K^2

There is quite a bit of matter in the bomb. All of it turns into a superheated plasma during the explosion. For the Orion, they supplement it with additional "propellant" material. About half of all that gets ejected into the space. But the ship has a damper plate on the back that absorbs the rest, giving ship impulse.

ISP is primarily limited by chemical energy. There can be other limiting factors, but maximum vacuum ISP can be close to theoretical maximum. Things like aerospike are an example of ways to get around some of these limiting factors and get closer to maximum. But if your ISP comes out higher than thermodynamic maximum, something went wrong. You can bet on it.

Janus and Epimetheus are by far the coolest moons in the entire Solar System, and of course, they are not on the list.

That is paragraph 3 of the text you just quoted.

It absolutely does. Energy out is greater than energy in. The reason it breaks down is because you should be adding energies, not velocities. This will bring it down to something in the 300s range.

The software I'm using is called a C++ compiler. Also some Mathematica to help avoid stupid mistakes in algebra where relevant. This isn't something you can just plug into standard simulation software. Especially, since I'm planning to have a curved metric. Although, there are certainly libraries that make working with lattice QED/QCD way easier. Because this is a lattice computation, it would inherently look at the ground state of the system. I'm not going to look at how outgoing flux of gamma radiation is going to affect the system. What I'm worried about is black hole munching on the electron cloud, which can be determined from the ground state. Since everything is far above Plank scale, QED is sufficient to describe it. Whether or not the flux is going to be sufficient to blow away the electron cloud is a separate question, but that can be estimated separately from ionization energy, which this computation will provide me. I might be completely wrong about being able to reduce degrees of freedom for this problem, though. If I have to run an actual 3+1 dimensional simulation, I won't have sufficient computing power. And I don't think I have access to any super clusters anymore. I miss being able to just SSH into a system that gives me access to 800+ GPUs for parallel computing. *sigh*

This, basically. But I'm a little worried about the overlap between electron cloud and the Schwarzschild radius. S-orbitals will partially overlap with the actual black hole, just like they overlap nucleus in ordinary atoms. That means the black hole will be munching on these electrons. I just don't know how fast. It's an interesting problem. Ground state should have cylindrical symmetry to within a phase, at least. So I should be able to get the actual electron distribution around the black hole with a lattice QED approach. And since it's going to be 2+1 dimensional, instead of 3+1 dimensional, I should be able to run it on ordinary PC instead of needing a cluster. I'm going to give it a shot.

You can't throttle a black hole. Its output grows as it evaporates. You feed it matter to prevent it from exploding. Although, you will have a few years between the time you've stopped feeding it and the time it actually explodes, so this isn't a safety factor.

I don't think it's humans that are impossibly unlikely. If we didn't have true Eukaryotes, we'd have complex life made up of symbiotic colonies of simpler stuff. Either way, as soon as they figure out sexual reproduction, whether on cellular level or colony level, it's kind of downhill from there. I think it's simpler. I think any self-replicating machine will eventually fall into the same trap. A tiny error in programming that managed to slip all of your error correction codes could give a specific machine a tiny bit of advantage in one particular environment. No, it's no longer competitive in all environments, the way its creators envisioned, but it's going to outnumber "healthy" machines in that one specific environment. From there, it starts to adapt. Sooner or later, it will drop any restrictions on mutation that were supposed to prevent it from doing so, and be capable of out-adapt in any particular environment. And then we're back to having plain old life, which will compete with itself and settle into a niche. It's Red Queen and Prisoners' Dilemma rolled into one package with Chaos Theory. There is only one way that can go. Basic understanding of field theory and differential manifolds, preferably with focus on GR, QFT, and their dualities.

I'll give you plausibility. But that's enough for me to take down your entire argument. It's plausible that extreme FTL method exists, and it's plausible that grey goo or Von Neumann probes with similarly scary reproduction rates can be created. We aren't currently being devoured by infinitely replicating machines, so we can conclude that no civilization in all of space has managed to achieve both. We can also throw in "or was crazy enough to let it loose," but you'd figure there would be at least one Dalek civilization somewhere out there that'd be bent on building berserker probes. So we conclude that with very high certainty, one or the other is not achievable. And I could leave it at there, but I'm going to propose one more thing. Suppose that it was possible for a reasonably intelligent civilization to construct such self-replicating machines. Say, Humans at some point later in their development. There are, by all indications, billions of worlds in our galaxy alone that would have supported some sort of civilization at some point between galaxy's formation and now. Many of these are completely gone now, along with their stars. Some might still be around. And it'd only take a million years to cross galaxy end to end at mere 0.1c. If you can figure out why you're not being devoured by some sort of grey goo made by some civilization in Milky Way a billion years ago, I'm sure you'll quickly find that reason applicable to why you wouldn't need to worry about a civilization with super FTL drives several superclusters away from here.

