Note that this is not a 3D crystal of electrons floating in vacuum.
It's a 2D crystal of electrons that live in a thin semiconductor that is sandwiched between two layers of other semiconductor. You can't pick it with a tiny gripper.
Moreover, I don't understand all the details, but IIUC the surrounding semiconductor provides an effective force that makes the electrons attract each other when they are not too close. So in some sense, the crystal is formed by the electrons, but this does not break the expected behavior of a 100% pure negative particles in vacuum.
On a slightly different topic: do you think it would theoretically be possible to build stable 3D structures composed on positrons and electrons (and not have them annihilate each other)? I don't really understand the physics of why electrons don't collapse into the positive nucleus, since positives and negatives should attract, but I'm wondering if the same interaction keeping protons and electrons apart in an atom could come into play with smaller particles like electrons and positrons alone.
> On a slightly different topic: I don't really understand the physics of why electrons don't collapse into the positive nucleus, since positives and negatives should attract.
Good question- this was a clear and troubling problem in the classical atomic models before quantum mechanics. Thinking of electrons as little balls whizzing around, being attracted and repelled by various field forces does seem to lend itself to this question.
The current understanding is that since electrons are quantum particles, they can only gain or lose energy through quantized packets, and can only occupy certain energy states. In fact, it's much more accurate to describe electrons by their probability fields, and not as those little balls. Quantum mechanics then describes probability shells called Sommerfeld orbits, where the chance of finding an electron at any given point peaks. Unless energy is added or removed from the system by those aformentioned quantized packets, electrons tend to remain at their respective energy levels and shells.
> The current understanding is that since electrons are quantum particles, they can only gain or lose energy through quantized packets
Just to clarify. An electron moving freely through a vacuum can move at any speed; it is not restricted to certain energy levels. (Speed and therefore kinetic energy is relative to the reference frame anyway.)
The quantization of energy comes into play when the electron is spatially confined in some system. This is related to the wave behavior of the particle, and because energy is related to wavelength. Much like how a standing wave on a string can only have wavelengths such that an integer multiple of them fit on the string.
Great answer! I'm still left wondering exactly what it is about the behaviour of an electron in the lowest orbit that is stopping it from getting closer to the nucleus. Maybe even thinking of it as 'stopping' at all is my problem. Guess the standing-wave analogy below is actually pretty good for understanding that aspect and also accepting that it's a probability field, which does have nonzero values 'inside' the lowest orbital, so it can be 'found' (measured to be) closer in, just much less often.
I'd guess having an intuition about why only the first orbital is spherical is probably part of understanding this all properly too, will keep-on reading!
> I don't really understand the physics of why electrons don't collapse into the positive nucleus, since positives and negatives should attract
My (student of physics) answer to that would be that they are pretty much collapsed as much as they can. It’s just that under quantum mechanics that least energetic state is not the one in which the electron is perfectly co-localized with the positive charge. (As that perfect co-localization is not even physically attainable.)
It's maybe worth mentioning that, pre-quantum mechanics, this was so far from being a naïve question as to be one of the motivating concerns of early-20th-century physics. It's not the same thing as, but is closely related to, the ultraviolet catastrophe (https://en.wikipedia.org/wiki/Ultraviolet_catastrophe).
> (As that perfect co-localization is not even physically attainable.)
But then, you have (or would have.. I think it's not experimentally verified) degenerate states of matter, like in a neutron star, where pressure is so big that the electrons collapse into protons to form neutrons.
> It seems to me this is simply a statement that an electron is a fermion not a boson, right?
Not really, that's a property of any quantum particle, bosons also. They don't occupy a single point in space like you would imagine classical particles do. They also cannot occupy a single point in space relative to another particle.
> It's a fermion, but why should it be?
Well there's the spin-statistics theorem in quantum field theory which starts from some likely assumptions and then shows that particles with non-integral spin must be fermions while particles with integral spin must be bosons. Other than that I take it simply as an experimental fact. I don't think there's a nice reason for it one could give (today, that is).
Fascinating! I would love to gain more of an intuitive grasp on how subatomic particles all work and fit together, i'm not a physicist though. Could you suggest any good introductory reading?
I like to read Wikipedia and popularized stuff. The problem is I come away unsatisfied, because even the best writing directed at people who aren't good at math, is more about giving the feeling of understanding than actual understanding.
My point about bosons and fermions, is I read the summary on Wikipedia, but they are just labels to me. I don't have the intuition or math except that it says the one kind of thing can "overlap" in ways the other can't.
Richard Feynman's "QED: The Strange Theory of Light and Matter" has been much praised though. What did I get out of it? I guess that quantum mechanics has something to do with multiplying complex numbers.
I'm not sure exactly what I'm missing, but I get the impression that if I could understand Hamiltonians, Lagrangians, or variational calculus, then I would have some insight into modern physics.
Some of it sounds tantalizingly straightforward, but at the same time beyond my mental capacity - imagine a space, a field, etc. - but it's infinite-dimensional or something. Or it's a space of functions.
Still, on Wikipedia you can keep clicking on things - what's a "fiber bundle", etc.
Ah whoops! It sounds like we're in a very similar boat indeed! All good, nice to meet a like-minded soul on HN.
