K^2

You can make changes in magnetic field arbitrarily abrupt as well. Just not infinitely. The whole point is that it has to remain differentiable or you do break absolutely everything. If fundamental constants are not continuous, then their derivative is undefined in at least the points of discontinuity, and then we have quantities not defined along the discontinuity. It's identical to use of every other field. In fact, the moment you start tuning them locally, they are a field. There will be symmetries, and conservation laws, and associated bosonic fields creating new fundamental forces. There will be all kinds of new physics. It just can't violate conservation laws due to space-time symmetries (energy, momentum) and thermodynamics. And the reason thermodynamics keeps working is exactly the same as with every other field you could use to mess with kinematics. So long as change isn't truly discontinuous, there is a gradient. And so long as there is a gradient, there will be some sort of a compensating force. The only way to break it is to either have discontinuity, creating region of space where physics is undefined, or breaking either temporal or spatial symmetry leading to energy and momentum to no longer be conserved quantities.

Making discontinuous anything is impossible. So I don't see why you are assuming otherwise with the control of fundamental constants. log3(-1)/3 = ln(-1)/(3 ln(3)) = root(-1) pi / (3 ln(3)). Not a very useful choice of units, honestly. Still get actual irrational pi in it.

I don't know! You'd have to break local rotational symmetry somehow. That tends to be way more flimsy than translational symmetries. So, maybe? But I can't think of a specific mechanism. My gut feeling would be to use the existing limitations of angular conservation laws. For example, if you have a system with zero net momentum, its center of mass cannot move without at least borrowing momentum from external source. But with rotation, you can have a system with zero net angular momentum, and it can still orient itself to any angle without ever gaining any angular momentum, ending in exactly the same configuration but oriented in different direction. Maybe if you manipulate constants, you can create the same kind of sink for angular momentum, effectively turning it into an angular quasimomentum.

@wumpus The standard for "obvious" got better due to Google v. Oracle battles, but if you're trying to make it obtuse for use in DRM, lockout, etc, it's just as easy. So as far as relevant to topic, it's all the same. Just a little easier on engineers just trying to make a product.

You can make legality of it ambiguous enough for nobody wanting to deal with it. It's the same trick used with software. There are legal ways to reverse engineer almost anything, but you have to set up very clean separation between the project doing the taking apart and the project of putting something based on the findings together, because you have to be able to prove that you didn't copy anything that's legally considered copyrighted. And there are things you can put into your design to make it very, very difficult. For example, an algorithm cannot be copyrighted, but it can be patented. If something in your design depends on a patented algorithm, then reverse engineering might have you violating either copyright by copying or patent by replicating function. There is some obfuscation you can do on physical level as well. You can hide tool marks or even create false ones to hide how the part was made. But that's a speed bump more than an actual block. Just makes it that much harder to put a replica into production. This used to be a much bigger deal before CNC and 3D printing. If you couldn't figure out a reasonable process for making a part, you're done. But now you can x-ray the part and find some way to replicate it. Might not be efficient, might be too expensive for mass production, but you'll be able to make something that works. And once you do, you can start working on a knock-off part that will do the same thing that you know how to machine.

You can get same effect by applying a magnetic field to one side of the chamber. Any orbitals with non-zero Lz will shrink a little, and that will propagate out to other orbitals because the repulsion will be a bit weaker. Granted, it'd take a formidable field for a very small change in radius, but you can actually create slightly different corrections to ideal gas law on both sides without having to invent new physics. So if your suggestion worked at all, you ought to be able to generate a small temperature difference with just a big magnet, which would already be a violation of thermodynamics principles even if the difference isn't large enough to be practical. Working out why it doesn't work this way might be an interesting exercise, but the main take away for me is that being able to have different atomic sizes in different sides of the box isn't sufficient to generate free energy. In fact, I'm pretty sure it's flat out impossible by varying any parameters in space only. You need to be able to change parameters as function of time to either generate energy directly or have Maxwell's Demon. That's why in original thought experiment, the demon opens and closes the door. This is your time-dependence.

