Starkiller base versus the ideal gas law

Partial eclipseMy friend Stuart explains why the Death Stars and the Starkiller Base in the Star Wars universe are inefficient ways of taking over the galaxy. I generally agree: even a super-inefficient robot army will win if you simply bury enemy planets in robots.

But thinking about the physics of absurd superweapons is fun and warms the heart.

The ideal gas law: how do you compress stars?

My biggest problem with the Starkiller Base is the ideal gas law. The weapon works by sucking up a star and then beaming its energy or plasma at remote targets. A sun-like star has a volume around 1.4*1018 cubic kilometres, while an Earthlike planet has a volume around 1012 cubic kilometres. So if you suck up a star it will get compressed by a factor of 1.4 million times. The ideal gas law states that pressure times volume equals temperature times the number of particles and some constant: PV=nRT

1.4 million times less volume needs to be balanced somehow: either the pressure P has to go down, the temperature T has to go up, or the number of particles n need to go down.

Pressure reduction seems to be a non-starter, unless the Starkiller base actually contains some kind of alternate dimension where there is no pressure (or an enormous volume).

The second case implies a temperature increase by a factor of a 1.4 million. Remember how hot a bike pump gets when compressing air: this is the same effect. This would heat the photosphere gas to 8.4 billion degrees and the core to 2.2*1013 K, 22 TeraKelvin; the average would be somewhere between, on the hotter side. We are talking about temperatures microseconds after the Big Bang, hotter than a supernova: protons and neutrons melt at 0.5–1.2 TK into a quark-gluon plasma. Excellent doomsday weapon material but now containment seems problematic. Even if we have antigravity forcefields to hold the star, the black-body radiation is beyond the supernova range. Keeping it inside a planet would be tough: the amount of neutrino radiation would likely blow up the surface like a supernova bounce does.

Maybe the extra energy is bled off somehow? That might be a way to merely get super-hot plasma rather than something evaporating the system. Maybe those pesky neutrinos can be shunted into hyperspace, taking most of the heat with them (neutrino cooling can be surprisingly fast for very hot objects; at these absurd temperatures it is likely subsecond down to mere supernova temperatures).

Another bizarre and fun approach is to reduce the number of gas particles: simply fuse them all into a single nucleus. A neutron star is in a sense a single atomic nucleus. As a bonus, the star would now be a tiny multikilometre sphere held together by its own gravity. If n is reduced by a factor of 1057 it could outweigh the compression temperature boost. There would be heating from all the fusion; my guesstimate is that it is about a percent of the mass energy, or 2.7*1045 J. This would heat the initial gas to around 96 billion degrees, still manageable by the dramatic particle number reduction. This approach still would involve handling massive neutrino emissions, since the neutronium would still be pretty hot.

In this case the star would remain gravitationally bound into a small blob: convenient as a bullet. Maybe the red “beam” is actually just an accelerated neutron star, leaking mass along its trajectory. The actual colour would of course be more like blinding white with a peak in the gamma ray spectrum. Given the intense magnetic fields locked into neutron stars, moving them electromagnetically looks pretty feasible… assuming you have something on the other end of the electromagnetic field that is heavier or more robust. If a planet shoots a star-mass bullet at a high velocity, then we should expect the recoil to send the planet moving at about a million times faster in the opposite direction.

Other issues

We have also ignored gravity: putting a sun-mass inside an Earth-radius means we get 333,000 times higher gravity. We can try to hand-wave this by arguing that the antigravity used to control the star eating also compensates for the extra gravity. But even a minor glitch in the field would produce an instant, dramatic squishing. Messing up the system* containing the star would not produce conveniently dramatic earthquakes and rifts, but rather near-instant compression into degenerate matter.

(* System – singular. Wow. After two disasters due to single-point catastrophic failures one would imagine designers learning their lesson. Three times is enemy action: if I were the Supreme Leader I would seriously check if the lead designer happens to be named Skywalker.)

