How big might real wormholes be?

AFAICT, there is no actual evidence for real wormholes existing, they are merely interesting ideas not obviously forbidden by known physics.

That said, they are fun to think about. Quoth Wikipedia: “The quantum foam hypothesis is sometimes used to suggest that tiny wormholes might appear and disappear spontaneously at the Planck scale and stable versions of such wormholes have been suggested as dark matter candidates.”, so I just decided to see how big such a wormhole might become if it popped into existence right before the Big Bang inflationary period began and lasted at least until the end.

Inflation itself lasted for an unknown time, but a minimum bound is that it expanded the universe by a factor of e^60 (≅ 10^60), which means 1 Plank length would expand to… 1.8458 nanometers. Tiny though that is, it would still be very useful for communications. I wonder how many of those you’d need to have in the universe for their existence to even be testable with current tech?

Fiction, mathematics, Science, SciFi, Technology

SciFi: The unexpected problems with gravity

Artificial gravity in science fiction falls into three categories:

  1. Applied Phlebotinum works via made-up technobabble. Examples include the gravity plating in Star Trek.
  2. Spin gravity is where inertia wants you to keep going in a straight line, but centripetal force from your outer hull keeps pulling (or pushing) you towards your axis of rotation, creating what feels like centrifugal force. Examples include the titular space station in Babylon 5, and in real life fairground rides and your car doing a sharp turn at speed.
  3. Acceleration gravity is similar to spin gravity, in that what you’re feeling is the reaction of your hull against the inertia of your body, but is based on your engine constantly accelerating you. Examples include many of the ships in The Expanse, and in real life rocket launches and drag racing.

If you want to write hard science fiction, you will ignore Applied Phlebotinum. Spin gravity may be fine, but will probably have a noticeable Coriolis force in practically sized ships and stations; notably, in the film 2001: A Space Oddesy, the spin-gravity habitation ring of the Discovery One was so small you could expect people to get dizzy from the Coriolis force messing with your sense of balance if you turn around, bend over, or other everyday motions (Arthur C. Clark was reportedly well aware of this, and overruled in the name of cinematography). This can be challenging to get right, but you may want to do it anyway.

If you don’t want to use spin or space magic, you only have acceleration gravity: In principle, there are plenty of atomic rocket designs could get you Earth standard gravity for most interplanetary trips out to about Jupiter, and some of the fancier fusion designs (let alone antimatter) could give you 1 gee to all the rest. Unfortunately, speed is a serious problem.

Consider Mars. Launch from Earth always requires you experience more than Earth gravity (the natural gravity adds to that of the acceleration), so let’s approximate this trip as 1 gee of linear acceleration rather than 1 gee subjective experience.

The distance from Earth to Mars varies from 4 light minutes to 20 light minutes. The turn-around point is half that, take the high end and you get 10 light minutes. The time taken to get there is given by s = 1/2 at^2, i.e. 10 light minutes = 1/2 (9.8 m/s^2) t^2 ⇒ sqrt((20 light minutes)/(9.8 m/s^2)) = t = 191600 seconds (about 2 days 5 hours), peak speed is v = at = (9.8 m/s)(191600 s) = 1.88e6 m/s.

Nuclear fusion starts getting noticeable when the ions have an average speed of about 2e6 m/s, and the speed of the solar wind is enough to make up the difference on sunward flights.

The other problem is the density of the solar wind — space, despite being very empty, is not completely empty. While it varies depending on solar activity, location, and nearby magnetic fields, the interplanetary medium near Earth is around 5 particles per cm^3, which is 5e6 per m^3; at a peak speed of 1.88e6 m/s, every square meter of the hull’s cross section to motion will be hit by (5e6 particles per m^3)(1.88e6 m/s) = 9.4e12 particles per square meter second. If they are all hydrogen atoms, the kinetic energy per second of this is 27.8 millijoules (does anyone say ‘kinetic power’? They should. The kinetic power is 27.8 milliwatts). This does not sound like much, but there is no difference at all between hitting a proton at this speed and sitting next to something radioactive emitting protons at that speed, so this 27.8 mW is in the form of somewhat penetrating radiation — at best the front of your ship will absorb it, filling internal voids with hydrogen gas and eventually flaking off (a process like this is already used industrially to produce very thin sheets of expensive materials such as computer-grade silicon); at worst, a small fraction of this will undergo spontaneous nuclear fusion with your hull, producing much harder radiation. The only good news here is that fusion is difficult precisely because this is a low-probability event, and the fusion power flux will be less than the directly absorbed power flux from the IPM.

