How Big Is a Proton? | Hacker News Reader

How Big Is a Proton?

sparkonit.com

91 pointsconse_lad51 comments

>> The new measurement puts the size of the proton to around 0.833 femtometers, against the previously accepted figure of 0.842 femtometers.

1 femtometer = 10^−15 metres. Also commonly called a fermi.

It's a quick read, worth the click to read how they measured it, and at least see CERN's imagined rendition of what the "turmoil of quarks and gluons" that make up a proton might look like.

> The new measurement puts the proton's radius to around 0.833 femtometers, which is 4 percent less than the previously accepted figure.

How is 4 percent less equal to 0.833?

  0.96 * 0.842 = 0.808
  1.04 * 0.833 = 0.866

Well, that rules out the obvious possibilities.

0.842 is also an experimental result, not the official figure.

I should probably have reread the full section. It's more clear in context that 0.96 * 0.8768 = 0.842.

4% less than the official figure of 0.8751 fm.

I was somewhat disappointed to see the rendition fail to follow color confinement :(

Could you elaborate on this please?

Due to how quantum chromodynamics works, free particles should be white (or colorless). That is, their constituent particles (in this case, quarks and gluons) have a “color” (red, green, blue for quarks, and their inverses for antiquarks) and they must come together in such a way to cancel out in any free particle like a proton.

So here the 2 red 1 blue means 2 up 1 down, right? And the QCD color is different from this, and so it's misleading?

Oh, is that what the color represents? I thought it must have been color charge…

That artist's rendition of a proton looks like how I imagine a Shoggoth from HP Lovecraft.

We really are made of just a bunch of wibbly-wobbly "stuff".

We are mostly nothing to a very very precise approximation of 100%.

Well, for sure, yes. But that nothing is definitely wibbly-wobbly, right?

This makes me think about just how bizarre we are at multiple levels. Quantum foam of nothing and probabilities, atoms and electrons and forces, then molecules making up DNA and cells, and then us enormously huge humans.

One of the most interesting molecules is the Ribosome, the 'player' if you wish of an RNA molecule that assembles proteins out of the soup it floats in.

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

It's a real life nano-assembler and there are billions of them in your body (and about 10 million give or take per cell).

> 10 million give or take per cell

That just astounds and confounds me. An astonishing amount of stuff in just one cell! We're amazing beings at so many levels. Thank you for that link :)

Wait until you realize that the total length of all the DNA in a single cell is 3 Km... How's that for folding@home ;)

I find this somewhat baffling. 4% just seems like such a huge disparity, especially for such a ubiquitous particle. It seems like any experiments before 2010, that used the size of a proton in the calculations should have noticed something was wrong. Fermilab has spent the last couple years trying spruce up an old experiment to measure the dipole-moment of the muon down to 0.14 ppm[1][2] Apparently that small of a discrepancy in theory and experiment was interesting enough to throw a huge amount of time into. How is it that we are trying to verify the 9th significant digit in the dipole moment of an obscure particle, while something as mundane as the size of the proton was off by 4%? Obviously, I'm missing something.

[1]https://en.wikipedia.org/wiki/Muon_g-2

[2]https://www.youtube.com/watch?v=UckuqHDB08I

The proton is so small that its finite size only shows up in a few purpose-built experiments such as the one explained in the article. Since the effect is very small, measuring it to high precision is extremely difficult.

It is also worth noting that protons are much more complicated particles than muons and their theoretical description is much less well developed.

>When a hydrogen atom is in its lower energy state, the electron not only orbits around the proton, but rather stays inside it.

This is the first time I have ever learned this is possible in all my years of schooling and working in science. Fascinating, this article changed how I think about the universe.

You should not think of the electron as occupying some fixed point in space. It makes more sense to talk about the probability distribution of the position.

We have decades of ball and stick models along with solar system like atomic diagrams to thank for that. And it's compounded by the fact that we say electrons orbit so people immediatly think spherical planet like objects orbiting a sun like nucleus.

Yes, and Bose Einstein statistics can be obtained either by assuming indistinguishable particles, or that this probability distribution fluctuates uniformly. No experiment can decide between these explanations; the physics comes out the same. These are two stories to go with the joint distribution, which is what we actually observe. One could wonder why we need "thought glue" at all to explain particle physics in the language of human-scale physics. The joint distribution is what it is. No need to accept the second story; there are likely others. But one is entitled to roll one's eyes when hearing about indistinguishable particles.

Ditto for the proton itself.

Another article that fails to mention two out of three accurate measurements done on regular hydrogen since 2010. The news article about the most recent measurement gets it right: https://news.yorku.ca/2019/09/05/scientists-measure-precise-...

