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I Are superposition, uncertainty principle, duality the same?

  1. Sep 28, 2016 #1

    eow

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    Are quantum superposition, heisenberg uncertainty principle, wave/particle duality the same thing? Do they imply each other?

    They all seem the same to me like the wave-like nature of photons -> superposition, and superposition means there's not definite position -> uncertainty principle.

    Sorry if it's a dumb question. I have no formal physics education (trying to learn on my own).
     
  2. jcsd
  3. Sep 28, 2016 #2

    DrClaude

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    Staff: Mentor

    No, they are different things.

    First, there is no wave-particle duality. That's an outdated concept fro the beginnings of quantum mechanics. Quantum objects have properties that can't be reduced to simple classical concepts such as wave and particle.

    Second, quantum superpositions come about because the the Schrödinger equation is linear: any linear combination of solutions is itself a solution to the Schrödinger equation. Therefore, quantum systems can be in superpositions of states, where is state is a solution to the time-independent Schrödinger equation. Note that there is nothing special about superpositions, since they correspond to different point of views. If a photon is left-circularly polarized, that's a single state, but also a superposition of linear polarizations along x and y. Likewise, a photon linearly polarized along x is in a superposition of left and right circular polarizations.

    The Heisenberg uncertainty principle comes from the fact that different observables correspond to operators that do not commute. This means that both attributes can't be defined at the same time. For example, if an electron is in a spin state pointing along z, you can't say anything about its spin along x or y.
     
    Last edited: Sep 28, 2016
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