If your ship is flying out to 90377 Sedna, you have slightly worse problems; the interplanetary medium gets significantly thinner (inverse-square law), but particles/second is proportional to speed (which is proportional to time when acceleration is constant), and kinetic energy per particle is the square of the speed, so under constant acceleration, the IPM power flux is (roughly!) proportional to your total distance from the sun. As it’s mostly in the form of a plasma, your ship design could use a magnetic field to deflect most of it; you might expect the downside of this to be that the magnetic field will massively increase your ship’s drag, and indeed it will, but you’re starting from such a low threshold that even a massive increase is negligible — solar sails, even M2P2 magnetic sails, have very small total forces despite trying to explicitly maximise this very effect.

And all that’s ignoring the effect of hitting a 1 milligram fleck of dust at 1.88e6 m/s — the kinetic energy of which is roughly equal to 420 grams of TNT.

Health, Psychology

Why do some people hate masks?

A bit over two weeks ago, I wrote the following on a nerd forum:

I wear masks outside, because sometimes I encounter a bus stop where the entire volume of the bus exits exactly where and when I happen to be walking.

Also, a mask, like wearing trousers, is a trivial cost.

I still will wear one after being vaccinated, because I expect the effects to be multipliers: 80% protection from a vaccine and 90% from a mask is 1-(1-0.8)(1-0.9) = 98% protection.

Gaining me net +4 karma.

Somehow, someone took such offence at this that rather than reply in that forum, they went to this blog, and posted three insults obliquely referencing the words “trivial cost” while spewing poorly-aimed keyboard-bile.

Why, for the love of sapience, does a small additional piece of clothing cause so much hate? Because it’s not just random blogger and random commenter — non-compliance with basic safety measures like this was an issue with the Spanish Flu a hundred years ago, and an issue with trying to contain HIV forty years ago.

I can understand being sad about it, but hate? Even nudists know about PPE like towels and shoes.

Futurology, Science, Technology

Bioprinted fairy drones

As Arthur C. Clarke wrote, any sufficiently advanced technology is indistinguishable from magic. In the case of bioprinted fairy drones, the tech only looks like magic because it isn’t advanced enough.

Bioprinting is the 3D printing of organic material. It’s been demonstrated for years in various different capacities, but the current state-of-the-art suggests that we’re as far from printing a fully-functional organ as a we are from inorganic 3D printers printing a fully-functional car — you can do something that superficially looks right, but doesn’t have all (or even a bare minimum) of the functionality.

Some of the problems bioprinting has are even the same problems that inorganic 3D printing has: There are a lot of different cell (/material) types, and you can’t get away with using the wrong thing. Just as jet engines don’t work too well when 3D printed out of pure plastic, you don’t want to mix up kidney cell types (plural: there are multiple types) with artery cell types.

Other problems are unique to bioprinting: while houses and boats (or rather, the empty shells of houses and boats) are limited only by the range of the printer, organic material has a tendency to die very quickly if it doesn’t get any oxygen, and getting oxygen into tissue without a heart is very difficult. Difficult, but for small things, possible, and that’s where fairies come in.

Fairies, at least in their Victorian-era depictions, are tiny. Not actually small enough to deal with all the oxygen diffusion issues by themselves, but small enough that it’s plausible tissue could be printed in a cryo-preserved state (which does work, just not for human-sized creatures), and then the complete organism thawed out alive when printing is finished. Their diminutive size also makes their wings actually plausible, whereas a human-sized biodrone would need ridiculous wings to fly.

