A single line from a blog post I read got me wondering if maybe (just maybe) the answer to a key quantum question has been figuratively lurking under our noses all along.
Put as simply as possible, the question is this: Why is the realm of the very tiny so different from the larger world? (There’s a cosmological question on the other end involving gravity and the realm of the very vast, but that’s another post.)
Here, the answer just might involve the wavelength of matter.
I’ve been working my way through The Principles of Quantum Mechanics (1930), by Paul Dirac. (It’s available as a Kindle eBook for only 6.49 USD.) It’s perhaps best known for being where he defines and describes his 〈bra|ket〉 notation (which I posted about in QM 101: Bra-Ket Notation). More significantly, Dirac shows how to build a mathematical quantum theory from the ground up.
This is not a pop-science book. Common wisdom is that including even a single equation in a science book greatly reduces reader interest. Dirac’s book, in its 82 chapters, has 785 equations! (And no diagrams, which is a pity. I like diagrams.)
What I wanted to post about is something he mentioned about qubits.
One small hill I had to climb involved the object I’ve been using as the header image in these posts. It’s called the Bloch sphere, and it depicts a two-level quantum system. It’s heavily used in quantum computing because qubits typically are two-level systems.
So is quantum spin, which I wrote about last time. The sphere idea dates back to 1892 when Henri Poincaré defined the Poincaré sphere to describe light polarization (which is the quantum spin of photons).
All in all, it’s a handy device for visualizing these quantum states.
The word “always” always finds itself in phrases such as “I’ve always loved Star Trek!” I’ve always wondered about that — it’s rarely literally true. (I suppose it could be “literally” true, though. Language is odd, not even.) The implied sense, obviously, is “as long as I could have.”
The last years or so I’ve always been trying to instead say, “I’ve long loved Star Trek!” (although, bad example, I don’t anymore; 50 years was enough). Still, it remains true I loved Star Trek for a long (long) time.
On the other hand, it is literally true that I’ve always loved science.
I think we all agree 2020 has been, as the curse puts it, an “interesting” year. Going into it, I had intentions about making changes. Most fell by the wayside due to COVID-19; I still haven’t taken the bus to watch the St. Paul Saints play. Or the bus-light rail combo to Target Field.
As a life long hard-core introvert, “social isolation” mostly meant I shopped for groceries less often but stocked up more when I did. The pain was fewer occasions of meeting a friend for tasty food, drink, and chat. I’m really looking forward to dining out again.
All-in-all, the last four years, this year… It’s been exhausting.
Since I retired, I’ve been learning and exploring the mathematics and details of quantum mechanics. There is a point with quantum theory where language and intuition fail, and only the math expresses our understanding. The irony of quantum theory is that no one understands what the math means (but it works really well).
Recently I’ve felt comfortable enough with the math to start exploring a more challenging aspect of the mechanics: quantum computing. As with quantum anything, part of the challenge involves “impossible” ideas.
Like the square root of NOT.