/sci/ - Science & Math

How to define the quantum mechanical path integral rigorously? I heard physicists use hand-waving when it comes to path integration but somehow it still works. How can a calculation without fundamental rigorous explaination just work?

>>12117794
Quantum physics implies that we do not. Quantum pehnomena are much, much more computationally intensive to simulate than classical physics. It is like Nature does not care about computational efficiency at all. Exactly the opposite of what we would expect from simulation hypothesis.

https://en.wikipedia.org/wiki/Path_integral_formulation

>>12001264
Except that QM is the very opposite. All the possibilities affect the result. Making quantum simulations is much, much more computationally expensive than classical simulations. Hence why we can easily simulate millions of classical particles, but struggle greatly with dozens of quantum particles...

https://en.wikipedia.org/wiki/Path_integral_formulation

>>11711696
>When unobserved, it only calculates the end result

Wrong, and the opposite is true, it calculates ALL possible results.

https://en.wikipedia.org/wiki/Path_integral_formulation

Quantum mechanics points towards simulation theory being incorrect, if anything. More here:

https://motls.blogspot.com/2013/03/we-dont-live-in-simulation.html

http://backreaction.blogspot.com/2017/03/no-we-probably-dont-live-in-computer.html

>>11033259
>>11033289
>>11033302
>>11033321

>one of the best ways to save computational power ... only doing atomic/subatomic level calculations when the simulated scientist denziens of the simulated universes performed scientific expirements or procedures which required results from those levels of existence. Afterall, if no one is observing the results of those levels of existence, why bother taking the power to simulate all the atomic and subatomic processes in trillions of galaxies if no one is actually observing the results?

Except that this is the very opposite of how quantum mechanics work. To simplify it, quantum mechanics is not about "not computing when nobody is looking". It is about "computing every possibility when nobody is looking, then adding them up in a clever way". It does not save computation, it GREATLY INCREASES required computation. Hence why we can do classical simulations with trillions of particles easily, but struggle with 100+ quantum particles simulations. Quantum mechanics implies that universe does not give a fuck at all about saving computational resources, and almost goes out of it's way to "waste" computation at the drop of a hat.

https://en.wikipedia.org/wiki/Path_integral_formulation