At this point, normal people will be asking ethical questions about their brains and lifespan. As they’ve been printed, this is absolutely the wrong question: you absolutely should not even try to print a brain into them in the first place — and not just because of the ethical dimension! We couldn’t even design a functional brain yet because we don’t actually understand brains very well (if we did, every A.I. question from self-driving cars to social media moderation would already be solved), but even if we understood brains perfectly, the brain and nerve tissues are particularly awkward one to print as axons and dendrites give them pointy bits which go all over the place in ways which directly matter to them being useful.

So, instead of giving them brains, give them WiFi. Instead of eyes, give them cameras. Congratulations, you now have a bioprinted fairy drone.

You may ask: Why?

Fair question. Other than size-fetishists, who benefits from a tiny flying humanoid robot? Well, pretty much everyone. While they couldn’t do any heavy lifting, the entire history of human invention all the way back to the inclined plane, the wheel, and fire, has been to minimise our heavy lifting. What tiny flying human-shaped organic robots can do is not limited to themselves, but part of the entire ecosystem of machines in our world, one of which is swarm robotics that lets them work together much more effectively than a mere team of humans, and at basically the same range of tasks.

So, my answer to “why” is a slight variant on an old meme of a question: Would you rather compete against a single 1.8m tall human, or a thousand pocket-sized fairies all working together?


Baryon asymmetry

One day, I might learn enough physics that my questions don’t sound like nonsense to physics graduates. Today is not that day — my working assumption is I sound like a freshman at best, and a homeopath at worst, and will remain so until I put numerical simulations of standard results in general relativity, quantum mechanics, and Navier-Stokes equations onto my GitHub page.

The baryon asymmetry problem is that matter and antimatter are always created and destroyed in equal quantity, yet the universe clearly has more of one than the other.

If you can make or destroy one without the other, in isolation, then you also get to violate charge conservation, which would mean that quantum field theory is wrong because something something Noether’s theorem. (Of course quantum field theory might be wrong; it’s known that general relativity and quantum physics can’t both be true because if they were both true the universe would’ve collapsed instantly at the very beginning).

The only way you can conserve charge but take antiparticles out of the system is if the process requires an equal number of antiprotons and positrons.

Both of these options — either violate charge conservation or take out multiple particles at once — have interesting consequences which can probably be tested, although not by me, given my degree is in a totally unrelated field.

If charge conservation is violated, then the universe should have a net electric charge. This charge should change over time, as there are still natural processes creating positron-electron pairs but not (at least to the same degree) proton-antiproton pairs. I don’t understand what this would do to the Einstein field equations (only that it would do something; given the effect on black holes I have to ask if it could be dark energy?), but I’m fairly sure lots of free electrons in the interstellar or intergalactic medium should be noticeable.

On the other hand, if antiprotons combine with positrons and that composite — possibly but not necessarily, given how conjectural this already is, an antineutron — either that composite is stable or it has a way of decaying into something other than an antiproton and a positron. The obvious question this raises is: could this be dark matter?

The obvious counter-point to the question “what if antineutrons are stable” is “surely someone would have noticed”, which is a fair question that I cannot answer — I genuinely do not know if anyone would have noticed yet, given how hard it is to make antimatter, how hard it is to trap antimatter, how hard it is to trap even normal neutrons, and the free-neutron half-life.

I can say other people have thought about neutron-antineutron oscillations, which might well solve the baryon asymmetry problem all by itself without any consequences for dark energy/dark matter:

(Another thing I definitely don’t know, and which my physics MOOC won’t teach me, is how to separate legit ArXiv papers from the bogus ones; that reflects badly on me, not on the authors of that paper).

Health, Minds, Personal

Truthiness & COVID denial by the dying

Enough people believe enough odd things that I was not surprised when I learned of COVID deniers; not just because the same happened a century ago with Influenza, but also my own former (as a teenager, now embarrassing) sincere belief in the occult.

