Physics

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If the vacuum collapses, everything gets messy

It’s Wednesday morning now, and I feel slightly better than I did yesterday, which should probably be no surprise.  I went back to the house last night, and I had a decent sleep‒for me, anyway‒and no major evening issues.  Now I am working my way toward the office.  It’s payroll day, so it should be at least mildly more hectic than most other days, but it shouldn’t be too unbearable.

Well, it shouldn’t be unbearable at all.  I mean, the state of being unbearable or not is a purely binary thing, isn’t it?  Either something is bearable or it is not.  If something is unbearable, then it cannot be borne.  So, saying something is not “too unbearable” is probably almost always nonsensical.  I suppose one could imagine something being only just unbearable, so that one could almost be able to bear it…but not quite, and one would finally be forced to succumb to whatever outcome that entailed, despite one’s possibly heroic struggles.

In some ways that sounds like it could be worse than something being thoroughly and unequivocally unbearable.  If one can see that something is truly unbearable, one will probably be less likely even to try to bear it.  One would not bother attempting to style out the brunt of a supernova; if one could not get far enough away, one would presumably just close one’s eyes and grit one’s teeth and take what comfort one could in knowing that the explosion will probably happen and obliterate one faster than any nerve impulse could propagate.

That’s one of the (tiny) comforts about the possibility of there being a “vacuum collapse” of the universe, in which the present “dark energy” vacuum state could, hypothetically, quantum tunnel down to a lower, truer vacuum state than the present one*, releasing that potential energy drop in such a way that wipes out all currently existing particles/fields.

This would erase everything in our visible universe (the “visible” part is deliberate and crucial; do you see why?**) in a sort of wave of collapse that starts at the site of the first state change, like the propagation of ice crystals forming in hitherto supercooled water.  But though it would be a shame, from our point of view, it would be one we would never experience, since the bubble of state change would expand at the speed of light.  It would thus be literally impossible to see it coming, because once you could see it, it would already be there, and you would be wiped away before you could possibly be aware that it was happening.

By the way, this possibility is “only” hypothetical; we aren’t even sure it could happen, not least because we’re not sure whether the vacuum state of the universe is as low as it can go or not, among other things.  But don’t worry:  if the vacuum collapse of the cosmos doesn’t kill you, something else will.

Even my truly immortal vampires in Mark Red might be wiped out by vacuum collapse.  I suspect they would, which might be a comfort to many of them, so to speak.  Of course, that would depend very much on how the “supernatural” forces in that book’s universe interact with the vacuum state and other quantum fields.  It’s not inconceivable that they might survive even that.  How’s that for horrifying?

These are odd thoughts for a Wednesday morning, aren’t they?  I mean, on a Thursday they wouldn’t be that odd, and even less so on a Friday.  On a Saturday they would be almost boringly predictable.  But on a Wednesday morning?  That’s just, well…odd, as I said.

I’m being silly.  My apologies.

I guess it’s more uplifting than is the prospect of universal Armageddon***.  Though, really, the Tao te Ching (in the version with which I am familiar) encourages us to embrace death with our whole hearts because that will help us to be prepared for most everything else we can encounter.

It does not encourage us to love death or to seek it; quite the contrary.  We are merely encouraged to accept it, not just intellectually but viscerally, to internalize***** it.  This is one of those curious circumstances in which the Tao to Ching and the movie Fight Club give the same advice, which is no indictment of that advice in either direction.

I try not to indulge in the vice of advice, but I will express my hope that every one of you who reads this post today or any of my other posts has a particularly good day, today and every day hereafter.

You’ve suffered enough already.

*This is analogous to what is thought to have happened when the “inflaton” field dropped down to a much lower energy level about 13.8 billion years ago, releasing the differential energy as the very hot soup of elementary particles that eventually became the universe we see.

**Okay, fine, I’ll explain.  It’s not just that the wave is expanding at the speed of light and so one would “see” it only as it hits.  But, given the current, accelerating expansion of the universe, the wave of change could never, even in principle, reach areas of the cosmos that are outside our cosmic horizon, because those places are receding from us faster than the speed of light/causality.  There is no causal influence from us that can ever reach them, or vice versa (assuming no wormholes or warp drives or similar).  Likewise, someplace beyond our horizon****** could be collapsing already, but we need never worry, because that collapse is not going to reach us (unless it changes the rate of overall cosmic expansion or even reverses it, which is not inconceivable.  We might then find ourselves in (or near) an anti-deSitter space, in which case, well…yeah).

***Not to be confused with the often misused**** term “apocalypse” which is basically just synonymous with “revelation”.  It’s become associated with the end of the world (and with lesser catastrophes) because one of the alternative titles of the book of Revelation is “The Apocalypse of Saint John the Divine” or whatever they called that nut bar.

****That rhymed, and it had a good rhythm too, both quite by accident.  I did that in yesterday’s or Monday’s post as well, but I didn’t call attention to it.  Can you find it now?

*****I would love to be able to use the term to grok it as in Heinlein’s Stranger in a Strange Land, but much as when Fuckerberg stole the term “metaverse” from me, likewise Elon Musk and the would-be tech boys who idolize him have arrogated the term “grok” and made it embarrassing to use.  Don’t even get me started on the disgusting theft of the word Palantir by Peter Thiel.  He deserves to be tortured interminably for the unmitigated gall he has shown in daring to use that term, but I would accept his immediate, painless disintegration and that of his company.

******Speaking of horizons, it is interesting to wonder what a vacuum state collapse would do to currently existing black holes.  I suspect they would basically be impervious to it, since the vacuum state is something that exists within spacetime, with the gravitational field as the backdrop of other quantum fields, but we don’t necessarily know enough about quantum gravity to feel very sure, as far as I know.  I suspect it might change the specifics of Hawking radiation at the level of the event horizon, and thus change the specific rate of black hole decay.  Also, I think in the first rush of particles generated by such a vacuum decay, most black holes would grow briefly with the influx of newly released energy all around them that had previously been bound up in the vacuum energy.  But that’s just my initial intuition.

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Noisy events on the horizon of my attention span

It’s Tuesday, isn’t it?  Well, I guess it may not be Tuesday when you’re reading this, but it’s Tuesday as I’m writing it.  It’s the second day in the latest of a seemingly endless stream of utterly pointless “work weeks”.

Welcome to our world.  Welcome to our world.  Welcome to our world of noise.

That’s a paraphrase of the song that was (and may still be) sung by the dancing animatronic puppets in the main front area of the big F.A.O. Schwartz store that sits just by the southeast corner of Central Park in Manhattan.  I’m not sure why I felt like including it there, but it definitely expresses the sentiment I have that nearly everything in the universe is effectively “noise” in the information theoretic sense.  At the very least, the signal-to-noise ratio in the world is vanishingly tiny.

