Friday, September 1, 2023

A Different View of Quantum Mechanics

I see lots of articles and posts about Quantum Mechanics (QM). Most, including the ones written by professional science communicators, are written by people who have such a tenuous grasp of the subject that they misinform far more than they inform. Others do have a good grasp of the subject but they violate a rule that I think is far more important than most people do: Simplify as much as possible, but no further. If you need to oversimplify then either your explanation needs to be better or your subject isn't appropriate for the level of understanding you assume your audience has.

The best models of reality that we have are in a category known as Quantum Field Theory  (QFT). Any attempt to explain it would violate the rule I stated above so I'm going to just use a few ideas from it. There exists everywhere in space a field that corresponds to each fundamental "particle". Fields are abstract entities that are very common in physics and some of them aren't too hard to wrap your head around. You can represent the temperature in a room as a temperature field, the value of the temperature at any point in the room. There can also be an air motion, or wind, field. It gives the direction and magnitude of air motion at every point. In QFT there is a field for every type of object. Also, there are wave-like excitations in this field. The wavelength of these waves is related to the momentum of the object. As shouldn't be too much of a surprise, since these are quantum fields, these excitations come in distinct, quantized, elements. These quantized excitations are what we call "particles".

In the first, incredibly successful, QFT there are two fields. The electromagnetic field, a concept that should be familiar to most readers of this, and an electron field. This theory is called Quantum Electrodynamics and it is often, justifiably, called the most accurate theory in all of science. The quantized elements in this theory are called photons and electrons.

These excitations are different from the objects that we experience in everyday life. One of the most important differences is encoded in the Heisenberg Uncertainty Principle (HUP). This is usually, and incorrectly, described as a limitation based on our ignorance. Or the effects caused by attempts to measure the position or momentum of quantum objects. The principle is more fundamental than that. Since objects are wave-like excitations of the underlying field their edge can't be defined in the way that everyday objects are. Like waves, they don't have abrupt edges. Instead, they are spread out. To use a bit of jargon, they can't be localized precisely. You may have noticed that I have avoided the word "particle" and when I did use it it was in quotes. That's because the word "particle" implies that the object can be localized precisely and that is simply not the case.

The most common version of the HUP relates the position of an object to its momentum. As stated above the momentum of the object sets the wavelength of the excitation of the field. So the HUP is a statement about the wave-like nature of QFT objects. The higher the momentum, the shorter the wavelength of the excitation, and the more abrupt its edge can be. One more strange concept will be helpful here. Momentum space. Just like locations are in the space of positions we can imagine an abstract space where positions are values of momentum. With this abstraction, we can state the HUP more precisely. The extent of an object in position space times the extent of the object in momentum space can never be smaller than a certain size.

In practice, this translates into a kind of pressure. Attempting to constrain a quantum object to a confined space requires increasing the momentum of the object so that it pushes against whatever is “holding” it in place. Let's look at that in a particular situation. An electron in an atom. The negative charge on the electron causes it to be attracted to the positive charge of the nucleus. This attraction tends to constrain the electron to be near the nucleus. The HUP acts like a pressure that resists this attraction. These effects are in balance in atoms and we can calculate, to pretty good accuracy, the size of an atom from this effect alone.

It is common to say that the electrons in an atom are whirling around the proton very quickly and the quantum mechanical orbitals are blurred approximations of its position. This is wrong. The electron simply doesn't have a fixed position. It is unlocalized because it is a wave whose extent is determined by the HUP.

Another, but closely related, incorrect statement that you will frequently read is that the atom is mostly empty space. This is based on the same oversimplification as used in the previous paragraph. The volume of the atom is not empty. It has as much electron in it as the laws of physics allow.