No, a black hole can’t be used as a rocket

With a headline like that, I need to introduce some concepts.

First, a black hole: if you have enough stuff in a small enough volume, the outside is causally disconnected from the inside. This is normally phrased as “nothing, not even light, can escape”, but that’s a little misleading because…

Second: Black holes emit Hawking radiation. The exact mechanism is not important, what you need to know is (1) that it behaves exactly like the black hole is a hot object (the scientific term is “black body radiation”, the hotter it gets the brighter and bluer the light), (2) that it gets hotter as it shrinks, and (3) that it shrinks because it’s emitting light.

(The reason we can’t see black holes despite their Hawking radiation, is that the converse of #2 is that bigger ones are colder — at the size of all the black holes we know about, they are actually colder than the cosmic microwave background of deep space).

Light has momentum. Not much momentum compared to the energy — burn 9 litres of oil, gather all the light emitted together, it will have the same momentum as an apple tossed lightly — but it does have some. This means you can use it to propel a space ship! The idea is easy enough: shine or reflect light one way, you go the other. However, the idea of rockets is equally straightforward, and yet building them isn’t.

Deliberately crude drawing of photon thruster (top) and de Laval rocket nozzle (bottom) to illustrate that science is easy part of rockets, it’s the engineering which is hard.

Because Hawking radiation goes up as black holes get smaller, even without knowing the maths you can clearly see that at some level the Hawking radiation is sufficient to move whatever you want it to.

The maths of Hawking radiation

Indeed, the “sweet spot” is black hole weighing 606,000 metric tons, which initially has a power output of 160 petawatts, and has a 3.5-year lifespan before all its mass turns into Hawking radiation. With such a power output, the black hole could accelerate to 10% the speed of light in 20 days, assuming 100% conversion of energy into kinetic energy and no payload. (arXiv:0908.1803 [gr-qc])

Now for the problems.

First, 160 petawatts is roughly the same as the power of all the sunlight falling on the planet Earth. Because that’s not exact and the Earth is (nearly) a sphere rather than a disk, this means you’d have to put the black hole in the middle of a 7136 3568 km radius sphere for your spaceship to only be getting as warm from it as you get from direct sunlight at ground level on a sunny day. Assuming you only have a half-sphere, this means your mirror has to weigh 6.8 milligrams per square meter if you don’t want the ship to out-mass the black hole. If this mirror was made from aluminium, it would have to be 25 nanometers thick.

You might be thinking at this point, “why do you want to be that far away, it’s a shiny mirror, it isn’t going to get that hot?”. Unfortunately, the effective temperature of the radiation means that no known material will act like a mirror, because…

Second, such a black hole would have a Schwarzschild radius of 0.9 attometers, which means the Hawking radiation is identical to a black body with a temperature of 223 trillion Kelvin, which in turn means most of the photons of light in the Hawking radiation have enough energy to not just cause spontaneous positron-electron pair production, but also proton-antiproton pair production[*]. This means your spaceship has to be made out of something other than normal matter, which is a fairly big problem all by itself — at this level even if you stabilised tau particles and used them instead of electrons, not only will it still not solve your problems (the Hawking radiation will make tau-anti-tau pairs too) — but even then, because of tau particles’ greater mass giving them more compact wave functions compared to electrons, you would increase the density of your mirror so much it would exceed the mass of the black hole. Particles massive enough to not be evaporated by the matter-antimatter creation due to the light hitting them would always make the mirror significantly more massive than the black hole itself unless the black hole was significantly cooler, but that in turn requires it to be more massive.

To get down to photons that “only” photo-ionise normal matter (about 6eV), you need a black body to be “only” about 70,000 K. That in turn means the black hole is now about 1766 trillion tons, and has a power output of 114 microwatts.

For both these reasons, black hole engines make mere antimatter rockets look safe and (given that even with Clarktech materials the minimum possible mass of everything else is so high), efficient.

* As an aside, I think the photons being at this energy level implies that it’s no longer appropriate to assume the black hole is only emitting photons, but most discussion of Hawking radiation don’t go into that depth and I don’t have the physics degree I’d need to start combining the relevant equations.

Arguments, hill climbing, the wisdom of the crowds

You ever had an argument which seems to go nowhere, where both sides act like their position is self-evident and obvious, that the other person “is clearly being deliberately obtuse”? I hope that’s common, and not just one of my personal oddities. Ahem.

In the current world of machine learning (yes these two things are connected), one of the well-known methods is a thing called “hill climbing”. You have some relationship between two things, and you want to learn the relationship between them — the function — so that you can maximise the thing you want to have more of (fun), or minimise the thing you want less of (pain). This function might have any shape and might represent any relationship. If you were to plot the whole thing on graph paper, it would be easy to see where the best place was:

A graph of an upside-down parabola with a peak at (x, y) = (1, 1)

But in the real world, data collection is expensive and you can’t just plot a graph and look at the whole thing and call it a day. When you can’t look at all possible solutions, then instead of merely guessing where the best might be, you might want to follow a standard method, and this is where “hill climbing” comes in. With the hill climbing method, you start with some measurement, then you measure what’s around that point, and take a “step” in the “best” (for the thing you care about) direction. Say you start at x = 0 on the graph above, you look at x = 0.1 and x = -0.1, you see that x = 0.1 is best and use that as your next measurement. If you imagine the graph is a hill, you are climbing to the top of that hill (sometimes the description is reversed and you’re trying to get to the bottom of the valley, but that doesn’t change anything important).

