Meet the new day; same as the old day. Or at least, in everything but the trivial details, every new day is indistinguishable from the previous oodles of days. It’s just a full rotation of the Earth around its axis, such that when it’s done, the same points on Earth are lined up with the same…
…well, okay, here there’s some variation depending on how you’re measuring the day. There are solar days (our usual measure), which are reckoned when the same line of latitude points “directly” at the sun again. But, of course, the Earth is moving relative to the sun, and at a noticeable rate: it goes roughly one 365.25th of the way around the sun in one day, and so it takes slightly longer to get back to the original orientation toward the sun than it would otherwise.
Then there are sidereal days, in which we reset when the same point on Earth is aligned with the same relatively distant stars. Such distance means the angular change to those stars caused by Earth’s motion is much smaller than the angular change to the sun. So those day lengths are, I believe, more consistent, but they are actually slightly less than 24 hours long.
I suppose, at our current level of technology and understanding, the most consistent day measure would be Earth’s rotation relative to specific spots on the cosmic microwave background radiation, which would basically be as far away as anything we can measure.
The Milky way is moving slightly relative to the CMB though. I think this is called proper motion*, but I may be misremembering that term. Still, that rate of motion is tiny relative to the scales involved. Although, come to think of it, since the Earth is moving within and along with the Milky Way, it’s possible that the Earth’s motion relative to the other, relatively distant stars within the galaxy may be smaller than its motion relative to the CMB.
I don’t know whether or not that is the case. If anyone out there knows off the top of your head, I would be delighted if you would let me know. But don’t bother Googling it, or asking some LLM about it; I can do that for myself if we’re going to resort to such tactics.
Speaking of relative motion and such, I did something relatively new yesterday afternoon with respect to reading. Allow me to set the stage**.
I recently started dabbling (very inconsistently) in the online courses at MIT (and other universities) on their YouTube channel(s). I started with Quantum Mechanics and then also started the General Relativity course, since I have some personal curiosities related to that subject that I’ve yet to see answered.
In the first lecture, the GR professor went over the main texts they would be using. Well, I already have two of them, so I figured I would get the third. I ordered it in paperback (the hardcover was ridiculously expensive, whereas the softcover was about the same price as any good-sized trade paperback). After it arrived, it sat rather forlornly on my desk for some weeks.

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Now, as I’ve said, I’ve been having a hard time reading fiction or nonfiction lately. But a softcover textbook is no heavier than my lapcom would be, unlike the two hardcover GR texts I own. So I brought the text General Relativity, by Wald, with me when I left the office yesterday.
The cool thing is, I actually read from it while waiting for the train and then while on the train. I completed the preface/introduction and chapter one! It’s not a long chapter, of course, and it mostly reviewed concepts of special relativity and so on***, which I know relatively (har) well.
Still, I feel reasonably pleased to have done this, and I hope to continue the process. Maybe once I get this book under my belt, I’ll feel more inclined to do similarly with Sean Carroll’s Spacetime and Geometry, which is hardcover but not too terribly heavy. Gravitation, on the other hand, is a book comparable in scale to Harrison’s, the “bible” of internal medicine. It’s not a book one tends to carry around (though it provides its own rather pointed example of the effects of gravitation).
Anyway, with any luck, maybe I’ll inaugurate a more useful commuter reading schedule. And maybe I’ll achieve enough skill at GR that I might be able to explore my perennial question. At least, I should be able to learn more stuff, and that’s always a good thing.
I hope you all have a good day.
*Actually, no, in astronomy “proper motion” has to do with angular movement with respect to more distant stars, or something along those lines. I don’t think it’s a great term for that. The motion of a galaxy relative to the CMB is apparently called the “peculiar motion”, which seems like a rather peculiar choice to me.
**I don’t know how you could stop me even if you so wished.
***It has one practice problem, which is a version of the classic barn door paradox aka the ladder paradox, but I didn’t work the problem. I know the basic answer already; it involves the relativity of simultaneity in special relativity, and the author asks us to draw a spacetime diagram demonstrating the basic issue. I had no resources to do this on the train.



