K^2

Sure. There is no local experiment that can tell you if you're in a gravitational field, but tidal measurements are inherently non-local. Although, I'm not sure you need to go to these lengths. You can measure relative position in space to within a few kilometers using pulsars pretty much anywhere humanity likely to ever get, and if you know your orbital radius and period, you can estimate the mass of the body you're orbiting and get all the same info with way better precision than you're likely to get from tidal force measurements.

I'll have to do a deeper dive, but so far, I'm not seeing anything that's going to solve the actual problem. We already know equations that describe everything derived from same principles as all the rest of physics - Gauge Theory. We have a combined "theory of everything" master equation that should describe everything we can observe. Problem is that we can't solve it. Worse, if somebody just gave us a result that is a particular solution to particular initial conditions, we wouldn't be able to even verify it. It's infinite sums over infinities divided by more infinities that must be canceling somewhere, because universe exists, but we don't know how - in general. We have some narrow, approximate special cases solved. For example, if we consider that gravity isn't a factor, we get Standard Model of particle physics, where there are still infinities divided by infinities, but we have math tricks to cancel them out and get nice numerical results that match experiment. (Mostly - mass of vacuum is a bit of a problem.) Likewise, if we throw away interactions due to intrinsic degrees of freedom (electromagnetism, nuclear forces, etc.) we get General Relativity. We can even do fancy things like particle physics inside a neutron star, where both quantum and space-time curvature are factors, but on different scales, so we can treat equations as if they were separable, and this does give us predictions about neutron stars that we wouldn't get from either theory alone. So there's a very good chance that Gauge Theory is fundamentally correct on all levels. It just happens to be mathematically useless when we try to load it with absolutely every known degree of freedom at the same time. What I've gathered from published Wolfram work is that it manages to reproduce features of Standard Model and General Relativity. Which screams at me that it is probably equivalent to Gauge Theory via some mathematical transformation. And that itself isn't terribly surprising, because both are playing off concepts in topology. Moreover, anything that has a chance of working as theory everything kind of has to have this equivalence, at least in limiting cases, because it has to have theory that we already know works. What isn't clear, and in fact, I don't see any attempt to verify this one way or another, is whether this new approach lets you work around any of the divergences we get in Gauge Theory when we are dealing with curved space-time. And if not, which seems more likely barring evidence to contrary, then it's still going to have the same bumps with Quantum Gravity that exist in Gauge Theory. It is possible that with the new formalism, we will see new mathematical methods develop that let us work around these problems. That's always the hope. But this isn't the first time somebody tried to introduce a new formalism, and so far, nothing got us closer to a working model. So I'm very curious to see where theoretical physicists can take this, but I wouldn't pop the champagne just yet. tl;dr - Very exciting mathematics, TBD if it helps at all in theoretical physics - unless I missed something huge in all of this.

Interestingly enough, speed of light isn't the problem. If universe wasn't expanding at an accelerated rate - even if expansion was constant and FTL, you'd still be able to reach every part of the universe eventually. It seems counter-intuitive, but because space itself is expanding, the fact that something is retreating from you at FTL speeds doesn't prevent you from catching up eventually. That's because as you travel forward, you'll be making progress at an inverse rate to the elapsed time, meaning that total time to reach destination is not infinite, but actually exponential. Consequently, if universe continued to expand at constant rate, it would take much, much longer than current age of the universe to reach the edge of visible universe, but you'd be able to do that in finite time and to even go past it. However, all indication is that universe is expanding at an accelerated rate, and that means that there are parts of the universe we can see right now, but will never be able to reach without figuring out FTL means of travel. A light signal we would send in that direction would never reach its destination.