It’s not zero, mind you.  There’s some info hiding in all the nonsense.

Of course, whether something is signal or noise depends very much on what signal you’re seeking.  If you’re trying to detect gravitational waves, then nearly everything else around is “noise” in the sense that it is not evidence of gravitational waves, and is just going to make that evidence harder to find.  But if you’re an ornithologist, then at least some of that seeming noise might be the birdsong “signal” of a rarely seen species there in Louisiana, which I think is where the first LIGO observatory was constructed*.

And, of course, if you’re a seismologist, what you consider a significant signal would very much be noise to the LIGO people.  If there were a gravitational wave strong enough to be seismically significant, it would have to be from a very close and catastrophically violent event.

We don’t expect there to be such a thing any time soon.  And apart from such events, gravitational waves are so relatively weak‒gravity being by far the weakest of the “forces” of nature‒that so far they can only be detected from things like black hole and/or neutron star mergers, which are ridiculously violent events.

Incidentally, apparently recent observations of one such merger has given confirmatory evidence for Stephen Hawking’s black hole horizon theorem**.  That states that when two black holes merge, the (surface) area of the new, combined event horizon must be at least as large as the two prior event horizon areas combined.

In this, as in other things, black holes and their horizons act very much like the 2nd Law of Thermodynamics, and that is consistent with the Bekenstein-Hawking thesis that the entropy of a black hole is proportional to the area of the event horizon, as measured in square Planck lengths.  Indeed, the maximum entropy‒the maximum information‒of any given region of space is that which would be encoded upon an event horizon that would hypothetically enclose such a space.

As for the volume of a black hole within the event horizon…well, that’s harder to quantify.  The apparent radius, as judged from the sphere of the event horizon‒the Schwarzschild radius for a non-rotating black hole‒is almost certainly much smaller than the radius that would be perceived by someone within the horizon, for spacetime is very distorted there.  Indeed, I suspect that, at least by some measures, the volume within a black hole‒or at the very least the radius from the “center” to the horizon‒is infinite, with the “singularity” actually stretching down away forever.

Of course, an asymptotically infinite well of that sort need not always have infinite volume.  There is, for instance, the counter-example of “Gabriel’s Horn”, a shape made by rotating a truncated function (y = 1/x for x ≥ 1) around the x-axis.  This shape has infinite surface area, but it has a finite volume(!).  So you could fill it with paint, but you could never finish painting the inner and outer surface.  Weird, huh?

Of course, the dimensionality of things within a black hole’s event horizon is probably at least one step higher than things in the Gabriel’s Horn comparison, so the finite/infinite comparisons may not translate.

I’d like to be able to do a better job working that out with more than my intuition; that’s one reason why I own no fewer than four fairly serious books on General Relativity.

That’s not the only reason, of course.  I would also like to try to solve what happens to a space ship that accelerates near enough to the speed of light that its relativistic mass and relativistic length contraction puts it below its own Schwarzschild radius (at least in the direction of motion).  Also, how would that figuring be changed if the ship were rotating around the axis of its motion***?

Unfortunately, I rarely have the mental energy to put into pursuing adequate mastery of the mathematics of GR, and so I can (so far) just try to visualize and “simulate” the spacetime effects in my imagination.  That’s fine as a starting place, but even Einstein had to master the mathematics of non-Euclidean geometry and matrices and tensors before he could make General Relativity mathematically rigorous.

It’s almost certainly a pipe dream that I will ever get to that level of expertise.  My chronic pain and chronic depression (dysthymia) combined with the effects of my ASD (level 2****, apparently) and the effort that’s required for me to act “normal” enough to get along just really wear me out mentally.  It’s frustrating.  I have a stack of pertinent texts above my desk at work, where I hope they will entice me.  I even have a copy of my old Thomas and Finney college calculus text there too, so I can do some reviewing in that.

If only I were able to spend some time without pain and to get a good night’s sleep once in a while, I might even make progress.  I suspect that such things are not in the cards, however.

I would love to be dealt The Magician (in Tarot cards) but I fear that I am just The Fool.  Oh, well, that’s all just metaphorical, anyway.  It’s possible to predict the future, of course, but it is difficult, and it’s very unlikely that any set of cards‒however cool they may be‒is the way to do it.

*I remembered correctly.  It is in Louisiana.

**The theorem, being a theorem, is mathematically rigorous, but the question remains whether it describes the way our universe actually works.  That is always a matter of credences rather than “proof” in the mathematical sense.  In the real world, probabilities may come vanishingly close to zero or to one, but they never quite reach them.

***In Special Relativity, when something is traveling around a circle at a significant fraction of the speed of light, length contraction has the effect of “shrinking” the circle from the “point of view” of that which is moving at that speed.

****”Requiring substantial support” according to the official definition.  I do not have such support.

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“The sun is the same in a relative way, but you’re older.”

Okay, well, here we are.  It’s Wednesday.  I don’t know what else there is to say about the day.  I guess…yeah, I don’t know.  It’s another day.  It’s a stretch of (roughly) 24 hours, the specifics depending on whether you’re using solar time or sidereal time or just the “self-contained” UTC time*.

UTC time is kept on a variety of clocks around the world and is based on the oscillations in the hyperfine transition frequency of the Caesium-133 atom.  That frequency has been defined as 9,192,631,770 Hz.  The international measuring community thing, whatever they call themselves, thereby agreed on defining the second as exactly 9,192,631,770 of those Caesium-133 oscillations.

Of course, oscillations of atoms, like all other processes that take time, slow down with increased spacetime curvature and with increasing speed relative to any given observer.  This is why the GPS satellites have to adjust their own time to account for both special and general relativity.  It’s pretty cool; you’re carrying proof of Einsteinian relativity in your smartphone.

You probably already knew that.

Then, of course, once they’ve decided on the precise value of a second‒knowing that the speed of light (or more precisely the speed of causality) is constant‒they then defined the meter as how far light travels (in a vacuum) in⁠ 1/299,792,458⁠ seconds (approximately 30 2/3 “vibrations” of a Caesium-133 atom).  Mind you, two observers moving relative to each other will see their meters as different each from the other, but c’est de la relativité.

It can be easy to imagine that definitions of units in science (and related fields) are not merely arbitrary but circular, almost tautological.  But really, given that these are attempts to codify specific attributes of reality itself, they would almost have to be self-referential with each other to be useful.

