# Particles like neutrino have zero mass and zero charge

## Main Question or Discussion Point

Hi friends,
I have read that particles like neutrino have zero mass and zero charge.Yet it has the spin value (1/2).How it is possible?It is difficult even to imagine an item of zero mass spinning.Is it right to call an item of zero mass as a particle?If yes,What is a particle ?Can someone help me in knowing what is spin?And how it is determined?Why it is always in multiples of (1/2)

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As i understand it, spin doensn't mean the particle is spinning. Its just a property attributed to it like charge. Quarks have "colours" which obviuosly doensn't mean they actually have coolur. Its just a property

Spin has almost nothing to do with the classical angular momentum. Spin is a property you need to calculate the direction in which the correspondanding particle will go if there is an external magnetic field. (There are two spin values, spin up and down and thus two direction a particle can go by applying a magnetic field).

jtbell
Mentor
kiru said:
I have read that particles like neutrino have zero mass
Your book (or whatever) is out of date. In the past few years most particle physicists have come to believe that neutrinos actually do have a small mass, revealed by the phenomenon of "neutrino oscillations."

Of course I know little that the the value (1/2) is due to the probability value.If you say that neutrinos have small mass,in beta decay, wont it affect the balance of the equation?
Also does anti neutrino differ from neutrino only in spin?

No, no an antineutrino can have the same spin as a neutrino. Spin values can be positive or negative, i.e. +1/2 and -1/2 in your case. A neutrino and antineutrino can have both, spin +1/2 and -1/2.

Kruger said:
No, no an antineutrino can have the same spin as a neutrino. Spin values can be positive or negative, i.e. +1/2 and -1/2 in your case. A neutrino and antineutrino can have both, spin +1/2 and -1/2.
If so what differs a neutrino from anti neutrino?

Gokul43201
Staff Emeritus
Gold Member
For one, the lepton charge (or lepton number).

Gokul43201
Staff Emeritus
Gold Member
kiru said:
Of course I know little that the the value (1/2) is due to the probability value.
How do you say that ? 1/2 is not some probabilistic mean over a range of values - it is exactly what you will measure for the spin of say, a single electron.

Gokul43201 said:
How do you say that ? 1/2 is not some probabilistic mean over a range of values - it is exactly what you will measure for the spin of say, a single electron.
Oh! I thought that a particle may spin in clockwise or anti-clockwise direction both of which having a 50-50 probability and hence the value (1/2).Is it not so?

Gokul43201 said:
For one, the lepton charge (or lepton number).
Will you give me proper article on any webpage about lepton charge?

kiru said:
Will you give me proper article on any webpage about lepton charge?
I don't have an article, but electron number, muon number and tauon number are always observed to be conserved. Electrons and electron neutrinos have an electron number of 1, positrons and electron antineutrinos -1, likewise for muons, tauons and their respective neutrinos and antiparticles. I think this is a consequence of observed particle decays, rather than fundemental principal (that is, they are conserved because that's all we've seen).

On spin, the funny thing is that the choice of axis is entirely aribitrary. No matter how you measure the spin of an electron, say, you will measure the same value had you measured some other axis of spin. This is why it is not helpful to picture it as something actually spinning. When people say a particle is 'spin half', they mean the quantum number s for that particle is 1/2, from which the possible actual spin values S are deriveable in the same way as actual quantized angular momentum.

kiru said:
Oh! I thought that a particle may spin in clockwise or anti-clockwise direction both of which having a 50-50 probability and hence the value (1/2).Is it not so?
No. The spin up and down come from the eigenvalues of the spin up and spin down spinors which are hbar/2 and -hbar/2.

jtbell
Mentor
To tie everything together, a "spin 1/2" particle has spin quantum number $s = 1/2$. The magnitude of the spin angular momentum is $S = \sqrt{s(s+1)} \hbar = \sqrt{3/4} \hbar$. These are both fixed, constant values.

The z-component of the spin angular momentum is quantized according to $S_z = m_s \hbar$. When $s = 1/2$, $m_s$ can be either +1/2 or -1/2. Therefore $S_z$ can be either $+\hbar / 2$ or $-\hbar / 2$. These are the "spin up" and "spin down" states, and for an isolated particle should each occur with 50% probability.

Dirac spinors

Recently I have learned a little bit about Dirac spinors and have written a paper with my view of them:
http://arXiv.org/abs/math/0601262" [Broken]
Maybe it will help you. Anyway, I would like to continue learning the elementary particles physics, so it would be best to discuss them here.

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Metric connections for Dirac spinors

The next paper is on metric connections for Dirac spinors in a gravitational field:

http://arxiv.org/abs/math.DG/0602359" [Broken]

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