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Comment by nabla9 | Hacker News Reader

Yes. It's just an equation. The complexity of quantum system that can be simulate is limited.

https://marl0ny.github.io/QM-Simulator-2D/index.html

From the above link you can look single slit, double slit, triple slit, step, spike, or load an arbitrary image as a potential and do experiments in 2d box.

>This WebGL program simulates the quantum mechanics of a single particle confined in a 2D box, where inside this box the user can create new potential barriers and scatter Gaussian wavepackets off them. The full instructions are found here.

https://github.com/marl0ny/QM-Simulator-2D

btw. Wave function collapse in quantum physics is completely speculative phenomenon. There is only apparent wave function collapse.

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> btw. Wave function collapse in quantum physics is completely speculative phenomenon. There is only apparent wave function collapse.

To be more precise, the Born rule non-linear adjustment of the wave function to a single real value after a measurement is strictly necessary for QM to match experiments. Whether this should be interpreted as a physical phenomenon of wave function collapse, or as entanglement with the environment (MWI), or as an update of probabilities for hidden variables (Pilot wave) or some other phenomenon is speculative, but the wave function must be "collapsed" to a single real value after a measurement to correctly predict experimental results.

Adjustment is just cutting interference terms from equation. Mathematically apparent wave function collapse is caused by quantum decoherence.

Wave-function collapse as a priori process is just speculation. Finding that it actually happens would be new physics.

In which case, where does the Born rule come from?

https://en.wikipedia.org/wiki/Gleason%27s_theorem

Huh. I can't believe I missed this. Thanks.

In quantum computing the consequence of the theorem (as I understand it) is that once you have asked every yes/no question there is to ask about the state, the state has collapsed.

I didn't think you needed the theorem for that; quantum entanglement behaves very similarly to information theory (specifically, information provenance).

As far as I can tell, that is just explaining the numeric value of the Born rule, not the wave function collapse/update. I have not found any claims that Gleason's theorem (which I was unaware of, so thank you for pointing it out!) solves the measurement problem.

Quantum decoherence may give you a diagonal density matrix but you still need to "collapse" that to a single outcome in some way or another.

However you put it, [to a classical observer] the wave function still "collapses" after a measurement. This is most famously seen by adding a detector inside one of the slits for the double-slit experiment: the original wave function is not consistent with the experiment, you have to update the wave function after the interaction (or lack of interaction) with the detector.

Sure, in MWI the wave function of the universe never collapses, but something similar still happens for "parts" of the universal wave function.

If you like that simulation you might also like my own webGL Gross-Pitaevskii Equation (GPE) solver. It uses RK4 to simulate a 2D box of ultracold atoms undergoing Bose-Einstein Condensation.

The GPE models a condensate as a single-particle quantum wavefunction with a non-linear form of the Schrödinger Equation, so you get some interesting behaviour from the non-linearity while the simulation remains computationally feasible.

You can interact with the potential term by clicking and dragging inside the 2D box.

https://georgestagg.github.io/webgl_gpe/

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