K^2

If you can give me a rough number for acceleration rate over these 6 months, I could do an estimate. Basically, we need to know the distance and power loss we are willing to tolerate. But lets say that the beam is to extend .1ly. That would put average acceleration at about .8g. Which would probably be higher early on, and drop off as the power drops with distance. So that sounds reasonable. Also, at these powers, we probably want a nuclear-pumped X-Ray laser. There has been some research on that during the Cold War. US didn't manage to build one that's large enough to function, and Soviet research on the matter is, well, classified. (I'll just say that their goals were a little different, so their results aren't immediately applicable.) But in Avatar universe we can definitely see a giant X-Ray laser like that being built for powering propulsion of an interstellar ship. We probably couldn't get the optics for particularly hard X-Ray regardless of how big the thing is, so lets go with 500eV for the X-Ray energy. That puts us at .5nm for wavelength. And .1ly is about 1Pm. (Peta-meter, or 1015 meters.) There is a simple result in wave optics that states that h/L = λ/d. Ratio of minimum spot you can see or project onto to the distance is equal to ratio of wave length to the optics diameter. So lets say we are willing to tolerate a 75% power loss. In other words, h = 2d. And, of course, L = 1Pm and λ = .5nm. I can re-write the above equation as hd = 2d² = Lλ = 5x105m². That gives us d = 500m. Naturally, a nuclear-pumped X-Ray laser that's 500m in diameter is kind of insane, but not all together impossible. It's not the worst idea for the "first stage" of the interstellar rocket.

Right, but there is a lot of EM noise coming out from the device itself, and the photon drive based on quantum plasma will have a broad radiation spectrum. So yes, it should be possible to detect, but it might be difficult to distinguish it from background. At least, until you get into high enough power ranges where it becomes unmistakable. The current problem is that in this experiment they claim to measure 2 orders of magnitude more thrust then there should be at that power consumption. Now, they have a bunch of BS about universe as reaction mass to explain it, but that's just hand-waving. QFT predicts that any momentum transferred to quantum plasma will be emitted as radiation. Id est, a photon drive. And if on the output you have photons with certain amount of energy, you must have expended that much energy. They have absolutely no theory to go up against that. What they do have are measurements with a lot of noise, where their claim of measuring thrust precisely enough to say anything more than, yeah, there is some, is overstated. So for now, assume that it should read 300kW per 1mN of thrust, and 3x107s of ISP, and the numbers they state are experimental errors. Now, if they do manage to reduce noise and show that they really are getting more thrust, that will be very interesting, and we'll need new physics to explain it. But it's not going to happen. Just like there were no faster-than-light neutrinos or anti-gravity superconductors. Just experimentalists getting way too excited way too early and not checking their wiring properly. That said, QT might still turn out the best damn photon drive we can come up with, and that's worth investing research money into.

A collimated beam does not follow the inverse square law. Instead it follows something like 1/(r+k)². The constant k depends on how you achieve the beam, but it can be quite large. And so long as your distance is smaller than this parameter k, you don't experience any significant drop off in power. Of course, eventually, you will get far enough from the source, and it will start going to follow inverse square law. (Because r is so much greater than k.)

All of the operational quantum thrusters are just a variation on photon drive. The nice thing about it is that they can be way more energy-efficient as photon drives than something like a laser. The downside is that they are still just photon drives. That means you need 300MW/Newton of thrust. Everything else is errors and misreporting.

That's actually completely wrong, because neutron is heavier than proton and electron combined. Hence, neutrons aren't stable, but protons are. If this wasn't the case, the only kind of matter in the universe would be neutron matter. That's a gross oversimplification. By this logic, neutral pions should be uu-bar particle. But they are not. They are uu-bar - dd-bar mix. Difference in current masses of up and down quarks is almost insignificant compared to energies of nucleons. It's important in the dynamics, which makes neutrons and protons not quite identical, but to say that neutron is heavier simply because down quarks are heavier is an oversimplification.

These things do make perfect sense.

I think he claimed that that's where he was aiming all along. Figuratively, if not literally.

Our understanding of physics at different scales is way more detailed than that. That's not to say that there can't be something very weird going on at larger scales, but it's very, very unlikely. An unobserved form of energy would make more sense. That said, people did say the same thing about aether.