I might be misunderstanding something, but I'm not sure that works. Forgetting Mun/Minmus for a moment, if you're already in circular orbit around Kerbin, or any other body for that matter, direct burn to escape the system is always cheaper than performing a dive and doing your escape burn at lowest possible altitude. And if you are orbiting Mun/Minmus, the most fuel-efficient way to leave the SoI is to drift out with minimal velocity left over, leaving you in circular orbit around Kerbin. Granted, if you are doing direct ascent, you win a little bit back by burning directly to a return trajectory, making the dive a little cheaper than it would have been from circular orbit around Kerbin, but that isn't nearly enough, as the entire dive only costs you about 20m/s and burning to escape just over Kerbin's atmosphere vs directly from Mun puts you more than 200m/s in the red. You can probably come up with a multiple gravity-assists trajectory for leaving Kerbin system from Mun/Minmus that's going to be cheaper, but it's going to be gravity assists that help you with that, not Oberth effect.

Well, all of the universe started as a single point, or as close to one as we could tell. If so, then if there was a statistical imbalance between matter and antimatter very, very early in the inflation, you could, in principle, end up with matter and antimatter being separated by immense distances once things settle down. I don't really know enough about the inflation to say whether it'd be possible for all the antimatter to end up beyond the boundaries of visible universe. I think, all of the cosmological models assume visible universe = universe, but that's probably only because due to how universe was expanding, nothing that's currently outside of the visible universe could ever have been part of visible universe except, possibly, really, really, really early on, and it means it couldn't have impacted evolution of visible universe, so we can pretend nothing outside visible universe exists without getting any disagreements with experiment. If nothing in our understanding of cosmology contradicts the notion that universe >> visible universe, as in greater by a lot, then I can't think of any reason why it couldn't be that all the antimatter is simply beyond the boundaries of the visible universe. But this stretches my understanding of cosmology past the breaking point, and I don't even know any cosmologists to ask. We had one theoretical astrophysicist in our department, and she specialized in neutron stars.

Yes. That's basically same as above. Also correct, and you can actually derive this with some math from the first one. That's very poorly phrased. Relativity is relevant, though. Not Special or General relativity, but Classical Relativity, also known as Galilean Relativity. The gist is that kinetic energy of a body depends on coordinate system of choice. Trying to explain Oberth through this is going to be awkward, and will essentially be the same as previous point. Another poorly phrased one. We've established that rocket gets more kinetic energy due to Oberth Effect. A natural question is "Where does the energy come from?" And that has to do with propellant. People usually think of rocket engine as converting chemical energy of the fuel into kinetic energy of the rocket. But the cool thing about a rocket is that it also converts part of the kinetic energy of the fuel into additional kinetic energy for the ship! If you're going fast enough, most of the energy of the rocket is gained from kinetic, not chemical energy of the fuel. Of course, that fuel had to be brought up to speed in the first place. Usually, you burn a lot of fuel early on to get the rocket and fuel moving. But if you use Oberth effect, the planet gives you extra energy to work with. In case of the solar sail, the extra energy comes from the fact that reflected light is going to be red-shifted. So there are no exhaust gasses, but there's still an exhaust of sorts. That one isn't right. Once you finished the burn and are climbing out of the gravity well, your energy isn't changing. Sure, kinetic energy of the ship is becoming gravitational potential energy of the ship, but the total is constant. Oberth effect lets you actually gain more energy. You end up in an orbit with higher total energy if you burn prograde at periapsis than if you burned at the apoapsis. And the burn can be very short, not long enough for gravity to impact you while you are using your engines. So this explanation is wrong. But planet's gravity does play a role as outlined in the previous one. It's either adding or taking away the kinetic energy from your fuel, which you are using to gain more energy for your rocket. As a side note, there are two parameters that determine shape of your orbit around a single body. It's energy and angular momentum. People who play around with rocketry generally know that you gain most energy at the low burn. But you gain most angular momentum as far away from the planet as possible. And to go from a low circular orbit to a higher one you need to increase both energy and angular momentum. Which is a somewhat hand-wavy explanation of why a Hohmann transfer is so efficient. You do first part of your burn at the lowest point to maximize energy gain and second part at the highest point to maximize angular momentum gain. This is just to point out that you don't always care just about kinetic energy gained there are other parameters of your orbit that you might need to adjust in the most fuel-efficient manner, and for these, burning low isn't always a good thing.

