It’s Wednesday, June 21, 2023 (AD or CE, as you prefer), and I’m writing this on my laptop, but it’s not on my lap.  It’s resting on my desktop at the office, because I stayed here overnight last night.  I had a bad day—personally, not professionally—at the office, yesterday.  I felt just rotten, partly due to how poor a sleep I had, even for me, the night before.

I considered leaving early, but we were rather busy, and I didn’t feel I could justify cutting out on everyone.  Also, I had the nagging concern that, if I left early, I might never come back, because I really felt at my wits end, and though I had no specific plan in mind, I thought I might take some kind of drastic action to make it impossible for me ever to do anything again.  I just wanted to go to sleep and to sleep and to sleep and perhaps never to wake up.

Anyway, it really started to thunderstorm rather badly near the end of the work day, so I decided I would just stay at the office.  I’ve had a hard time getting up to my usual status on the payroll this week so far, and it has to be finished by today, so eliminating the commute time will better allow me to finish that.

But everything is getting too onerous for me.  I’m so tired, and I have no internal drive or purpose of significance, just habit and stubbornness, which can’t really ever make up for the real thing in the long run.  I don’t know what I’m going to do.  I need help, but I doubt I’ll get any, and I don’t think I’m capable of seeking it.

I can’t make myself believe that I deserve or am worthy of any help.

Speaking of long runs (I was, you can go back and check) today is the Solstice—the summer one in the northern hemisphere, and the winter one in the southern hemisphere.  Thus, it is the “longest” or the “shortest” day of the year, depending on one’s location.  I use scare quotes because it’s not the actual length of the day that varies on this date, or from day to day in any kind of steady way, but the duration of daylight, the time in which the sun is overhead, or at least visible in the sky (barring clouds).

But, of course, the length of a day really does change a bit from time to time, though not in anything like as regular, nor as dramatic, a fashion as daylight does regarding solstices and equinoxes and all that.  The earth is a rotating mass, and is subject to the laws of angular momentum.  Thus, when enough mass changes position on the surface of the planet, it can have an effect on the overall rate of rotation of the planet.

The stereotypical “demonstration” of this process is a skater spinning on the ice, who speeds up when bringing his or her arms close to the body and slows down when extending them.  This is because, crudely, the angular momentum is mvr, the mass times the “tangential” velocity (of the mass), i.e. the speed at which it goes around the center of rotation, times the distance from the center of rotation.  Thus, since angular momentum is conserved, if the radius shortens, the velocity around the center of rotation increases proportionately, and vice versa.

The instantiation of this is somewhat complex, as is usually the case, but this really is the gist of it.  The conservation of angular momentum is related to the rotational symmetry of the universe, as per Noether’s Theorem—i.e., the laws of physics aren’t dependent upon which direction you happen to be facing.  This is similar to how conservation of linear momentum is related to symmetry of translation—i.e., the laws of physics don’t depend upon where you happen to be along any linear direction.  And conservation of energy (locally) has to do with the symmetry of time.  This last one can be tricky when taking the universe as a whole, because conservation of energy doesn’t necessarily apply to the whole cosmos, nor is time fully symmetrical on the largest of scales, or so it seems, but locally it is true.

Physicists, please correct me if I made any gross errors there.

Anyway, back to the rotation of the Earth and the length of days.  Movement of significant amounts of mass on the surface of the planet (or within the planet) can change the rate of rotation of the planet.  I’m led to understand by the program QI* that a massive hydroelectric project in China cause the “elevation” of a large enough mass of water to slow the rotation of the Earth by a measurable—if inconsequential and utterly unnoticeable—amount.

I sometimes wonder if the periodic gathering of millions of people near the mouth of the Ganges has any potentially measurable effect on the momentary rate of the Earth’s rotation.  I’m not aware of anyone having made such a measurement.  Even if it’s true that it changes the rotation rate, it may be too small to detect.

I also wonder whether, as glaciers on mountains and across Greenland and similar melt, with the water thus previously elevated seeking a level closer to the center of the Earth, the planet’s rotation might well speed up.  I wouldn’t expect glacier melt in Antarctica to speed up the rotation in quite the same way, because those glaciers are all far closer to the axis of rotation in the first place, and so might have limited effect in shortening the “lever arm” of rotation.  Indeed, if they raise sea levels significantly enough, I could imagine the “center of mass” of the Earth’s rotation moving slightly outward, especially as the seas bulge more at the equator, thus slowing the motion of the planet down.

The odds of this perfectly balancing seem small, but I imagine it would require very complex calculations and—more importantly—quite fine measurement to ascertain the net balance.  And, of course, the balance is likely to shift over time.

In comparison, it’s relatively** easy to calculate the balance between special and general relativity required to keep GPS satellites in synchrony with the ground.  In this case, the speed of the motion of the GPS satellites slows down their local passage of time relative to the surface of the Earth, by a calculable and quite constant amount, but their greater distance from the center of the “gravity well” makes their time go faster relative to the surface of the Earth, again in a quite calculable and rather constant rate.

It’s the latter effect that predominates, and this is routinely accounted for in the GPS process.  If it were not, GPS would have huge and increasing errors as the timing in the satellites and of ground-based clocks diverged steadily, and the errors would very rapidly become far too great to be useful.  So, your use of smartphones to find where you are and how to get where you’re going depend on both of Einstein’s theories of relativity.

I guess you all already knew all that.  Sorry to be boring.

Anyway, that’s my bit*** of trivia for the day.  It will probably be the most interesting thing to happen to me in this particular Earthy rotation, but I hope all of you are having more interesting days than I am.  I’m just very tired, and discouraged, and worn out…and it’s only a little after five in the morning.

I’ve been in pain for twenty years, and I haven’t seen my kids (in person) nor interacted with my son at all (barring one email) in over ten years, and my last remembered restful night’s sleep happened in the mid-1990s.

If I could just find way to get restful nights’ sleeps, that would be a start.  Everything else would be easier, or so I suspect, if I could find a way to make that happen.  Then again, perhaps it wouldn’t help, and I would simply be faced with the tragic irony of having that wish come true only to find that it didn’t make the other things better, and might even make them worse.

Never underestimate the potential for things to get worse.  Reality has no bottom.

There’s that symmetry of translation that implies, by Noether’s Theorem, that momentum will be conserved.  Which brings me full circle, thus recapitulating the conservation of momentum/symmetry of rotation.  It’s neat, isn’t it?  Time, however, is a trickier bit of possible symmetry, as Pink Floyd recognized only too well.  But at least after Time has passed, when on The Dark Side of the Moon, one can look forward to the beauty of The Great Gig in the Sky.

If you haven’t listened to that album in a while, why not listen to it today?  Or if you’ve never listened to it, treat yourself.  It’s well worth it.  What the hell, it’s the longest day (or night) of the year.  Indulge yourself.  And if the cloudbursts thunder in your ear—you shout and no one seems to hear—and if the band you’re in starts playing different tunes, I’ll see you on the dark side of the moon.

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*Which has, upon occasion, been incorrect, but it does, in the long run, try to correct prior errors, often in hilarious ways, usually at the expense of Alan Davies, as in the running conflict over the number of moons the Earth actually has.

**Ba-dump-bump.

***Well, actually, probably a few thousand bits, albeit redundantly encoded.