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.
He commented:
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?
Skulls in the Stars 