The length of a day is something that happens for real.  Thanks to the base 6 and 12 numbering system of the Babylonians, the day was long ago arbitrarily divided into 24 hours, each 60 minutes long, and each 60 seconds long, so a second was 1/(24 x 60 x 60) days or 1/86,400 of a day.

That worked well for a long time, especially since, before Galileo et al, humans couldn’t really measure time very precisely, anyway.  And then, until railroads allowed rapid travel between cities, it wasn’t necessary to worry too much about having the same time in different places.

But eventually that did become useful and necessary for many purposes, and eventually it was realized that a day wasn’t exactly what we were calling 24 hours, and indeed, that the length of a day varied slightly from day to day and year to year; also, a year isn’t a whole number of days long.  Also also, a day could be measured relative to the sun‒which is close enough that a day doesn’t end quite exactly after one full rotation since the Earth moves relative to the sun over the course of a day‒or with respect to distant stars, by which estimate a day comes closer to being exactly one complete rotation.

For most people most of the time, though, this precision, and that upon which it is based, are probably not merely irrelevant but unknown and unguessed.

Likewise, I don’t know how many people know about how Celsius made his temperature scale 100 degrees between the freezing and boiling of water at sea level pressure (a pretty reasonable choice, though I’m led to understand he initially had 100 assigned as the freezing point and 0 the boiling point!).

Then it was discovered that there existed a minimum possible temperature in principle, and they decided to set that scale, the Kelvin scale (named after William Thompson Scale**) using degrees of the same size as Celsius, but with zero defined as‒understandably enough‒absolute zero.

It’s all fairly interesting, if you’re in the right frame of mind.  But, alas, there’s every reason to suspect that all this information will be rendered moot and useless and perhaps even lost as the world winds down, or if life is replaced by artificial intelligence, or everything ends in some other way, as seems more than possible even in the relatively short term.

In any case, the laws of physics, as we know them, seem clearly to predict that the universe will tend toward ever-greater entropy and eventually all life, all structure will end.  Sometimes, I think it cannot happen soon enough for my taste.

Then again, there are cyclic universe proposals, such as Roger Penrose’s Conformal Cyclic Cosmology.  It bases its model on the fact that entropy, though always tending to increase, is not really an absolute quantity, not a substance, and that our universe’s “maximal” entropy may be the next universe’s low-entropy beginning, just on different scales; it doesn’t even require any “inflationary” burst of expansion to explain the uniformity of the CMB, I think.  I haven’t yet finished Penrose’s book about CCC, because though he is a stunningly brilliant mind, his writing can be a bit plodding and dry.

I guess it’s hard for any person to be good at everything, though Penrose has many strengths.  If memory serves, he invented a set of shapes which can be used to tile an infinite plane (in principle) with no gaps and no repeating patterns.  Supposedly this has been proven to the satisfaction of professional geometers, though I am not familiar with that proof.  Still, if it is a mathematical proof, then it is one of those rare things that we know to be certainly true, given its set of axioms.

It’s not necessarily useful in any practical sense, of course.  For instance, I think it’s probably true that any tiling system that can tile an infinite plane without repeating could not be used to tile a closed, finite, simple geometrically shaped portion of a plane‒such as a rectangular room.  I think you would always have to cut some of the tiles as they reach the wall, no matter how big the room is, as long as it is finite.  I do not know this for certain, that’s just my intuition.

Well, I guess I’ve wasted space and time enough here for now.  It’s no more wasteful than has been my entire existence, I guess, but also no less wasteful.  Or is it?  I don’t know.  In any case, for now I will stop wasting your time.

Please have a good day.

*Yes, it’s probably redundant to say “UTC time”, but the order of the acronym is sort of Yoda-esque‒it did not originate with an English term‒so I feel it’s tolerable to use it this way here.

**That’s a joke.  He was really William Thompson, the first Baron Scale***.

***I mean the 1st Baron Kelvin, of course, all joking aside.  A baron scale sounds like some long forgotten and unused (i.e., barren) bit of laboratory apparatus, left for eons, gathering dust in an abandoned world, like the broken statue of Ozymandius.  It’s very sad.

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I’ll have blogs more relative than this

Hello and good morning.

It’s Thursday again, if you can believe it.  It feels like it was just seven or eight days ago that it was Thursday last time, and here it is again.  I don’t know how this keeps happening.  Weirdly enough, though, from within, this week has felt as though it’s moving very slowly, and yet, it also feels as though Thursday has come again sooner than I expected.

The mind’s time sense is clearly not entirely objective and consistent.  Then again, why would it be?  Extremely precise long-term time-keeping would not have been a particular evolutionary advantage in the ancestral environment, certainly not one worth the inescapable biological (metabolic) cost of maintaining such a thing.

In any case, now we have incredibly precise time-keeping mechanisms which rely on some fundamental and consistent physical laws.  And though time does pass (so to speak) at different rates depending upon one’s relative velocity and the local curvature of spacetime (i.e., gravity), thanks to Einstein, we know how to adjust our disparate measurements of time with enough precision that we can maintain contact with a bunch of satellites in orbit, and they with each other, and use them to “triangulate” our precise position on the surface of the Earth to within a few meters (there’s generally more than one such triangle, thus the scare quotes—there is probably something more like a tetrahedron).

Of course, we don’t quite know completely just what time is, or at least, we don’t know for sure whether it’s fundamental or emergent from a deeper underlying set of physical laws.  We do know, based on General Relativity alone, that time would be in many ways “an illusion”, because simultaneity is not a consistent thing, and what counts as “now” relative to you depends very much on the direction and speed of your travel compared to other people.

From that point of view, all of spacetime in a sense “already” exists, and our experience of change is an illusion produced by the fact that we are within the block of spacetime.  Like characters and events in a movie on a DVD (or in any other stored medium) the events of the future are already laid out for us, and the end of the movie is as real and as permanent as the beginning, even when we watch the movie for the first time and don’t know what’s going to happen.

I think I talked a bit about this phenomenon in a post on Iterations of Zero called “Playing with spacetime blocks”.  If you want a better introduction to the ideas than anything I could give you, Brian Greene described it really nicely in either The Fabric of the Cosmos or The Hidden Reality.  I’m sorry that I don’t recall for certain which of the two books it is, but they’re both really great and are well worth your time.

Now, as it often does, quantum mechanics puts a bit of an onion in the ointment of fixed 4-D spacetime blocks, and the questions it raises depend—or so it seems to me—on which “interpretation” of quantum mechanics one applies.  In the standard version(s), in which there is such a thing as the collapse of the wavefunction when a quantum interaction occurs that leads to decoherence, there is a fundamental unpredictability to the outcome of such interactions when “measured”.