Of course. And why should manipulation of the fundamental constants be any different? I mean, you CAN start with assumption that, "We can tweak fundamental constants without adding or removing energy," but then your claim is, "If we were given means of violating conservation of energy, we could use it to violate conservation of energy!" You don't need a Maxwell's Demon. You're given the keys to the whole castle from the start. Alternatively, we can look at what a self-consistent theory where fundamental constants are tunable can look like. And solid state physics is a good example of what might be. You are still dealing with a field theory of some sort. It might look weird and have bizarre emergent properties, but it's still a field theory with an action over the fields. And where there is action there is Hamiltonian. And then so long as the rules applying to universe as a whole don't change in time, the Hamiltonian is translationally invariant in time, and we have conservation of energy as consequence. The energy may not be conserved in sub-system we are manipulating, but it has to come from somewhere. If you are changing the constants to increase mass of matter in your fuel tanks, you will need to supply energy to make it happen. That's only fair. And mathematically self-consistent. I'm not following this argument at all. Why should there be preferential movement? Is the door actuated by something? Or just constantly open. If it's the later, then what you're describing has time-independent Hamiltonian and will conserve energy. Thermodynamics should take care of it. The only thing I can see changing is the average size of molecules and their binding energies. I don't see how that should affect energy distributions to cause one side to heat up. Otherwise, this is still very similar to welding two different metals together, each of which has different energies of electron gas.

Right. I'm familiar with the concept. You're not explaining how you build a Maxwell's Demon. I'm telling you explicitly that we have systems where effective energy of the particle changes when it transitions from one material to another. If you need to make it time-dependent, there are materials where you can adjust that energy with external electric field, for example. So we have technology to do this in limited, controlled settings. If you can explain to me how to turn that into Maxwell's Demon, you can be generating free energy right now.

Hey, who are you calling basic? But yeah, good point. They say "water droplet", but in Venusian atmosphere these droplets would need to be diluted with more water before you can use them safely for battery acid. It does occur to me that, for example, DNA will certainly be completely destroyed by this pH level. I know terrestrial extremophiles generally adapt their biochem to environment, but in this case, I'm not sure that's even possible if this life was to evolve from oceans. Seems like the only way to combat it is a cell wall that can withstand the environment and some powerful proton pumps. I wonder if that's even viable, and whether something like that, if existed, would be less picky about pH.

One of the speculations has been that small droplets of water can form occasionally and be brought up to cloud layer with air currents. If some airborne spores exist, they can be dormant until they encounter such a droplet, then use it to reproduce until the droplet dries up, and form new spores. This is plausible with what we know of atmosphere of Venus and with types of life we know on Earth. Whether this is viable long term and if it could have evolved from ocean life when the oceans evaporated remains entirely unknown, of course, but that's a way Venus could have life without needing to invent a new solvent. Of course, if this is the case, the cloud cities start sounding like a really bad idea. It's one thing to deal with scarcity of some resources, and completely another if atmosphere is filled with what's basically Venusian anthrax. Life that's all about capitalizing on any moisture droplets it finds is going to do bad things to human lungs.

We already have such device. We have different metals that have different band energies for electrons. From perspective of how it affects energy of electrons, it's identical to changing binding strengths. You can weld two of these metals together and generate energy at one of the junctions. However, these devices only generate energy when there is a temperature difference. What you are describing is not Maxwell's Demon, but rather a variant of Seebeck Effect.

Nah, most of the mass is dynamically generated. Higgs mechanism provides a symmetry break in the electroweak bosons, but that's just one of contributions to mass. You could, of course, change mass of electrons by tweaking Higgs coupling, but you'd get better results playing with strength of electrostatic and weak forces. Likewise, your best bet on changing mass of protons and neutrons is going to be messing with strong force, as by far most of the mass comes from gluon and meson exchange. That said, none of it makes for more matter. Just heavier matter. And even that's not free. The energy for it has to come from somewhere. Here's simple example. I have buckets of water on my ship that I want to use for propulsion. Someone asks, "Can I make more buckets by adjusting how much water goes into each one?" Well, no, you'd be making heavier buckets. You'll run out of them eventually, though, that might be good enough. The bigger question is where does the water come from, and why don't you just point a hose back and use water for propulsion directly with same efficiency? To put it back into original terms, if you have the energy to manipulate the mass of propellant, it's going to be more efficient to just use that energy directly for propulsion as a photon rocket.

