# Just what the hell is quantum physics anyway?

I learned about quantum physics probably the same way as everyone else. First, you see some blog post, magazine article, or BBC special mentioning the latest mind-bending thing scientists have discovered. Then, you go and read up on more popular expositions touting the magic and mystery of the quantum. Finally, you get so frustrated that you go and spend 15 years trying to understand what the hell is going on, and the only thing you end up having to show for it is a t-shirt that says, “I went to the quantum realm and all I got was this lousy Ph.D.”

But, there is one thing I discovered that has saved me a lot of grief, and I am going to share it with you. I hope this will be especially helpful if you are desperate to understand quantum physics, or just want a bit of comfort as you embark on your journey of quantum enlightenment.

I’m certainly not claiming this is The Answer. But, this is probably the best default position you should subscribe to. Think of it as Basecamp. You can try all you like to ascend the mountain of confusion, but Basecamp is always here to fall back on when you hit a dead-end — which I promise you is all you’ll ever find up there.

# The trouble with quantum physics

Science fiction often takes “natural laws” to the extreme but more often it intentionally breaks them. The trouble with quantum physics is that its laws need not be broken to create science fiction. Hence you can have “quantum jumping,” “quantum healing,” or “quantum” whatever-you-want and there will be some interpretation of quantum physics, espoused by some expert, that supports it.

The problem is that everyone, including science students, is consistently censored from the reality that the “natural laws” we teach them are facts not about nature, not even about our knowledge of nature, but facts about the way a particular majority of scientists have chosen to think and speak about nature. So when we are told that quantum theory is full of mystery and magic and that these are facts about the world, it is no surprise that we have “quantum marketing” and “quantum love.”

Prior to quantum physics, the mathematical elements of a physical theory corresponded nicely with elements of our experience. For example, the position, the mathematical symbol ** x** in Newtonian physics, of an apple falling from a tree is something we can all point to out in the world and agree upon. This is no accident; theories were built as abstractions of our direct senses — I see an apple, it has a place, call it position, label it

**. Quantum theory, on the other hand, is taught the opposite way; it starts with mathematical abstraction and we have been struggling ever since to find the intuitive world which it abstracts.**

*x*In broad terms, that struggle defines the interpretations of quantum theory program. This goal is often based on the premise that quantum theory is either the “truth” or the next step to it. But we need not attempt to make sense of quantum theory from the point of view that it is sacrosanct. We can have a look from an outsider’s perspective.

# And one model to rule them all

The rise of quantum information theory, the promise of quantum computing, and maybe some government money brought a rush of mathematicians to the scene with none of the traditional physics upbringings that are usually considered prerequisites for entry into the quantum physics club.

Now, if you enroll in an introductory course in quantum information theory you will get a vanilla introduction to quantum theory revealing its limits but at the same time not introducing anything beyond its operational structure. That is, the model is a list of mathematical objects and a rule for combining them to make predictions. These “axioms” are as follows:

1. To each experimental arrangement, we assign a complex vector space.

2. Each preparation procedure is represented by a positive semi-definite matrix ρ with a trace of one. These matrices are called the states.

3. If the state changes, the change is accomplished by a completely-positive map, Λ: ρ ↦ Λ(ρ).

4. Each measurement procedure is represented by a set of positive semi-definite matrices {A, B, C,…} where each represents an outcome of the measurement and the set satisfies A + B + C + … = 1.

5. The probability of an outcome, say A, of the measurement {A, B, C,…} given the state at the time of measurement is ρ is given by the rule Probability of A given ρ = trace of Aρ.

Sure, there’s some complicated-sounding mathematics in there, but that’s it. That’s all of quantum theory.

Now, you may be thinking, *this is just mathematics* — *there is no “physics” in these axioms.* Is that such a limitation, though? In other words, what are the predictive limits of this model? None, in fact. There are no probabilistic predictions which these axioms rule out. Any prediction can be accommodated by these axioms by a clever, or trial-and-error, choice of states and measurements. So, quantum theory is not a model of a feature of the world but a mathematical model for models.