But if the permanence of spacetime as a whole that appears to be implied by General Relativity is correct, even those seemingly unpredictable events, countless numbers of which happen every second of every day in Dorset alone, are actually fixed and unchangeable.  This implies a mechanism of sorts for “superdeterminism”, or so it seems to me.

Of course, the Everettian “many worlds” version of quantum mechanics—which doesn’t require a deus ex machina wavefunction “collapse” that has to be added “by hand” to the calculations—seems to imply that, if spacetime is fixed in the GR sense then the state of being so fixed includes a fixed set of every outcome of every quantum interaction that would lead to so-called branching of the wavefunction of the universe.  That can be put into the works of GR, and it would give spacetime an added dimensionality of sorts—the dimension in which those “branched” paths exist.

But it would leave in the reality that we ourselves could not say which future “we” would experience, because every possible one actually happens; we just experience one at a time, so to speak*.  It would still be deterministic, just not as a “local” experience for those within spacetime.  Reality would be more like a “choose your own adventure” story than a fixed, scripted movie, but as with those books, all outcomes of any path are still fixed ahead of time.

I think I’ve rehashed a lot of the stuff I discussed in that blog post from IoZ, though I haven’t the will and patience right now to go check.  The specifics of my take on things are probably different this time; certainly, I think I understand all of the pertinent subject matter better than I did when I wrote about it before.  So, hopefully, this has given you at least something new.

Whatever the case, I cannot have done any differently than I have—unless I cannot help but do every possible different thing, but each branch of me, being a branch, only experiences its subset of the universe.  Even if, in a sense, you go both left and right at every metaphorical turn, you still only experience one direction.  It’s just that there is more than one of you, in a sense, experiencing each direction itself but unable to experience the other(s).

It’s really wild and cool stuff, isn’t it?  Science is amazing and awesome and fun.  Thomas Dolby sang that She Blinded Me With Science, but it’s really a way of removing blinders, of wiping the lenses of one’s glasses (and eyes) and focusing more precisely and rigorously on what’s really there, i.e., what’s happening whether anyone believes it or is there to experience it or not.

That’s probably enough for now.  I hope every possible version of you—even if there is only one—has a wonderful day today.

TTFN

*Please don’t make the mistake of thinking that it is human (or other creatures’) choices that determine the branching points of Everettian many-worlds, as seems to be implied by the movie Sliding Doors among other things.  It is quantum interactions resulting in decoherence that lead to the “splitting” of the wavefunction, and they are rarely the result of human choices, at least outside of places where experimental physics is done.

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Gravid questions of time and gravity (and labor)

It’s Monday, the first of September, which was “originally” the seventh month, but which is now pushed back to the ninth by the two “caesarean” months.  Speaking of such things, it’s also Labor Day in the US (I’m not sure about other countries) a day on which we celebrate labor by giving most people the day off.  This isn’t quite as perverse as it might sound.  After all, what woman would want to work while in labor?

Ha ha.

Anyway, my workplace is open today, though only for half a day.  It has become more and more common for nearly everything to be open even on huge holidays like New Years and so on, let alone “ordinary” federal holidays.  The reasons are fairly straightforward, and they have nothing to do with any kind of formal, deliberate, corporate conspiracy such as is imagined by so many naïve people on social media.

It’s just the same problem‒or situation‒that leads trees to grow tall when it would make much more sense for them all to stay closer to the ground and not waste so many resources on trunks and xylem and phloem, on getting water and nutrients from the ground up to their highest leaves*.  The trouble is, if all the trees were low but then one variant appeared that was slightly higher, it would have a significant advantage over its species-mates (and other species), so it would be more effective at reproduction, ceteris paribus.  Its offspring would come to dominate, unless and until yet other variants occurred that tended to grow even higher.  And thus the “arms race” would begin.

So in the human world:  if everyone else worked four days a week, but one worker was willing/able to work more days or longer days, especially if for the same or only slightly higher pay, then that worker would have a job advantage, (again, ceteris paribus).  And so competition leads at least some workers to strive to outdo each other to the extent they can, and so on, working for local, individual advantage that inexorably leads to less pleasant outcomes for everyone.  It’s just game theory applied to economics.

Anyway, that wasn’t what I wanted to discuss this morning.  I wanted to discuss two physics-related ideas I’ve had in the last few days.  The later one is just a bit of silly fun, but the other is more interesting to me.

The second one happened this morning (at about 2 am, when I was awake, because of course I was).  I put on a YouTube video of Star Talk in which a string theorist was the guest, and Professor Tyson asked her about the possibility of more than one dimension of time, and she said most such theoretical possibilities fall afoul of paradoxes and trouble with causality.

But it occurred to me, if there were a situation with time travel involving, for instance, the “grandfather paradox”, maybe the fact that preventing one’s grandparents from meeting makes one no longer there to prevent the meeting doesn’t necessarily unravel the universe, but maybe the paths and events correct and change each other in a closed, repetitive loop of time, interfering with each other** until only one, complete resonant spacetime line is there.

It’s analogous to a plucked string*** in which all sorts of vibrations and waves go back and forth between the fixed ends, but most waves/vibrations end up canceling each other out except the ones that fit an even number of times within the confines of the fixed string.  So maybe the actual events of reality could thus only be the ones that are resonant within that spacetime…whatever the hell that might mean.

Anyway, that’s the frivolous question; though it’s a bit fun, it probably doesn’t really have anything to do with our actual world (though it could…remember my thought a bit ago about forces traveling backward and forward in time and interfering until only a fixed number of outcomes resonate****?).

More interesting to me, really, was a question that occurred to me while I was reading Lisa Randall’s Warped Passages, a physics book (of course) and a particularly good one.  It was not really discussing the question that popped into my mind, other than that Professor Randall was reviewing the particles in the Standard Model.

We know that fermions cannot pile up one on another (cannot share quantum states), and that bosons can (e.g., in lasers).  We also know that massless force-carrying bosons such as gluons and photons travel at c, the “speed of light”.  The W+ and W- and Z bosons of the weak force do not because they interact with the Higgs field and so have “rest mass”.

Anyway, that’s not really the point.  The point is that gravitons, the hypothetical force-carrying particle of the gravitational field, are also massless bosons, and gravity travels at the speed of light*****.  But something popped into my head that had never occurred to me before and I’m not sure why:  do gravitons come in different frequencies?

We know that light has a limitless number of possible frequencies, across a very wide range, and that higher frequencies/shorter wavelengths are associated with higher energies per photon.  We also know that all matter radiates photons at a spectrum of frequencies that depends on temperature‒the so-called black body radiation.  Well, we also know that all matter “radiates” gravitons, or at the very least it all interacts with the gravitational field.  What if matter gives out gravitons in a spectrum that depends on total mass?