There is also the issue of the amount of energy needed to run the base. Sucking up a star from a distance requires supplying the material with the gravitational binding energy of the star, 6.87*1041 J for the sun. Doing this over an hour or so is a pretty impressive power, about 1.9*1038 W. This is about 486 billion times the solar luminosity. In fact, just beaming that power at a target using any part of the electromagnetic spectrum would fry just about anything.

Of course, a device that can suck up a star ought to be able to suck up planets a million times faster. So there is no real need to go for stars: just suck up the Republic. Since the base can suck up space fleets too, local defences are not much of a problem. Yes, you may have to go there with your base, but if the Death Star can move, the Starkiller can too. If nothing else, it could use its beam to propel itself.

If the First Order want me to consult on their next (undoubtedly even more ambitious) project I am open for offers. However, one iron-clad condition given recent history is that I get to work from home, as far away as possible from the superweapon. Ideally in a galaxy far, far away.

Dampening theoretical noise by arguing backwards

WhiteboardScience has the adorable headline Tiny black holes could trigger collapse of universe—except that they don’t, dealing with the paper Gravity and the stability of the Higgs vacuum by Burda, Gregory & Moss. The paper argues that quantum black holes would act as seeds for vacuum decay, making metastable Higgs vacua unstable. The point of the paper is that some new and interesting mechanism prevents this from happening. The more obvious explanation that we are already in the stable true vacuum seems to be problematic since apparently we should expect a far stronger Higgs field there. Plenty of theoretical issues are of course going on about the correctness and consistency of the assumptions in the paper.

Don’t mention the war

What I found interesting is the treatment of existential risk in the Science story and how the involved physicists respond to it:

Moss acknowledges that the paper could be taken the wrong way: “I’m sort of afraid that I’m going to have [prominent theorist] John Ellis calling me up and accusing me of scaremongering.

Ellis is indeed grumbling a bit:

As for the presentation of the argument in the new paper, Ellis says he has some misgivings that it will whip up unfounded fears about the safety of the LHC once again. For example, the preprint of the paper doesn’t mention that cosmic-ray data essentially prove that the LHC cannot trigger the collapse of the vacuum—”because we [physicists] all knew that,” Moss says. The final version mentions it on the fourth of five pages. Still, Ellis, who served on a panel to examine the LHC’s safety, says he doesn’t think it’s possible to stop theorists from presenting such argument in tendentious ways. “I’m not going to lose sleep over it,” Ellis says. “If someone asks me, I’m going to say it’s so much theoretical noise.” Which may not be the most reassuring answer, either.

There is a problem here in that physicists are so fed up with popular worries about accelerator-caused disasters – worries that are often second-hand scaremongering that takes time and effort to counter (with marginal effects) – that they downplay or want to avoid talking about things that could feed the worries. Yet avoiding topics is rarely the best idea for finding the truth or looking trustworthy. And given the huge importance of existential risk even when it is unlikely, it is probably better to try to tackle it head-on than skirt around it.

Theoretical noise

“Theoretical noise” is an interesting concept. Theoretical physics is full of papers considering all sorts of bizarre possibilities, some of which imply existential risks from accelerators. In our paper Probing the Improbable we argue that attempts to bound accelerator risks have problems due to the non-zero probability of errors overshadowing the probability they are trying to bound: an argument that there is zero risk is actually just achieving the claim that there is about 99% chance of zero risk, and 1% chance of some risk. But these risk arguments were assumed to be based on fairly solid physics. Their errors would be slips in logic, modelling or calculation rather than being based on an entirely wrong theory. Theoretical papers are often making up new theories, and their empirical support can be very weak.

An argument that there is some existential risk with probability P actually means that, if the probability of the argument is right is Q, there is risk with probability PQ plus whatever risk there is if the argument is wrong (which we can usually assume to be close to what we would have thought if there was no argument in the first place) times 1-Q. Since the vast majority of theoretical physics papers never go anywhere, we can safely assume Q to be rather small, perhaps around 1%. So a paper arguing for P=100% isn’t evidence the sky is falling, merely that we ought to look more closely to a potentially nasty possibility that is likely to turn into a dud. Most alarms are false alarms.

