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B Is this a good understanding of superposition?

  1. Apr 11, 2017 #1
    Say you flip a coin and place your hand above it before you view it.
    Now the coin is in a super position where it's both heads and tails.
    Once you look at it, you'll know what side is up and the wave function collapse.

    Say you are flipping two coins instead. The odds of both being heads is 25%.
    Both are hidden from you and thus are in a super position state of both heads and tails.
    By viewing one of the coins you find out it's tails and therefore the odds of both being heads is 0%. You've successfully ruined both wave functions by simply viewing one coin. Welcome to entanglement.

    Is this a proper analogy for super position?
     
    Last edited: Apr 11, 2017
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  3. Apr 11, 2017 #2

    PeterDonis

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    A coin is not a good example because it's a macroscopic object. You need to think of a quantum system with a two-dimensional Hilbert space, i.e,. a qubit.
     
  4. Apr 11, 2017 #3
    Yes it is. It's called a Bell state.
    https://en.wikipedia.org/wiki/Bell_state
     
  5. Apr 12, 2017 #4
    As PeterDonis mentioned, there are several features of the quantum cases that do not easily carry over to the classical analogies.

    One thing about two entangled coins is that separately they behave randomly, but together they're not. For example, if you have many pairs of entangle coins, then you could take one of each pair into one room and then flip them, and the other of the pairs into another room and also flip them. In each room the person flipping them will measure a completely random sequence of heads/tails but when they compared their sequence afterwards they will find that their random sequence was exactly identical (or exactly opposite depending on which entangled state they used). This feature is not captured by your classical analogy.

    Also, for both superposition and entangled states, you need to remember that they are only in a superposition in a particular basis. If you take the same state, but measure in a different basis you can see an eigenstate. For example, the state |+> = |0> + |1> is a superposition in the 0/1 basis, meaning you measure randomly 0 or 1 every time, but if you measure in the +/- basis you get the same result every time. The randomness is basis dependent. This is also not captured in your classical analogy.
     
  6. Apr 12, 2017 #5

    PeroK

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    No. When you have your hand over the coin, it is definitely heads or definitely tails. It is not a mixture.
     
  7. Apr 12, 2017 #6
    No, this is a very bad analogy. Extremely bad. Actually, it is a perfect way to misunderstand quantum mechanics from the very beginning.

    As for "entanglement", your analogy is also inappropriate.

    Practically we do not have in a regular macroworld anything analogous to superposition or entanglement. Except may be for two waveves interference - that may somehow model (to some limited extent) what superposition is.
     
  8. Apr 12, 2017 #7

    bhobba

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    Interestingly a critical analysis of the QM formalism shows entanglement is what separates ordinary probability theory and QM:
    https://arxiv.org/abs/0911.0695

    We know that the simplest generalized probability model is ordinary probability theory, but the next simplest is QM and two things separate them.

    1. If you want continuous transformations between so called pure states then you must have QM.
    2, If you want entanglement then you also need QM.

    We understand the QM formalism a lot better these days than when it first came into being about 1925-1926 but what it means, or even if it meaning is an issue - :-p:-p:-p:-p:-p:-p:-p:-p

    Thanks
    Bill
     
  9. Apr 12, 2017 #8

    Nugatory

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    A very long thread hijack that started with the claim that "I do not think that superposition, as I think you mean it, actually exists in the quantum world" has been removed from this thread.

    A number of members had put a fair amount of work into thoughtful responses to that post; if you want a copy of your work please ask any of the mentors.
     
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