Superposition always exists, 2.2.1

Decoherence and the Collapse, 2.1 | Quantum decoherence 7.2.1

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But wait! Doesn’t this mean that the “consciousness causes collapse” theory is wrong? The spin bit was apparently able to cause collapse all by itself, so assuming that it isn’t a conscious system, it looks like consciousness isn’t necessary for collapse! Theory disproved!

No. As you might be expecting, things are not this simple. For one thing, notice that this ALSO would prove as false any other theory of wave function collapse that doesn’t allow single bits to cause collapse (including anything about complex systems or macroscopic systems or complex information processing). We should be suspicious of any simple argument that claims to conclusively prove a significant proportion of experts wrong.

To see what’s going on here, let’s look at what happens if we don’t assume that the spin bit causes the wave function to collapse. Instead, we’ll just model it as becoming fully entangled with the path of the particle, so that the state evolution over time looks like the following:

\displaystyle{|O, \uparrow \rangle \to \frac{1}{\sqrt{2}} |A, \downarrow \rangle + \frac{1}{\sqrt{2}} |B, \uparrow \rangle \to \frac{1}{\sqrt{2}}\sum_i \left( \alpha_i | i, \downarrow \rangle + \beta_i |i, \uparrow \rangle \right) = | \Psi \rangle}

The interference has vanished, even though we never assumed that the wave function collapsed!

And all that’s necessary for that is environmental decoherence, which is exactly what we had with the single spin bit!

A particle can be in a superposition of multiple states but still act as if it has collapsed!

You might be tempted to say at this point: “Well, then all the different theories of wave function collapse are empirically equivalent! At least, the set of theories that say ‘wave function collapse = total decoherence + other necessary conditions possibly’. Since total decoherence removes all interference effects, the results of all experiments will be indistinguishable from the results predicted by saying that the wave function collapsed at some point!”

But hold on! This is forgetting a crucial fact: decoherence is reversible, while wave function collapse is not!!!

Now the two branches of the wave function have “recohered,” meaning that what we’ll observe is back to the interference pattern!

— Decoherence is not wave function collapse

— MARCH 17, 2019

— SQUARISHBRACKET

— Rising Entropy

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This is the original link:

Decoherence is not wave function collapse

In case the original link does not work, use the Internet Archive version:

https://web.archive.org/web/20210124095054/https://risingentropy.com/decoherence-is-not-wave-function-collapse/

— Me@2021-01-24 07:14:50 PM

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A particle can be in a superposition of …

Note that it is not that the particle is in a superposition. Instead, it is that the system is in a superposition.

— Me@2021-01-24 07:16:49 PM

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2021.01.25 Monday ACHK