What would it mean for a graviton to have higher frequency or lower frequency?  Would that entail a stronger (and weaker) gravity?  Or would it correspond to something else entirely?

Of course, I know that gravitational waves are of varying frequencies depending upon the source‒that frequency and intensity (amplitude) increase as, for instance, two mutually orbiting black holes get closer and closer, orbiting faster and faster, before they coalesce.  Is that analogous to them producing large numbers of gravitons of those increasing frequencies?  Or are gravitational waves different types of things than “ordinary” gravitons?  Is ordinary gravity propagated by “virtual gravitons” much as the electromagnetic force is carried by “virtual photons”, which are really just mathematical shorthand for perturbations in the quantum field of electromagnetism?

I suspect that, because we don’t really have anything like a good quantum theory of gravity, there would be few clear answers to my questions about gravitons, but there may be constraints based on what we already know that would make my questions answerable or moot.

I mean, I know that “we” know that gravitons would be spin-2 particles, meaning that to rotate them 180 degrees would leave them unchanged******.  I don’t know how this or other aspects of gravitons would affect possible frequencies, though.  Also, can gravitons be polarized in a manner analogous to light?  I’m not sure whether my graviton questions are sensible or pertinent or utterly off the mark.  If anyone out there is a physicist specializing in such things, please, if you can spare a moment, let me know?

This post has gone on for a long time, I know.  I could meander around much longer on these subjects, probably for pages and pages and pages, but that would be a bit much for a daily blog post, if it isn’t already.  Maybe because it’s a holiday, at least some of you will have the time and interest in reading such thoughts, but I don’t want to push my luck.

However, I welcome any comments on the above subjects if you have an interest, and especially if you have relevant expertise (though I welcome all interested thoughts).

In any case, please try to have a good day.

*A fascinating physical process that’s only possible because continuous liquids can actually have negative pressures.

**Not in any inappropriate way, just that they interact and waves can cancel out.

***Not a “superstring” or heterotic string or what have you, just for instance a guitar string or a cello string.

****This is not unlike Feynman’s path integral/sum over histories notion, really.

*****We know this is so because there was a neutron star merger detected by LIGO and VIRGO that was quickly looked at using “light” telescopes as well, and the timing matched up (As a silly aside, since gravitons are bosons and could thus in principle share quantum states, one might, in principle, be able to create a coherent beam of them…a GRASER or GASER if you will).

******Spin-1 particles basically return to their identical state if you rotate them 360 degrees.  And for spin ½ particles, you need to rotate them 720 degrees (!) for them to return to their prior configuration.  Once you’ve rotated them 360 degrees they’re kind of the opposite of their prior configuration.  If that’s hard to think about, just imagine traversing a Mobius strip laid out in a “circle”:  once you’ve gone 360 degrees, you’re on the opposite “side” of the strip than that on which you began, and you have to go another 360 degrees (so to speak) to get back where you started.  Neat, huh?

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Is it a sine of the (space)times that we are where we are in the week?

TBIF* or TDIF**, either way, it’s Friday.  It’s the last day of the work week.  I started writing “It’s the end of the work week” (emphasis added), but I realized that, since it is early in the morning, and I am just on my way to work, this time could not accurately be called the end of the work week.  One could, in fact, say that 20% of the work week yet remains; that can hardly be called an end, any more than a B minus can be considered a perfect score (unless one radically changes the grading system one is using).

Such are the random things that spring forth from my brain via my fingers when I am writing my blog posts in the mornings (in this case on my laptop computer, which is literally on my lap***).  I’m sure you’re well aware of that, if you’ve read this blog for any length of time.  I don’t really know ahead of time what I’m going to write, unless I have a specific subject to address.  Even then I often address subjects in ways that surprise me.  This is because when I write I am really “thinking out loud”, although in this case, “out loud” is figurative.

Do my thoughts meander like a restless wind inside a letter box?  Well, they’re probably more like a restless discarded Cheetos® wrapper in the wind of a nearby tornado; one should almost certainly use a junk food metaphor when describing the way my thoughts spontaneously arise.  Not that I think my thoughts are “junk”, no more so than anyone else’s are.  I just think it’s rather appropriate to consider many of them as having a bit of a temporary amusing effect, but without any real nutritional substance.  Junk food has its place****, after all.

I don’t know what else to write today, but I’ve only written about 450 words so far, including the first four footnotes below.  I would say that I don’t want to shortchange you, the reader, but you’re not actually paying for this in any sense other than spending your time.  And since time cannot be used as legal tender—when you “spend” it, I don’t receive any from you—I guess I shouldn’t consider it to be shortchanging you.

In any case, whether you spend your time reading my blog or doing something else, your time passes all the same.  You could slow it down relative the those around you by accelerating to relativistic speeds, but you would still require the same amount of your “proper time” to read a blog post.  And to those watching you pass at some substantial fraction of the speed of light, it would seem to take you longer than it would take us.

Remember, from a particular, mathematically precise, point of view, you’re always moving at the speed of light—it’s just that most of your motion is through time.  This is part of why you cannot ever reach the speed of light through space:  As you tilt your motion vector toward faster motion through space, less of your motion is through time, until it would stop for you completely.

It’s a bit analogous to moving (say, driving or flying) in particular compass directions.  Imagine your default motion is all northwards, so there is no east or west component to your momentum, but that your momentum vector is always the same length, i.e., you speed in your direction of travel is constant.  If you start to veer eastward a bit, going at that same fixed speed now in a north-northeast direction (for instance) the component of your motion that is northward is smaller than it was*****.

As you veer more through northeast toward east-northeast and beyond, staying at your same speed but in your new direction, the component of your motion that is northward becomes smaller and smaller.  Finally, of course, if you go due east, there is no longer any component of your motion in the northerly direction.

This is close to being the same thing that would happen if you could somehow achieve the speed of light through space, except that the geometry of spacetime is (if memory serves) hyperbolic.  This means “relating to or described by hyperbolas”, it doesn’t mean that the geometry of spacetime exaggerates things all the time.

In any case, though, an object or person traveling at the speed of light (through space, so to speak) would cease to experience any “proper time”.

And with that, I think we’ve come to the proper time to bring this week of blog posts to a close, even if the work week still has a fifth of its time remaining.  I hope you all have a good day (whatever day on which you may read this) and then a good weekend (whenever the next one is for you) and a good week and so on and so on and so on.

*Thank Batman it’s Friday.

**Thank Doom it’s Friday (I suppose one could use TDDIF, Thank Doctor Doom it’s Friday, but that would eliminate the parallel with the more traditional version of the acronym).