Both matter and antimatter have positive energy, so they move along the same trajectories in space-time - just in opposite directions. So the fact that the universe is expanding at an accelerating rate pretty much excludes that possibility.

There is a common statement that protons and neutrons are made up of 3 quarks. That's not actually the case. Both of these are actually a soup of quarks and fermions. But if you take a snapshot of the proton or neutron at any given time and start matching up particles with anti-particles they could annihilate, you'll be left over with 3 quarks. These are called valence quarks and they're always there. You can't say that it's these three specific quarks over there, because that's purely arbitrary, but in the count, there will be 3 left over. Well, what about all the other particles? A lot of them really are just these three valence quarks bouncing back and forward in time! And in fact, there are only two possibilities for a lone particle. Either any given particle is part of that valence quark trajectory, or it's part of a loop. And loops are even weirder, because it's one particle on a closed trajectory that covers some stretch of time resulting in interactions as if it was a whole bunch of particle and anti-particles, returning to the exact point in space and time where it started. What makes all of this a lot worse is that no particle takes just one trajectory. Each particle moves along every possible trajectory, meaning we can't say for sure if a particle is part of a loop or a valence trajectory. It can be both. One of Feynman's important contributions was the mathematical description of this fact as part of path integral formalism. At some point, you're really forced to accept that the very idea of a "particle" is just us trying to assign familiar properties to unfamiliar math, not unlike people of antiquity assigning human personalities to forces of nature. It's still convenient for making some explanations easier to follow, and Feynman's diagrams are a fantastic tool for sorting through math, but you can only take the particle analogies so far before it breaks down, and it's something you have to be careful with.

The only problem with this approach is that you continue increasing ship's momentum. First of all, it means you have to keep increasing your warp/translation speed, which might require energy or could even saturate. Second, once you drop out, you will have all that momentum, so now you're not at rest anymore, unless you spent equal amount of time "slowing down". That's inconvenient. But there's a way to fix this. Suppose, you didn't have warp, but did have that thruster that you can burn "for free" for a constant 1g. You could put your ship into a circular trajectory, using your engines to accelerate towards the center constantly. It's just like being parked on a very large rotating station, minus the station. You're still rotating the ship, but you don't need counterweights or moving parts. But now, with warp/translation you can do even better. Using translation you can keep your ship put while it's momentum keeps turning in a circle. So effectively, instead of translating along a line, you're translating along the circle at a constant rate. It does mean that the ship still needs to rotate to point its engine in different directions, but if effective orbit you are compensating for would have been hundreds of kilometers in diameter, the rotation of the ship can be very, very slow. Say, one revolution per day.

If one ship is strictly pursuing, the other is strictly evading, the evading ship has advantage and in general will always be able force pursuer to run out of fuel first. Suppose, pursuing ship already invested some fuel to get an intercept. Now the evading ship can perform a correction to avoid intercept. Pursuing ship has option to match or abort and go for a different intercept later. In the former case, it's the evading ship that chooses the burn and therefore, can always chose one that's going to be fuel-efficient for evading ship. If pursuer aborts, they have to get new intercept, which will require even more fuel down the line. Either way, evading ship can keep evading until pursuer runs out of fuel.

