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Comment by jordanpg | Hacker News Reader

It's unfathomable to me that anything about the universe would be pinned at some integer value.

My intuition is that particles come in infinite numbers of "generations" and we just so happen to be only able to measure three of them right now.

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Evidence suggests that's not the case, however. Consider the neutrinos, which also are observed to come in three generations. Cosmological evidence suggests that the sum of the three masses is ~1 eV. Detector experiments suggest that the lightest neutrino must be at least 0.05 eV.

Now suppose there's a fourth generation of neutrinos. Per the weak interaction, the Z boson can decay into a neutrino/antineutrino pair through the following diagram:

  Z -> 2 v

(one of these neutrinos v would be an antiparticle). Therefore so long as the decay is kinematically permitted, ie m_Z > 2 m_v, we will eventually see the decay.

But just what is the mass of the Z? Well, experiment has its value pinned ~45 GeV -- at least 10^10 times larger than the heaviest of the three lightest neutrinos. If there is a fourth generation of quarks, then the mass the mass hierarchy must be something like*

  v_1 :  0.00000000005 GeV 
  v_2 :  0.00000000010 GeV 
  v_3 :  0.00000000100 GeV 
  v_4 : 22.50000000000 GeV

And of course, v_4 could be larger! There's nothing physically preventing a fourth generation of quarks from being so massive (at least, that we know of), but to a particle physicist that would be a highly unintuitive discovery.

* The mass splittings for the quarks is known, but not their actual values. Don't quote me on these values -- they're just for illustration!

Cardinality is fundamentally integral, so if the basal layer of reality consists of discrete non-infinite configurations it should not be surprising that you see it resolve in some integral constants. Also, physical infinities have never actually been observed so you should definitely be more skeptical of that notion just on a prior basis.

Also, even if we take as given your supposition r.e. infinite types of particles, a variant of the question is just as interesting: why are only threes of them observable and why do our models seem to do a decent job of explaining reality with only threes of these infinite variants?

Everything in the universe is pinned at integer values. That's the reason quantum mechanics is called what it is.

Our model for everything in the universe is pinned at integer values. I think that's gp's point.

No, the physical evidence shows that everything in the universe is pinned at integer values in point of actual physical fact. It's not just our models. It goes all the way back to blackbody radiation and the ultraviolet catastrophe of the late 19th century. The evidence for QM is overwhelming. It's not just an artifact of our modeling.

The ultraviolet catastrophe is for sure a good example of this phenomenon.

What's the spin of an electron?

Yeah, so that's a core part of the unintuitiveness of Quantum Mechanics. Nature itself, it turns out, is fundamentally quantized. And also random too.

It objectively cannot be broken down into a continuum.

Neither of these are scientific conclusions — they’re philosophical positions built around an interpretation.

The sloppy way people present the Copenhagen interpretation as a scientific conclusion is likely what’s stalling science: it’s fundamentally built on an extraneous assumption, but everyone pretends their assumed interpretation is a conclusion.

We’re not gonna get progress until people assuming an extraneous assumption drop it and redo the last couple generations of physics to not depend on it.

Would you say the same for the number of dimensions? :-)

BTW, related to your idea... IIRC, Schuster and Toro had some work using continuous spin particles (just a special representation of Lorentz algebra) with a similar motivation. Can’t recall the details right now, but feel free to check out their papers/talks.

PS: To all the uptight commenters pooh-poohing parent... relax, and lay off it... this is a legitimate research question/direction that physicists think about. We just don’t have satisfactory or appealing answers yet.

“Unfathomable”? Why would you expect your uninformed amateur speculation (“intuition”) to be more plausible than the best modeling and experimental observation of generations of the world’s foremost experts?

We all have our own mental models of the world and expectations that derive from them. I don’t think that the parent is trying to say that their intuition is more plausible, only stating their surprise.

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