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/sci/ - Science & Math


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10489137 No.10489137 [Reply] [Original]

why is quantum superposition linear?

>> No.10489148

>>10489137
it's quadratic?

1/sqrt(2) |a> + 1/sqrt(2) |b>

>> No.10489167

Cause it's waves, and wave superposition is linear

>> No.10489169

>>10489167
why is wave superposition linear?

>> No.10489172

>>10489169
Because any linear combination of solutions to the wave equation is also a solution.

>> No.10489243

>>10489137
All differentiable functions are indistinguishable from linear for small enough inputs, and given how long the wavefunction has had to spread out the true amplitude of anything must be incredibly tiny. We usually ignore this because we focus on the part of the wavefunction we're actually remotely likely to interact with and normalise that to unit total measure.

>> No.10489252

>>10489172
this. the wave equation is linear.

>> No.10489263

>>10489172
>>10489252
but nonlinear wave equations exist

>> No.10489275

>>10489243
any nonlinear quantum phenomena then?

inb4 wave function collapse

>> No.10489287

>>10489263
and in conditions where such equations apply, the superposition principle isn't valid
>>10489275
condensed states?

>> No.10489290

>>10489275
There is absolutely no evidence that a wavefunction has ever collapsed. Nothing is known to be nonlinear in the amplitude, although you wouldn't be able to tell if it only showed up for high amplitudes. You can set up all kinds of nonlinear systems in qm, all of classical physics for example, but that's nonlinear in things other than the amplitude, so it's not what people are talking about when they say qm is linear.

>> No.10489451

isn't

>> No.10489646

>>10489451
What isn't and how do you know?

>> No.10490078

This thread is what happens when you "get into" QM without knowing prerequisites such as mathematical physics and ODEs/PDEs.

>> No.10490441

>>10489137
>why is quantum superposition linear?
otherwise we'd have interaction terms between timelines. your question is identical to "why are timelines separate?"

>> No.10490515

>>10489137
Damn she is CUTE!

>> No.10490834

>>10490441
Timelines do interact though. Qm is linear in the amplitude, not the probability.

>> No.10490884
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10490884

>>10489137
The answer is one that applies to many similar questions:
We try to model physical phenomena using frameworks that we are able to solve.

Say there's a much better non-linear theory. It might be hard to find and even if found, hard to solve. We are glad we find a linear theory that still works.
Same spiel applies with "conservation of energy" and integrate systems. Those are the ones we are able to solve and so people desperately try to find theories that fall into that framework. E.g. when the nuclear physics theory broke conservation of energy, the neutrino was hypothesized to add another particle that made conservation of energy work out after all, and in that case it worked out and new experiments could be explained with that theory.
Of course for every theory that works out, there are 1000 that don't. Consider e.g. these list of 80 or so post 1900 bust still classical theories of gravity that turned out not to make it
https://en.wikipedia.org/wiki/Alternatives_to_general_relativity

tl;dr we know of theories that are comparatively simple by the nature of us being able to deal with them

>> No.10491093

>>10490834
iirc timelines interfere but do not interact.