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Comment by unholiness | Hacker News Reader

Stopped reading after "Yet in the mathematical equations that define the Standard Model, the eight gluons are distinct from one another in the same way that the W and Z bosons differ."

W and Z bosons, photons, etc have fixed masses, charges, interaction strengths with other particles. These properties can exactly be listed and looked up in a table of elementary particles with discrete rows.

Gluon color is continuous property in a vector space. Gluons can have any color in that space, with any combination of the 8 basis vectors (and that choice of basis is also completely arbitrary). The color |g1> is no more valid than the color (|g1> + |g2> + |g8> / √3) or any other of infinite combinations.

Calling this "8 gluons" is like saying there's "3 photons" because they can have momentum in 3 dimensions. If you want to argue there's infinite kinds of gluons, go ahead, but there aren't 8.

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> W and Z bosons, photons, etc have fixed masses, charges, interaction strengths with other particles.

But you can form a continuous set of linear combinations of these things, just as you can with gluons. Indeed, what the article calls W and Z bosons (and photons) are just such linear combinations--the ones that appear in the low energy limit after the electroweak phase transition occurs. Before that phase transition, different linear combinations (i.e., a different basis of the electroweak vector space) are the ones that naturally appear. So saying that there are two W, one Z, and one photon is really counting basis vectors in the electroweak vector space, just as saying there are 8 gluons is really counting basis vectors in the gluon sector of the strong interaction vector space.

In a hypothetical scenario where we were inventing the standard model in the first 10^-11 seconds after the big bang, you're right there would be an analogy there. But in that scenario, our standard model would say there was one electroweak particle, not that there were 8 gluons.

In our own universe, the fact that electroweak symmetry breaks ensures there are 4 electroweak particles and not other combinations. There's no corresponding thing to contain gluons to individual particles, you'd need laws of physics we don't have to add that constraint.

> in that scenario, our standard model would say there was one electroweak particle

No, it wouldn't. There would still be four; they would just be called W1, W2, W3, and B. The electroweak vector space doesn't change when the electroweak symmetry is broken; it has 4 basis vectors before, and 4 basis vectors after. All that changes is which basis is the most "natural" to use in describing physics at the given energy scale.

(And there would still be eight gluons as well--what I say below about those applies just as well above the electroweak symmetry breaking energy scale as below.)

> There's no corresponding thing to contain gluons to individual particles

If you mean that there is no "natural" choice of basis for the gluon vector space, that's not quite true either. The Gell-Mann matrices are a natural choice of basis for the adjoint representation of SU(3) (or, equivalently, the defining representation of the Lie Algebra of SU(3)), which is the gluon representation. Those eight matrices are what physicists typically are referring to when they refer to the eight gluons.

The gluon with color (|g1> + |g2> + |g8>) / √3 is just a superposition of the gluons with colors g1, g2 and g8, the same way you can make superpositions of any other particles. You are right that the choice of basis vectors is arbitrary, but that doesn't make it wrong to count the number of dimensions. It also doesn't make it fundamentally different than, say, polarizations of photons or even flavors of quarks. You can have superpositions of photon polarizations or quark flavors.

All of these are continuous properties in an n-dimensional vector space.

8 color indices, why not call that 8 particles what is the point of commenting like you are better than the article when you so clearly show you are not in one sentence never speak on physics again please

It’s how gauge theories work:

- fermions (charges) are in the fundamental representation of the gauge group, here SU(3) so 3 Colors

- bosons are in the adjoint représentation, for SU(3) that 8 dimensions

And the different charge W bosons are just the same particle, via time reversal symmetry.

Huh, I didn't even know we had sub-species ID of gluons now

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