Expansion of the universe is accelerating. General Relativity requires average stress-energy density to have considerable pressure for this to happen. The mysterious source of that pressure is what scientists call dark energy. Though, what that actually is, or if that's even what's really happening, nobody knows. But it's the best explanation for accelerated expansion that we have for now.

It qualifies as more of a prediction, since it's based on established theory. But that's almost a semantics point in this case.

What's the problem here? You can compute mean anomaly. You can compute true anomaly from that. The orbit can be any conic section, it doesn't matter. (You do have to be careful with periods of hyperbolic orbits, but if you are comfortable with complex math, equations generalize to this case as well.) The difficulty is with real planets/moons only, because their orbital elements evolve over time. In KSP, orbital elements are fixed, so equations are very simple.

Shouldn't be all that much different. You are going to be either predominantly influenced by one of the objects, or by system's barycenter. If this wasn't so, that binary system couldn't have moons of its own anyways. Naturally, there are going to be a whole lot of perturbations and corrections, so a general orbit might ending up a bit weird, but so long as you have means of predicting your path, you can always make corrections for this.

Somewhat related to the plot of Falling Free by Lois McMaster Bujold, part of Vorkosigan Saga. Good read.

Kepler's Second law is just conservation of angular momentum. Angular momentum of the planet is given by Ér². While the triangle the line r sweeps in some short amount of time t has height t and base vt = Ért. So the area is tÉr²/2. Since Ér² is a constant, the area of the triangle is also a constant.

Not really. Gravity, as in the force of gravity, is just an artifact of acceleration. The force you are experiencing while standing on the surface of the planet is exactly the same as the force you are experiencing while standing inside a centrifuge. In both cases, the force of (artificial) gravity is a fictitious force arising due to accelerated frame of reference, and in both cases, what is actually important is the real force with which ground pushes against your feet. Even the equations you'd use to derive the force of gravity in General Relativity can be applied to a centrifuge, and you will get correct answers. The difference between the artificial gravity we can make with acceleration and gravity of the massive bodies is a bit more subtle. If I have a centrifuge, and I attach my coordinate system to it, then I have to introduce a centrifugal force and a Coriolis force to explain motion of the objects inside. But that's just a "bad" choice of coordinates. I can always chose an inertial coordinate system, say, from perspective of an observer floating outside of a rotating space station, and describe everything without using centrifugal force. The normal force supporting artificial weight of objects in the station, in this case, is just there to provide centripetal acceleration of the objects. F=ma, and nothing else. With gravity, I can always choose such a coordinate system locally. A space station in orbit of the planet is in effective free-fall, and therefore, I can attach a coordinate system to it and call it my inertial system. But no matter how I try, I can't come up with a coordinate system that's inertial everywhere once I have massive bodies involved. There is formal way to describe all of it, and it has to do with symmetries of space-time, but the important bit is that while there are very important distinctions between gravity of large bodies and artificial gravity we can make, the force of gravity and the force of artificial gravity are absolutely equivalent in every way.

You mean magnetos? The reason magnets in magneto lose their field has more to do with engine heat, vibration, and impacts that are all part of normal operation for a magneto. By the way, not just vintage engines. Some modern airplane engines use magnetos for better reliability. It also lets you kill all of the power in case of electrical fire, and still have the engine keep going. Of course, this only makes sense with carburetor engines. And yeah, an iron magnet, especially something with a needle shape, can lose its strength over time. The field near end points is very weak, allowing domains to drift over time. But if that's a concern, all you have to do is use stronger magnets. Neodymium magnets are, for any practical purpose, absolutely permanent. At any rate, they can certainly outlast any machine you'd build with them.

Conservation laws are formally written as current conservation laws. For example, you are familiar with the law of conservation of electric charge. You can create some negative charge, but you have to create some positive charge to compensate, so net charge in the system remains the same. Well, the way it's written formally is ∂ÃÂ/∂t = ∇∙j. "Rate of change of charge density equals to divergence in current density." In simpler terms, if amount of charge you have changed, then the change is equal to amount of charge that flowed in minus the amount that flowed out. (By the way, this formula is way more elegant in Special Relativity, but that's way off topic.) Alright, so any conservation laws you might be looking at, be it energy, momentum, charge, baryon number, or whatever, will have an associated current. And any physical way of traveling from one universe to another would involve currents. So while the total amount of stuff in a particular universe might have changed, that change is only due to an incoming current, and so the fundamental conservation laws are fine. Of course, how exactly this is going to work out is going to depend very much on how exactly you define the universe, and what sort of structure the underlying multiverse has. Since we have no evidence of other universes, the question is mostly academic. But if we can't count on conservation of conserved currents, then the rest might as well be voodoo, and it's no longer a scientific question.

