Research

I am interested in quantum stochastic calculus and in particular its relation the GRW interpretation of quantum mechanics. The measurement problem has long been an issue in quantum mechanics having to do with the actualization of the possible states allowed in quantum mechanics. In quantum mechanics, a system can be in a superposition of possible states, but these superpositions are never observed macroscopically. Physicists have long speculated over the mechanism that causes the collapse from the possible states in a superposition to the single observed laboratory result. Below is an animation of a superposition of possible position states of a harmonic oscillator, akin to a quantum spring. The animation starts with the particle able to occupy approximately 4 different position states at the same time, visualized by the red line having about 4 bumps and signifying that there is a higher probability for the particle to be in these positions. The green and blue lines represent the real and imaginary parts of the state. As the system evolves according to GRW rules the red line evolves into a state where the particle is in one state which oscillates back and forth like a classical spring. In this way the superposition of the 4 most likely positions collapses to one classically moving position.

Entanglement is one of the central features of quantum mechanics. While it has a very natural description within the framework of quantum mechanics, it gives rise to mysterious correlations that defy classical intuition. Below is an abstract conceptualization of how entanglement could work, inspired by David Bohm's view of implicate and explicate orders and a holographic approach to entanglement. The mechanism which generates the animation is a simple operation on a few polynomials treated as vectors. When their roots are plotted, a complex 'entangled' looking order develops. This is symbolic of how entangled states in the position space of a system can emerge from purely quantum systems, which have relatively simple descriptions in the appropriate space (the implicate order), but have complex structure when projected onto a different space (the explicate order).

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