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.)
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 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.
> 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...
A more nuanced description (which is not exactly quantamagazine's forte) would note there is a conundrum about the proton size. The article describes a measurement that falls under "spectroscopic methods" in the wiki .
Why eg scattering measurements should yield a different value is not at all clear.
This reminds me of a joke. An experimental physicist walks into a theoretical physicist's office with a really cool experimental result, shows the printed out graph to the theoretician. He thinks for a while and says, "this is perfectly in line with theory, let me explain how". The experimentalist looks at the graph, scratches his head, says "uh, this is upside down", and rotates the paper 180 degrees. The theoretician thinks a while more and says, "well this can also be explained".
The results from Hessels were announced as preliminary results more than a year ago -- it's great that they are finally out peer-reviewed. But the community at large didn't stop back then when the results came out, with more experiments planned all over the world, especially but not only in the scattering sector. We made progress, but the puzzle isn't dead yet. There is actually a conference starting next week on this topic: http://ecsac.ictp.it/ecsac19/
It's a rare occasion where nuclear physics and AMO overlap. Another one is the Zemach radius, which also requires knowledge of the proton magnetic form factor.
I think if we were closer to ideal science, we'd work harder to verify numbers as a first step. More replication means stronger foundations and less wasted work.
There will always be some bad results that stick around for a long time before being overturned. But the median lifetime of bad results can change based on how we prioritize research. That statistic might currently be far from optimal.
However, I wanted to commend your reply. It seeks to educate without judgement. Cheers.
The problem is, and has always been, that these alternative theories are never as accurate or precise as GR and their observational evidence is never as good as what we have for DM and DE.
It's not a conspiracy that scientific consensus is that they both exists, and no one is preventing research into alternatives being done. Significantly more money goes into research that accepts their existence, yes, but that's because most scientists do as well. What outcome do you want? To force scientists to work on theories they don't put any stock in? There is still plenty of interest in research papers written by people advancing alternate theories. Good ones are widely read by the entirety of the community, but you make it sound like the scientific community is actively suppressing anyone from researching anything that casts doubt on the existence of dark energy and dark matter, and that's just not true.
I wonder if we figure out how to regrow a damaged heart into a healthy heart with a simple injection and 10 weeks of physical therapy if hope will die in all those cardiologists out there who no longer are able to push the boundaries in heart transplant surgery or heart substitutions.
What is the effect on people who have spent their lives becoming an expert in a field or subject which now seems to be "done." I could imagine they might lose hope.
I mean, I clicked because I thought, "Hope dies? I'm sure that's an exaggeration..."
I'd say the writer has a tendency to write gloomy headlines: https://www.quantamagazine.org/famous-experiment-dooms-pilot...
It's pretty sickening to watch the (sadly predictable) HN sneering and mockery around the topic of someone's (anyone's) mental health. It's such a cruel, distorted and completely non-constructive conversation. Do you guys really not have anything more interesting to say?
You get all this from "make sure they're doing ok?".
So... how do we know that we will not find some bizarre scenario in the future the throws the Standard Model into a similar existential crisis?
I say keep your mind open.
"On the role of the Michelson-Morley experiment: Einstein in Chicago" http://philsci-archive.pitt.edu/4778/1/Einstein_Chicago_Web2...
It seems that the development of quantum mechanics has been much more driven by experimental results, although there are exceptions, such as Dirac's prediction of the positron.
Though we'd have to hope that, unlike that novel, we don't accidentally set off a vacuum collapse. That would be unfortunate.
We just need to observe the collisions happening at these energies - we don't necessarily need to produce them ourselves.
Some physicists are starting to think about how we might be able to observe naturally occurring collisions at these energy levels rather than producing them ourselves.
I'm having trouble finding the articles I've read on the subject - I'll follow back up if I do manage to find 'em.
- The standard model doesn't explain any of the rest masses of the fundamental particles nor any of the coupling constants and a bunch of mixing angles. I think in total there are more than 30 input parameters that are completely unexplained
- Neutrino oscillation/masses are NOT part of the standard model as it predicts them to be massless
- Gravity is just not part of the standard model and currently cannot be combined properly with the other fundamental interactions
the harder it is to find flaws in the Standard Model, the harder it would be to use such new physics in engineering.
Basically I'm curious whether continuing failures to find new physics can be taken as evidence that, if and when we find the new physics, it will be very difficult to apply.
I'm not against science for its own sake, however. Just more of an engineer than a scientist, myself.
But it might be just more difficult qualitatively, like some different and non-intuitive way of interpreting everything, which might only require switching a few equations and changing some procedures.
I think people have been misled by science fiction. Stories posit all sorts of interesting and exciting physics not because that's plausible, but because it makes interesting stories.
But maybe it's under a completely different rock, that we haven't thought of turning over.
I think that is very likely, but not necessarily guaranteed. I use similar logic with regard to FTL and time travel; if physics has not quite entirely ruled it out, the window is getting smaller and smaller, and is already to the point it's entirely plausible that even if it's theoretically possible there may be no conceivable engineering path to get to it, even for a hypothetical civilization that can fling black holes around.
However, we can't entirely rule out the possibility that some new physics will come along that will reveal how to easily "flip" matter into anti-matter (there seems to be no fundamental reason why this is impossible, it's just... too hard to be useful), or enable the creation of some state of matter or energy that may be exceedingly unlikely to be created naturally , but once created could be leveraged into something useful, or other such things. Stabilized muon fusion ? Relatively & QM fusion will certainly reveal something new about gravity; it can't be entirely ruled out that it will in some way be useful to engineering. (Although in this particular case, remember we can eliminate not just the "scientific" theories, but also observe engineers have yet to blunder into anything that seems to indicate any manipulation of gravity in any sensible way. Every real-world device ever built is also a test that shows that particular device must not be doing large-scale gravity manipulation.) Will quantum computers reveal some limit of reality's ability to calculate, and will that limit somehow itself turn out to be useful? Maybe.
Still, I tend to think that as much fun as flights of fancy about time travel, FTL, or bizarre alien tech can be, that the most likely hypothesis by far is that we are indeed very unlikely to discover anything in particle physics anymore that will be of any engineering value.
But I wouldn't counsel disappointment. There's still a lot of room at the bottom. We're not going to run out of technology in our lifetimes. If particle physics bores you, check out what's going on in materials science. They're making qubits sing and dance on command. It may still not build UFOs, but they're doing weird stuff in there.
: As a sort of example, see: https://en.wikipedia.org/wiki/Strangelet#Dangers (Stranger Danger has nothing on Stranglet Danger.)
Albert A. Michelson, 1894, just 11 years before Einstein first published about special relativity.
But see https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_p...