However, it is easier to generate theoretical noise than resolve it. I have spent some time working on a new accelerator risk scenario, “dark fire”, trying to bound the likelihood that it is real and threatening. Doing that well turned out to be surprisingly hard: the scenario was far more slippery than expected, so ruling it out completely turned out to be very hard (don’t worry, I think we amassed enough arguments to show the risk to be pretty small). This is of course the main reason for the annoyance of physicists: it is easy for anyone to claim there is risk, but then it is up to the physics community to do the laborious work of showing that the risk is small.

The vacuum decay issue has likely been dealt with by the Tegmark and Bostrom paper: were the decay probability high we should expect to be early observers, but we are fairly late ones. Hence the risk per year in our light-cone is small (less than one in a billion). Whatever is going on with the Higgs vacuum, we can likely trust it… if we trust that paper. Again we have to deal with the problem of an argument based on applying anthropic probability (a contentious subject where intelligent experts disagree on fundamentals) to models of planet formation (based on elaborate astrophysical models and observations): it is reassuring, but it does not reassure as strongly as we might like. It would be good to have a few backup papers giving different arguments bounding the risk.

Backward theoretical noise dampening?

The lovely property of the Tegmark and Bostrom paper is that it covers a lot of different risks with the same method. In a way it handles a sizeable subset of the theoretical noise at the same time. We need more arguments like this. The cosmic ray argument is another good example: it is agnostic on what kind of planet-destroying risk is perhaps unleashed from energetic particle interactions, but given the past number of interactions we can be fairly secure (assuming we patch its holes).

One shared property of these broad arguments is that they tend to start with the risky outcome and argue backwards: if something were to destroy the world, what properties does it have to have? Are those properties possible or likely given our observations? Forward arguments (if X happens, then Y will happen, leading to disaster Z) tend to be narrow, and depend on our model of the detailed physics involved.

While the probability that a forward argument is correct might be higher than the more general backward arguments, it only reduces our concern for one risk rather than an entire group. An argument about why quantum black holes cannot be formed in an accelerator is limited to that possibility, and will not tell us anything about risks from Q-balls. So a backwards argument covering 10 possible risks but just being half as likely to be true as a forward argument covering one risk is going to be more effective in reducing our posterior risk estimate and dampening theoretical noise.

In a world where we had endless intellectual resources we would of course find the best possible arguments to estimate risks (and then for completeness and robustness the second best argument, the third, … and so on). We would likely use very sharp forward arguments. But in a world where expert time is at a premium and theoretical noise high we can do better by looking at weaker backwards arguments covering many risks at once. Their individual epistemic weakness can be handled by making independent but overlapping arguments, still saving effort if they cover many risk cases.

Backwards arguments also have another nice property: they help dealing with the “ultraviolet cut-off problem“. There is an infinite number of possible risks, most of which are exceedingly bizarre and a priori unlikely. But since there are so many of them, it seems we ought to spend an inordinate effort on the crazy ones, unless we find a principled way of drawing the line. Starting from a form of disaster and working backwards on probability bounds neatly circumvents this: production of planet-eating dragons is among the things covered by the cosmic ray argument.

Risk engineers will of course recognize this approach: it is basically a form of fault tree analysis, where we reason about bounds on the probability of a fault. The forward approach is more akin to failure mode and effects analysis, where we try to see what can go wrong and how likely it is. While fault trees cannot cover every possible initiating problem (all those bizarre risks) they are good for understanding the overall reliability of the system, or at least the part being modelled.

Deductive backwards arguments may be the best theoretical noise reduction method.

Awesome blogs

I recently discovered Alex Wellerstein’s excellent blog Restricted data: the nuclear secrecy blog. I found it while looking for nuclear stockpiles data, but was drawn in by a post on the evolution of nuclear yield to mass. Then I started reading the rest of it. And finally, when reading this post about the logo of the IAEA I realized I needed to mention to the world how good it is. Be sure to test the critical assembly simulator to learn just why critical mass is not the right concept.

