# Q & A: Why does an electron have spin 1/2 ?

Q:
Pls tell me why is spin of an electron +1/2 or -1/2 and not something like +1 or -1?
- Tridib Banerjee (age 16)
Kolkata, West Bengal, India
A:
Dear Tridib,   This is a very deep and fundamental question.  The Nobel Prize winning physicist Richard Feynman was once asked for a simple answer to this question (actually it was for a related phenomenon, the spin-statistics relationship, why spin 1/2 particles are fermions). He came back the next day and said "I can't do it.  That means we don't really understand it".   All we can say that by performing experiments we can  measure its spin, and that it is 1/2 h-bar.
See, for example:   .

LeeH

If you go on in physics, after you've learned some special relativity and quantum mechanics, you should get to learn the spin-statistics theorem, which at least tells  why particles have either half integer or full integer spin, and why the former are fermions and the latter are bosons. What it doesn't say anything about is why any of those spin 1/2 particles should actually exist or why one of them should have the mass and charge of an electron.  Mike W.

(published on 05/14/2009)

## Follow-Up #1: why is electron spin 1/2?

Q:
i want know why spin is 1/2 for electron? plz tell me
- arul josheph (age 18)
delhi,india
A:
I assume this question isn't about why we give the name "electron" to a particular spin-1/2 particle. Perhaps you're asking why there's a particular set of properties: unit charge, spin-1/2, a rest mass of around 500 keV, etc. that happen to go together as a packet. So far as I know, the current state of theory doesn't account for much of that. The "Standard Model" puts many of these features in by hand.

What is known is why particles have to have either integer or half-integer spin, and why the former must be bosons and the latter must be fermions. We've discussed that a bit in answers on spin-statistics.

Mike W.

(published on 10/03/2011)

## Follow-Up #2: half-integer spin rotation

Q:
When particles have spins that aren't whole, I read you only have to spin them that much to see the same side, so an electron you only spin it a half a rotation and you see the other side. What causes this? Or was the book wrong? This property is confusing me a lot, and seems impossible to me.
- Jack Gifford (age 12)
Hanover, Maryland, The USA
A:
Wow, what was the name of that book? It sounds as if it got things seriously confused.

Elementary particles, such as spin-1/2 electrons, don't even have "sides" in any normal sense of the word. What changes as you rotate a particle like that is something more abstract, its quantum phase, a complex number that rotates in the complex plane. Sorry if those are unfamiliar concepts, I just can't think of some other way to describe it.

Anyway, here's the part that's really opposite to what you got from that book. A particle with a whole-number (integer) spin comes back to the same state after rotating around once. A particle with half-integer spin comes back to minus its starting state after a whole rotation. It has to rotate twice to get back to the starting state.

Mike W.

(published on 12/22/2011)

## Follow-Up #3: rotating two electrons

Q:
Alright, I am beginning to understand why you need to rotate an electron twice to see the same side again, however, if you had 2 electrons, and rotated them against each other, such as 2 gears would, would this affect the spin? Would it prevent the spin from being "weird"?
- Jack G. (age 12)
Hanover, Maryland, USA
A:
There's really no "sides" to an electron, but I'll move on to your next question, which gets at something quite important.

If two electrons form a combined state the possible total spin can be either 0 or 1. In the spin-zero case, there's no change at all as you rotate it. In the spin-1 case, the change isn't weird- one full turn restores the starting state.

There can also be a dependence on rotation from the spatial form of the wave-function, but that type of dependence is never weird.

Mike W.

(published on 12/23/2011)

## Follow-Up #4: Do electrons have sides?

Q:
You say "There's really no "sides" to an electron." but this sounds puzzling because if an electron is truly rotationally symmetric how can you differentiate the electron that has rotated from the one that has not? and if "spin" is something always stuck with an electron, does this "spin" not break the rotational symmetry of an electron? I mean, you can tell the axis of the spin which has a direction. Is this not a "special side(direction?)" of an electron?
- Anonymous
A:

You're right that electrons are not rotationally invariant. I guess if you wanted you could then say that means they have "sides", although I think you can see that the resulting picture would be pretty misleading.

As for the specifics you mentioned, yes, there are physical symptoms of rotation. For example, start with an electron spinning up along the z-axis. A rotation of say 90° along the x-axis then gives an electron with only 50% chance of being up along z, if that property then gets measured. So obviously the electron changes under rotation.

Rotating that same electron around the z axis produces more subtle effects. Send the electron to a beam splitter, which leaves equal amplitudes of electron wave on two different paths. Bring the two paths together and then detect the electron on a screen. Do the same thing with lots of electrons and you'll see a pattern on the screen of where the two beams interfere constructively (lots of electrons) or destructively (few electrons). Now insert a device to rotate one of the beams by 360°.  Your gut says that a 360° rotation should leave things unchanged. What you'll see is that the interference pattern reverses! In other words, the 360° rotation changes the sign of the wave pattern, indicating that the particle has half-integral spin. Weird.

Mike W.

(published on 07/24/2012)

## Follow-Up #5: Why do Bosons have integer spins?

Q:
Why do bosons have "integer" spins?
- Saurav (age 14)
Bangalore, India
A:
It's a matter of definition.   It is determined by experiment that a certain class of fundamental particles like electrons, protons, etc,  all have half integer spin values in terms of the fundamental unit of angular momentum  h/2pi where h is Plank's constant.  These are called Fermions, so named after Enrico Fermi who studied their properties.  A separate class of particles, such as pions, photons, W and Z particles, all have integer values of spin.   These are called Bosons in honor of the Indian physicist Satyendra Nath Bose.
In the realm of quantum mechanics the wave function for a pair of identical fermions changes algebraic sign when the two particles are exchanged.   For bosons, there is no change of sign.
See:     for details.

Lee H

(published on 11/17/2012)

## Follow-Up #6: spin of He 4

Q:
I understand that the concept of half-integer spin came from the Stern-Gerlach experiment. The beam of silver atoms was split in 2 because silver atoms have half-integer spin (1/2). What would be the result if the beam were helium-4 atoms (integer spin) rather than silver atoms?
- Anonymous
A:

4He does have integer spin, but the integer is zero. So a beam wouldn't split in a Stern-Gerlach experiment.

An ordinary O2 oxygen molecule is a nice example of a spin-1 particle. A beam would split into three parts in a Stern-Gerlach experiment.

Mike W.

(published on 02/13/2019)