Understanding Interference Between Spin States

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Discussion Overview

The discussion revolves around the concept of interference between spin states, particularly in the context of quantum decoherence and superposition. Participants explore the conditions under which interference can occur, especially regarding orthogonal states like up and down spin states.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant expresses confusion about how interference can occur between orthogonal spin states, suggesting that interference is only possible if the states are not orthogonal.
  • Another participant distinguishes between interference and coherence, stating that while orthogonal states cannot directly interfere, they can exist in a coherent superposition that allows for interference under certain conditions.
  • A request for an example of a transition that could lead to interference between orthogonal states is made, indicating a desire for clarification on the concept.
  • A further explanation is provided regarding transition probabilities, noting that if the phases of the states are randomized, only certain terms contribute, while coherent states allow for additional cross terms that enable interference.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the nature of interference between orthogonal states, with some suggesting that coherence allows for interference while others remain uncertain about the implications of this distinction.

Contextual Notes

The discussion highlights the complexity of quantum states and the conditions necessary for interference, with participants acknowledging the need for further examples and clarifications regarding transitions and coherence.

metroplex021
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I'm reading about decoherence, and I've found I don't understand the most basic thing. Interference between terms in a superposition is only possible, I thought, if the two terms are not orthogonal. But then how can up and down spin states (with respect to some direction) interfere with one another?!

thanks!
 
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It would help to hear more about the context, but I think you have to make a distinction between interference and coherence. If two states |ψ1> and |ψ2> are orthogonal they can't directly interfere with each other. Nevertheless they may be in a coherent superposition α|ψ1> + β|ψ2>, meaning there remains the possibility of interference between them following a transition to another state |φ>.
 
Thank you... I am fundamentally confused! Could you maybe give an example of such a transition that could lead to inference between orthogonal states?
 
What I'm suggesting is that when you ask for the transition probability to a state |φ>, if the phases of |ψ1> and |ψ2> have been randomized you'll just get two terms, αα*<φ|ψ1><ψ1|φ> + ββ*<φ|ψ2><ψ2|φ>. But if the states are coherent you'll get as well the cross terms αβ*<φ|ψ2><ψ1|φ> + α*β<φ|ψ1><ψ2|φ>. I may be off base, but I think this relates to what you're asking.
 

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