What is the most correct way to think about electrons?

Question

I'm sorry for this question, I know it's been asked before What is an Electron? but the answer doesn't really help me..

Studying chemistry the teacher tried to explain what atoms are, what electrons are etc but in a very simplified way. I've never studied quantum physics or any advanced physics so sometimes, trying to read what electrons are, I get pretty confused and I don't understand. My question is: what is the correct way to think about electrons?

Studying electromagnetism we think about electrons as negatively charged particles, "little balls" that have a negative charge and are attracted to protons and that repel each other.
Other times, as in the question I linked above, people say "the electron is a standing wave".
Here instead you can read "they are both waves and particles all the time, and don’t just change from being one to the other depending on what’s done to them." and this defintion really doesn't makes sense to me.. electrons can't be two things at the same time, maybe they can behave like two different things, but they have to be one single thing. I'm typing right now using my fingers, which are made of atoms, which have electrons, I just can't believe that I have on my hands two different things at the same time (look at your hands right now and think about it for a second..).
Last example, the spin number was introduced thinking about that the electron could rotate. The definition, taken from Wikipedia, is "In atomic physics, the spin quantum number is a quantum number that describes the intrinsic angular momentum of a given particle." but then it takes very little to find something that contradicts it Why can't I just think the spin as rotating?

If this is not confusing I don't know what is.. I think all these concepts are not consistent with eachother (all true at the same time).. It makes me even question if what we study is correct.. like when in electrostatics we study Coulomb's law etc.. Do we really know what electrons are at least? From pages like this I would say "if they don't even know, I shouldn't even mind trying to understand", but at the same time, since they are extensively used (in physics, chemistry, electronics etc etc) I keep trying to understand.

What is the most recent, pratical and intuitive way to think about electrons?

Answer 1

Here is my way of looking at electrons, I hope this helps. Sorry if it is too simplistic.

An electron is a fuzzy ball of electric charge that has mass but as near as we can tell, no size: it is a mathematical point surrounded by an electric field. In free space, at any temperature above absolute zero it zips around like a bee, but if you try to confine an electron to a small space, it clumps up into a cloud and its precise location inside that cloud is impossible to pin down. Some people refer to that confined cloud as a standing wave, especially if the thing that is confining it is the attractive force of a proton nearby.

Depending on exactly how you try to pin it down for a closer look, that electron can either behave like a wave (exhibiting a wavelength and both reflection and diffraction) or like a particle (transferring momentum in discrete units when it smacks into another object, and having well-defined mass).

You can think of this as if the electron were a speeding water balloon: if you try to determine its speed by seeing how hard it collides with a wall, it gets transformed from a ball into a pancake, during which its speed is changing all the while. Or if you try to measure its size by putting a pair of calipers on it, it pinches into a dumbbell shape and tries to squeeze out from between the caliper jaws. Whoops, now it is moving! So, what is a water balloon? Is it a sphere, or a pancake, or a dumbbell? It depends.

Now the thing that makes an electron both wave-like (as in a cloud with finite size) or particle-like (as a speeding bullet with no size at all) is its very tiny size: it exists firmly in the domain of quantum mechanics, where such counterintuitive behavior (is it a particle? is it a wave?) holds sway, and you can't pin down its position without altering its velocity, or measure its velocity without altering its position.

Answer 2

Historic experience shows that physics knowledge has always been transitory, even though at least in a kind of convergent way. Probably you may think of it that way: if you only took for real what you are absolutely sure of, you would be forced to memorize all physical experiments that have ever been done before and if you want to answer some question, you could only do that if an experiment had already been performed earlier that exactly corresponds to this question. This would be a huge load on your brain, absolutely certainly several orders of magnitude larger than what you complain about.

Compared to that situation, which one could call an "empiricist's hell", it is already a terrific improvement, if some sets of experiments can be summarized by certain formulae and procedures, which enable you to predict the results of some experiments-not-yet-performed. Consequently you only have to memorize some key experiments and some sets of formulae and procedures in order to get a pretty good description of nature.

What you probably want are two or three equations that explain everything without much thinking about when to apply these equations, just put in the numbers into the calculator and hit the "=" button. This kind of theory does not yet exist in physics, and if it ever will exist, it is already pretty certain that it will comprise a lot more than only two or three equations. It will be complex in a way that it will not help you much in answering even the most basic of questions, because every answer will have to be built from the grounds up. Only, imagine feeding a computer with all the initial positions and velocities of all DNA, proteine, sugar, fatty acid and water molecules inside your fingers in order to predict what next letter you will be typing.

So, this illustrates that you should be more modest with respect to what you expect from the laws of physics. In case of the electron (or any other quantum mechanical particle), you should be thankful that physics has discovered certain experimental scenarious where an electron behaves like a particle, and other experimental scenarios where the electron behaves like a wave. If you want to understand what the electron is, you don't need to memorize a million of different experiments, you just need to know a few and the contextual information that allows you to apply the formulae that physics has discovered for describing them.

For the electron, as Richard Feynman has pointed out, a lot is already contained in the double-slit experiment. Before and after the double-slit, the electron behaves like a wave. When detected on a screen, the electron behaves like a particle. For the former you need to know Schrödinger's equation, for the latter you need to know that the squared magnitude of the electron's wave function is the detection probability on the screen. That's all. The vast majority of all other aspects of the electron are just variants of this basic experiment.

Take the atom as an example: the electron behaves like a wave that basically bounces back and forth within the bounds that the Coulomb field of the nucleus defines. Eventually, after all initial disturbances have waned, the electron develops to a standing wave in the nucleus field, kind of similar to the standing wave that develops between the fixed ends of a guitar string after it has been plucked with a plectrum. Of course, the details are a little different, but the general analogy holds. Now, if you want to measure the electron's position in the atom by any method, it will again leave this standing wave state, and do as you commanded: it will show up at a random location, only that the probability of this position is determined by the magnitude squared of the former wave function. By the measurement, you have changed experimental context and have caused the electron to change to something else (which can again be described by a wave function after the measurement, but this time an initially very much more localized one) like a chameleon.

Be glad that you only need to memorize a few, apparently contradictory experimental scenarios. Nature is complicated, but it could also be way more complicated.

Answer 3

Spin is a rather unfortunate name. Early models of the electron saw the electron as a spinning ball of charge. Unfortunately that proved not to be the case, but the name stuck anyway. Physicist aren't very good with names of particle properties e.g. quark truth, beauty, charm, color etc. None of those names make any sense and are really just whimsical.

So unless you really want to get deep into the maths, I suggest that you just treat electron spin as (1) something that can take 2 values ('up' and 'down' - just more whimsical names) and (2) spin points in a specific direction. (The early model compared the electron to a spinning top with the 2 values corresponding to spinning clockwise or anti-clockwise - but this analogy is ultimately incorrect as pointed out in your link to a previous question)

Is an electron a wave or a particle? It turns out you are in great company. There is considerable debate about exactly what an electron is. Enough to say that sometimes a wave, and sometimes a point particle...

Answer 4

The properties of an electron can be associated with a wave packet of finite size. The amplitude of the wave at a given point determines the probability that the electron will interact with something else at that point. An electron orbital in an atom is a resonant 3D standing wave bound by the electric field from the nucleus.