Ooo. That gives me all sorts of ideas. We've decided on a charged black hole, right? What if we shield it partially by dropping in a bunch of electrons? They will form countless shells, with potentially an absurd energy spectrum. These can block nearly all of the gamma and convert it down to something much more manageable. Perhaps to the point where, yeah, you'll really just have a solar sail. Powered by its own tiny sun. I really need to run at least some rough estimates on all of these, though. Otherwise I'm just going to carry on making stuff up.

Alrighty. That's about an order of magnitude higher than I thought it was. And apparently, they go even higher. So I stand corrected. Bad idea. Thank you.

@Kerbart That's not entirely fair. The actual turbine stage on a car turbo is exactly what you want for a cheap turbo pump. Author might not have been aware of it, and then your comparison stands, but at least through dumb luck he wasn't that far off. Compressor from a turbo charger, however, is completely the wrong type. It will not pump fluids. Still, the pump is the easy part. So if you want to build a small-ish rocket engine at home, starting with car turbo is a pretty good idea. What you want to do is take the car's turbo apart, separating the turbine from compressor. You can throw compressor away, but keep the common shaft. Then grab two centrifugal pumps, the kind that are typically used with electric motor to pump water out of wells. You want high RPM, low torque pumps, which electric driven ones typically are. Then connect both of these pumps to the common axle from the charger. Now you can feed gas from your pre-combustion stage into the turbine, and it will power the pumps. The output from the turbine goes into your main combustion chamber, and output from pumps should be split between pre-combustion chamber, main combustion chamber, and regenerative cooling piping as appropriate. This wouldn't be exactly commercial grade rocket pump, and it'll be far more likely to fail under the real launch conditions. but on the flip side, it should be sufficiently powerful for either a heck of a hoby rocket or even a second stage of a small orbital rocket. P.S. I should warn, though, that this is getting into seriously dangerous stuff territory. I don't expect OP to be able to build a complete rocket engine, but if you just get pre-combustion chamber going, or even simply feed the system from external pressure source for testing, this thing can pump ludicrous quantities of fuel and ox. I would strongly advise not trying a live test without a full engine built. What you can do reasonably safely is to test the concept by feeding water through both pumps and using something like a leaf blower to power the turbine. P.P.S Ok, on closer inspection, I might have jumped the gun on that "second stage" thing. I'm not seeing a lot of commercial, easy to find centrifugal pumps that go above 0.5 MPa, and you need at least ten times that to have an efficient RP-1 engine. In fact, charts I've found don't even start until about 1MPa. But 0.5MPa isn't terribly bad for a hobby engine. Of course, at mixture ratios that involves, you're kind of building a giant turbo charged flamethrower...

Oh, man, that totally slipped my mind. I was just thinking of impulse received, but with radiators you have to expel the same amount. On one hand, great! You can double your impulse with directed beam! So you'd get 50% efficiency instead of stated 25%. On the other, it means you effectively need to build an incandescent light bulb that generates half of your impulse. :/ I'm not even going to do the math for it. That's silly. What might not be silly is active radiators containing hot plasma in magnetic confinement. Hawking radiation of a tiny black hole is extremely hot, putting output firmly in gamma ranges, so even at a temperatures of a hot star in the radiator, there should be organize net wins on energy. I'll run the numbers for that to see what's actually plausible.

Titan came to mind, but its orbit makes it tricky. It's tidally locked to Saturn, with orbital period of 15 days. Which means the counterweight would have to be suspended above L2. Unfortunately, it's quite a bit out given the orbital period and mass of Titan, and Hyperion's orbit is going to pass close by. While odds of actual collision between elevator and Hyperion are negligible, it can pass close enough to the tether to provide considerable lateral forces, which would be all kinds of bad. Otherwise, Titan would have been one of these rare exceptions for which a space elevator actually makes sense.

