In a recent post, Chad at Uncertain Principles addresses an interesting criticism of one of his posts. In short, he attempted to summarize the essential features of quantum mechanics that set it apart from other, classical theories of physics. As Chad notes,
So, what’s the issue? The strongest single objection probably comes from Peter Morgan, who didn’t like my element 2):
2) Quantum states are discrete. The “quantum” in quantum physics refers to the fact that everything in quantum physics comes in discrete amounts. A beam of light can only contain integer numbers of photons– 1, 2, 3, 137, but never 1.5 or 22.7. An electron in an atom can only have certain discrete energy values– -13.6 electron volts, or -3.4 electron volts in hydrogen, but never -7.5 electron volts. No matter what you do, you will only ever detect a quantum system in one of these special allowed states.
NOOOO!!!!! You need to talk about measurement operators, not about states, if you want to say “discrete”.
Perhaps: Measurement operators that have discrete spectra are used to represent measurement apparatus/procedures that produce discrete measurement results. Measurement operators that have continuous spectra are idealizations that do not correspond to real experimental data that is written in lab books or in computer memory.
The state space is usually taken to be vectors in a Hilbert space over the complex field, or density operators (arguably always one of these, by quantum physicists?), which are pretty much continuous linear spaces.
Leaving aside the technical details, the real issue between poster and commenter is one that’s often on my mind: how much description is necessary to properly explain a physical phenomenon? This is relevant not just to authors of blog posts, but also to educators in general. Science is complicated, and we want to simplify it as much as possible for our students/readers. There is clearly some point, however, at which the simplifying just becomes misleading. The question, then, is: how does one draw the line?
My impression is that it depends — it depends on who you are trying to reach, when you are trying to reach them, and what you are trying to convey.
It’s probably somewhat obvious, but one provides a different level of detail about a subject when explaining it to a physics major than when explaining it to an “average joe”. One also provides a much different level of detail to a first-year undergraduate than to a first-year graduate student.
On a deeper level, though, it is worth noting that every level of explanation used is simultaneously partially wrong and partially correct. Every possible explanation one can give of a phenomenon is partially wrong because it is always an approximation and simplified model of the real physical processes that are taking place. I tend to think of an explanation as being partially correct if it pushes the audience’s understanding in a positive direction.
An example of what I’m thinking would probably help! When I taught a class on “modern physics” (relativity and quantum mechanics) for undergraduates, I begin with a discussion of the Bohr model of the atom. In this model, discussed in this post, electrons are treated as point-like objects orbiting like planets around a nuclear “Sun”, with Bohr’s groundbreaking hypothesis that the electrons can only orbit in states of discrete (quantized) angular momentum.
Bohr’s model is “wrong” on many levels: electrons possess wave properties, and do not “orbit” in any classical sense of the term. However, the model captures many of the essential parts of quantum mechanics: the quantization of electronic states, the release of a single quantum (photon) of light when the electron goes from a higher energy state to a lower state. If I used Bohr’s model to explain quantum mechanics to a complete novice in the subject, I would feel comfortable that the student had walked away with some “positive” knowledge. In fact, looking at the historical evolution of quantum mechanics, it is hard to imagine the theory being developed without someone making the intermediate conclusions that Bohr did. It is natural to teach the subject by at least partly following the historical path of discovery, because we know that’s how scientists originally learned it!
The learning process in science, and really all subjects, is a layering of increasingly fine details on top of one another. Most of these subjects are too darn complicated to be digested all at once, so we learn the rough details, then build upon them with the finer points. It is almost inevitable that some of the rough descriptions will lead to misunderstandings that need to be corrected with later teaching.
As a research scientist who has spent his entire adult life fiddling with the finer details, it is often easy to forget this. Academia has plenty of professors who have forgotten what it is like to be an outsider struggling with basic concepts in a field of study. One of my major motivations for starting a blog in the first place was to keep myself connected to those basic concepts, and those struggling with them.
Another example of the conflict between simplicity and accuracy was in the comments of my recent post on Lord Kelvin versus the aether. After describing Kelvin’s investigations on the aetherial matter, I concluded with:
Kelvin’s musings do illustrate nicely that the evidence was piling up against the aether; in only a few short years, in 1905, Einstein would, in essence, find the smoking gun against it.
A commenter pointed out, correctly, that the aether theory did not immediately die with Einstein’s paper. However, as a first approximation, I feel relatively comfortable saying that Einstein’s relativity was the turning point against aether belief. The statement captures the essence of the history as best as one can capture it in a one sentence conclusion to a post primarily about something else!
I’m not sure if there’s a very definite point to this post; to some extent, I think I’m agreeing — in a rather long-winded way — with the point of Chad’s post, which I summarize* as “more detail is not necessarily more enlightening”.
* It would be wonderfully ironic if my post on the challenges of simplifying and summarizing a topic for a specific audience ended up misrepresenting Chad’s point!