Is the hydrogen atom two hard little balls of matter orbiting one another, as we were taught in primary school, or are they a probabilistic soup with various, vaguely localized extrema?
If the latter, how do you even define the notion of diameter?
The definition is somewhat arbitrary, but still has some real physical significance. In actual fact, a proton is a field, so it doesn't have sharp boundaries. But the amplitude of the field still dies off very rapidly with distance from the center, so you can pick some arbitrary small value and say "the point at which the amplitude becomes less than this value is the radius of the proton". What matters is not really the number that you get out of this, but the fact that the experimental results of measuring this value appeared to change in the presence of muons. This was a phenomenon that was not predicted by present theory, and if it had held up, would have been a major breakthrough. One of the biggest problems in physics right now is that there are no experiments (except possibly this one) whose results are at odds with the Standard Model. That makes it hard to improve the model!
The thing about those particular questions is that they only tell us that the standard model is incomplete. Gravity exists. The fact that it's not in the standard model doesn't necessarily mean that the model is broken, just that gravity needs to be added somehow.
What we need more of are instances where the standard model makes a precise numeric prediction and it's dead wrong. That puts a spotlight on every piece of the standard model that went into the prediction.
(Edited for the pun I didn't intend.)
https://en.wikipedia.org/wiki/Charge_radius
It is one of several distinct possible notions of "size" for a particle.
Yes, I know that. I am simply giving a link to more detailed information about what lisper was describing.
What about Neutrino masses? Or the Muon 'anomalous' magnetic moment?
Is the wavelength fixed? Is it in meters?
Is it the field of a proton made up of multiple frequencies/modes?
Is a proton’s influence on fields extend to all space or is there a point (within the hubble sphere) at which a proton does not influence fields at all?
- A quantum mechanics wave function does not necessarily have a wave length or a frequency. It is a different concept from waves, although classical waves are a consequence of it.
- In QM all particles influence all of space. It is also too small an influence to make any difference.
If we say that new physics comes from inconsistencies (either between theory and experiment, or simply within a theory), then there is plenty of new physics to be done, for example the pretense that an electron is a fundamental particle results in the inconsistency with predicted infinite mass. (I claim to have a solution, but I am sitting on it because I believe with a bunch more effort it can explain the dimensionless number that relates planck charge with electron charge, essentially explaining planck's constant and QM in quasiclassical terms...)
My comment indicates unwillingness because I think I can deduce more from the insight. (resolving the infinite mass inconsistency was not in the original scope of my attempt, it just happened to roll out while trying to deduce the dimensionless ratio)
Anyway, the main point I was making was that there is plenty of work to be done, because theres plenty of unresolved problems left.
The usual deadlock picture (that theorists can't proceed if experimentalists don't bring new data, and experimentalists can't proceed if theorists don't bring good discriminative tests) hides either laziness or ignorance.
Usually these are describing expectation values of radial positions.
For the well-understood example of the hydrogen electronic orbit, the Bohr radius is the expectation value of the radial position of the electron. The electron has a wavefunction Ψ; When you calculate the expectation value of the radius r using Ψ (= \int_0^\infinity Ψ* r Ψ dr ) you find a value of about 0.5 nm.
People will drop the subtlety of the "expectation value" and just say "the hydrogen atom has a radius of about 0.5 nm".
The issue for the proton radius that the article did not delve into: There is currently more than one way to measure the proton radius. One is scattering (pitch another particle at the proton, look at how it "bounces" off), and another is spectroscopically (look at the energy levels of the electron, deduce the proton radius from the interaction of the electron orbit and the proton.) These methods do not give the same answer.
This paper[0] says that it is defined in terms of a "probability amplitude that an interaction between a photon of four-momentum q^μ (Q2=−q2) and a charged constituent of the proton can absorb such a momentum with the proton remaining in its ground state." So, not exactly a radius, but "radius" is an okay conceptual mnemonic.
Also, mass has nothing to do with size, or "stuff"-ness. A proton has about 100 times more mass than its quarks (from binding energy), but an atom has less mass than its protons and electrons added up (from the loss of potential energy). A top quark has about as much mass as an atom of gold, but again is just a point particle. And photons have no mass but the energy of photons bouncing around in a confined space does have mass.
Interactions between particles, waves, fields, etc. are quantized, which means there is a set of distances at which a given interaction can happen, and a set of distances at which it can't. This creates a boundary, often spherical, which can be described as having some "radius", and thus some "diameter".
Depending on the interactions you choose, a particle might have multiple diameters, or even boundaries with different topologies, but they're usually somehow related to each other for any given particle.
Yes.
> which means there is a set of distances at which a given interaction can happen, and a set of distances at which it can't.
... that's not how quantization works. The exact ways in which quantum effects are actually discrete is much subtler than in most popularizations. In fact, sharp effects with distance are more likely to be seen in classical models than in quantum ones because the quantum models often allow for classically forbidden effects to happen with small probability, which decreases as the distances increase. You only really see sharp transitions for "bound states"; for everything else (e.g. scattering experiments) there are wider or narrower peaks of more likely to occur depending on both spatial and other parameters.
The radius really is measuring "over about how much space is this particle spread", and while the exact details of how you define that can give different numbers, they are all measuring interaction widths -- how close something has to be to feel its direct effect. I say direct effect, because obviously the indirect effects such as through the EM field can be felt at great distances.
Note that this measure of spread is distinct from the how the wavefunction of the center of a particle is spread, which in the right states can be highly delocalized, even though the particle hasn't gotten any wider. Electron orbitals, for instance, can have different radii in different states (or topology, as you note, if you pick a cutoff that splits high-density regions in two), but the electron still has the same negligible (usually modeled as zero) radius in comparison to any orbital.
