Information Theory on Wave Function Collapse

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Discussion Overview

The discussion revolves around the relationship between wave function collapse, superposition, and information theory, particularly focusing on the concepts of entropy and energy associated with quantum states. Participants explore the implications of these concepts in the context of measurements and the nature of quantum states.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions how information is related to different eigenstates and what happens to the information during wave function collapse, suggesting a connection to Schrödinger's equation.
  • Another participant explains that both eigenstates and superpositions are considered pure states with zero entropy, emphasizing that the choice of basis affects the interpretation of superpositions.
  • There is a discussion about the process of collapse during measurements, where a pure state transitions to a classical probabilistic mixture, leading to increased entropy, but the mechanism for selecting a single outcome remains unclear.
  • A participant seeks clarification on whether energy is associated with different superpositions and questions where that energy might go, indicating a desire for mathematical or logical explanations.
  • Another participant notes that arbitrary states can be expressed as superpositions of energy eigenstates, pointing out that energy is not well-defined in such cases and that average values change during measurement interactions.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the relationship between energy and superpositions, and there is no consensus on how information and energy interact in the context of wave function collapse.

Contextual Notes

The discussion highlights limitations in understanding the mechanisms behind wave function collapse and the definitions of energy in superposition states, as well as the dependence on measurement interactions.

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I was trying to understand wave function collapse in terms of superposition, but I ran into some problems when relating back to information theory/entropy. It is given in the definition of information in terms of entropy energy is needed to transfer information. That is something we have always been taught, but if that means information is associated with different eigenstates, what happens to the information associated with different collapse forms of a particle? Is it that there is no energy associated with the information of the superpositions of a particle, but if that were the case, how could those states exist in the first place? Perhaps the answer is in Schrödinger's equation. Any help is welcomed! Thanks.
 
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Time_ said:
That is something we have always been taught, but if that means information is associated with different eigenstates, what happens to the information associated with different collapse forms of a particle?
Eigenstates of an observable and superpositions of such eigenstates are not different regarding their (von Neumann) entropy: both are so-called pure states and have zero entropy. When you think about superpositions you should keep in mind that every state can be a superposition of states. This is just a question of which basis you chose. Physically, this corresponds to which observable you are going to measure.

Collapse only occurs during measurements, where additional degrees of freedom are introduced. The interaction with the measurement apparatus leads the initially pure state to a classical probabilistic mixture of states, which has a higher entropy (this is called "decoherence"). However, there is no universally accepted mechanism how a single outcome is chosen from this mixture. So I'm not sure, if there is a satisfying answer to your question.
 
Alas I feel the same way, I cannot find definitive answer, however, could you answer this, mathematically, or logically? Is there energy associated with the different superpositions? If so, where does that energy go? I have a thought, but I'd like to hear others opinions first.
 
Time_ said:
Is there energy associated with the different superpositions? If so, where does that energy go?
What do you mean by the first question? Arbitrary states |ψ> can be decomposed in a superposition of energy eigenstates. If you have such a superposition, the energy of the state is not well-defined. The best you can do is to talk about average values. During a measurement, this average value changes due to the interaction with the measurement apparatus. So the apparatus is where the "energy goes".
 

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