There’s a problem with this, though. Hills don’t usually look so simple, so let’s make the graph more complicated:

A more complicated function with two peaks; the peak bellow 0 is bigger than the peak above 0

In this case, starting hill climbing at x = 0 will always give you the smaller of the two peaks. And of course in the real world things are even more complicated than this, with countless peaks and valleys, and if your goal is Everest, you will definitely fail to reach that peak using this algorithm if you start anywhere in the Americas, Australia, Antarctica, or any island.

There are a lot of different ways to upgrade hill climbing to avoid this problem. One in particular is called either “random-restart hill climbing” or “shotgun hill climbing”. It’s a simple, and surprisingly effective, method: do normal hill climbing many times with random starting values, pick the best.

In a flash of insight this morning while pouring milk into my cereal, I realised that this could be an explanation for both how those annoying arguments happen (because we’re on different metaphorical hills in our models of reality or language) and may also contribute to why the wisdom of the crowds can be so effective (because everyone’s on a random hill and the crowd can pick the best).

This doesn’t diminish the usual problems with wisdom of the crowd — when there is an actual right answer, experts do better and everyone else just dilutes rather than reinforces; if the crowd is allowed to deliberate rather than all voting independently, then the crowd follows a charismatic leader and you get groupthink — and it comes with a testable prediction: things which can help you randomise-and-restart can help you make better models of reality, so long as you can ignore the old mental model right up until it is time to compare the new and old models:

1. Every language you learn should make it easier to learn more; and 5 hours of nothing-but-$new_language should be better for learning the structure of the language than 10 minutes of $new_language every day for a month, because 10 minute blocks are short enough to keep thinking in $old_language about $new_language.
2. Any psychotropic substance which lets you restart from scratch but without deleting old memories (temporarily suppressing them is fine) would be a nootropic.
3. If it’s possible to delete a cognitive anchor, doing so would lead to modelling reality better.

My German is nowhere near as good as I want it to be, so I’m going to try #1 for a bit, the intention is 5 hours once per month, which is going to be in addition to all my various 10 minute per day vocabulary memorisation apps (memorising doesn’t require understanding, and I need both).

Blasphemy, LARPing, mandatory vaccination

Back in the olden days, when Lord of the Rings was new, my brother introduced me to LARP — live action roleplay — which in his case meant Fools And Heroes, a swords-and-sorcery themed game with foam-rubber weapons and vampires dusted with flour[0]. In Fools And Heroes, there is a pantheon of gods. My brother claimed that, in-universe, nobody is an atheist: if someone denies the existence of these gods, the gods literally mark them on the face for their naughtiness.

I didn’t like this.

It wasn’t that this isn’t a very good reason for in-universe characters to believe in these gods (clearly it is), but rather that people aren’t that rational: people frequently deny what should be undeniable, and for any issue (at all) you can almost certainly find someone convinced that the opposite is true. My brother didn’t buy my argument. Still, as it’s a game, I didn’t push it — all games have something unrealistic, it doesn’t matter.

In real life, it does matter.

Vaccination. I’ll take any vaccine offered, to me all modern medicine is basically the closest we can get to superpowers — compare a superhero film where someone is immune to Zombie Plague versus real life immunity to smallpox — yet I knew even before the word COVID was coined there would be people who would reject masks[1] and vaccination and isolation, simply because such things happened in Spanish flu (masks), Typhoid Mary (isolation), smallpox in Sweden 1873-74 and MMR in modern times (vaccination).

Of course, if I can spot that in advance, I assume almost every government is capable of knowing this too. But if the executive is run by people who assume that nobody can possibly believe an untrue thing because of immediate severe consequences, as with the divine punishment in Fools And Heroes, then we may have a problem: failing to plan, as the saying goes, is planning to fail.

(I still don’t get why face masks couldn’t be successfully marketed as “tactical cameo face armour” to reach the loudest anti-mask voices that made it here from America, as this is one of the few situations where a cargo-culted military costume can be useful outside fancy dress parties. This probably means I’ve not understood the interests of non-military types who dress up in military uniforms. #IHaveNoticedMyConfusion).

[0] because it’s self-raising

[1] sometimes it isn’t just rejecting masks for oneself, it can be rejecting other people wearing them, which confuses me even more: https://kitsunesoftware.wordpress.com/2021/06/14/why-do-some-people-hate-masks/

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?

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.

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.

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?

Point an infrared thermometer at the sky

The temperature of a night sky in Berlin, 2021 February 12, 23:40 local time

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: https://arxiv.org/abs/0902.0834

(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).

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.