A playlist on quantum spin
I am watching a playlist on quantum spin. The following are some of my thoughts about quantum theory.
We live in three dimensional real world, real here means real number instead of complex number. From time to time, theories built on complex numbers seem simpler. For example, sine and cosine functions often are simpler when written in complex exponential functions.
In quantum physics, however, complex functions become essential in the construction of the theory itself. This I don’t understand. Quantum spin is the simplest quantum phenomenon. Learning quantum spin may help me gain a foothold for further understanding.
Spin is very simple. It is simply up and down. But its mathematical model is quite perculiar. It is a two dimensional complex number model. We live in a three dimensional real number world. Why can’t we build a model in a three dimensional real world?
Specifically, there is 180 degrees between spin up and spin down in physical space. But spin up and spin down are orthogonal to each other in the mathematical model. This means spin up and spin down are 90 degrees apart in the mathematical model. Why the difference?
I have learned a lot from watching the videos. But quantum physics is always a mystery to me.
The following is the link to the playlist.