I don't think a lot of people appreciate that about rocket propulsion and rocket equation. The power output of a rocket increases with velocity, thanks to the kinetic energy of propellant being used as additional energy source. It's all kind of counter-intuitive, and the idea that rockets must have fixed power output, and therefore can't go much faster than the exhaust, was pretty popular. These days, we're used to having rocket equation as a tool and the fact that rockets, well, work, so we tend not to even think about this bit that would have made some otherwise competent engineers in the olden days argue that reaching orbital speeds with a rocket is impossible.

Right. Inherent assumption in all of the derivations above is that your vessel starts out as a closed system in vacuum. If you have external medium or external power source, that changes everything. Extreme case being a solar powered airplane, which requires neither its own power source nor propellant to generate significant thrust. For a more interesting example, modern field theory predicts huge zero-point energy of vacuum (in fact, seemingly impossibly large, but that's another story,) but it's fundamentally impossible to push from it. Explanation for why you can't push off from vacuum despite it having mass until you excite it is a bit mathy, but in a nutshell, excitations are what carries momentum, and these excitations are also presented as particles, so you need to either have or create particles to push from. However, if we are missing something in Standard Model, there might be something in zero-point vacuum that we can push from. That would allow not truly reactionless, but certainly propellantless drives. It seems extremely unlikely that such a feature exists, because we'd be almost guaranteed to see some side effects, but it's hypothetically possible within framework of fundamental principles we understand to be true. It would kind of put it on the same level as an idea of hyperspace. Hypothetically possible, but entirely speculative, with absolutely no evidence for it found. At this point, we have good enough coverage on experiments that I expect any novel propulsion method, if ever discovered, to come from sound mathematical model first. It's not going to be something we stumble on by accident. And with things like EM Drive, whose "theory" is entirely bogus, if it were to work, it would be entirely by accident. We don't have theoretical framework that predicts that something like this should work.

Yeah, that's garbage. The only reason it "works" on paper is because authors don't account for the mass flow responsible for making capacitor heavier or lighter. Gravitational mass is part of a conserved current of a fundamental symmetry from which gravity arises in the first place. Conservation of momentum follows from the same conserved current. So all they're doing is constructing a classic proof by assuming falsehood. "If we assume a violation of Poincare symmetry, we can derive this thing that violates Poincare symmetry." Well, no crap. Except that this would also mean that General Relativity isn't correct, and we have pretty good evidence for it. To be specific, when considered along with other gauge theories, such as Quantum Electrodynamics, we have better evidence for symmetries in GR than any other scientific theory. And within confines of that theory, what they're proposing there is mathematically impossible by contradicting Noether's Theorem. To properly emphasize, time travel doesn't have nearly as many constraints on it, and would be far more believable. To show that any such device is a violation, you don't need to understand anything about the physics of the abstract device. Take the device in inert state. Take a coordinate system where total momentum of the device and its surroundings is exactly zero. Place an imaginary bubble fully enclosing device and activate the device. If device never makes it out of the bubble, then everything is fine, but it's not much of a drive then either. If device makes it out of the bubble, it must pass certain amount of mass through the boundary. That would mean that energy density at the boundary increases from zero. Because energy is part of a conserved current, it means there is momentum flowing through the boundary. (In a fixed frame, rate of change of energy at a point is equal to divergence of momentum flow.) As the device passes outside, it carries some amount of momentum with it, so this quantity of net momentum has been taken out of the sphere, and inside the sphere we now must have something containing the exact opposite quantity of momentum. If the device produced no exhaust, and the sphere is empty, that is impossible. Q.E.D. Exhaust can take any form. It can be matter, it can be light waves, and it can even be gravity waves. But in order for you to start from rest inside an imaginary sphere, and then leave that sphere, you have to have had produced exhaust of some kind that either stays inside the sphere or passes through it in the opposite direction. Absolutely anything else would violate local Poincare Symmetry. The other thing to keep in mind is that if exhaust has no rest mass, such as light or gravity waves, then we have a very simple formula for minimal energy use of such a drive. For massless fields, E = pc, so you expect about 300MW of power for 1N of thrust. And that's the absolute best you can do for any drive if you don't bring propellant with you.