Well, the heat exchangers are required for both. So that's no advantage to either one. I suppose, depending on how your antimatter confinement works, it could actually be worse than an NTR overall, yes. But again, this is specific to thermal rocket, where you convert energy to heat and use it to heat up propellant. But there have been other proposals for antimatter rockets that are way, way more efficient. Including ones that can theoretically do short interstellar runs in reasonable time. Wikipedia has an article on antimatter rockets which might be a good starting point if you want something a bit more powerful than an NTR. Of course, if you want to do practical interstellar runs with a rocket, you probably want to have a black hole drive, as that has the same 100% matter-to-energy efficiency and doesn't require antimatter confinement. A black hole drive is only practical as a torch and you can maintain a 1g proper acceleration throughout the trip for a ship in a few thousand metric tons range. Which means you can do a round trip to center of the galaxy within human lifetime of the crew. Of course, 45,000 years would pass on Earth in the mean time. Not great for interstellar commerce, but if your goal is to seed the galaxy with life, quite doable. If you can figure out how to deal with drag, radiation, etc. If that's not good enough, and you want to actually be making interstellar round trips in reasonable time in Earth years, then you do have to go FTL, and some variant on warp drive is probably the best bet for that. That's the place where math of General Relativity gives us some idea of what is and isn't inherently possible, but beyond that, completely unknown area as we lack all kinds of basic requirements to conduct the most rudimentary experiments. So at that point, we're dealing with pretty much pure fiction.

That works. Of course, now orbital maneuvers are irrelevant. You just have to make it far enough out from gravity sources to engage the translation. I wasn't complaining about propellant. I was complaining about it being a thermal rocket. With thermal rocket, you always use hydrogen, because that's the lightest stuff we have that's electrically neutral and stable, and the only two factors determining efficiency of a thermal rocket are melting points of components and how light your propellant is. NTRs already have about as high of an efficiency as you can get. By switching to antimatter as energy source in a thermal rocket, all you're ditching is the fuel core, and that's not even the heaviest part of NTR. All of the heat exchangers are, and you have to keep them for any thermal rocket. At this point, you might as well just go conventional NTR. If you insist on burning antimatter for energy, the most efficient propellant is light. You have pure energy from your fuel - there's no reason to dilute it with anything. But that assumes you can bring all of your fuel mass as equal parts matter and antimatter. If you are limited in how much antimatter you can bring, either due to costs or because there are technological limitations, then you start thinking about what propellant to use. Again, if you're trying to do a lot better than an NTR, we're talking about energies that will turn any propellant you use into fine plasma. Since nothing can contain these sort of temperatures mechanically, that becomes a moot point, and you either go for magnetic nozzles or use ablative dampers, or whatever you need to do to protect your ship. Since temperature is no longer a factor, neither is the mass or composition of your propellant. You can literally use anything. If you are trying to reduce space, you probably want dense propellant. If you want it to flow, maybe mercury will do! Or maybe you want it to be cheap, abundant, safe to handle, and easy to transport. Then why not just use water? There are a lot of good options that depend entirely on what kind of rocket you're trying to build here.

Acceleration is a vector. Which way is the ship accelerating? And you can't say "same direction as the ship moving." If you're riding a bike due North and I'm passing you by on a car going faster, you're going North relative to a person standing on a sidewalk, and you're moving south relative to the car. Would accelerating in the same direction be accelerating North or South? We can still talk about bike speeding up or slowing down in absolute quantities, because we take motion relative to the ground for granted. You don't have that in space. Just within Solar System the planets are moving fast enough to make that relevant as I've illustrated above. Are you accelerating in direction you're moving relative to planet you're departing or planet you're arriving at? Because that can be almost exactly opposite directions. And why should either of these matter? Any object or imaginary point is as valid a reference point as any other. So saying the ship accelerates in the same direction as it's already moving is nonsensical. Relative to the ship, the ship's never moving at all in any direction ever by definition. So which direction are you accelerating in?