None of these, because it's a dumb concept for every single one of these objects? I'm not sure why that's not an option, given that it's an obvious one. Except for Earth, all of the other bodies don't have enough atmosphere/gravity to interfere with direct magrail to orbit launches. Mars will require some rocket propulsion, but it will still be way cheaper than building a space elevator. And for Earth, there are way better options. like launch loop. If we don't want to build a full size launch loop, we can get away with using a smaller one for suborbital launches, and assist with a space teather.Again, way cheaper and more efficient than space elevator could ever be.

A 660,000 ton black hole, which is considered a "sweet spot" for a black hole drive, would have a Schwarzschild Radius of 2.2x10-19 meters. This is smaller than a single proton. It's not just subatomic. It's sub-nuclear.

Do you seriously not see the irony of telling a high energy physicist with experience and an actual publication in cellular biology that he doesn't understand the physics of reproducing machines? This would be appropriate if you were yourself an expert, with tons of expertise in cellular biology. Heck, I would settle for an ambitious undergrad who can construct a coherent argument and do some actual research, cite some papers at least. But you literally have nothing to back your claims other than some popular science literature you've read. If you happen to be right, it's by sheer accident at this point. But no, you have audacity to claim that your position is infallible. I have offered to argue physics with you. Make your point. I am well versed in Statistical Mechanics of the small and Classical Mechanics of the large. I even happen to be familiar with software involved in actual manufacturing and rapid prototyping, simply because I do my own 3D printing, so I'll happily discuss with you the finer points of tolerances in manufacturing. But you aren't defending your claim. Other than insisting that "this isn't how it works," you've literally made no attempt to actually defend your position. I've had students like you. They don't last long. You need to revise your attitude. I don't care what you take out of this argument, but you seriously won't make it in academia if you keep this up.

That's not quite correct. Our current understanding of physics suggests that FTL may very well be possible, but way beyond what we could imagine ever building. To be even more precise, speed of light has existed as an absolute, impossible to exceed limit in our understanding of physics for about a decade. Between publications of Special Relativity and General Relativity. And for the past 100 years, our understanding of it went from, "There might be ways to achieve this," to "Here are some plausible conditions under which it should be possible." Which doesn't sound like all that much progress for a century of thought, but it is progress. So I wouldn't bury the hope that we'll have it one day. Still, I suspect we'll end up making attempts at interstellar probes, at very least, long before we'll have any practical laboratory experiments on FTL travel. Barring some completely unforeseen breakthroughs in theoretical physics, of course.

It's floppy and statistical precisely because of the scale. It's called Statistical Mechanics for a reason. Your entire argument is that complex machinery necessary for a factory style reproduction cannot evolve. A cell is a perfect counterexample. You are retreating into, "Oh, it works slightly differently," without even looking at the fact that every argument you've made about why it can't evolve is perfectly reproduced in the cell. Complexity, check. Self repair, check. Reliance on individual components, check. You cannot invent a single distinction between a biological system and a factory that would allow for one to evolve and prevent the other from evolving. You keep talking about "dead zones," but it's totally just a buzzword for you that you've picked up and haven't even thought about. Exactly the same "dead zones" should have prevented evolution of Eukaryotes. Do you happen to recall how they managed to evolve these capabilities, at least? See, this is the kind of attitude that prevents you from actually learning anything. Critical thinking is a key requirement in science. So is making an argument. If you want to simply take that attitude and give up on defending your point, I suggest you give up on your career. I'm nowhere near as stubborn as most of your reviewers are going to be. P.S. I bet I have more publications on cell biology than you do. XD

A living cell already uses a good chunk of periodic table, including heavy metals. A living cell already has fibers inside that are as strong as carbon fiber. A living cell already has machinery inside it that does repair and delivery of necessary components. mRNA logic is Turing Complete. These are facts. I don't know if you simply opted not to take any courses in cellular biology or slept through them. Here is a video that demonstrates just a few of the processes in construction, replication, and material delivery inside the cell that we happen to understand. There is a protein there that works as a frigin' forklift. How much more "factory" do you need it to get? And this is just tip of the iceberg. About the only thing you are correct on is that we can't reliably reprogram any of that, because we don't understand it all. Its way more complex than anything we have ever built. It has more moving parts and more complex programming than anything we have ever built. This is precisely what it takes to build a factory that copies itself. And whether we adjust existing ones, or build it from scratch, we'd have to understand that level of complexity. We don't. But of course, there are experts who claim they can do better. Oh, and if you really insist on burring yourself deeper with your plane/bird analogy, do you know what else jet engine and a mitochondria have in common? They both use a literal mechanical turbine to generate power. And if you think living cells are incapable of guzzling power, you are absurdly wrong. Living cells have sufficient power generation reserves to cook themselves. The limiting factor is, once again, heat generation and dissipation. And if you've studied anything about cancer cells, you should have some idea of just what sort of reproduction rate living cells are capable of. Living organisms limit their reproduction and energy consumption so as not to wipe themselves out and go extinct. This is a fundamental limitation for any self-replicating machinery. We can throw living cells into overdrive and cause them to reproduce at far faster rate. It's been done in the lab. There is no limitation of biological system that actually enforces the reproduction rates we see in nature. Faster reproduction is simply not sustainable.