# Physics is in the features

The axioms form a syntax that allows the user to perform probabilistic calculations in a very general operational setting. Some features of the world whose models satisfy the axioms have the following in common: they are well isolated from their surroundings, they are unpredictable, the act of measuring affects them and the measured quantities are discrete. These features some would call characteristically “quantum”.

But the axioms themselves do not imply all of these characteristics. To see this, note that experiments that one might consider “classical” also satisfy the axioms — the simple roll of a die, for example. When the term “quantum theory” is understood as just this set of mathematical axioms, it is not a model in the usual sense.

A better understanding of quantum theory is in terms of “quantum models”: a collection of models about electrons, photons, atomic spectra, Stern-Gerlach apparatuses, superconductors, lasers, cats in boxes, and so on — those features of the world which have certain characteristics. Perhaps these are the characteristics described above, perhaps not. Like all things in life and science, it is a matter of personal taste as to which models one considers “quantum.”

However, there is an enormous amount of agreement on some specific models. For example, the models used for lasers on an optical table, nuclei in a magnetic field, or ions in an electrical trap, most would consider “quantum.” A model of the outcome of a dice roll, although it satisfies the same axioms, most would not consider “quantum.” All of these models happen to use the same mathematical machinery of the axioms, but they make other assumptions as well — assumptions that clearly set them apart from other models which also satisfy the axioms.

When the first set of axioms was written down by Dirac in the 1930s it solidified the transition from the “old” quantum theory to, well, just *quantum theory*. The “old” quantum theory of the early 1900s was a scattered mix of experimental facts explained by haphazard “corrections” to classical physics. The “new” quantum theory arose to explain the common structure behind them. This abstraction gave rise to an explosion of new results. By showing the connection between otherwise disparate ideas, the gaps could be filled, expanding the range of applicability of existing experiments, techniques, and explanations. More than that, though, the new quantum theory showed what else was possible by pointing the way to entirely new and unobserved phenomena, such as anti-matter and new fundamental forces.

But even though the axioms have led to new “physics,” they are still just mathematics. The axioms serve as a guide for what models could be. They are not much use to a student entering the laboratory. For every laboratory set-up, one must consult an expert on the prescription of what mathematical objects correspond to what knobs and buttons. This leaves us wondering if the axioms have anything to do with something tangible in the real world.

# The reasonable effectiveness of mathematics

To those who extrapolate “classical” ideologies from their domain of usefulness, the aspects of certain features of the world whose models most would consider “quantum” — such as the act of measuring causing unavoidable effects — are obviously surprising. But this is not something that is unique to quantum models. For example, the tenets of Einstein’s theory of gravity are certainly surprising to those who steadfastly cling to the ideologies derived from Newtonian theory.

Do the mathematical objects in quantum theory have intrinsic meaning? No. Again, to see meaning in the equations of quantum theory is an unwarranted extrapolation. Even the axioms themselves are no more than a convenience invented out of necessity. They do not represent truths about the world but are a useful way to talk about a particular set of features of our experience.

Science is not a collection of facts but a method to convey to each other what we find important or useful about the patterns in nature. True to human nature, this method consists of telling a story. Scientific stories are often written in the language of mathematics, which we call models, to reveal the essence of what we find interesting about a certain feature of the world.

There is no right model and it is a matter of personal taste how complex, intricate, accurate, beautiful, or insightful the model should be. Since all models idealize their respective features, they must necessarily deal with uncertainty and hence probability.

The beauty of quantum theory is in providing a mathematical syntax for calculating probabilities in *any* operational setting. As such, the term “quantum theory” should not refer to any specific model but a collection of models. Indeed, for any given phenomenon we may have several models. Laser light, for example, could be countless corpuscular photons, a complex dynamical wave, or excitations in an abstract field. Or, it could just be an imagined colored line connecting its source to a glowing spot on the wall. These are all valid stories with a utility that depends on the goals of the storyteller and the desires of the audience.

Stories need not compete in an arena where one is crowned true and the others false. The well-equipped intellectual explorer holds a map, or several, which they know does not represent the truth but is a useful guide anyway. The best explorers are the ones who can choose the best stories, or create their own, without being trapped by conviction.