Relative to what? Lets illustrate with a simple example. Your ship is orbiting Earth prograde with Earth's rotation and is on the day side when it engages its translation engine. Relative to Earth, it's traveling at 7km's and will be translating out of Solar System going retrograde with respect to all the planets. Relative to the Sun, it's still moving at about 23km/s prograde, because of Earth's orbital velocity, and so the ship should be leaving the Solar System prograde. So which direction does it go? And relative to potential destination, it could be completely different direction of travel. You can't say that two things are moving in the same direction but at different speeds. That only works when you're referencing anything relative to some fixed medium. So it makes sense when you talk about cars or boats. Not spaceships. And so a drive with this description isn't just non-physical, it's inherently inconsistent even as far as basic story-telling goes. As soon as your ship starts traveling between planets, let alone stars, the whole thing breaks down narratively. There are additional concerns regarding physics of something like this, but they really stem from the same root inconsistencies. You just pick up additional baggage of conservation laws and having to make sure they are satisfied. This one's just... why? You've taken one of the only two known ways to generate energy with 100% efficiency and combined it with the worst known way to generate thrust. It's like sticking a nuclear reactor core into a 19th century steam locomotive. I mean, it'll work, but if you can build a nuclear reactor in the first place, you can do better for your engine.

We rarely even see hydrogen as a fuel these days. People are mostly trying to build better kerlox or methane rockets. Sure, you need less fuel with LH2, but you need heavier tanks, so by the time you have a rocket, a lot of advantage is gone. And if you build your rocket reusable, it's just cheaper to refuel it with RP1 or some other cheap fuel. In order for us to consider a toxic, expensive, highly specialized, highly corrosive fuel that will require special plumbing from pumps to nozzle cooling, which will also reduce lifetime resource of the engines, the advantage on ISP would have to be something like 2:1 or better, not 10%.

F-15 also has a fly-by-wire system specifically designed to adaptively deal with combat damage. I would imagine so would Su-35, since both aircraft are inherently unstable and both are built to have snot beaten out of them and keep flying. This is similar to how you can usually land a conventional airplane with any one control surface stuck near neutral position by utilizing combined input from all the others. (Yes, you can roll your plane with rudder, just not very well.) The difference is that a modern(ish) fighter is built to be aerodynamically unstable for improved maneuverability and efficiency, so it has a computer keeping controls coordinated. You don't control anything with flight stick directly - just telling flight computer what you'd like the airplane to do. If you lose a control surface, flight computer usually adapts input to all others to try to give you as much of authority back as possible. According to the pilot from that F-15 incident, had he known how bad the damage was, he would have bailed. But due to the fly-by-wire simply rerouting control to all remaining control surfaces, he thought the wing is merely damaged and so went ahead with the landing.

