An electronic story

Or "Drop the Schrödinger's cat jokes".

How do we handle complex ideas in our head? How do we manage to use a brain that, in all its power, was designed to grasp concrete ideas to hunt, organise small groups of people and preserve itself, and put it to manipulate concepts that cannot be seen? At the peak of their era, Romans have conquered pretty much all the known world, and yet they were using a numerical system that could only count up to 10,000, and the concept of zero was yet to be mastered!

We’ve always dealt with our Universe assuming that we as mere humans can understand what is going on, that everything is rational, and that our theories are fallible: we’re getting less and less wrong one step at a time.

That’s maybe one of the reasons why Quantum Mechanics is so confusing: it both challenge human understanding with its complexity (you have to deal with advanced mathematics to grasp its conclusions) and at its basic assumption: Quantum Mechanics implies that we can no longer be deterministic about our world. When we are in the atomic world, we stop dealing with certainties. This is an idea that we are not used to, and thus unprepared to deal with.

That’s probably why ordinary people still holds the idea that electrons are tiny particles that, like planets, orbit around the nucleus of the atom, with well-defined paths, even circular ones. Electrons doing that would steam radiation that would make them collapse into the nucleus. The common idea about the atom is plain wrong.

Why do we still keep such analogy between the solar system and the atom? For starters, it’s easy to grasp, and grasping easy concepts is what our brain is train to do. All the smart kids in high school know that we cannot travel faster than the speed of light and are nevertheless taught a physics model that doesn’t deal with that problem: gravity is -9.8, and using a calculator you can predict that, if accelerated in such a way, you only need 30.6 million seconds, or less than a year, to surpass the speed of light. Is that true? Of course not, but when you are 15, you are taught a simplified version of reality that is easier to grasp than the state of affairs in Physics.

Secondly, we keep the solar system analogy because it makes useful predictions in Chemistry. An electron jumps from Cl and goes to Na and then you have NaCl, which is the formula for salt, and that electron jumping is what keeps the atom together. It’s just the next level of abstraction from what juniors in high school are told about it, but abstract enough for chemists to create an empire of chemical technology that has eradicated from Earth illnesses that only 100 years ago were devastating for the human race.

And third, because reality is very complex. Again, Quantum Mechanics has proved to be particularly challenge, and counterintuitive. Trying to explain someone that the physics of a football is deterministic while the atoms that make it up isn’t is not easy.

An electron, not being entirely a particle, can be thought of a probability cloud that extends on the entire Universe. Even though that is strange, there is a clear analogy: pinpointing the exact location of your best friend on a map. You can definitely tell he or she isn’t far from home, or work, or maybe on vacations, but not sure where (maybe Thailand or New York or on the Mediterranean sea on a cruise). If your friend is the next Neil Armstrong, he or she might be in the ISS right now. The truth is, you can never tell with precision. Same happens with an electron.

However, and stretching a little bit more the “find your friend” analogy, even if you cannot tell where he or she is, you can at least say “well, I’m almost positive that he or she isn’t at the gym.”. You can map out the probability that an electron can be found on a certain point in space. In fact, we can cluster certain areas in space that are mostly probable, what are commonly known as orbitals (the solar system analogy is really rooted in this). Orbitals are defined to contain 95% of the total likelihood of the electron’s whereabouts for a certain level of energy and angular momentum (the two factors that determine an electron in space, other than the spin). The remaining 5% is contained…everywhere else.

Up until here, everything is more or less fine: a cloud, probability instead of actuality, an electron isn’t a particle, we can live with that. Are the clouds in the sky particles of water, or just clouds that contain, somewhere within, millions of drops ready to go? Who cares. Thing is, we are abstracted from what is going on inside, because all external effects are indifferent to both explanations. Then, it rains.

Thing is, what if the electron is outside the orbital, somewhere across the Universe? Is the atom stable? Are the positive charge in the core and the negative charge outside it compensated?

Here is the part that gets tricky, where the analogies do not apply anymore.

See, all the cloud interacts with the nucleus and adds up its own contribution, no matter how minimal, to the sum. Is the probability of an electron being in a certain point in space also the negative charge it carries with it? In a sense, it is, provided that you include the distance involved between that point and the core, and the fact that there isn’t anything in that point of space to “carry” it. At this point, an electron is more of a concept rather than an actual particle.

Now comes the hard part: does this hold in experiments? Is this consistent with what the scientific community has seen in experiments? In fact, it is indeed. An electron is both a particle, because trying to experiment with it releases all properties that can be attached to a particle (you can trace its charge when using drops of oil, like Milikan did). At the same time, you can never tell with absolute certainty where an electron is, given the fact that the energy is always discrete, that is, it “jumps” from one state to the next without going “in-between”. These and more leave us in an impossible middle ground between particle and wave that physicists still try to get their heads around nowadays.