Keith’s Conundrums: Cosmic Puzzles

March 2026

Keith Douglas

Recap

Last time, I wrote about “the large”. I have been given the chemical (a so-called “empirical”) formula for the (universe, I guess the Hubble volume) via an XKCD cartoon that was shared with us! Thanks!

Now, try to write the structural formula. 😊

For this month…

This month, I’d like to present a few cosmology / (astro) physics puzzles. Some of them are pretty common as questions in the textbooks and will actually be routine to anyone who does a literature search (never mind having any relevant qualifications in the subjects; I might even be rightly accused of sophistry). However, they are fun to think about and have sometimes rather subtle answers and complexities. Happy thinking.

Our first is named “Olber’s paradox”. If the universe is infinitely old, there would be starlight arriving from the farthest stars – as it has had “all the time in the world” to get here, and hence it would be bright all the time, etc. So (?) the universe must be finite in age.

Moving on to the next, called the Fermi paradox. It is as follows: It seems plausible if one looks at what sorts of planets can support life, how big even just our galaxy is, etc., that we should be flooded with radio signals from all over the place advertising us soap, asking us if we want to MAKE MONEY FAST or join the Galactic Federation (or the Rebel Alliance). We are not. Why? (And no, I don’t mean the English version of those, of course.)

If one takes a certain parameterization of the expansion of the Hubble volume, the so-called York time results, and with that, the time since the big bang diverges, is this telling us there is a sense in which even the local Hubble volume is eternal? (Be very careful with this one!)

On the relativity of motion. If all motion is relative, weren’t both Galileo and the Inquisition wrong about the motion of the Earth?

Consider the electric force due to a point particle. In elementary electricity and magnetism, the electric field due to a point-like particle is infinite right next to it (as it is zero distance away). Yet we are also told how to perform some integrations to calculate the field due to (say) a line of charged particles, all at zero distance from each other. The calculation ignores the self-interactions. Why?

In quantum mechanics, one often appeals to “FAPP” – “for all practical purposes” – to explain the quantum-classical “split”. What exactly is this appealing to? Time? Unlikeliness?

Classical solid bodies have a well-defined boundary. We all know that even the highest boiling point stuffs do produce small amounts of “outgassing”. So, where’s the boundary in a real object? This one I will give you my idea – borrow one from quantum chemistry, rather – and you can tell me what you think. Boundaries are probabilistic. In some cases, over short enough time scales, the rock has the shape we can pretend we drew, model as a surface in topology, etc. Those of you who have studied psychophysics might want to ask if there’s a psychophysical relationship here too, in the object segmentation of our (say) vision for object permanence (of a very strange character, no doubt).

What’s a metal? (I leave that one just as is.)

The so-called Wheeler-DeWitt equation has been interpreted as saying that taken as a whole, the (multiverse, everything, etymologically correct use of “universe”, etc.) does not change. Is this correct as an interpretation? (HINT: I have no view on this.)

All the electrons – perhaps some of the smallest things there are – seem to be exchangeable (are “identical” in a sloppy sense). What is the smallest thing for which we can guarantee “individuality” – i.e., that the system (whatever that is – see above about boundaries) has nothing like it exchangabilitywise anywhere?

Also on the “wee electrons”, as it was put to me once, we have another puzzle. All of them are also seemingly (modulo a few other twists) also “identical” to the positrons – provided one looks at them as being temporally reversed with respect to each other. The great physicist J. A. Wheeler apparently was fond of saying that this astonishing fact is because there is in fact one only one electron (= positron). Comment.

Finally, let’s return to Descartes for a moment. Descartes thought that empty space (like Democritus’ kenon (void) – see my earlier columns on “nothing”) was a self-contradictory notion. Yet something like what he describes as preventing the horror vaccui sort of happens. In particular, an isolated body surrounds itself with a gravitational field, so it seems both vacuism (of bodies only) is correct, and plenism also – if one generalizes a notion of matter to fields. (Note that the same sort of “propagating process” also happens with charged particles and the electromagnetic field.)

Thanks for reading, see you next month. What do people think we should tackle?