If a proton is a [probability] cloud, what exactly does the size measure? where that cloud's probability goes to zero?

It's defined as the slope of the electric form factor at Q^2=0. Since that is not a very helpful definition, with some hand-waving, you can say it's the root-mean-square radius of the electric charge distribution. The proton has also a magnetic radius, defined via the magnetic form factor. And something called a Zemach radius, which is a combination if them both.

I was thinking more or less of the same question. Our intuition of what a particle "is" has a lot to do with how we perceive macroscopic objects. But particles are not really the same kind of thing. Or are they? Is their size correlated with their mass? Do particles consists of some "fundamental matter" or are they more like little machines?

I suppose that if you measure a probability-cloud long enough, you can arbitrarily bring down the inaccuracy of the size (?)

Square of the complex probability doesn't go to zero anywhere IIRC, the radius is at some arbitrary threshold.

It's really incredible what our everyday mundane world is made of... especially taking into account the quantum realm.

Yes. For example it’s mind boggling that most of your mass is due to kinetic energy of quarks zooming around each other at relativistic speeds pulled by the strong force.

This seems really interesting. Could you explain more about the strong force and this "kinetic mass" effect? I thought quarks had mass, and that's where my mass comes from?

the quarks have it own (rest) mass, but quite tiny compared to when you include binding energy (9 Mev vs 900 Mev)

Rest-mass being a somewhat difficult concept if your particle only "exists" in bound systems, i.e. is confined. But yeah, forget the Higgs, almost all the mass you see around you is generated dynamically by non-perturbative QCD.

Edit: More explanation: If you take the quark masses as unbound rest mass, it's not clear why the proton is bound -- it would have higher energy (=mass) than the unbound constituents. This is different from atoms, as a hydrogen atom has slightly less mass than the sum of a free proton and free electron (13.6eV in the ground state).

I first read about it here.

https://profmattstrassler.com/articles-and-posts/particle-ph...

Omg, I love this idea -- it's comprehensible. Is there a source for this?

Here's one... https://www.fourmilab.ch/documents/golden_glow/

https://www.youtube.com/playlist?list=PLsPUh22kYmNCLrXgf8e6n...

Wait, I thought my mass is due to Higgs boson, no?

Not really! The Higgs mechanism explains why elementary particles, such as quarks and electrons, have non-zero mass.

Almost all of the mass of ordinary matter is composed of nucleons (protons and neutrons), which are made of 3 quarks each. But the quarks' masses only account for about 1% of a nucleon's mass. The quarks are bound together incredibly tightly by the strong nuclear force (mediated by gluons), and it's the mass-energy associated with this gluon field that is responsible for the remaining mass.

https://en.wikipedia.org/wiki/Proton#Quarks_and_the_mass_of_...

The quark mass is somewhat misleading: It's not the mass of a "free" quark, that doesn't exist, because of confinement. The incredible strong nuclear force actually /lowers/ the mass of the proton compared to the sum of the unbound constituents, from "infinity" to some finite value. Strange, I know, but similar to what happens with the hydrogen atom: In the ground state, it's 13.6 eV less massive than the sum of the mass of proton and electron.

Wow. Where can I read more about this?

https://www.amazon.com/Mass-understand-matter-quantum-fields...

or you can hear the author explain the key bits here:

https://www.youtube.com/watch?v=HfHjzomqbZc

"The Dreams that Stuff is Made Of"

Physicists have "observed quarks" for a long time in the sense that if you scatter protons against protons or other particles, you can see that the proton scatters particles as if it was made up of three little particles.

Not a physics guy, so my understanding is probably wrong. Aren't all particles infinite in size and are just blips in the fields behind our universe?

The "wave function" that we use to model a particle's state has indefinite extent, but when the particle actually interacts with something else, it does so in a single, small location (from our perspective.)

When they talk about the proton radius, they're talking about the radius of that interacting object, not its wave function. The wave function can be thought of as describing the probability of an interaction finding the particle in a particular location.

Isn't there a contradiction in your answer? Since the probability of interaction far away is not zero, why is it not included in the "radius of that interacting object".

"Radius of the interacting object" was poorly worded. I was referring to the radius of the interaction itself, which is much smaller than the extent of the corresponding wave.

For example in the double slit experiment, the interaction occurs on a detector screen in a single, small location with a radius on the order of 10^-15 meters (subatomic), whereas before it interacts with the screen, the wave extends throughout the experimental apparatus.

A neutron star is so dense that a matchbox sized portion of one would weigh 3 billion tons.

https://clearlyexplained.com/neutron-stars/index.html

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