They do have airfoils, and they have exactly the same aerodynamics limitations as airplanes. There is no magic in physics. Again, you are not addressing the fact that every Eukaryote is literally a factory. Your entire complaint from the start was that a factory can't replicate without any one component, and therefore, cannot evolve. A Eukaryote cell is literally that. I am waiting for a detailed rebuttal, where you explain the difference between Eukaryotic cell and a factory.

And just how much do you need? And how are you going to do error-checking on all that data during replication? Eukaryotes have that. They have active transport and direct supply. Every single living cell in your body works exactly the way you describe, and you are still trying to prove to me that it's impossible to evolve. Unless your thesis is that original Eukaryote was created by God, you already lost this argument.

You don't. You put a damper on your ship that covers 2π of the solid angle, and get 1/4 of max impulse that way. I'm perfectly happy with 25% thrust efficiency on an engine that has 100% mass-to-energy efficiency. You'll need massive radiators to cool that damper, of course, but you can put some steam generators in between and generate all the power you could possibly need on a ship this side, including powering ship's magnetosphere for rad protection. Sensible. However, you were talking about containment failure. In this scenario, you still get an explosion before you can jettison the reactor. Yes, a smaller one, perhaps in just a few hundred ton range now, but it's going to be enough to breach containment on the next reactor, and a chain reaction is a go. You still have a single point of failure, except now you've reproduced it in every reactor. Accidents will happen with this kind of ships. All we can do is make them infrequent. Not even touching that one. My thesis is, "Maybe some day we'll figure out how to make a black hole. Then we can start building reasonably reliable, reasonably fast interstellar ships." Yes, we can build generation ships either way, and we'll probably build them eventually. They just won't let us build an interstellar civilization. It will be many disjoint civilizations of common origin that might share knowledge with each other. To really call it going to the stars, we need ability for people to reach other worlds within their life times. And short of FTL, that requires torch ships. And there are only two things that can power an interstellar torch ship. Antimatter or black hole. Because these are the only two things known to human kind that allow for sufficiently efficient matter-to-energy conversion.

It's a question of constraints. Yes, I'm absolutely sure we could engineer a machine that will briefly be capable of reproducing at far greater rate than any living organism. Hell, we could probably find a way to just throw an existing living cells into overdrive and get a factor of ten at least on their reproduction rates. But living cells don't do that, despite increasing in number being the primary goal of a living thing. Why? You are mostly right about it being the matter of how building materials and energy are supplied. Where you are completely wrong is suggesting that all we need to solve is build a conveyor. Living cells are perfectly capable of doing that. You seem to focus on simplest living organisms, that are entirely at a mercy of environment and random processes. But eukaryotic cells have overcome that billions of years ago. They have literal conveyor belts, cables, pipes, and other delivery systems built within the cells. Ones that take necessary materials and send them to where they are needed fast. Everywhere it made enough of a difference to bother with, it has been done. What it really comes down to is adaptability. Living things need to be adaptable to survive changing environment conditions. A lot of evolutionary "decisions" seem like they are a waste of resources, but really, they are critical in making sure that the organism doesn't survive just today, but a million years from now. And a Von Neumann probe is going to be the subject to same restriction. If some alien species builds machines that are simply better than living things at making copies of themselves by sacrificing adaptability, yes, they'll be able to spread rapidly. Then they'll get wiped out by the first unforeseen event, change in environment, or even an external agent. In order to actually survive and keep spreading through the stars, they have to adapt. They have to evolve. And that's just life. Also, if you think airplanes are more efficient than birds, I suggest you mention that to an aeronautical engineer and watch his response. If there was ever a biological need for birds to fly faster, they would have. As it stands, they fly quieter, stay in the air longer, and consume far less energy doing it. Because these were the specs.