## Why quantum mechanics does *not* say a particle can be in two places at once

This post is about understanding the difference between a mathematical model and the physical system that is being modeled. Confusion between the model and the physical system is especially prevalent in quantum physics and leads to statements such as: A particle can be in two places at once An object is spread out in space … Read more

## The Quantum “Finite Step” problem

The Probability Wave: The Wave Function: This is an animation of the Finite Step problem, as described in a typical undergraduate quantum mechanics textbook. The top animation shows the evolution of the probability density function. The bottom animation shows the full wave function . The real part is blue and the imaginary part is red. … Read more

## The Twins

This is an animation of the relativistic “twins” scenario. One twin stays on Earth. The other travels away at a high rate of velocity and then comes back. Typically when you see this situation analysed in a textbook, they have the travelling twin doing something like going out at half the speed of light then … Read more

## Liouville’s Theorem

The idea of this animation is to give an example of Liouville’s theorem in phase space. I’m using a Hamiltonian suggested by Josh in the Portland Math and Science Group: Leading to the update equations: This Hamiltonian is not intended to represent any actual physical system. I’m using it simply because it exhibits an “interesting” … Read more