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Comment by Koshkin | Hacker News Reader

The article keeps talking about "the size of the proton", its "radius", etc., but I would like to point out that the proton is not a sphere and does not, in fact, have a size in the normal sense, being an aggregate of three other particles; so in this case the notion of "size" itself must be defined in some pragmatic fashion before any meaningful statements about it can be made.

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It's true that there's a sense in which the size of the proton is undefined. But there is also a sense in which it is very precisely defined, which is the root mean square of the electron scattering cross-section. This can be measured very accurately. And that's what the article is talking about.

https://en.wikipedia.org/wiki/Charge_radius

> the root mean square of the electron scattering cross-section

Thank you, and I wish the article had said that.

While you can measure it via scattering, it's not the square root of the scattering cross section. The radius is defined via the slope of the proton electric form factor at Q^2=0. This translates to the root mean square radius, that is the sqrt of the integral of r^2 weighted with the density, i.e. sqrt ( Integral r^2 rho(r)).

Hmm...perhaps it has been edited since but that's exactly what the parent says.

I feel it necessary to point out that the proton is only an aggregate of three other particles on average. It's three quarks, plus several gluons mediating interactions between the quarks, and lots of virtual quark-antiquark pairs.

... and the muon that "spends more time inside the nucleus", according to the article.

(You direct your sarcasm at an easy target; it is also too easy to turn a blind eye to all the glaring omissions and gross misrepresentations - i.e., effectively, lies - purposefully made in popular texts for the sake of making the material more "accessible" for the general reader.)

Well, it's not so far off. Every time you "look", the wavefunction of the lepton collapses to a point. For the muon, that point is more often inside.

That is understood, although it leaves me wondering if this could be interpreted as the hydrogen atom being only slightly larger in "size" than its nucleus. (Point being, nothing is "obvious" at that scale.)

The proton is something like 100000 times smaller than the orbit of the electron. Both are not usual object, so there are a lot of technical details about how you define the size of each one, but the proton is definitively much smaller than the hydrogen atom.

The electron is inside the proton only a tiny amount of time [1] but it's enough to measure it.

[1] A better explanation should use probabilities and wave functions, but the main idea is that.

That's a kind of common misconception. Nothing collapses. Measurement system (e.g. your eye) just gets entangled with particle in the same way particles get entangled to each other, in a particular state.

Well, the question of measurement in QM is somewhat deep one, and no theory should be dismissed off-hand. The notion of "collapse", in particular, can be seen as expressing the non-unitarity that is intrinsic to considering measurement as a non-reversible process (which means that it there's too many things that get entangled with the particle - not just the eye but also systems in your brain, for example, so that the process becomes effectively irreversible; one can also say that the process that has lead to creating information cannot be undone).

It can be undone though, right? https://en.wikipedia.org/wiki/Quantum_eraser_experiment

Or do you mean that the point where it can no longer be undone in principle can be considered as a cutoff for "collapse"?

Irreversibility is essential in creation of information, i.e measurement.

I thought that unitarity was also preserved in quantum mechanics, which is linked to the law of preservation of information , which induces reversibility. This was the central question about black holes destroying information being a problem, which gives rise to the problem of black hole firewalls. If information is truly destroyed, then quantum mechanics has a deep flaw

Even if information can be destroyed ("erased"), it is not by way of reversing the process that lead to its creation, the latter thus being necessarily non-unitary. This, in fact, is a requisite for the notion of measurement to make any sense.

The point here is to consider what the claimed "non-reversible process" means in a quantum theory that as of current does _not_ allow for destruction of information.

It might be more correct to say three valence quarks?

Technically nothing has "size" in the sense that you are intuitively defining it to be. All matter in the universe is collections of point-like (but also wave-like) particles without defined shape. It'd be totally fair to throw the critique back at you.

I don't think it would - for the obvious reason that when we talk about the size of, say, a desk, there is never a concern about its meaning, and we rarely, if ever, think about the object itself in terms of waves or particles. Protons etc., on the other hand, is a totally different matter, and since everyday notions cannot be trivially applied to such objects it becomes important to be clear concerning the meaning we choose to give to the word.

That says more about the weirdness of our intuitions than reality. Reality is not weird. We are.

Maybe. More likely our inferred assumptions about the things we can't see are off or wrong.

Why do you say that's likely? The data points otherwise.

Desk size is the same - sqrt mean square of scattering cross section of people, books, etc. with the desk :)

I just hope it doesn't collapse when anyone looks at it.

See it’s not my woodworking skills at all, it’s just the nature of matter in our Universe.

Technically, the point-like properties come out of the mathematics used, not the experimental measured. The problem with point-like is that this brings singularities to the fore when we do not measure singularities.

Singularities makes the mathematics simpler (an approximation to the reality being worked with). Keep in mind that QM and all of its associated trappings are approximations (useful but still approximations). This is no different to the use of mathematics in any other field.

The point-like properties don't just come out of the mathematics used. You can fire electrons at each other and they scatter as if point particles so that aspect of them is an experimental observation also.

Particles absolutely interact as points as well as as waves. Neither model captures their behavior accurately. They are a wave-particle thingie and that’s just what reality is.

> The article keeps talking about "the size of the proton", its "radius", etc., but I would like to point out that the proton is not a sphere and does not, in fact, have a size in the normal sense

The "normal sense" for _any_ measured value, in order to be considered a reliable measurement, whether it be length, weight, or number of electrons contained within, must necessarily be established as an average of independent samples sufficient to narrow the measurement error to within the desired precision boundaries. You might as well say that you don't have a height in the normal sense because some days you stand slightly more erect than others, except that would be a misunderstanding of "normal sense" and also "height". If you can only reliably measure protons along a single particular dimensional axis, and then only on average through sampling, then you have no way of saying that it isn't actually, factually, literally a sphere, and using spherical measurement terms is reasonable. If you want, feel free to mentally prepend the word "approximately" any time you read any measurement of anything. It will always be slightly more accurate, even when just counting things.

Also https://en.wikipedia.org/wiki/Spherical_cow

It's a pop-sci article, and it does a wonderful job explaining what's going on

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