Another awesome blog is Almost looks like work by Jasmcole. I originally found it through a wonderfully over the top approach to positioning a wifi router (solving Maxwell’s equations turns out to be easier than the Helmholz equation!). But there are many other fascinating blog essays on physics, mathematics, data visualisation, and how to figure out propeller speeds from camera distortion.


A sustainable orbital death ray

Visualizing lightI have for many years been a fan of the webcomic Schlock Mercenary. Hardish, humorous military sf with some nice, long-term plotting.

In the current plotline (some spoilers ahead) there is an enormous Chekov’s gun: Earth is surrounded by an equatorial ring of microsatellites that can reflect sunlight. It was intended for climate control, but as the main character immediately points out, it also makes an awesome weapon. You can guess what happens. That leds to an interesting question: just how effective would such a weapon actually be?

From any point on Earth’s surface only part of the ring is visible above the horizon. In fact, at sufficiently high latitudes it is entirely invisible – there you would be safe no matter what. Also, Earth likely casts a shadow across the ring that lowers the efficiency on the nightside.

I guessed, based on the appearance in some strips, that the radius is about two Earth radii (12,000 km), and the thickness about 2000 km. I did a Monte Carlo integration where I generated random ring microsatellites, checking whether they were visible above the horizon for different Earth locations (by looking at the dot product of the local normal and the satellite-location vector; for anything above the horizon this product must be possible) and were in sunlight (by checking that the distance to the Earth-Sun axis was more than 6000 km). The result is the following diagram of how much of the ring can be seen from any given location:

Visibility fraction of an equatorial ring 12,000-14,000 km out from Earth for different latitudes and longitudes.
Visibility fraction of an equatorial ring 12,000-14,000 km out from Earth for different latitudes and longitudes.

At most, 35% of the ring is visible. Even on the nightside where the shadow cuts through the ring about 25% is visible. In practice, there would be a notch cut along the equator where the ring cannot fire through itself; just how wide it would be depends on the microsatellite size and properties.

Overlaying the data on a world map gives the following footprint:

Visibility fraction of 12,000-14,000 ring from different locations on Earth.
Visibility fraction of 12,000-14,000 ring from different locations on Earth.

The ring is strongly visible up to 40 degrees of latitude, where it starts to disappear below the southern or northern horizon. Antarctica, northern Canada, Scandinavia and Siberia are totally safe.

This corresponds to the summer solstice, where the ring is maximally tilted relative to the Earth-Sun axis. This is when it has maximal power: at the equinoxes it is largely parallel to the sunlight and cannot reflect much at all.

The total amount of energy the ring receives is E_0 = \pi (r_o^2-r_i^2)|\sin(\theta)|S where r_o is the outer radius, r_i the inner radius, $\theta$ the tilt (between 23 degrees for the summer/winter solstice and 0 for equinoxes) and S is the solar constant, 1.361 kW/square meter. This ignores the Earth shadow. So putting in \theta=20^{\circ} for a New Years Eve firing, I get E_0 \approx 7.6\cdot 10^{16} Watt.

If we then multiply by 0.3 for visibility, we get 23 petawatts – is nothing to sneeze at! Of course, there will be losses, both in reflection (likely a few percent at most) and more importantly through light scattering (about 25%, assuming it behaves like normal sunlight). Now, a 17 PW beam is still pretty decent. And if you are on the nightside the shadowed ring surface can still give about 8 PW. That is about six times the energy flow in the Gulf Stream.

Light pillar

How destructive would such a beam be? A megaton of TNT is 4.18 PJ. So in about a second the beam could produce a comparable amount of heat.  It would be far redder than a nuclear fireball (since it is essentially 6000K blackbody radiation) and the IR energy would presumably bounce around and be re-radiated, spreading far in the transparent IR bands. I suspect the fireball would quickly affect the absorption in a complicated manner and there would be defocusing effects due to thermal blooming: keeping it on target might be very hard, since energy would both scatter and reflect. Unlike a nuclear weapon there would not be much of a shockwave (I suspect there would still be one, but less of the energy would go into it).

The awesome thing about the ring is that it can just keep on firing. It is a sustainable weapon powered by renewable energy. The only drawback is that it would not have an ommminous hummmm….

