"Now," says Po'mi, "if fundamental physics has nothing to do with consciousness, can you tell me why the subjective >probability of finding ourselves in a side of the split world, should be exactly proportional to the square of the thickness of >that side?"
There is a great terrible silence.
"WHAT?" says Yu'el.
"WHAT?" says De'da.
"WHAT?" says Nharglane.
"WHAT?" says the entire audience of Ebborians.
"WHAT?"
That's not how it works in QM. It comes out as squared amplitudes because they're orthogonal. If you had them in one dimension as described, it would be linear.
That's not how it works in QM. It comes out as squared amplitudes because they're orthogonal.
Isn't that just a tautological consequence of how orthogonality is defined in Hilbert space? One way to develop quantum mechanics is to start with the pure states for some observable, which is all that you ever "actually experience", and then define an inner product on Hilbert space such that these states are orthonormal.
Today's post, Where Physics Meets Experience was originally published on 25 April 2008. A summary (taken from the LW wiki):
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