K^2

Funnily enough, the central argument of Holographic Principle is that, "So is every other kind of force."

*sigh* Yeah, but it's one of these topics which doesn't lead to anything good when discussed with lay-persons. Let me just drop a few bullet points, and for anyone who wants to understand this better, there are a few universities I can recommend. Technically speaking, the idea of looking at our 3D space (or 3+1, really, because time) as a section, boundary, or some projection of space with higher dimension is related to Holographic Principle and various models involving this are sometimes known as holographic interpretations. The one that comes up most frequently as an example is the AdS5 which leads to the gauge/gravity duality. The most important thing to understand about this is that no holographic interpretation produces better results than Standard Model. In fact, they can't even fully match SM. So far, they have all been just interesting mathematical models; at most, a different way to look at already understood physics. Kind of like gravity in General Relativity can be interpreted as consequence of Space-Time geometry, or it can be viewed as just another gauge field. Ultimately, all of the math is the same, but some interpretations are easier to grasp intuitively in certain contexts. Nonetheless, there are still some very serious physicists who think that it's the key to Unified Field Theory. Again, not because it's inherently different, but because it's the same field theory seen from completely different perspective.

It would work, but it wouldn't be most efficient. Given these sort of conditions, I would expect different light-absorbing molecules to evolve. And most likely, what little of light is in visible red would probably be thoroughly absorbed. Now, if there is local fauna with different sort of vision, it might see actual "color" to the plants. But to us, it will look black or dark brown in all likelihood.

Conventions on that sort of things seem to be in a bit of flux. Modern convention is to include multiplicative identity in the definition of the ring, with these algebras lacking identity getting called something like pseudo-rings. But yeah, good call on watching out for it. It's kind of like m in modern physics representing rest mass, whereas some of the older papers, especially these written by Einstein himself, used m as the symbol for relativistic mass. Rest mass in such papers is denoted as m0. And if you don't know about it, it can cause much confusion. Like with the E = mc², which is absolutely true with Einstein's notation and not generally true with modern notation. Fortunately, once you are aware that these things are out there, figuring out which convention is used is easy from context.

Can't speak for Europe. US has a pretty bad school-level education, but starting with University it picks up. Sure, most graduate students in good schools are from abroad, but they finish their education in US and they stay to work in US. It'd be nice if US fixed their K-12, then we wouldn't need to import so many engineers. But there are a lot of qualified people working in aerospace. I cannot say the same thing about modern Russia. Most of their qualified engineers are pushing retirement age. And there are no replacements. Education system doesn't produce nearly enough, and of these many leave the country for better income in US and Europe. And Russia can't afford to import enough engineers. I have no idea what the plan is with Federation, but I'd be shocked if it comes to fruition.

You'd probably need to make an entire star system with a red dwarf sun to make it authentic. Not that it really has to have anything besides that planet and a few rocks. P.S. If anybody actually wants to try this out, I can easily crunch numbers for a particular spectral type and tell you exactly what color sky, water, ice, etc. should be.

The star needs to be at least orange-yellow to get enough blue for a blue tint on things. I think it would qualify as a yellow dwarf by that point. I would expect something in brown-orange-tan sort of colors for water and sky. With black vegetation and what likely appear to human eye as red ice caps. What a sight!

Once you throw in momentum, the famous "E = mc²" becomes E² = p²c² + (mc²)². Physicists often use "natural units", where c = 1. So this becomes E² = p² + m². If you graph the three components of momentum p and the mass m together, all allowed values form a hypersphere of radius E. This is called the Mass Shell. There is a fundamental reason for this shell's existence. Only propagators that are on the mass shell preserve amplitude. Translated to what it means for the particle, in order for a particle to propagate freely in space over a "large" distance, it must be "on the shell". Off-the-shell propagators are a mark of virtual particles. They do not satisfy the above equation, but neither can they propagate freely. They have to be absorbed after a very short jump. Typically, we are talking about distances between atoms or less. Because of this, no matter what Quantum weirdness is happening within a particular drive, if we step back a little, and draw an imaginary boundary around our space craft, everything leaving the spacecraft must satisfy the mass shell equation. This is why Quantum Thruster is possible, but it must produce an exhaust that's on the shell somewhere downrange. And this leads right back to conservation of momentum and energy. If the net exhaust from the drive has m = 0, then we have a trivial E = pc. That's 300MW per 1N of thrust. Mind, even a drive that achieves precisely that would be fantastic, because we have no idea how to build anything close to 100% efficient photon drive. It wouldn't be immediately useful, but we'll find a use for it in the future. If mass of the exhaust is not zero, then the spacecraft is shedding that mass. Whether it's doing so directly, like a conventional rocket or an ion drive, or converts energy into mass doesn't matter. Because in craft's own frame of reference, any energy it has on board contributes to its total mass. E = mc². So regardless of mechanism, the best we can have is an equivalent of a really efficient ion drive. That doesn't work, either. Vacuum is a medium. You can push from it, but like with any medium, the only way to do that is to excite the medium. Even if you are swimming in a pool and push from water, from perspective of field mechanics, what you are doing is creating all kinds of quasiparticles in the water which you use as a form of exhaust. Now, you can do that with vacuum. But all of the excitations in vacuum follow the shell rules above. You still need a minimum of 300MW per 1N of thrust if you didn't bring any propellant on board.