In both models, the object can follow either orientation, depending on how fast it's spinning. If the satellite spins at 1 revolution per orbit, it will follow orientation in Fig 1. (Or five revolutions per orbit! That's called aliasing. But now I'm off on a tangent.) However, if we insist that the object is not spinning, it will be closer to Fig 2. Now, the reason I'm saying "closer" is because in Newtonian physics, there's an exact notion of what it means for object to not spin, and then we get Fig 2 and that's that. In General Relativity things get a little more complicated. In Newtonian Physics, we assume that motion is relative. You can't answer the question of how fast you are going. Only how fast you are going relative to something else. But you can always answer a question of how rapidly you are rotating. In Newtonian Physics, there is a globally inertial frame of reference. You can pick a direction and always know that direction, and if you keep facing in that same direction, you aren't spinning. Simple! And so a non-spinning satellite always faces the same direction, and we have Fig 2. I'm sure that's clear, but I wanted to walk through this to set things up for General Relativity. Well, in GR, things get complicated. Imagine that you are standing on the surface of Earth at the equator. You start out pointing your hand directly North. Now you walk North until you reach the pole. (I don't know, water's frozen, or something.) You are trying to keep pointing in the same direction, but along the surface, and nothing really changes until you make it to the pole. You then start going directly to your right. So you're moving South, but 90° of latitude from where you started. If you kept pointing your hand in the same direction, you are now pointing it East. And once you're at equator, you can move directly West until you're back where you started from. You always tried to point in the same direction, but somehow, you started out pointing North, and ended up pointing East. That's result of curvature. Things get further more complicated because time is a dimension and so, just like space, is subject to curvature. That's why gravity pulls on objects that aren't moving - they are still "moving" through time. And so in general, just like you can't be sure of direction you're pointing when moving through curved space, even if you aren't going anywhere, keeping track of what's the same direction as you age through time is also impossible. So how can we tell if something is spinning if we can't say if the orientation an object is pointing at now is same or different than orientation a few minutes later. Well, we still have concept of parallel transport. Just like you could keep pointing in the "same" direction as you moved along the surface of the Earth, you can maintain the "same" direction. And so while there is no global inertial frame, there is always a local inertial frame. And because of that, a notion of whether an object rotates local to that object. For a satellite, that's a local free-falling frame along that satellite's orbit. And relative to that, we can absolutely say if the satellite is turning or not. But in general, you, standing on the ground, might disagree with measurements on the satellite itself. This is the part where I would have to drag in a lot of heavy math to derive these things, so I hope you take my word for it. (Or ask someone else who understand the math and whom you trust more than stranger on the internet!) If Earth was a perfect sphere and was not rotating itself, nor had significant electric charge, the curvature it would produce is described by Schwarzschild Metric. It's one of the earliest exact solutions to Einstein Field Equations that we know. It's also why we knew to look for black holes and made many other discoveries. If our satellite was completely irrotational relative to its local free-falling frame of reference in Schwarzschild Metric, it would also perfectly follow Fig 2. The reason satellite moves in a circle but the chosen "forward" direction doesn't curve with it is related to why a much faster satellite would curve less. Even light moves through time as well as space, and what we need for a reference is a straight line in space only, and that does not curve in this particular metric. But Earth isn't a perfect sphere and isn't even electrically neutral. But it's Earth's rotation that throws a biggest wrench into our assumptions. There's another exact solution to Einstein's Field Equations that describes space-time near a massive rotating object. It's called a Kerr metric. And Kerr metric is weird. It doesn't get too wild until you have something really heavy with a lot of angular momentum, like a supermassive black hole, but technically, it's still a better description of what happens near Earth. And in that metric, there's something called frame dragging. It's named so because it's almost as if rotating object was pulling space-time itself along, creating a bit of a twist. And that twist does mean that an object orbiting above, one that's perfectly steady relative to its own local frame of reference, will appear to rotate ever so slightly from perspective of someone standing on the surface. Of course, from perspective of the satellite, it's the rest of the universe that'd be drifting around ever so slightly. And just to be clear, I don't expect that effect to be remotely measurable. There are too many other things going on. There are tidal forces that make measurement of rotation much harder. There is the fact that Earth isn't a sphere, and gravitational field will vary, generating various torques that you'll have to exclude. And even external forces due to light pressure and what little of air resistance there is making it impossible to keep things steady enough. But mathematically speaking, there should be a tiny amount of drift.

I've never seen any indication of a stable, even remotely, particle with any quark count other than 3. And if stable arrangements exist for antiquarks, we should have ones with quarks as well. So we're still back to the question of why more of one than the other. There are purely topological explanations for matter-antimatter imbalance as well. As a toy example, imagine our universe structured as an onion. Each moment of time is a shell, and inner shells happened "before" the later ones. Big bang is the point in the center of that onion. In that configuration, you don't have a question of what's before the big bang, because if you pass through the center, you start going to the future again, but on the opposite end of the universe. And you also don't have to have anti-matter. If all "matter" is radiated away from the center, all charges are conserved by what's happening on the opposite side of the universe. After all, the only difference between matter and antimatter is direction of propagation in time (to within TCP symmetry), and everything on the opposite side of the universe is propagating in the opposite direction. This simple model doesn't explain everything, but it's a start. Yet other models allow for lepton families to oscillate beyond just flavor. So all the antiquarks are... electrons! Why we ended up with more of one less of another? Could be purely random. And there are other problems with these models, primarily because of predictions of supersymmetry that don't seem to pan out. But the point is, there are a lot of reasons the matter-antimatter imbalance could be. We shouldn't be coming with a theory to explain that. That's a sure way to lead yourself along the path of ad-hoc theory and confirmation bias.