Indeed, even when it comes to people denying the existence of COVID even in their dying breath (and despite claims that these reports are, if not incorrect, then exaggerated), I find this scenario very plausible thanks to the unfortunate path of my father’s bowel cancer.

Bowel cancer, as you might guess, can require a colectomy and the subsequent use of a colostomy bag. As one function of the colon is to absorb water, skipping it means you must increase your consumption to compensate. My father did not drink more water, and therefore suffered kidney failure just as I arrived for that year’s family Christmas — so I got to listen to his nurse telling my father all of the things I’ve just written about in order to explain to him why he now had an emergency hydration drip going in one arm and an emergency kidney rescue drug going in the other. Despite this, my father absolutely denied there was anything was wrong with how much water he was drinking.

He died two months later.

Fiction, Politics

If you wanted to steal an election…

Let us say that you were in charge of the Ministry for Shenanigans, tasked by the Supreme Leader with interfering with the democratic elections in Freedonia, not to ensure the current Prime Minister of Freedonia remains in power, but to sow dissent amongst its people.

The current Prime Minister of Freedonia is known for saying random nonsense, but is not actually known for having the competence to pull off any of the conspiracies everyone knows he would like to engage in.

If anything, he is so mindbogglingly incompetent that nobody would dare try to involve them in a conspiracy, because everyone knows that if you tried, he would boast about the plan the next morning in the middle of a breakfast TV interview that was supposed to be a fluff-story about cheese exports. Everyone knows this, because during the last election he openly asked you to interfere, and then went on to boast about getting your help, even though you actually didn’t bother that time. The fact you genuinely didn’t help him then is the only reason he has not already been removed from office and inserted into a prison cell.

So, what do you do given that it is absolutely vital that all of your actions are deniable? Remember, the goal is not to get this moron elected, it is to cause civil disorder within Freedonia. To make Freedonia care more about its internal affairs than whatever the Supreme Leader is doing.

You wait.

You wait for the Prime Minister to say or do something corrupt and stupid. Perhaps he will claim that suicide bombers are plotting to blow themselves up in the polling stations, and therefore all voters must be naked, even though the election is in the middle of November. Perhaps he will make spurious claims about postal voting. Perhaps he will require people to show a voting-specific ID card but only send those cards out to people likely to vote for him.

It doesn’t really matter what nonsense he comes up with, because Freedonia has a constitutional separation of powers that limits the damage the Prime Minister can actually inflict.

What does matter is that he will say these things, and many voters will see this as a threat to their vote and (quite understandably) be very angry. They will organise. They will suggest ways around his schemes. They will think themselves very clever. Broadly, they will also have no idea how anything works.

You will use your fake social media accounts to join in. You will seem real, genuine, pro-democracy. But… the ideas you will be feeding the Freedonian electorate are those which sound good and yet do not work. Ideas like “online voting with blockchain” (you know how easy it is to break into a Freedonian government website) or “posting your vote directly to the $insert_address_here” (oh, but post that goes there never gets read).

Most of the public won’t be able to tell which advice is good and which is bad, so if experts warn against listening to bad advice, the public are still just as likely to do the wrong thing as the right thing.

Either way, an increasing number of people start distrusting the result. When the results come in, they have an excuse ready and waiting for why they lost: not because their politics were unpopular, but because the other lot corrupted the vote.


Hᵤ(2, 2) = 4 for all u>0

A bit of recreational mathematics. I’d be (pleasantly) shocked if this is novel.

2+2 = 2×2 = 2² = 4 🤔

Hᵤ is the set of hyperoperations, e.g.
H₁(a, b) = a + b
H₂(a, b) = a × b

Hu(a, b) = Hu-1(a, Hu(a, b-1)) when u≥3 & b≠0
∴ Hu(2, 2) = Hu-1(2, Hu(2, 1)) when u≥3

also Hu(2, 1) = Hu-1(2, Hu(2, 0)) when u≥3

also Hu(2, 0) = 1 when u≥3

∴ Hu(2, 1) = Hu-1(2, 1) when u≥3
∴ H3(2, 1) = H2(2, 1) = 2
∴ H3(2, 2) = H2(2, 2) ⇒ 2² = 2 × 2 = 4

also Hu(2, 1) = 2 when u≥3
∴ Hu(2, 2) = Hu-1(2, 2) when u≥3
∴ ∀ u ≥ 3 Hu(2, 2) = 4

as H₁(2, 2) = 4 and H₂(2, 2) = 4, ∀ u ≥ 1 Hu(2, 2) = 4

i.e., for any hyperoperation ∘ other than the zeroth (successor) operator, 2 ∘ 2 = 4