***Does the term “laptop computer” imply that there could be a “lapbottom computer”?  What would the bottom of a lap look like?  Would it just be the “bottom”, in which case it really has nothing to do with the lap, since your lap disappears when you stand up, but your ass doesn’t?  If there is no lapbottom (i.e., if laps are instead bottomless) then why use the term laptop?  Why not just call it a “lap computer”?  If people wanted a foreshortened version of that, they could just call it their lapcom.

****That place is 7-11™.

*****By how much?  Why, one only need apply the Pythagorean Theorem to the components of your momentum vector.  It’s dead simple.  If you prefer, you can use trigonometric functions, such as the cosine of the angle of your motion relative to full north, but mathematically there is no difference.

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Oblivion is cold comfort, but it’s all the comfort I have to offer

Well, it’s Monday.  Meet the new week‒same as the old week.  There is nothing new or interesting happening, as far as I can see.  Nothing is new in my personal interactions with the world, and nothing is new in the world at large.  There may seem to be new things, and there are probably some details that are unique.  But then again, every snowflake is supposedly unique, but they’re all just flakes of snow, airborne ice crystals, and the overall behavior is nothing different despite all the trivially new specific flakes.  The phenomenon of snowfall is still just overall the same.

“So in the world,” as Shakespeare’s Julius Caesar said.  “‘Tis furnished well with men.  And men are flesh and blood, and apprehensive.”  He goes on the claim that he is unique in the next sentence, but immediately thereafter, Brutus, Cassius, et al, demonstrate that he too is merely flesh and blood like all the rest.

All the heroes, all the villains, all the ordinary people‒they are all functionally identical, despite all their trivial differences.  What percentage of the people who have ever lived are remembered at all?  A smattering, a handful, if that‒not even a rounding error compared to the total of all people who have lived.  And many of those we do remember are probably highly fictionalized and may not have actually existed at all.

What are the odds that Gilgamesh and Enkidu were real people?  How about Achilles and Hector?  For crying out loud, we know that even Richard III, presented as Shakespeare’s most thoroughgoing villain (perhaps matched by Iago) and deformed as well, was pretty much nothing of either sort in real life (or that’s what the historical evidence suggests).  He was simply defeated and then vilified by those who had defeated him, presumably to help justify their own actions.

And, by the way, who remembers them?

This sort of fact is part of why I sometimes refer to people (and other lifeforms) as virtual particles.  They pop into existence, persist for an infinitesimal period of time, and then literally vanish again, without a proverbial trace.

Well, actually, as with all virtual particles (which are not actually a thing but are merely mathematical and pedagogical tools) the collective effects of us virtual particles‒aka living things‒can have impacts on the world as a whole.  It’s even conceivable that, in just the right circumstances, as with the “real” virtual particles*, a virtual personicle can become actual.  I’m not sure what that would mean in the real world, though, and I’m not convinced that it has ever yet happened.

All this is part of why I have no patience for people who become fanatical about their particular ideologies and such.  They’re all just equivalent to some fanciful imaginary imaginings by a group of photons or neutrinos or what have you.

Don’t get me wrong, it’s perfectly reasonable for someone to approach their current affairs and ideas as “important” in their local** transient bailiwick, for some things to be important to them.  But it would be silly in a pronounced (but unfortunately not funny) sense for anyone to imagine that they had access to some final, consequential knowledge about the nature of the world and particularly about how people should behave.  If someone had such knowledge, I suspect it would be obvious to any intellectually honest person, including intelligent but disinterested aliens.

Humans and their dogmas are transient and transitory and ephemeral (and other synonyms as well) as are all other specific forms of life and ways of life.  Life overall is transient; as far as we can tell, it cannot even in principle go on forever.  That’s not just referring to individual lives, but to life as a phenomenon.  We could be wrong about this; there is much we don’t know, and in principle, our descendants could discover ways around the Second Law of Thermodynamics.  But that’s quite a big “if”, as it were.

Sorry to be such a downer; it’s just my nature, apparently.  Look not for comfort from me, as the ghost of Marley said.  It comes from other regions and is delivered by other ministers to other sorts of people.  Though, in this case, I’m not sure about what sorts of ministers and people would be involved, let alone what “regions” might produce such comfort.

In any case, I have no comfort, so I can offer none to anyone else; I cannot give what I do not have and what I do not even hope to have.  The best I can offer is to say that, well, oblivion seems to be the only viable alternative to discomfort offered by this universe.  It’s not much to offer, I admit, but it’s the best I have.  And, as pointed out above, as far as we can tell, it’s waiting for us all, eventually.

I won’t say that I look forward to it, because that really doesn’t make much sense.  But I am tired of trying to continue despite having almost no good reason to do so.

I hope you, the average reader, feel better than I do.  Batman help you if you feel worse.

*There’s an oxymoron.

**That “local” can, in principle, include the entire planet.  The point is merely that it is quite finite and limited.

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Had we but time enough, and space…

It’s the beginning of a new week but the end of an old month:  Monday, June 30, 2025, AD (or CE, if you prefer).  After tonight at midnight, we will be in the second half of this year, for whatever that’s worth.

Of course, one can debate whether Monday is really the beginning of the week or just the beginning of the work week.  Many consider Sunday to be the start of the week, at least here in this region of the “West”.

But, of course, since mainstream Christianity sees Sunday as the sabbath day, a day which is supposed to commemorate the day on which God rested after creating the world, seeing Sunday as the beginning of the week doesn’t make a lot of sense.  In the “original” observance of the sabbath—the Jewish one—Shabbat falls on Saturday (beginning Friday at nightfall), which makes more sense.  Then, Sunday really is the beginning of the week.

Not that any of this actually signifies anything real.  The start of the week or the start of a month or the start of a year are all just as arbitrary as one’s choice of the location of the origin and the x and y axes in setting up a system of coordinates in Euclidean space (or a plane, in this case).  As long as one is consistent in applying them, any calculations involved will turn out the same.  It is, in a way, a kind of symmetry, which would—in physics, anyway, if one were applying Noether’s Theorem to such as absurd situation—imply a conservation law of some variety.

I suppose there is a sort of conservation of days and months, in that one cannot by adding or subtracting days or months on a calendar change the length of a year or of a lunar cycle.  Although, with a big enough rocket or explosion or whatever, one could noticeably alter those things—it would be catastrophic for creatures on Earth, but this is science we’re talking about here, and if life on Earth must suffer for the advancement of science, then so much the worse for life on Earth!