Same way you do in derivation of rocket formula. Instead of considering all of the energy at once, you compute delta-V for each individual detonation. You can then work in rest-frame of the ship for each detonation, since incremental delta-V changes are going to be the same. Then you add all of these together. Since early detonation work against the full mass of the ship, and later detonations push a ship that's a few nukes lighter, you will end up with something resembling a logarithm in the rocket formula.

Doesn't work this way. Kinetic energy is frame-dependent. Adding 1m/s to something stationary takes a lot less energy than to something that's already going 100m/s. This is why you balance momentum, not energy, when deriving rocket formula. And honestly, rocket formula is still a very good estimate for NPP. You can play off the fact that sum 1/n is very closely approximated by ln(n) to within a correction term. So as long as you can estimate the ISP of your pulses, you can simply treat this as a continuous burn rather than series of pushes. And for estimating ISP you could go with energy conservation approach, but you'd be using energy to find the velocity of the propellant. Of course, you'd have to know how much energy you'd straight up lose in NPP, and I suspect, it's a rather large fraction.

To accelerate air with laminar flow you need a velocity gradient. Velocity gradient is where energy losses happen. This might not be a big deal on model scale, but as you go bigger, you increase gradients to get more thrust, you increase the air flow, and you increase the volume in which these losses are happening. So it's going to be an unpleasant power law from length scale. Even going from their quarter-scale model to full scale is probably going to absolutely kill performance. Until they show a full scale engine with good specific thrust and fuel efficiency, I chose to remain highly skeptical on this.

I think grounding the cover is the key, yes, which is why I remembered More Magic. But I don't think it has anything to do with RF. For starters, completing the circuit could only reduce RF interference inside, which should have made things better. No, I suspect something somewhere else was shorting against the case. That's usually your first suspect. Change in capacitance could also do it, but that's a scary thought if something in the circuit is that sensitive. The most annoying case of ground doing weird things I've had to debug involved an unintended short circuit caused by the fact that oscilloscope used to diagnose the circuit and the power supply the circuit was fed from shared ground by virtue of being plugged into outlets on the same grid. Swapping the leads on the oscilloscope fixed the problem. The circuit was actually fine and operating as designed. Until that day, I never would have even thought to consider the two outlets and the wiring behind the wall as part of the circuit I'm debugging.

You forgot to put the switch into 'more magic' position.

There are trajectories near L1-L3 that are somewhat stable. A capture could get briefly stuck in either of these, but it wouldn't last. L3 is the most interesting case here, because that can lead to Janus/Epimetheus type orbit.

Absolutely. You pick your favorite boson field, preferably one with a zero rest mass. Then you polarize the vacuum in that field, flip the polarization, and repel from vacuum. Easy. For example, lets pick electromagnetic field. Vacuum is a dielectric, so you can apply electric polarization. Start alternating the electric field in your generator, and you will get a reaction force propelling the craft forward. Of course, you'll be producing electromagnetic waves, but you have to have something carry away momentum, so that makes perfect sense. Congratulations, you just invented a photon drive, AKA, pushing yourself with a flashlight. It has best-in-class ISP of over 30,000,000s, or nearly 100,000x better than kerlox! The only problem is that it does take a bit of power. 300MW per 1N of thrust, to be specific. So you better bring some matter/anti-matter fuel or a black hole to power this thing. There's a reason why we don't discuss propellant-less thrusters outside of science fiction topics. Energy-momentum is a conserved current, which means you either bring mass to propel yourself with, or you waste an enormous amount of energy to stand in for that mass. Anything else violates the most fundamental of underlying principles - local symmetries. You can think of it as being geometrically impossible to do better than this. That said, there are ideas out there that involve moving yourself places without actually accelerating. Warp drives, wormholes, etc. Sadly, nobody figured out yet how to do any of this without negative energy densities and enormous amounts of ordinary energy. A black hole drive is way more realistic at this point, and that's all that needs to be said on the matter.