I Unraveling the Mystery of Particle Spin Numbering System

[bbbl67]

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.

 

[DrClaude]

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.

 

[bbbl67]

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.

 

[DrClaude]

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.

 

[Nugatory]

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.

 

[Nugatory]

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 :)