I was kidding with that last bit there.  I am currently alive and on Earth—though at times I rue both facts—so I don’t actually want to treat life on Earth frivolously for my own curiosity’s sake.  Also, and more importantly, the people who matter most to me live on Earth*.

Anyway, over time the orbit of the moon is going to lengthen, as the moon very slowly draws farther and farther away from the Earth (which it is doing).  The length of a day and of a year both also slowly and subtly change over time.  Those time scales are long, though, and probably the sun will go red giant before either rate has changed enough to cause significant trouble, barring some large-scale asteroid collision or something similar.

This does, however, raise a point about the relationship of symmetry and conservation laws, à la Emmy Noether’s theorem.

It is the symmetry of translation—moving something from one place to another doesn’t change the laws of physics—that implies conservation of momentum.  And it is the symmetry of rotation—it doesn’t matter in what direction you’re oriented, the laws of physics are the same—that implies conservation of angular momentum.  And it is the symmetry of time—the laws of physics don’t change from one moment to the next—that implies the conservation of energy.

But here’s the rub:  on the largest of scales, the universe is not time symmetric; the past is significantly different than the present (and the future).  And so, on long time scales, the conservation of energy does not apply.  This is not merely a case in which I’m playing word games, by the way.  In this instance, I am speaking the truth about the nature of energy at the level of the cosmos according physics as it is understood today.

It’s an interesting question whether our local asymmetry in time—i.e., that the direction toward the “Big Bang” looks quite different from the other direction in time—is really just a local phenomenon.  That may seem strange, but perhaps it will be useful to consider an analogy with the various dimensions of space.

In space, in general, there is no directionality to the three dimensions.  One can go up and down, back and forth, and from side to side with equal ease, at least in space in general.  However, if you live on the surface of the Earth**, there is a very real difference between “up-down” and the other two sets of directions.

This apparent directionality to space is caused, of course, by the gravitational effect of the mass of the Earth itself.  It is an entirely local directionality, caused by a local phenomenon.  And similarly, the seeming directionality of time may be merely because we are “near” (in time) to a local, powerfully influential phenomenon:  whatever caused the Big Bang and produced a region in time of extremely low entropy and significant expansion, whether it is cosmic inflation or something else.

It seems pretty clear that, as entropy increases “over time”, the difference between past and future will become less and less noticeable, until eventually, there will be effectively no directionality to time***.  And so, in the “heat death” of the universe, the conservation of energy would steadily apply more and more, even at cosmic scales.

Not that there would be anyone to notice.

Of course, one can ask if there exists more than one time dimension.  I have asked this before, myself, I think on my other blog, Iterations of Zero.  But now there are some serious physicists entertaining the notion.  This sort of thing always makes me feel at least a little bit clever:  when I thought of something before the mainstream physics articles were published (or at least before I encountered them).

Anyway, that’s enough of that for now, this morning.  I hope you all have as good a week as you can.  Well, you will inevitably have as good a week as you can, but I hope it will subjectively be good  for you, too.

*I am not one of those people.

**As I suspect most of you do, at least physically.

***Very much in the way that, as one gets farther and farther away from the surface of some strongly gravitating body, like a planet, the difference between up and down becomes less and less prominent and finally vanishes into undetectability.

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The stochasticity of quantum interactions and the names of days of the week

It’s Wednesday today.  That’s a weird way to spell a day, and a weird way to spell a version of the name of the god Wotan or Odin, after whom the day is named (unless I am quite, quite mistaken).

Our days are peculiarly and seemingly haphazardly named here in the English-speaking West.  We’re not the only ones with inconsistent weekday names, but ours are certainly a strange hodgepodge.  Sunday and Monday are relatively straightforward:  they’re named for the sun and the moon.  Then, weirdly, we suddenly switch to Norse (!) mythology and name the next four days after four of the old Scandinavian deities.  Then, abruptly, we switch to a Roman god, Saturn, for Saturday.

This “names of the days of the week” thing was clearly not planned out.  It just sort of happened.  But that’s the way so many things occur in the real world—indeed, perhaps everything just sort of happens, and at multiple levels—not randomly but nevertheless stochastically and in a way that is functionally unpredictable, at least in its details.

The various quantum fields just sort of interact in ways that, at their lowest stable energy levels, give us quarks and gluons and electrons and photons and W and Z bosons and various neutrinos and a nonzero Higgs field that interacts with some (but not all) of the other fields.  The quarks and gluons just happen to form up stably into protons (and some neutrons, but neutrons are only stable within an atomic nucleus—they decay with a half-life of about ten minutes when existing freely).  And the protons happen to interact, via the electromagnetic field, with the electron field, and they stably pair up, and neutrons come into play “afterwards”, stabilizing larger atomic nuclei (though that’s not all they do).

Then, on large scales, the graviton field (if there indeed is such a thing, which is suspected but not certain) interacts with all the other fields, and where the density of stuff is slightly higher it pulls that stuff in towards itself, and where it is less, that rarefied stuff gets thinned out further as its components are pulled by neighboring stronger areas of gravity.

This process undergoes positive feedback—as stuff gets denser, its gravity gets more prominent, and that in turn tends to make the stuff get denser still.  And if there is any net angular momentum to larger collections of the stuff—and there almost always is some net angular momentum, since there’s only one way to have zero angular momentum, and there is a functionally limitless number of ways for it to be nonzero*—the stuff starts to rotate around a net common axis.

And then, of course, we get galaxies, and in those galaxies, we get stars, in which the interactions of the various quantum fields and gravity lead the protons and neutrons to get together into bigger clumps, some of which are quite stable (and the ones that aren’t stable simply don’t endure but transform into other states until they find ones that are stable).

Then stars run out of fuel, and the various field interactions and gravity produce various kinds of spectacular deaths, most of which involve scattering at least some heavier elements** out into the reaches of the galaxies.  Then we get next generations of stars, which (by the way) clump and develop angular momentum in a smaller but similar way to the galaxies.  And now, with heavier elements, we get planets, some of which are largely solid.

I think you know the broad strokes of the rest of the story.  If not, let me know.

Of course, this is a very general sketch of how stuff just came together to form the universe in which we exist, and there’s no indication that that is anything more than just small things—or esoteric things, really, such as quantum fields and their local perturbations—interacting with each other and making patterns on larger scales, much as water molecules can clump into fantastic patterns in the frost on windows or in snowflakes when they get cool enough.  Simple (well, relatively simple) rules at small scales can come together to produce surprising things at larger scales when they all interact at secondary, tertiary, quaternary and higher levels.

If you want to see how remarkable that tendency can be even in two dimensions, find a website that lets you play “John Conway’s Game of Life” and see how stable and active and interactive shapes can arise from even truly simple rules.