Fiction, SciFi

Trek head-cannon

In the real world, the “vaporise” setting in SciFi ray-guns comes from a desire to make extras disappear quickly when their characters are killed off.

As countless of pedants have noticed, a real-life weapon which vaporised a target would have all sorts of unpleasant side-effects, from the merely icky of inhaling your enemies to the potentially fatal of suddenly adding 80 cubic-meter-STP of (lethally hot) gas to your room in less than a second. There are also, shall we say, artistically convenient behaviours such as one scene in Star Trek VI where a pan is vaporised while the mashed potato inside is untouched.

None of these things ought to spoil your experience of Star Trek or similar — they’re character-driven space soaps, not hard SciFi. That doesn’t mean it’s not fun to invent some plausible-sounding rationale for how it fits into the in-universe technobabble.

So, phasers, with a digression via subspace.

In the Star Trek universe, “subspace” is treated as an extra dimension — not up-down, not left-right, not front-back, not future-past. If you’re “deep” in subspace, you’re “further” from the reality we know about. How this works precisely is never described, so let’s pretend that there are a bunch of different stable layers that matter can occupy, one for normal space and one more for each different integer warp speed; and lets assume that in the absence of anything pushing you between layers, you just stay on your current layer.

What if the “rapid nadion effect” is a nudge in the subspace-realspace direction?

All the atoms in your body are connected by relatively strong interatomic forces, while the interatomic forces between different objects are much weaker (not zero, but much much weaker). Let’s say you’re hit by a beam which nudges you in the direction of subspace: if its a weak push, the atoms hit by the beam are briefly a little bit outside normal space, but they rapidly return. This effect propagates through your body in exactly the same way that a sound wave would — each out-of-place atom drags nearby atoms with it, but they’re quickly restored to their original place. This could stun you or kill you, depending on how much it interferes with the chemistry that keeps you alive, in much the same way that a punch or a grenade both send waves through your body yet have very different impacts on your life expectancy.

If this nudge is strong enough to push your body to the next subspace layer, the part of your body first hit by the beam will seem to disappear entirely, without the inconvenience of exploding! All the atoms bound to the nudged-into-subspace patch of flesh will be dragged with it onto the next subspace layer, which does not have any air. If this happens at the speed of sound in water (5336 km/h), a 2m humanoid hit in the middle would disappear completely in about 0.7 ms. The effect you see on screen is a far more prosaic 8-15 km/h — again, don’t worry to much about that: Trek has very little in the way of scale or time consistency, but even if it did you should pretend it’s a dramatic slow-mo.

There’s no narrative requirement for subspace layers to be limited to three spacial dimensions, so we can also posit that subspace is (e.g.) 4 spacial dimensions. In 4D, a creature like us built in 3D space would fall to pieces in much the same way as you might expect a creature built out of a single layer of atoms sandwiched between two plates would almost instantly disintegrate if you took the plates away. One idea which would allow “being pushed into subspace” to be much more dangerous than “being in a starship when the warp drive is switched on” would be another fairly ambiguous piece of Star Trek tech: the inertial dampeners. The inertial dampeners are supposed to be space-filling forcefields which push every atom in your body at the same rate the ship accelerates so that you don’t feel any G-forces — vitally important when you go from zero to 0.25c (74,770 km/s, full impulse) in one second. Those very same force fields could (with enough technobabble) keep the crew from disintegrating even if they were in a 4D (or 5D or 6D or…) subspace domain.