - you can't observe it to get another pure state. Every time you observe it you get exactly the same pure state.

    Here is an example. Before you throw a dice the outcome is the number 1 to 6 with a probability of 1/6th. That's a mixed state. Throw it and you get 1 to 6. Lets say you get 1. Doesn't matter what you do unless you throw the dice again it will be 1 when you observe it.

    Now lets look at QM and see what happens in the famed Stern-Gerlach experiment:
    http://en.wikipedia.org/wiki/Stern–Gerlach_experiment

    We measure the spin in say the x direction and you get two possible values - called spin up and spin down - suppose it's up. Its in a pure state whose x direction of spin is up. Measure it again and you get the same value - fine. This is exactly the same as the dice situation - sweet. Now measure the the spin in another direction say y and you again get two values - up or down. Say its up so its in a pure state in the y direction of up. Great. But now measure the spin in the x direction - if it was like classical probability theory you should get up. But that's not what happens - you do not get the same value - sometimes its up and sometimes its down. Somehow measuring it in a different direction caused the value in the first direction to change. This is not like your answering question analogy. It would be like you answered question 1 then answered question 2 and somehow that changed the answer to question 1. Pure states do not remain 'fixed' like in classical probability theory.

    QM also has mixed states - which are randomly selected pure states - but it has the added feature observations can change pure states into other pure states.

    Check out:
    http://arxiv.org/pdf/quant-ph/0101012v4.pdf
    http://arxiv.org/pdf/0911.0695v1.pdf

    Thanks
    Bill
     
    Last edited: May 20, 2013
  4. May 20, 2013 #3
    I appreciate the feedback and references Bill. I'm hungry to learn more, so you gave me more to chew on.
    Thanks
    Dave
     
  5. May 21, 2013 #4
    Just to underline Bill's point a bit: there is no classical analogue of entanglement. I know it's helpful when learning someone to try to draw analogies between what you're studying and what you already know, but such analogies are very precarious in quantum mechanics. Some of the key ideas in QM, like entanglement, aren't like anything else you're already familiar with. So, the answer to, "Is entanglement like X?" (where X is some everyday thing) is always going to be no.
     
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