Saying magnets lose power over time and saying that they demagnetize if taken above Curie Temperature are two completely different things. In a strong permanent magnet, magnet's own magnetic field keeps domains aligned. No. Over-unity is prohibited by some extremely fundamental theorems. Not theories. Theorems. As in, mathematically proven. No. Which makes the rest of your questions completely pointless. You can't build a PM device out of permanent magnets. Can't. Even with perfect magnets which will never lose their strength. Again, there are theorems that say so. No, it's not. Because there are proofs for general configuration. Doesn't matter how many wheels, magnets, and so on you have.

A lot of very dangerous things could be justified this way. Sensible regulations should be followed. Especially, in cases when government gives you means of obtaining proper certification.

It can be. But I'm not the best person to ask. I'm planning to go into software once I finish up with dissertation and defense. It's not that I wouldn't like to keep studying physics, but things I'm interested in are difficult to get funding for. While in contrast, areas of research I can continue in, I find incredibly boring. I'm pretty sure it has to do with where we are as a civilization right now. Things that are really new and different are so far ahead of our current technology, that they are pretty much impossible to test. And things that can have practical use within the next half century are all built around tying up loose ends, which feels tedious to me. But your mileage can vary. There is a lot of very exciting stuff in materials and condensed matter in general. Not my thing, but it might appeal to you. The good thing about getting a solid education in Physics is that you still have choices even when you're nearing the end of your Ph.D. track. You'll definitely find applications of physics that you find interesting. And if you can make it through the Ph.D. program, you'd definitely be capable enough to make a career out of whatever it is. It can be in academia, private research, or some other technical field. You would definitely have to put some effort into keeping yourself up to speed in appropriate related fields if you want to branch out, but physics is one of your best options for building your skill set around, simply because study of physics taps into so many other disciplines and skills. It is tougher than most fields, though. If you are in any way not comfortable with mathematics or any of the sciences you've come across, have a backup plan.

Light cone coordinates, while they have their use, should not be used as a frame of reference in general. For example, say you are taking an aim at the target at the range using a laser sight. Then you fire. Now, relative to you, light from the laser is traveling at the speed of light. Relative to bullet, it also travels at the speed of light. So if it's fair to say that you are traveling at the speed of light with respect to the photon, same can be said about the bullet. So then you and the bullet travel at the same speed? But you fired the bullet. Clearly, it's moving with respect to you, so the speeds have to be different. See, it just falls apart like that. Ultimately, it has to do with the fact that from perspective of light, there is no longer a distinction between space and time. For a photon, the only direction that exists is forward. It's both its direction and its future. And if you only have one dimension, and it is both a space and time, how are you going to go about defining velocity of anything? So yeah, the short answer is that you simply can't use light as frame of reference like that.

Any charged particles that interact with your hull at these energies will result in a shower of particles, and you'll end up with enough of the total energy deposited in your ship to have a very serious problem.

And that's why every once in a while a large chunk of German population decides to go and have fun with gunpowder and explosives abroad. Pardon my abrasive humor. Anyways, in the States, rules are pretty lax. High-power rockets, defined as having more than 62.5g of propellant or more than 160Ns of impulse (H or above), do require a license. Anything bellow that, does not. You can just go and buy a G motor in the store. If you want to build your own rockets, limits are stricter. You need license to pack gunpowder over certain amount, for example. I don't recall what the limits are. Other fuels vary, but the only limitations are laws on explosives, and you can typically get away with almost any kind of propellant so long as you keep quantities low. You also have to be aware of the Destructive Device laws, which limit propellant to 4 ounces (113.4g). Anything over that would require permits from the Gov't which are a pain to obtain. Of course, you're well into high-power category by then. And as usual, there are various regulations specific to individual states. But they generally only restrict where you can launch.

There are no arrangements of magnets where magnets "create" motion perpetually. And it has nothing to do with magnets losing field. In fact, a good feromagnetic won't. Neither would a superconducting magnet.