To be fair, muon-catalyzed fusion is a thing. It's not what people usually mean by "cold fusion," but it's close enough for me to give sci-fi a pass on that.

You can't say that with a straight face while showing an instrument panel with literal nixies and VFDs.

Best we can tell, every point in the universe can be considered its center, because they all started being literally the same point at the big bang, or at least, as close as it's physically possible. Unfortunately, both the theory and our ability to make relevant measurements with sufficient precision break down when we are talking about the universe's very, very, very beginning. So there's a bit of wiggle room on whether universe started out as a literal point or just something incredibly tiny, but everything indicates all of space starting out at least from a very close neighborhood of the same point.

Actually, because space itself is expanding, everything in the universe is roughly at rest on average w.r.t. CMB. Granted, in some cases you have to average over huge distances, as even galactic clusters can be moving pretty fast relatve to neighbors, but expansion doesn't contribute either way. We aren't actually moving away from distant galaxies, just getting more space between us. And yes, it's a matter of choice of coordinate systems, but if you chose the one that's most at rest w.r.t. neighborhood, it actually ends up being the CMB rest frame, and in it, galaxies aren't really flying apart, just getting more space between them.

Honor Harrington series by David Webber covers this topic pretty well. The universe has interesting fiction for how both sublight propulsion and FTL work that actually does well to justify tactics similar to line of battle, and how development of such carriers changes the balance.

I don't know how much of it is going to be Sun moving through interstellar medium, and how much interstellar medium moving past the Sun. Hydrodynamics of galaxies is kind of weird. What I personally find more fascinating, although only tangentially relevant, is that we can measure how fast the Sun is moving relative to the "rest of the universe", or as close to the "absolute" rest frame as we can find, the rest frame of Cosmic Microwave Background. And it so happens that Sun is traveling at about 369km/s roughly in the direction of Beta Sextantis or 264°, 48.25° in galactic coordinates, to be more precise. And you might as well call that the true velocity of our Sun, because there is no other reference frame nearly as universal, and I do mean that literally, as CMB.

Kind of a guess, but if you're setting up a control loop, you'll have something like PID. In practice, probably something a little more complicated, but PID works for sake of discussion. Because the output of PID is desired force from control surface, the deflection angle will depend on velocity. The slow the rocket is moving, the more deflection you are going to need for the same authority, so that will feed into the control loop as well. And there isn't really an obvious lower cutoff point other than hitting the limiters on deflection. Since I'm pretty sure the fins are well balanced, there is probably no reason to explicitly shut this behavior off. So they probably just let it keep running, with gimbal on engine providing all of the authority and fins just going back and forward in futile attempt to help in the last moments of the landing. If it's not hurting anything, figuring out a shut-off timing is just one more potential point of failure.

Yup, that's the one. Good call. I must have only seen the first couple of episodes, because I don't remember the show at all, but that scene still stuck in my memory.

Problem is that it only works with the kind of arbitrary combination of selectively having gravity and aerodynamic forces that you get in soft sci-fi. And being that kind of sci-fi is not to detriment of Yamato, certainly, but it's also entirely in the realm of, "This looks cool," rather than, "This is practical," because rules for physics are arbitrarily adjusted to fit the sequence to make it look practical. Though, I agree that revolver style storage is probably way more practical in zero-G and would be a good way to house fighters in that scenario. You do need to consider how pilots are going to get in and out. And the exit can probably be slow, but if you require everyone to get to their cabin in vacuum and zero G inside a revolver system before launch, that's not going to work well. I'm trying to remember which sci-fi had cockpit pods that would get transported to the fighter proper on launch. That can probably work, as the room with cockpits can at least have air in it, and they can be slotted to fighters an instant before launch.

It's unlikely to be exactly like Kerr naked singularity, because Kerr metric is very symmetric, and we don't know exactly what to look for. There are people trying to come up with plausible metrics that include CTC via computer modeling. I would expect anything interesting to come out of that first before we attempt to detect whether anything like it is happening. Keep in mind that the way we are detecting events such as black hole merger is by comparing signals we get at gravity observatories to computer models. We don't really have a way to detect something new, other than getting a signal that doesn't match an existing model, at which point, the best we can do is shrug our shoulders and say, "We don't know what happened there, but it was energetic."