Collapse of Wave-Functions: What Does it Mean & How to Visualize It?

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Discussion Overview

The discussion centers on the concept of wave-function collapse in quantum mechanics, exploring its meaning and potential visualizations. Participants engage with theoretical aspects and seek clarification on the topic.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant requests an explanation of wave-function collapse and how to visualize it.
  • Another participant introduces the idea of a Hilbert complex vector space, suggesting that wave-functions can be represented as state vectors, with collapse described as the projection of one vector onto another.
  • A later reply reflects on the concept of projection, proposing a visualization of dominos falling towards a central point to represent the final observation event vector.
  • It is noted that both initial and final state vectors project upon each other through measurement.

Areas of Agreement / Disagreement

The discussion includes various interpretations of wave-function collapse, with no consensus reached on a singular understanding or visualization method.

Contextual Notes

Participants express varying levels of familiarity with the topic, indicating potential gaps in understanding and the need for further exploration of foundational concepts.

dlgoff
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There's an interesting thread on Conciousness in the
Metaphysics & Epistemology forum dealing with the collapse
of wave-functions.

Can someone explain what collapsing a wave function means
and how to visualize it?

Thanks in advance.
 
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Think of a (Hilbert) complex vector space, where each state vector represents an equivalent wavefunction. According to von Neumann, the probability between unitary states is the projection, or collapse, of the one vector upon the other, always less than or equal to one. (Visualize the projection of a hypotenuse upon a leg.)
 
Thanks for the reply. I just finished watching some Feynman lectures and I'm probably not ready (know enough) to ask.

According to von Neumann, the probability between unitary states is the projection, or collapse, of the one vector upon the other[b/]


Oh, I think I "see". Projection. That makes since. The final observatation\event vector has all other possible state vectors projected upon it? I visualize dominos falling in patterns to a central point. I'll look up hypotenuse and try to understand better. Thanks again.
 
Both the initial and final state vectors project singly upon each other by measurement.
 

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