Warp drive can't generate a measurable force, which is how it gets around that limitation. EMDrive actually generates thrust, so it can't qualify even for that loophole.

One day, perhaps, someone will figure out how to explain Quantum Mechanics in a simple way without saying a whole bunch of things that are simply wrong. Today is not that day. But good effort. It's definitely one of the better explanations of orbitals to a lay person.

Because it gains momentum at a rate that doesn't match the loss of energy. So it either generates off-the-shell exhaust, which is impossible, or it doesn't conserve momentum, which is even more impossible. If it interacts with some medium to produce this thrust, then it merely becomes very improbable.

You mean, if it works as described in most optimistic claims, with no requirements for a medium or stored propellant? Setting aside the fact that we'd probably have to burn all the physics textbooks written since, oh, late 19th century, the impact would be primarily on unmanned exploration. The net thrust is still pretty low, but it adds up over time if you don't have to bring any extra mass with you. So deep space probes, perhaps even some interstellar ones would be possible. It'd be quite handy in studying outer Solar System as well. If it works as described in every way except not needing propellant - that is, there is some sort of a leak it utilizes to get thrust - it can still be useful as a type of ion thruster that has better TWR than most other designs we've considered, as well as pretty good power-efficiency. Still great for Solar System exploration, but not quite there for interstellar. The biggest win for this outcome is that it doesn't break known physics, so we'd just have to account for phenomenon. Finally, the most likely possibility is that we'll find a glaring source of error, and this whole thing will be put to rest.

Photons have no rest mass, which is why they are difficult to push from. You need 300MW of power to generate 1N of thrust with a photon drive. EMDrive is measured to do at least 10 times better, which means that it pushes from something that does have rest mass.

Not all the mathematics. Just groups, rings, and other algebras which are required to have units. Without identity, you would be talking about a quasigroup or a semigroup, for example. Or even just magma in general. Trust me, if you've thought of something, mathematicians have considered it over 200 years ago and incorporated it into general mathematics theory. Any assumption we take for granted with what we usually think of as maths has been evaluated, and theory with different assumptions certainly exists out there somewhere. Some of these even find practical use.

Yup. Do you see now why I simply dismissed this as an option? Unless you can figure out how to turn these into giant, almost weightless sales, it's just not usable. You can improve the situation using a magnetic scoop, of course, but you end up with the same considerations with drag that ultimately buried the Bussard ramjet.

Take typical interplanetary ion densities. Take "engine" cross-section of 1m² orbiting the Sun. You can use solar wind speeds as reference for how much matter passes through your engine. Now boost all of that matter to 0.1c, which is well above the upper limit for EMDrive given Power/Thrust ratio. Look at the trust you get. I'll save you a Google search. Solar Wind is 3amu/cm³ at 500m/s. Now you just have to do the math.

I can totally buy momentum transfer at short, but not microscopic range, resulting in thrust from whatever ions are still floating in the chamber, something evaporated from the chamber, or perhaps even from the equipment used to measure the thrust. What I don't buy is virtual particle transfer of momentum over long scale. And by that I mean anything beyond a few centimeters at the most. If this is the principle of operation, it's still exciting, because it's really new. But useless in most operations that the EMDrive is being advertised for. If it happens to be a way to get thrust from surrounding ions, this could be a good system to keep small satellites, perhaps even cubes, in LEO orbit almost indefinitely. Which is something. But it wouldn't make it a practical deep-space drive, unless there is a way to convert it into a conventional, albeit potentially more efficient ion drive.

