Highly recommend looking at Jacob Barandes’ formulation of quantum mechanics as non-Markovian stochastic processes. It was the first introduction to quantum mechanics I could actually follow.
In a fews sentences: the evolution of a physical system (quantum and classical) can very successfully be modeled as a stochastic process, and ...
1. state of the system is a real-valued "vector" (could be a vector of with continuous indices), or to put it another way, a "point" in state space.
2. system evolution is described by a real-valued "matrix" (matrix in quotes because it is also possibly a matrix with continuous indices), defined by the laws physics as they apply to the system
3. evolution of the system is modeled by repeatedly applying the matrix to the system (to the vector), possibly with infinitesimal steps.
The major discovery Jacob made is that, historically, folks working on stochastic processes had restricted themselves to studying "markovian" stochastic processes, where the transformation matrix has specific mathematical properties, and this fails to be able to properly model QM.
Jacob removes the constraint that the matrix should obey markovian constraints and lands us in an area of maths that's woefully unexplored: non markovian stochastic processes.
The net result though: you can model quantum mechanics with simple real-valued probabilities and do away entirely with the effing complex numbers.
The whole thing is way more intuitive than the traditional complex number based approach.
Jacob also apparently formally demonstrates that his approach is equivalent to the traditional approach.
anotherpaulg|7 hours ago
suhputt|8 hours ago
ur-whale|8 hours ago
seconded
>might make sense to link to the actual material you're referring to
https://www.youtube.com/watch?v=sshJyD0aWXg
In a fews sentences: the evolution of a physical system (quantum and classical) can very successfully be modeled as a stochastic process, and ...
1. state of the system is a real-valued "vector" (could be a vector of with continuous indices), or to put it another way, a "point" in state space.
2. system evolution is described by a real-valued "matrix" (matrix in quotes because it is also possibly a matrix with continuous indices), defined by the laws physics as they apply to the system
3. evolution of the system is modeled by repeatedly applying the matrix to the system (to the vector), possibly with infinitesimal steps.
The major discovery Jacob made is that, historically, folks working on stochastic processes had restricted themselves to studying "markovian" stochastic processes, where the transformation matrix has specific mathematical properties, and this fails to be able to properly model QM.
Jacob removes the constraint that the matrix should obey markovian constraints and lands us in an area of maths that's woefully unexplored: non markovian stochastic processes.
The net result though: you can model quantum mechanics with simple real-valued probabilities and do away entirely with the effing complex numbers.
The whole thing is way more intuitive than the traditional complex number based approach.
Jacob also apparently formally demonstrates that his approach is equivalent to the traditional approach.
Really worth taking a read/listen at.