# Tangents of tangents of tangents, oh my!

It’s Wednesday, the middle of the week based on our usual reckoning of things.  Welcome.

Of course, the universe at large doesn’t give any preference to days of the week, or months, or whatever.  Days, per se, are more or less natural units of time, as are years.  Both are related to regular, physical phenomena in the solar system*.  Now, one could argue that since the moon’s orbit around the Earth is roughly twenty-eight days, that seven days in a week is a sort of natural division, since 28 divided by 4 is seven.  That’s not an unreasonable thought, but it is derivative, unlike the measure of a year or a day.

Of course, rather irritatingly, the days don’t evenly divide into the years, nor do the months (orbits of the moon, which itself isn’t quite an even number of days), which means we have to do all sorts of mucking about with the number of days in months to get a reasonable number of them per year, and only one of them has 28 days, but even that changes every 4 years, except every hundred years when it’s 28 again, except every thousand years when it’s 29 again, and so on.  And then, of course, we have to add and subtract “leap seconds” on an irregular basis to adjust things to keep them consistent, lest the seasons creep steadily in one direction or the other relative to the calendar as the years pass, even as the times of day and night also shift.

If the period of the moon’s orbit around the Earth divided evenly into the orbit of the Earth around the sun; and the length of days on Earth** also evenly divided into the orbit of the Earth around the sun; and if those divided evenly, say, into the orbits of the sun around the center of the Milky Way; and then if the second, as we decided it, turned out to be some round number of oscillations of a cesium atom being pumped by a particular wavelength of light—say 9 billion exactly, when measuring a previously decided interval of one sixtieth of one sixtieth of one twenty-fourth of a day…that would all be quite a collection of coincidences!  That would make me start wondering if the whole thing was designed by someone.  As it is, though, it looks very much like it just all kind of happened, with no inherent direction or purpose or goal.  Which makes more sense of most of human history and the natural world than the alternative does.

It would also be quite a coincidence if, for instance, pi turned out to be 3.141618110112114…or some other regular pattern alone those lines.  Especially if some similar pattern of interest showed up when it was measured using other number bases, like base 2, base 16, whatever.  That would be something.  Or imagine if pi were an exact integer.  Of course it’s hard even to imagine what it could possibly be that could make the ratio of a circle’s circumference to its diameter into an integer, how that could actually be achieved, since the number pi is something born of what appears to be fundamental geometry, constrained by internal logical and physical consistency.

Anyway, the universe looks very much like, as I said yesterday, a spontaneously self-assembled system.  For all we know, it’s just a collection of quantum building blocks of some kind that fall together in a bunch of spin-networks, if that was the right term, to form spacetime that acts like General Relativity when there are enough of them***.

And, maybe the other quantum fields are just emergent phenomena that develop as part of the properties of these conglomerated spin-networks, and the net result of their gross uniformity leads them to mutual repulsion, and then—rather like quarks being forcefully separated leading to formation of new quarks if you could do it, which you can’t—when spin-networks are stretched apart, they simply generate new, connecting networks in between, out of the energy from the tension of their repulsion.  Thus, spacetime can expand forever, generating new space-time as it does, and perhaps the other quantum fields, again, are mere epiphenomena that arise when enough spacetime exists.  And everything else, as we can already tell, is a bunch of epiphenomena overlying, or produced by, that.

Here’s a question that just occurred to me:  If spacetime can be continuously created by stretching of the preexisting network, in response to “dark energy” or “inflaton field” or whatever one might call it, popping little new nuggets of spin networks or whatever spacetime is made of into existence, can it, on the other end of things, be made to disappear?  Can quantum spacetime be unmade as readily as it is made?  I don’t think it would have to happen, say, in the “singularity” at the center of a black hole.  I can see that as potentially being a thin and narrow “tube” of spacetime stretching off and continuing to grow but only in one direction, like the function 1/|x| as it approaches zero, with a finite “volume” perhaps, but an infinite “surface area” that can keep growing indefinitely if spacetime really can just keep reforming itself.  Though maybe, if the chunks are of finite size, the tube can never narrow past some certain minimal “circumference”.  I wonder what the implications of that could be.

But can spacetime ever un-form?  Quarks that could be formed from, for instance, stretching the gluon field between two of them could, in principle, “un-form” if they encountered an anti-quark of the proper character.  They can even decay, I think.  But they wouldn’t simply disappear, they would convert into, presumably, some pair of high-energy photons, and maybe something else, too.  But spacetime itself doesn’t always obey the straightforward law of conservation of energy/mass, as GR has already shown.  Conservation of energy is a property of things within spacetime, and is born of the mathematical symmetry of time translation, as per Emmy Noether’s**** Theorem.  It doesn’t necessarily apply to spacetime itself.  So under what circumstances, if any, could it simply spontaneously disappear, and what affects would that have?

Well, that’s something I’m not going to figure out right here right now, I’m afraid.  But, boy, have I gone off on some tangents!  It’s rather like a moon or a planet suddenly released from the gravitational embrace of that which it orbits, to go off into eternity like a rock from a King David-style sling.  Or like the derivative of any continuous function, or the derivatives of derivative of derivatives, “most” of which end up settling out at some constant, if memory serves (but not the exponential function, ex!).

All this is, apparently, just what happens when one cannot stay asleep after three in the morning and so gets up very early and waits for the first train on Wednesday morning.  One thing leads to another, but with no inherent direction or purpose or goal.  Things just happen.

That sounds familiar.

*The rotation of the Earth and its orbit around the sun, in case you didn’t already know.

**Of course, there are different ways to define a day.  There’s a solar day, which—if memory serves—describes the time it takes for the Earth to turn until the same longitude line (so to speak) is facing the sun, which, because of the motion of the Earth in its orbit, is going to be slightly longer than a sidereal day, which—again, if memory serves—describes when the same longitude line returns to its place relative to the distant, “fixed” stars.  Of course, the stars themselves are not truly fixed, but their angular location changes so slowly that that’s an adjustment that doesn’t have to be made often.  I think there are other day measures, but they aren’t popping into my head right now.

***I realize that this is very loosely a description of loop quantum gravity, and that one prediction of one form of that model predicts that light speed even through a vacuum varies ever so slightly by frequency—and that our best measurements of light from distant quasars and the like seem to disconfirm that prediction.  But I don’t think the jury is completely in on that question.  And maybe that specific form of LQG is not quite correct, or the difference is smaller than expected.  I don’t know the subject well enough to opine.

****Look her up.  Einstein called her a mathematical genius.  Hilbert invited her to teach in the University of Göttingen (fighting against the powers that be that didn’t want a woman professor).  She should be a household name.  Her face should be on currency.  She should be bigger than every TikTok “influencer” combined.  That she is not should bring every human shame.