I completely know what you mean about the complex numbers and Hamiltonians etc. A lot of the time I think I could even have a reasonable chance of understanding the concepts given a few graphs/diagrams and some kind of translation to prose/pseudocode (or even just code) but there is so much symbolic syntax in both maths and physics (too much for me!) - I think it's probably hard to become fluent unless you use it every day I reckon.
I can also imagine something like a 'reasonably realistic' subatomic particle simulation framework in a 3D engine where one could fully control time space, energies, polarisation, quantum stuff etc and really examine the events in detail. I think one could perhaps start to get a feel for how it all fits together just by playing with the various interactions and watching/virtually-measuring carefully?
> Earnshaw's theorem states that a collection of point charges cannot be maintained in a stable stationary equilibrium configuration solely by the electrostatic interaction of the charges. This was first proven by British mathematician Samuel Earnshaw in 1842. It is usually referenced to magnetic fields, but was first applied to electrostatic fields.
I was confused by not seeing an explanation of where the attraction comes from (there shouldn't be any). Sounds like the top and bottom layers push the electrons together and the electrons settle into a hexagonal grid like a flat arrangement of balls would.
To me being able to measure/observe a thing like this is a whole other level of amazing.
It's too far from my area to be sure, but let's guess ...
Perhaps it similar to the Cooper pair effect. In this effect, it looks like electrons inside a conductor attract each other. From https://en.wikipedia.org/wiki/Cooper_pair
> Although Cooper pairing is a quantum effect, the reason for the pairing can be seen from a simplified classical explanation. An electron in a metal normally behaves as a free particle. The electron is repelled from other electrons due to their negative charge, but it also attracts the positive ions that make up the rigid lattice of the metal. This attraction distorts the ion lattice, moving the ions slightly toward the electron, increasing the positive charge density of the lattice in the vicinity. This positive charge can attract other electrons. At long distances, this attraction between electrons due to the displaced ions can overcome the electrons' repulsion due to their negative charge, and cause them to pair up. The rigorous quantum mechanical explanation shows that the effect is due to electron–phonon interactions, with the phonon being the collective motion of the positively-charged lattice.
This attraction is too small and is only important when the temperature is very low, and is the explanation of low temperature superconductivity.
<guess> So perhaps there is a Cooper-pair-like effect here, that creates the illusion that the electrons attract each other. They are using semiconductors, so perhaps it's caused not by the movement of the nuclei, but the movement of the holes in the other semiconductor.</guess>
> It's a 2D crystal of electrons that live in a thin semiconductor that is sandwiched between two layers of other semiconductor. You can't pick it with a tiny gripper.
Somehow as a layman I suspect it isn't a crystal in the lay "stays super stable for super long periods with no energy input" sense, but in some other scientific sense. Can a future, more advanced version of this structure theoretically store energy in this form?
Maybe faulty video decoder on your phone? (Or maybe another device, but that's rather unlikely due to instant fallback to software decode if there's a problem.) The video is in a weird resolution, so your decoder may tripped up there.
According to the article scientists have been trying to prove this structure for eight decades. Then two independent groups report having successfully done it in the same month! What are the odds?
There are quite a number of similar coincidences in the history of science. It seems to me that at some point the necessary knowledge or techniques are just there to make some discoveries almost inevitable.
It'd be cool if these could be made in a material transparent to protons, then it'd be a good anode for polywell fusion without the energy loss to Bremsstrahlung radiation.
Potential dumb question ahead: how, or does, this relate to the Uncertainty Principle? My five-year-old brain says that freezing the electrons in a lattice so that they don't move means that there's no momentum or velocity, and therefore we should have an infinite? uncertainty concerning position.
Obviously something is wrong in my understanding or in the precision of the article's discussion. Can someone ELI5?
They are not 100% frozen in a 100% perfect lattice structure. They still move a little around the positions where they "should" be. Something similar happens with atoms in a normal crystal.
> They are not 100% frozen in a 100% perfect lattice structure. They still move a little around the positions where they "should" be. Something similar happens with atoms in a normal crystal.
Thanks for the explanation. In retrospect this seems like it should be obvious (at least for some definition of obvious); I was probably reading a little too hard.
The distances between electrons in this lattice are enormous compared to the electron, even bigger than the typcial distances between atoms in a lattice, so being essentially dead still in the overall lattice structure doesn't imply much about the certainty of the position of the electron at the scale the uncertainty principle implies.
The uncertainty principle says something different than the common understanding.
It says that if you have an ensemble of identically prepared systems, the product of variances of non-commuting observables obtained by measuring different instances in this ensemble will have a lower bound.
“ Wigner participated in a meeting with Leo Szilard and Albert Einstein that resulted in the Einstein-Szilard letter, which prompted President Franklin D. Roosevelt to initiate the Manhattan Project to develop atomic bombs.
Wigner was afraid that the German nuclear weapon project would develop an atomic bomb first. ”
It's a 2D crystal of electrons that live in a thin semiconductor that is sandwiched between two layers of other semiconductor. You can't pick it with a tiny gripper.
Moreover, I don't understand all the details, but IIUC the surrounding semiconductor provides an effective force that makes the electrons attract each other when they are not too close. So in some sense, the crystal is formed by the electrons, but this does not break the expected behavior of a 100% pure negative particles in vacuum.