Addendum 14 December: I just realized an important limitation. Sunlight comes from an extended source, so if you reflect it using plane mirrors you will get a divergent beam – which means that the spot it hits on the ground will be broad. The sun has diameter 1,391,684 km and is 149,597,871 km away, so the light spot 8000 km below the reflector will be 74 km across. This is independent of the reflector size (down to the diffraction limit and up to a mirror that is as large as the sun in the sky).

Intensity with three overlapping beams.
Intensity with three overlapping beams.

At first this sounds like it kills the ring beam. But one can achieve a better focus by clever alignment. Consider three circular footprints arranged like a standard Venn diagram. The center area gets three times the solar input as the large circles. By using more mirrors one can make a peak intensity that is much higher than the side intensity. The vicinity will still be lit up very brightly, but you can focus your devastation better than with individual mirrors – and you can afford to waste sunlight anyway. Still, it looks like this is more of a wide footprint weapon of devastation rather than a surgical knife.

Intensity with 200 beams overlapping slightly.
Intensity with 200 beams overlapping slightly.


Somebody think of the electrons!

Atlas 6Brian Tomasik has a fascinating essay: Is there suffering in fundamental physics?

He admits from the start that “Any sufficiently advanced consequentialism is indistinguishable from its own parody.” And it would be easy to dismiss this as taking compassion way too far: not just caring about plants or rocks, but the possible suffering of electrons and positrons.

I think he has enough arguments to show that the idea is not entirely crazy: we do not understand the ontology of phenomenal experience well enough that we can easily rule out small systems having states, panpsychism is a view held by some rational people, it seems a priori unlikely that there is some mid-sized systems that have all the value in the universe rather than the largest or the smallest scale, we have strong biases towards our kind of system, and information physics might actually link consciousness with physics.

None of these are great arguments, but there are many of them. And the total number of atoms or particles is huge: even assigning a tiny fraction of human moral consideration to them or a tiny probability of them mattering morally will create a large expected moral value. The smallness of moral consideration or the probability needs to be far outside our normal reasoning comfort zone: if you assign a probability lower than 10^{-10^{56}} to a possibility you need amazingly strong reasons given normal human epistemic uncertainty.

I suspect most readers will regard this outside their “ultraviolett cutoff” for strange theories: just as physicists successfully invented/discovered a quantum cutoff to solve the ultraviolet catastrophe, most people have a limit where things are too silly or strange to count. Exactly how to draw it rationally (rather than just base it on conformism or surface characteristics) is a hard problem when choosing between the near infinity of odd but barely possible theories.

What is the mass of the question mark?One useful heuristic is to check whether the opposite theory is equally likely or important: in that case they balance each other (yes, the world could be destroyed by me dropping a pen – but it could also be destroyed by not dropping it). In this case giving greater weight to suffering than neutral states breaks the symmetry: we ought to investigate this possibility since the theory that there is no moral considerability in elementary physics implies no particular value is gained from discovering this fact, while the suffering theory implies it may matter a lot if we found out (and could do something about it). The heuristic is limited but at least a start.

Another way of getting a cutoff for theories of suffering is of course to argue that there must be a lower limit of the system that can have suffering (this is after all how physics very successfully solved the classical UV catastrophe). This gets tricky when we try to apply it to insects, small brains, or other information processing systems. But in physics there might be a better argument: if suffering happens on the elementary particle level, it is going to be quantum suffering. There would be literal superpositions of suffering/non-suffering of the same system. Normal suffering is classical: either it exists or not to some experiencing system, and hence there either is or isn’t a moral obligation to do something. It is not obvious how to evaluate quantum suffering. Maybe we ought to perform a quantum-action that moves the wavefunction to a pure non-suffering state (a bit like quantum game theory: just as game theory might have ties to morality, quantum game theory might link to quantum morality), but this is constrained by the tough limits in quantum mechanics on what can be sensed and done. Quantum suffering might simply be something different from suffering, just as quantum states do not have classical counterparts. Hence our classical moral obligations do not relate to it.

But who knows how molecules feel?