Comment by simcop2387 | Hacker News Reader

Comment by simcop2387 | Hacker News Reader

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Disclaimer: I have a theoretical degree in armchair physics, not a real one.

So that's where the fun of Quantum Mechanics and uncertainty comes in. Electrons are not just point-like particles, they're sort of both particles and waves. If you nail down exactly where the electron "particle" is, then you end up with it's momentum being less defined, meaning that you're not going to be able to say anything at all about where it came from, where it's going, or how fast. Similarly if you can nail down it's momentum perfectly it won't have a definition of where it is anymore. This isn't the Observer effect, where you making the measurements changes the system, but in fact that the other related property actually ceases to have a valid definition anymore (I'm not well versed enough to say it stops existing with any confidence but that's my understanding). This leads to a situation where you end up measuring a probability density of the property of the electron, so you get a density of it being "around this point +/- some amount" and with a "momentum +/- this amount, and sort of in this direction". This means that you now have a probability density of the electron where you'll see it's effects of the negative charge and kinetic energy and those are the things that describe that "cloud of negative charge". The main effect of this that affects things is that you end up with this cloud of all the electrons around an atom and you don't ever observe the individual electrons, just the shells/clouds around the atom and how they change as energy is inserted into the system.

My layman's understanding is that essentially as you make a measurement/system/whatever where it's designed to see the position more than the momentum you'll see more point-like particle behavior, but never only just that (you can't ever nail it down to an infinite precision, if you did it'd have a momentum that could send it off at the speed of light as if it had no mass) and in the other case if you could measure infinite precision on the momentum you'd end up measuring the electron as if it was "everywhere" in the universe all at once, which is just as nonsensical of a result as the first one.

Not bad for an armchair physicist. Disclaimer, my undergraduate degree was in physics but I'm not a quantum expert by any measure and my graduate work took me closer to statistical mechanics.

So for the simplest explanation for you and the parent is that as you said electrons are both particles and waves, there are experiments that we can demonstrate for that. But if you're thinking of the electron cloud then that exists partially because you aren't measuring the electron. Basically this particle(s)/wave(s) orbiting the atom can exist in a lot of different configurations at once determined by it's energy (which is influenced by its/they position and how fast it is/they are moving). For educational purposes we often treat them more exclusively as a particle (early electrodynamics) or a wave (early quantum) depending on what field we are talking about.

Of course there is greater definition I can give to what it is if we want to start talking about what protons and neutrons are made of and most of that is what occurs at the LHC. (But I'm heavily out of my depth in high energy particle physics).

The measurement uncertainty applies to some other properties as well basically your uncertainty in the electron's position (sigma_x) and uncertainty in the electron's momentum (sigma_p) are bound by sigma_p * sigma_x >= hbar/2

hbar is the reduced planck constant and sigma are statistical variance, but that condition must always hold so as sigma_x goes to 0 (you are more certain about the potential) sigma_p must get larger to compensate so you are less certain about the momentum. This measurement collapses the waveform and until enough time passes for the system to "normalize" the momentum will continue to be uncertain, after that you can measure the momentum but the position could be different too.

> I'm not well versed enough to say it stops existing

That's a small detail, but no, it's not that the particle "stops existing". It's that we can't describe the momentum and position of something with indefinite detail with mathematics that is still coherent. The data type we have for describing things can not go there (on the QM language, of course).

And the surprising thing is that QM predicts our experiments with as much detail as we can experiment with. So, we have this language that can't describe something with known position and speed, and as far as anybody is concerned, it's perfectly correct.

What does it mean though to say an electron is a particle? Isn’t a particle an excitation of a quantum field? What does it mean to talk about the shape of a field?

Yes an electron is a “quantized vibration” of a quantum field (the electron field). The vibration is quantized in the sense that you can only turn on the amplitude of vibration in discrete clicks, not in a continuous way. Two clicks would be two electrons.

Such a quantized vibration has all the properties of a particle: it has a certain mass, it has a certain momentum, it has a certain angular momentum, and when you look at it in another frame of reference, all these quantities transform just as would a particle’s. And, when you “perform a position measurement” it shows up as a single dot. If you don’t do a position measurement it spends most of its time quantum superposition of states of definite position; hence the “cloud” aspect.

Is it the superposition volume (volume of non-zero probabilities?) that is a perfect sphere?

No, the language of “perfect sphere” versus “bumpy sphere” used by the article is just an analogy with a classical object that would interact with an external electric field in a similar way. Even when it is in a single position eigenstate, an electron has another degree of freedom, its spin orientation, that has nothing to do with its position. This is “like” a spinning pool ball in the sense that it possesses angular momentum in a certain direction and reacts to torques like a spinning thing, but beyond this the analogy breaks down. For one thing, its spin can never be increased nor slowed; for another it has this intrinsic spin even when its position is localized to a dot.

Similarly, a non vanishing Electric Dipole Moment would be some preferred direction to its electric interactions in relation to its spin. Its electric field would be slightly oblong even when position is localized to a dot.

So to clarify, there are multiple senses of “electron cloud” at play — the superpositions of positions is what is usually meant by the term, as in electron cloud around nucleus of atom. The article’s use of the term is a tad sloppy since it invites confusion with this — it means something that generates an oblong electric field and reacts to an external electric field through a term in the energy of the form p.E (with p the EDM and E the external electric field).

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