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

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In summary, there is an interesting thread on the Metaphysics & Epistemology forum discussing the collapse of wave-functions. The collapse is explained by the projection of one vector upon another, with the probability always being less than or equal to one. This can be visualized as dominoes falling in patterns towards a central point. The concept is further explained by von Neumann's theory and the use of complex vector spaces.
  • #1
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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  • #2
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.)
 
  • #3
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.
 
  • #4
Both the initial and final state vectors project singly upon each other by measurement.
 

What is the collapse of wave-functions?

The collapse of wave-functions refers to the phenomenon in quantum mechanics where the probability distribution of a system's possible states changes suddenly and unpredictably upon measurement.

Why does the collapse of wave-functions occur?

The collapse of wave-functions occurs due to the act of observation or measurement. When a measurement is made on a quantum system, the wave-function collapses to a single state, known as the "eigenstate", corresponding to the observed measurement.

How is the collapse of wave-functions related to the uncertainty principle?

The uncertainty principle states that it is impossible to know both the position and momentum of a particle with absolute certainty. The collapse of wave-functions is a manifestation of this principle, as the measurement of one variable (e.g. position) causes the wave-function to collapse, making the measurement of the other variable (e.g. momentum) uncertain.

Can the collapse of wave-functions be visualized?

The collapse of wave-functions cannot be visually observed, as it occurs at the quantum level and is a probabilistic phenomenon. However, there are visualizations and simulations that can help us understand this concept, such as the double-slit experiment and the Schrödinger's cat thought experiment.

What are the implications of the collapse of wave-functions?

The collapse of wave-functions has significant implications for our understanding of reality and the behavior of particles at the quantum level. It challenges our classical understanding of cause and effect, and has led to the development of various interpretations of quantum mechanics, such as the Copenhagen interpretation and the many-worlds interpretation.

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