# Spin up or spin down

1. Aug 4, 2015

### xXDEMAMAXx

Hello,
I have read about Schrodinger's cat saying we do not know whether or not a particle has a spin up or spin down. It is only when we check it that we know which one it is.
I understand the concept however I do not understand what do scientists mean when they say "spin up/down".
What are 'spins'?

2. Aug 4, 2015

### Staff: Mentor

Spin is intrinsic angular momentum, the quantum-mechanical analog to the classical angular momentum of an object spinning around its own axis, like a spinning top or the Earth's daily rotation. Each elementary particle has a fixed amount (magnitude) of spin, which is a fundamental property of that particle, like its mass and electric charge.

There are only certain allowable values for the magnitude of spin, namely $S = \sqrt {s(s+1)} \hbar$ where $s$ can have either positive integer or half-integer values, or zero. Electrons have $s = 1/2$ so $S = \sqrt{3/4} \hbar$. (beware the distinction between lower-case $s$ and upper-case $S$)

Analogous to the way that we can orient a spinning top so its axis of rotation points in different directions, we can (loosely speaking) think of a particle's spin as being oriented in different directions. We describe this using the component of spin along a given reference direction which we customarily call the z-direction although it can actually be any direction we like. The z-component of spin is restricted to a set of values which depend on the magnitude of spin: $S_z = m_s \hbar$ where $m_s$ can have values from $-s$ to $+s$ in steps of 1. Electrons have $s = 1/2$ so they must have either $m_s = -1/2$ ($S_z = -\hbar/2$) or $m_s = +1/2$ ($S_z = +\hbar/2$). We call these two states "spin down" and "spin up".

Unlike a particle's spin magnitude $S$ which is fixed, we can change $S_z$ ("flip the spin") by various methods.

For further information see e.g. Wikipedia: https://en.wikipedia.org/wiki/Spin_(physics)

Last edited: Aug 4, 2015
3. Aug 4, 2015

### xXDEMAMAXx

Thank you so much for your help. I am now reading more about spins and quantum numbers. :)