Unraveling the Mystery of Particle Spin Numbering System

In summary, the particle spin numbering system is based on the angular momentum in units of ħ. Particles with spin 1/2 have a spin angular momentum of ħ/2. The difference between half-integer and integer spin particles is explained by the spin statistics theorem. While it may seem like it would make more sense to redefine the value of ħ or the elementary charge, these arbitrary choices have been made and changing them would only complicate equations and units. Ultimately, scientists choose units that are convenient for the problem at hand.
  • #1
bbbl67
212
21
Now, how did the particle spin numbering system come about? What I'm referring to is, why are bosons integer spins, while fermions are half-spins? Is this just a convention that we got stuck with since the early days of quantum theory? For example, instead of having half-spins, could they have just multiplied everything by 2 and all half spins become odd-integer spins, while bosons which currently have integer spins become even-integer spins.
 
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  • #2
It is the angular momentum in units of ħ. A particle of spin 1/2 has a spin angular momentum of ħ/2.

As for why half-integer and integer spin particles behave differently, you have to look up the spin statistics theorem.
 
  • #3
DrClaude said:
It is the angular momentum in units of ħ. A particle of spin 1/2 has a spin angular momentum of ħ/2.

As for why half-integer and integer spin particles behave differently, you have to look up the spin statistics theorem.
So wouldn't it have made sense to make ħ half of what it is now? Same thing with electric charges, since quarks have 1/3 electron charges, wouldn't it have made sense to make the basic charge 1/3 of an electron? I mean it seems to me that it was chosen this way because that's what it was chosen as back in the early days before they discovered something that could be less than the basic unit.
 
  • #4
Just to clarify something: I meant to say that the projection of the spin of a spin-1/2 particle is ħ/2. The actual spin is ##\sqrt{3}/2##.

There is no point in changing the value of ħ now. And would it make more sense to write ##E = 2 h \nu##?

As for the elementary charge, since quark can't be found individually, there is no point in counting the charge differently than what we do now.

If you really could go back in time and change things, it would probably be better to define the charge of the electron as positive, and take the circumference of the circle to be π times the radius instead of the diameter. Arbitrary choices have been made and we must live with them.
 
  • #5
bbbl67 said:
So wouldn't it have made sense to make ħ half of what it is now?
##\hbar## and ##h## show up in many other places, and those equations would acquire an unnecessary factor of two. For example, Planck's constant is defined by ##E=h\nu##; we'd have to rewrite that as ##E=2h\nu##, and it's not clear how that is an improvement.
Same thing with electric charges, since quarks have 1/3 electron charges, wouldn't it have made sense to make the basic charge 1/3 of an electron? I mean it seems to me that it was chosen this way because that's what it was chosen as back in the early days before they discovered something that could be less than the basic unit.
You'd be sentencing the chemists, atomic physicists, and solid state people to a lifetime of misery chasing factors of 3 and 33... And we care a lot more about the electrodynamics of charge-1 particles than of charge-1/3 particles.

What's really going on here is that we always choose units that are convenient for the problem at hand. Particle physicists measure energy in electron-volts instead of joules and relativists routinely set ##c## to one by measuring time in seconds and distances in light-seconds. Likewise, when you're doing quantum mechanics you set ##h## to one by choosing appropriate units... So redefining ##h## to make the spin-1/2 particles be spin-one wouldn't simplify anything much more.
 
  • #6
DrClaude said:
If you really could go back in time and change things, it would probably be better to define the charge of the electron as positive...
There's a classic xkcd cartoon somewhere around :)
 

1. What is the particle spin number system?

The particle spin number system is a quantum mechanical concept used to describe the intrinsic angular momentum of subatomic particles. It is a fundamental property of particles and is denoted by the symbol "s".

2. How is the spin number of a particle measured?

The spin number of a particle can be measured through various experiments, such as scattering experiments or magnetic resonance imaging. These experiments involve manipulating the particle's spin and observing its resulting behavior.

3. What are the possible values of the spin number?

The spin number of a particle can have both positive and negative values, as well as zero. However, the specific values depend on the type of particle. For example, electrons have a spin number of either +1/2 or -1/2, while photons have a spin number of either +1 or -1.

4. How does the spin number affect a particle's behavior?

The spin number of a particle affects its behavior in various ways. For example, it can determine how the particle interacts with other particles, how it responds to external forces, and how it behaves in different energy states. The spin number also plays a crucial role in determining the properties of materials.

5. Is the spin number a fixed value for a particle?

No, the spin number of a particle can change depending on the interactions and energy states it experiences. This phenomenon is known as spin flipping. However, the spin number is a fundamental property of a particle and is typically conserved in most physical processes.

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