Consider a perfectly spherical hollow shell of mass, and an observer inside the shell, will she be attracted to the center of mass of the shell? No, let's see why.
We know that gravitational field falls of with distance squared ( 1 / r^2 ). Consider a random observer position, and a random direction. Now consider a cone tipped at the observer with the random direction as its axis, and also consider a second cone with the same cone angle but the opposite direction as its axis. So the observer position is where the 2 cone tips meet. Then consider the distance between the observer towards each patch of the spherical shell. The area (and thus mass) of this patch will scale with the distance squared, so if one patch is say 3 times further away than the other, it will be 9 times weaker due to 1 / r^2 gravitational fall off, but also 9 times heavier due to geometric scaling of the patch, so gravity due to the patches will cancel, and since the direction of the axis was arbitrary, the gravity of each part of the shell will be balanced by the gravity of a corresponding opposite part of the shell.
So when you are in an elevator halfway down the radius of the hypothetical spherical Earth, all the layers of Earth above you will cancel gravitationally, and the gravitational field will only be due to the mass of the Earth that is contained in the sphere up to your altitute with respect to the center of the Earth.
Similarily, when the electron is far enough from the (assumed spherical) proton, we can somewhat pretend the proton is a point particle. but when the electron is inside the proton, then the effective charge of the proton will be lower because of all the charge of the proton that is farther from the proton's center than the electron is invisible to the electron (since the electric field also falls of like 1 / r^2 ).
I hope that answers the question?
I was illustrating how in principle radii can be derived in a phenomenological sense.
I didn't read the actual papers by the experimenters of the proton radius determination, but it would probably require a modification of the Hamiltonian for the hydrogen atom, since usually one treats the nuclei as point particles.
There are plenty of ways to wave your hands about it, and I have been doing this for a long time and could give 100 different explanations. At the end of the day what do I see in my head when I think about the "diameter" of the proton? Basically a probabilistic soup which is confined to a small area.
The "wave function" of a quantum particle can tell you where it is but is not the same as the particle itself. Standard QM assumes particles are infinitesimal points, in QFT this leads to infinities which can be resolved if you assume particles have a "smeared out" radius. This "smeared out" radius is what the proton diameter should be related to when the more complete quantum and gravity theory is discovered.
Say you had ten different light bulbs. Could it make sense to talk about their differing light output as "diameters"? It wouldn't be defined in terms of a physically measured length of the bulbs, rather a diameter could be defined to be about properties of a light bulb.
Remember all these words are in some ways arbitrarily chosen by people. If you replaced the word diameter everywhere with "fat content" would all the math still work?
The math would still work fine. The problem would be it's even less understandable than diameter, and it makes it less efficient as an abstraction that you can grok and reason about.
I dunno about simpler, but it certainly helps explain many of the weird effects we’ve observed in the universe. I recently went down the Quantum Field Theory rabbit hole (thanks to PBS Space Time on YouTube) and it’s an absolutely fascinating topic (even if the maths is beyond me) and QFT especially both makes sense to me and explains a lot of the “problems” with particle physics as I learned it in school.
I suppose you have to pick a probability criteria for the diameter.
> an electron [...] spends part of its time inside the proton (which is a constellation of elementary particles called quarks and gluons, with a lot of empty space).
Nuclei are quasi-classical little balls. It's electrons that are wacky quantum weirdness.
Which makes the current pedagogical emphasis on electrons, rather nuclei, as a foundation for understanding atoms... perhaps miss some opportunities for greater clarity. And that's even before getting to state standards that require teaching both "atoms are conserved in chemical reactions" and "atoms are electrically neutral, so if charged, they are no longer atoms, but ions". Sigh.
Nucleons overlap (not orbit), but nuclei aren't homogeneous, especially light ones. Light nuclei are well described as clusters of alpha particles, heavier ones as liquid drops. Ground states are generally more or less spherical. Though Neon looks like an old-style wine bottle, with a tetrahedron of alphas in the bowl, and a fifth making a neck. Non-ground states for lights are mostly rearranged alphas, for heavies, variously distorted balls. Fission is droplets stretching and necking apart.
A proton is a mix of odd shapes, but directly measurable properties are spherical. It's just a ball.
Nuclear mass and charge density are, to a good first approximation, colocated. You don't have mass concentrated one place and charge somewhere else. No surprises.
Electrons are a peak with exponential falloff, making choosing a radius quite arbitrary. What's the diameter of a cartoon volcano, that blends seamlessly into plains? Wacky, wacky electrons.
Nuclei have a flat-ish density plateau, then a steep slope, and only then a tiny exponential footlands (Woods–Saxon potential). So it's just a ball with a fuzzy edge, rather than a wacky exponential cloud thing.
Note the narrow range of sizes being discussed. No one is suggesting 10 femtometers, or 0.1 femtometers, or even 1.0 fm or 0.8 fm. "GEOID-Next committee tables discussion and heads to a bar, unable to agree on the shape of the Earth!!! News at 11!!!" But for most everyone, primary school up, that's "a femtometer ball".
A superball can be bounced, and crushed, and burned. You need polymer physics to understand just why it behaves as it does. But you can describe that behavior to a Kindergartener. They don't need polymer physics. Nuclei are just little balls.
Now look at the giant hairy mess of this thread. It's like, we teach "4/3 pi r^3, 4 pi r^2", but not "the volume and area of a ball are half of its box". But dialed way way up. Science education, variously distracted, failing to provide a coherent briefing on the physical world.
If anyone has ideas on how to describe this point, I'd appreciate them, as I've never come up with something nice.
Here's a tiny Neon pic. I just think Neon is cute. https://arxiv.org/abs/1406.2473 page 4. There's a nicer one somewhere...