Unraveling the Mystery of Particle Spin Numbering System

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    Particle Spin System
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Discussion Overview

The discussion revolves around the particle spin numbering system, specifically addressing why bosons have integer spins while fermions have half-integer spins. Participants explore whether this distinction is merely a convention from the early days of quantum theory and consider hypothetical alternatives to the current definitions of spin and charge.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants question the origins of the particle spin numbering system and whether it could have been defined differently, such as by multiplying half spins by 2 to yield odd-integer spins for fermions.
  • Others explain that spin is defined in units of ħ, with a spin-1/2 particle having a spin angular momentum of ħ/2, and reference the spin statistics theorem to understand the behavior of different spin particles.
  • One participant suggests that redefining ħ to half its current value would complicate existing equations, such as Planck's constant, and create unnecessary factors in calculations.
  • There is a discussion about the elementary charge, with some arguing that it would have made sense to define the basic charge as 1/3 of an electron charge, but others caution that this would complicate the work of various fields in physics.
  • Participants note that unit choices are often made for convenience in specific contexts, such as using electron-volts in particle physics or setting c to one in relativity.
  • One participant humorously mentions the arbitrary nature of some definitions, suggesting it might have been better to define the electron charge as positive.

Areas of Agreement / Disagreement

Participants express differing views on the implications of redefining fundamental constants and the historical choices made in physics. There is no consensus on whether the current definitions are optimal or if alternative definitions would be preferable.

Contextual Notes

Participants highlight the arbitrary nature of certain definitions and the potential complications that could arise from changing fundamental constants. The discussion reflects on the historical context of these choices without resolving the implications of such changes.

bbbl67
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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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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.
 
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.
 
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.
 
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.
 
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 :)
 

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