What was my point?  Sorry, I got distracted there for a minute.  Oh, right, I just meant to say that the things that happen and that all seem very real and important and even inevitable and fundamental are largely the products of stochastic processes interacting in ways that ultimately are far from being representable by any kind of linear equation.

It’s entirely possible and plausible that, if the rules of the quantum fields—or the specific types of quantum fields*** involved—were different, and thus interacted with each other differently, they might still accumulate into structures and functions on higher levels, and though they might produce a universe that would be all but incomprehensible to us, and in which we could not survive for an instant, they might nevertheless form structures and processes that could become what would have to be called “alive” and even “aware” and “intelligent”.

But in how many such universes would there be creatures that name the days of whatever passes for their weeks after various astronomical bodies (or whatever they have that is comparable) and random mythological figures from different places and times?

I leave it to the reader to speculate.

*There’s only so fast anything can be spinning, since no part of the spinning thing can exceed the speed of light.  Even black holes have a maximum angular velocity.  Nevertheless, both the angular velocity and the net axis of rotation can be more or less continuously variable.  If we can apply the real numbers—which ironically may not be possible in the real world—there is an uncountably infinite number of possible ways for angular momentum to be nonzero.  That makes zero really unlikely and unstable.

**Astronomers call any element but Hydrogen and Helium a “metal”, which is a very loose use of the term if you ask me.  I think many astronomers would agree, and sometimes I think I detect more than a tiny amount of embarrassment when they tell people that astronomical definition.

***Or the configurations of strings and branes if superstring/M theory turns out to be correct.

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Thoughts on real versus virtual keyboards, books, and quantum teleportation

It’s Friday, and I’m writing this post on my mini laptop computer, because although yesterday I forgot it and had to use the smartphone, it was really quite nice the other day to be able to type for real and not tap around on some simulated keyboard with no aesthetic appeal, on which one cannot feel the keys responding to one’s touch (and which gives this one arthritic pain in the base of his thumbs).

I remember when the notion of such a virtual keyboard first appeared to me—this was in Star Trek: The Next Generation.  I thought the idea seemed terribly unsatisfactory despite being very clever.  I mean, I recognized the efficiency of it, but when the characters would read books and such things on their little portable “tablets”, it seemed almost heartbreaking.

Obviously, in a star ship in deep space, they’re not going to have room for a vast physical library such as the virtual one they clearly have in the ship’s computer.  It’s much like the fact that I have many more books in my Kindle library than I have in my physical living space (though I used to have way more physical books than I have current Kindle books).  But something is lost a bit, nevertheless, at least for me, with such virtual collections.

Actually, it just occurred to me:  in Star Trek, they use replicators to make their food and so on, applying the transporter technology to reproduce scanned items that include food.  Why could they not use that to replicate books as needed, then scan them away when they were done?

Of course, the quantum mechanics of potential real world transporter-type technology is such that you couldn’t mass produce anything from “scanning” any one particular item; as part of the required entanglement process for quantum teleportation, one destroys the quantum states of the particles in the original item (or person, if it’s a person, so Dr. McCoy was right to be leery of the transporter).

Also, the entangled particles used to reconstruct the item by creating a new set of particles in identical quantum states to the original, could not be kept in their transitional states indefinitely; such states are not inherently stable.  Even if they could be maintained thanks to advanced technology, once they were used to recreate the original item or person, those entangled particles would also have their own quantum states irreparably altered, and could not be used to make another copy.

You can never make more than one copy of a thing sent by quantum teleportation, The Enemy Within notwithstanding*.

Still, maybe the people in TNG could “scan” a bunch of real books, as if about to transport them using the ship’s transporters, and just…save them for later.  You couldn’t make multiple copies, again because the originals would not still exist after being scanned—as I noted before, such scanning destroys the initial quantum states of all the constituents of the scanned item (or person).  But they could just be singly stored in the “buffer”, saving the quantum state of the entangled particles used to apply quantum teleportation.

But wait, I hear you say, storing all those books “in transition” would entail a tremendous amount of stored quantum information that would need to be maintained in its entangled state indefinitely, at presumably great cost in data and energy.  Not only that, one would have to have the equivalent of the mass of those items in the ship at all times, no matter** what.

You are very clever, and you are, of course, correct; it wouldn’t be efficient in any sense, and would add to the power requirements of the ship.  Also, in any serious disruption of the ship’s stability and power—such as happens in nearly every episode, so more than twenty times a year on average—much of that quantum information would probably be lost.

Maybe it really doesn’t make practical sense to try to do such a thing.  After all, I’m the person who has bemoaned the incredible data wastage necessary to store audio, let alone video, files rather than the much more efficient written word.  And I have not changed my mind on that set of subjects.  I could record a video, or even an audio, of me reading the words of this blog post, and it would have a file size in the hundreds of K at least; for a video, it would probably be many megabytes in size.

Meanwhile, my average blog posts, as stored in Word, are 16 to 20 K in size.  It’s quite a difference.  Even just using the RAM of this small computer (4 gigabytes) I could load up as many as a quarter of a million blog posts (assuming nothing else were in the random-access memory, which in not the way things work).  That’s about 250 million words.  Even I am unlikely to write that much during my lifetime.

More importantly, with the written word no one has to look at my ugly mug (though I will admit that my voice is absolutely lovely, so it might be worth hearing any audio file I produce…Ha-ha, just kidding).

Anyway, as I noted, it’s Friday, and I’m almost certain we’re not working tomorrow—I’m inclined to say that, even if the office is open, I’m not working tomorrow, but I tend not to follow through on such ultimata, because I’m a pushover—so there won’t be another post until Monday, at the earliest (barring, as always, the unforeseen).

I hope you all have a good weekend, but at least I know, as I pointed out yesterday, that you will have the best weekend you possibly can, since whatever happens becomes inevitable as soon as it happens, and it may have always been so (if quantum superdeterminism is correct).  Of course, that means you will also have the worst weekend possible.  But for most weekends, that’s a comfort.  For most such weekends, you could honestly say, “Well, if that was the worst weekend I could possibly have had, it’s not so bad.”

Usually, you could honestly say and feel that.  And it’s very likely that this weekend will be one such usual weekend.

Have a good one.

*In any case, that episode is really more of a fable than anything truly science fiction.  It assumes a bizarre kind of dualism between body and mind and a further, cleanly divisible dualism even in the mind itself, which in the episode is split into discrete but very broad personality aspects that can be separated out into different bodies.  It’s an interesting exploration of the tension between aspects of a person’s character, and engages speculation about whether a dark/violent side is a necessary aspect for a good leader.

**No pun intended, but I’m leaving it.