# Spin and the violation of the speed of light

1. Aug 19, 2012

### g.lemaitre

this is from Omnes' book Understanding QM

Has this problem been resolved or is it still outstanding?

2. Aug 19, 2012

### CAF123

The spin of an electron is not meant in the literal sense (ie like some sort of spinning top or rotating sphere). Instead, it is a vector quantity and we define a spin quantum number.

I believe a sort of rough calculation goes as follows:
$$\tau = \frac{dL}{dt} = Iα$$
If we define $L = m_l\hbar = \frac{\hbar}{2}$ and $I = \frac{2}{5}mr^2,$ an electron as a solid sphere with $r ≈ fm$

Then, $$L = Iω = \frac{Iv}{r} => v = \frac{Lr}{I} = \frac{5Lr}{2mr^2}.$$
Simplifying and inputting known data gives v ≈ 1011 ms-1, which is 1000 times the speed of light.

3. Aug 19, 2012

### g.lemaitre

So in other words the problem of the violation of the speed of light has not been resolved, right?

4. Aug 19, 2012

### CAF123

The above calculation assumes that the electron is behaving like a rotating sphere and so it is meant to demonstrate why we should not think of spin as a classical concept here.

5. Aug 19, 2012

### g.lemaitre

well if the electron is not spinning then what is it doing?

6. Aug 19, 2012

### CAF123

Just to be a little clear on the question:
What do you mean by 'what do they do?'

7. Aug 19, 2012

### Bill_K

The electron is observed to be pointlike, which means its size, if it has one, is smaller than we have so far been able to detect. (10-16 cm). As a particle, it has a number of properties: mass, charge and angular momentum. Angular momentum comes in two varieties: orbital angular momentum (r x p) and spin angular momentum. There is no motion associated with spin angular momentum, and so the electron does not rotate. The angular momentum it carries (ħ/2) is simply an intrinsic property.

8. Aug 19, 2012

### Staff: Mentor

The model (small, rotating sphere) which produced this prediction was wrong. Therefore, it is not a problem any more.

Spin is just another particle property, like its mass and charges (not just the electromagnetic charge).