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.

Lots of Effort, Terrible Result

 On June 13, 2023 a seminar was held at CERN to report some of the results and methods used by one of the major collaborations involved in the LHC. One of the motivations for this work is the fact that there is matter in the universe but very little antimatter. It is expected that whatever created the initial, very hot, universe would have produced as much matter as antimatter. These components would then have interacted and resulted in neither matter nor antimatter, just a lot of photons. We are an indication that this didn't happen.

Beginning in the 1960s and continuing into the 2000s experimental evidence showed that certain particle interactions violated matter/antimatter symmetry. This was incorporated into the Standard Model of Particle Physics back in the '60s. However the asymmetry involved wasn't enough to explain the amount of matter we see.

When the LHC was designed, many decades ago, it was produced with 4 interaction areas. One of these, LHCb, was specifically designed to determine how well the asymmetry predicted by the Standard Model matches experimental results. That shows how important this is to physics. The recent seminar presented the current status of that data analysis and it shows that the asymmetry is consistent with the predictions of the Standard Model.

So why am I writing this? I saw a post that linked to an article that was clearly related to this seminar. It also contained a significant amount of material clearly intended to provide background on the subject for readers that aren't familiar with the field. Why don't I say it was about the results from the seminar? Because what it reported implied the opposite of what actually happened.

Let's look at both articles. One says, correctly, "The weak force of the Standard Model of particle physics is known to induce a behavioural difference between matter and antimatter". The other says, incorrectly, the opposite, "The Standard Model of physics tells us that if we substitute a particle for its antiparticle, it should still operate within the laws of physics in the same way". There are numerous other examples of the second article getting things completely wrong. Most importantly in the way that the seminar's results are portrayed.

The first, the correct one, says "...  the new LHCb results, which are more precise than any equivalent result from a single experiment, are in line with the values predicted by the Standard Model". The other says, the results do "... not fully answer why there is more matter than antimatter in the universe, [the experimental results] will help constrain models that do attempt to explain this strange asymmetry". Although it isn't explicit it inplies that the results show something new, the exact opposite of what is true.

How does this happen? The "journalist" could simply have copied, or slightly reworded, the article linked above. Instead they clearly expended lots of effort. Unfortunately, they had essentially no understanding of any of the physics involved.

I was made aware of this when a link to the incorrect article was posted by a friend. Reading it made it clear that the veracity of the information wasn't trustworthy. A quick search found the article at the top of this rant. I sent the link as a comment to my friend's post. The fact that people are far more likely to come across popular articles on things like this is not a surprise. The problem is that articles like this almost always get some, or in this case essentially everything, wrong.

A Superposition of Errors

For a really long time, I've been trying to construct a simple explanation of Quantum Mechanics (QM) that could be understood without a background in the math used in the formal studies of the subject. I hope to eventually do that but there are several subtopics. I'm not sure which to tackle first and I keep getting stuck.

Recently I came across a science blogger's article about quantum computing that said:

Qubits exploit the quantum phenomenon of superposition, the ability for a particle to be in more than one state at once. A qubit can therefore be in any state between 0 and 1 inclusive, and in fact can be in every state from 0 to 1 at the same time.

Yes, Qubits exploit superposition. Essentially every other part of this is wrong. Superposition is not a quantum phenomenon. A qubit is not in more than one state at a time, it is a state formed by a superposition of other states. There are no states between 0 and 1, so a qubit cannot be in a state between zero and one. The assertion that it is "in every state from 0 to 1 at the same time" isn't even wrong.

So, thanks to this "incentive" I'll address superposition.

Superposition is a general property of an enormous category of mathematical relationships. One set of those is used in QM but it is not a "quantum phenomenon".

To explain the rest of these errors I need to explain a bit about superposition.

I'll use light waves as an example. As I hope everyone reading this knows, light is an electromagnetic wave. One particularly simple and useful way to view a light wave is that it has its electric field value changing like a sine wave in a single direction. Light like this is said to be polarized in that direction. 

A particular electromagnetic wave can be polarized in the vertical direction. Another possible wave is one that is polarized horizontally. Electromagnetic waves are in the category of mathematics that support superposition. This means that the sum of any solutions to the relevant equations are also solutions. So we can add the horizontal and vertical waves and the results will also be a valid electromagnetic wave. I chose these options because adding combinations, also known as forming a superposition, of vertical and horizontal waves results in an electromagnetic wave at any possible angle. (For those that aren't spooked by trig functions to set the polarization angle to θ from the vertical component is cos(θ) and the horizontal is sin(θ).) Any linearly polarized light wave can be constructed from a superposition of horizontally and vertically polarized waves. Light that is polarized at some angle to the direction in which the polarization is being measured is not in more than one polarization state at a time. It is a distinct polarization state that is formed by the superposition of other states. 

If we consider light as a series of photons we start to see some of the effects of QM. A photon of light is an all-or-nothing sort of thing. If the photon encounters a polarizing filter it either goes through it or it doesn't. The proportion of photons that will go through is related to the amount of horizontal and vertical polarization in the superposition. Each photon either passes through the filter or it doesn't. There are only two states possible, the photon has an intrinsic "two-valueness".

(The above treatment of polarized light ignores several very important aspects of the topic, like circular polarization and polarization measurements at arbitrary angles. These don't have any relevance to the topic of this entry, and they don't relate to the general topic of superposition in quantum computers.)

This superposition is, mathematically, the same as superposition in the context of quantum computers.

Many quantum mechanical systems can only be in discrete states. Let's consider the (so-called) spin of an electron. The spin, or angular momentum, of a regular object is a vector whose direction is the axis of rotation and whose magnitude depends on the distribution of mass and the rate of rotation. For an electron, the spin behaves in a way that has no classical analog. No matter how the electrons are aligned and no matter what axis the spin is measured along the result is always the same magnitude, either with or opposite that measurement axis. Explaining what this means and why it's so weird is far beyond the scope is this rant. This "two-valueness" is true for all qubits, not just the ones that can be reduced to electrons.

So, how should that article have described qubits? Here's a possibility.

Qubit is a portmanteau of quantum and bit. Qubits take advantage of superposition, a fundamental property of quantum systems that can make any combination of states a possible state. Qubits, like regular bits, have two states, usually called 0 and 1. Superposition allows qubits to be in other states, ones that aren't possible with regular bits, where the value is both 0 and 1 at the same time. When combined with another quantum behavior, entanglement, this greatly increases the amount of information that can be encoded in a set of qubits.