Monthly Archives: January 2019

Quantum Mechanics for Babies

I had a kid a year and a half ago. Because I’m a physicist, people bought me “physics for babies” books. We’ve got two: General Relativity for Babies and Quantum Mechanics for Babies. To be totally frank, neither book is particularly good, but the General Relativity one is a lot better and I think this serves as an interesting framing device for talking about the two theories. In particular, the character of quantum mechanics is extremely difficult to explain because it is, to a large extent, apparently abstract and detached from the physics as such.

All of the ideas in General Relativity for Babies are either intuitive or map neatly by analogy onto intuitive things. We, more or less, perceive mass directly and the sense of warped space is pretty easily given by a heavy object sitting on a bed. Of course, that hardly gives any sense of the unusual way that GR tells us that mass warps space-time, the way that events perceived by an external observer slow to a crawl as they enter ever more curved space time, or the way that a similar effect over the entire observed universe as one approaches the speed of light. But in a way, none of these things are metaphysically revisionary the way quantum mechanics is. Whatever distortions we see due to relativistic effects, they always preserve a causal account of things which is fundamentally familiar. In this way, GR underlines our typical perception of the universe, even if it stretches it out or otherwise distorts it.

Quantum Mechanics, on the other hand, involves a variety of phase transitions in thinking that are difficult to convey by any analogy, partly because it seems like at least some of the content of the theory has nothing to do with physics at all and instead derives entirely from a naive application of some basic principles about probabilistic explanation. This is a theme in R.I.G. Hughes’ book on the interpretation of the theory: that the unusual features of Quantum Mechanics inhere not so much in any physical circumstance but derive instead from using vector spaces to represent exhaustive, mutually exclusive events related to one another by some probabilistic process.

Ok, sure. But how would I explain Quantum Mechanics to a child? Like this:

  • It turns out that very small things are difficult to describe.
  • When we try, we find that we can only predict the probability of certain outcomes, sort of like how you can only predict that a coin will land heads or tails, but not which side.
  • Except in special cases, the exact result of a measurement is unknown, but the relative chance of each possible outcome can be known.
  • In the special case that we do know an outcome will occur, there are always other measurements which we only have probabilistic predictions about (no dispersion free states).
  • We use something called a wave function to calculate the probabilities of different outcomes. A wave function can be many things, but you can think of it as a field of values over all of space. The values tell us something about the probability of measurements.
  • In many situations, the physics combined with the wave function, tell us that for certain kinds of measurements, only certain values are observable. This is why we call the theory “Quantum” Mechanics – “Quantum” is a word which means “a discrete value.”
  • One example of this is the hydrogen atom. This is a small system with an electron and a proton. You can think of these as being like two small points. The electron and proton want to be as close to one another as possible, sort of like how two magnets pull on one another.
  • We can describe the position of each particle using Quantum Mechanics. That is, we can write a wave function which we can use to calculate, for instance, the probability that we find the electron at any position in space.
  • If we do this, we find that the energy of the system, which is sort of like how fast the particles are going plus how much they are pulling on one another (they pull harder on one another when they are nearby) is quantized. Even though we can find the electron at any position in space, if we measure the energy of the system, it only comes in a discrete set of values. Hence, the system is called quantized.
  • The fact that many systems are quantized in this way makes all sorts of things possible that would not otherwise be like atoms and molecules.
  • Measuring the energy means that we can only describe the probability of measuring a specific position. If we were to measure position after measuring energy, we might find the electron anywhere in space, and while some points in space might be more likely than others, we can’t tell where the particle is until we’ve measured it. Critically, this isn’t about the accuracy of our measurement – our uncertainty about the particle’s position is unavoidable because of the theory of quantum mechanics. It seems to be the case that nothing we could know would reduce our uncertainty about the position to nothing.

 

This is far from the level of “Mass bends space!” but I think its a relatively accurate and honest description of the theory that a young person could understand.