3D printer can handle printing foam. There are sufficiently flexible filaments available. It's all about how you convert the solid geometry into GCode. It'd take a custom program for sure, but it's nothing particularly insane. I could probably write an STL -> GCode foam program if you guys really want it. Just don't expect anything fancy. I have a simple 3D printer with a single print head, so that's basically the extent of features I plan to support. @Nuke, I wouldn't print wings. It's much better to print ribs, connect them to the spar(s) (e.g. aluminum tube), run some stringers, and then use a wing covering material specifically designed for RC, film or fabric. I might have an OpenSCAD script for generating NACA profile ribs if you want it. You'll have to CSG subtract spacing for your spars and stringers yourself.

Eh. Ternary is far more efficient. It's a shame we didn't go with it for the computers back in the day. Setting aside a huge boost in memory capacity and performance, even simply splitting data is more convenient. Instead of nibbles, we'd have sets of three trits, which is sufficient to encode 0 + 26 letters of alphabet, which would make for more convenient representation than hex. Alphanumerics would be sent with pairs of these allowing for larger alphabet and more error correction data, while a data stream would probably run in threes. A 9 trit instruction set would already put us close to 16bit machines with only a slight overhead over 8bit architecture. We'd probably have powerful personal computers half a decade sooner. The only downside is that powers of 3 don't fall close to powers of 10, and the base-3 logic is slightly less intuitive than base-2 logic. Although, tritwise-Z3 is always an option. Kind of like the bitwise XOR/AND make up a Z2 ring. In fact, calling the tritwise operators AND and XOR would work just fine.

Yup. Some bases are easier to get used to than others, but you can get used to pretty much anything.

Trivially solved with an electric motor. For a centrifuge of practical size and rotation speed, the power drain will be low enough so as not to break your power budget. And if you dual-purpose this aerodynamics for ventilation, you can drop net losses even lower. I don't know if it's the best way to do it, but it is certainly an option.

No, you don't understand. I'm taking into account the decline in power output. And I am not taking into account any subsidies from the government. Solar power is already flat out cheaper than fossil fuel electricity in most states and countries that have various environmental taxes against fossil. And very soon, it will be just flat out cheaper without any involvement from the government. That is the status quo. Solar panels aren't the cleanest way to get solar, but the waste produced during manufacture of panels is much lower than that produced by burning coal. And more importantly, the greenhouse impact of solar panels can be zero. And again, I point out that solar panels aren't the only way to get solar power. Solar collectors are virtually pollution-free.

I've addressed it somewhat in a post just above.

Depending on a battery, about quarter to half of the battery's average life-time will be necessary to recover the energy used in production. Which explains why they have such high up-front costs. However, it was less than a decade ago that it took more energy to produce a solar panel than it could generate in its life. So the only advantage was shipping off pollution to other countries. Fortunately, we're past that point, and solar panels are rapidly improving. Even more fortunate, solar panels aren't the only way to generate power on industrial scale. A lot of places would do better with solar collectors. They come with problems we still need to resolve, like frying birds in mid-flight, but if we bury the collectors instead of building up, we can avoid that unfortunate side-effect. In either case, solar is booming in US and Europe, with industrial nations expected to follow soon. Even with total lack of environmental oversight, solar energy is getting close to competitive in places like China. And once solar becomes cheap enough to start driving down actual costs of electricity for the industry and consumer, we'll see major changes introduced into transportation network. Many large cities already find it efficient to run public transit on electric, be it in form of trains or trolley buses. But imagine the sort of change we'll see when NYC cabs switch to electric cars, for example. Or all the rigs on the freeways. And it's not science fiction. We are really close to the breaking point where that will be simply cheaper for transportation companies to do that. How long do you think consumer market for gasoline cars last after that?

Cost is the only way to compete with electricity right now. Environmental concerns will always come second to price. Energy density of batteries is high enough. The only application we have where it's not is aircraft. And for large ships, it's still going to be cheaper to go with diesel. These are the only two applications where we can't go electric right now. That's not enough to keep expanding our infrastructure. Once street cars, trains, and trucks are all electric, the oil demand will collapse to a tiny fraction of what it is today.