Not Everything at Once

I’m midway through Philip Ball’s Beyond Weird. It’s about quantum mechanics. Thanks to popular media, the idea that the quantum world is weird is having its heyday. Multiverse – here I come! Perhaps weird isn’t the right word to use; I’d suggest counter-intuitive. Ball argues that the challenge is “our (understandably) contorted attempts to find pictures for visualizing it or stories to tell about it.” One can learn the math and do the calculations. The problem is that we feel compelled to add interpretations to kinda sorta explain what’s going on. This alludes to the fundamental problem – if quantum information forms the bedrock of all this funny business, then knowledge, observation, measurement, calculation, seem to merge although it’s unclear what exactly that means.

 

Today’s post is on a “chapter” of the book titled “Not everything is knowable at once”. Technically there are no chapters in the book and each section is bookended by a grey page instead of a white one with words on it. As a quantum mechanic, I appreciate the design choice even though it makes it infuriatingly harder to refer to things. (Thankfully, page numbers remained.)

 

The chapter is about Heisenberg’s Uncertainty Principle, although Ball argues that uncertainty is a misleading word. It makes us think that everything in quantum world is fuzzy. Neither is it “that if we want to measure one thing very accurately then we have to accept a commensurate blurring in the values of everything else.” I admit that I have even sometimes inadvertently misled students towards this interpretation. My G-Chem students, on first encountering it, think this is a ridiculous notion. But what’s going on is more subtle. Ball writes: “Quantum objects may in principle have a number of observable properties, but we can’t gather them all in a single go, because they can’t all exist at once.” Fundamentally, it’s a question about knowledge.

 

But this restriction only applies to certain pairs of (conjugate) variables – the ones often used are momentum and position. And it should be emphasized that it has to do with simultaneous knowledge of both momentum and position. It’s not just that we can’t measure them accurately to a great degree of precision. It’s that the two properties are linked in such a way that they don’t manifest separately all at once. Isn’t this language maddening? Counter-intuitive? Weird? Ball writes: “if the math says that we can’t measure some observable quantity with more than a certain degree of precision, that quantity simply does not exist with greater precision”, or that’s what Niels Bohr might say. It only affects certain pairs. Mass and charge can be known simultaneously; no problem there.

 

Ball makes the analogy that in matrix mechanics, the order in which you multiply two matrices matters: “M x N is not necessarily the same as N x M.” In contrast “3 x 2 is the same as 2 x 3”. Matrix mechanics is how Heisenberg formulated quantum mechanics. I am much more comfortable with Schrodinger’s wave mechanics, and so that’s what I teach students in quantum chemistry. Ball also suggests that instead of Uncertainty, we should call it Unknowability or Unbeability, presumably the ability to be or exist. I like this. You can’t have Everything, Everywhere, all at once. Simultaneity is the problem. But that opens up another can of worms. We think of simultaneity in terms of the time variable. But time and energy are conjugate variables. And as I tell my students, everything in chemistry is about energy. We don’t really know what it is, but we can count it, even as it morphs from one form to the other. Follow the Energy!