ZetaX

That's not an observation but a theorem: a conclusion that follows from the assumptions (GR) by purely logical means. I am not sure if you are serious about this part, so just a short answer: that's not the definition of "embedding" that is used in the statement. If that other dimension has neither an observable effect on the universe nor gives any advantage when doing computations and such, then there is no reason to even talk about it. If using it actually gives an advantage or is the best way to explain some phenomena, then it will be used; GR is an archetypical example where only considering space fails while considering space-time as a whole gives a nice theory. Nothing, but unless you have at least some observation or other reason to assume so, you should not assume it. That does not mean you should not look for one, though.

This is surely true if the universe is of infinite age or light has infinite speed, but I don't see how that argument should work when considering relativity. It surely fails if we just allow the universe into existence "as is", but maybe there is an argument coming from general relativity that I am missing. With all the usual definitions of universe I know and/or find in wikipedia, your statement is simply "what if we observe things that cannot be observed/that don't exist?", which is meaningless.

The "real world" should probably not be seen as the theorems following from your axioms, but as a model of them. This is much closer to how physicists use it, too. In particular, Gödel's theorem does not apply anymore that way. Furthermore, the undecidable statements could be things like "does this nucleus of Pu-238 decay in the next year¿" that are governed by quantum randomness. In other words, we already have some loopholes to 'hide' undecidable statements in.

This heavily depends on things like the rotation of the black hole and the direction of the orbit. Generally, inside the event horizon is definitely "too close".

I find that implausible to work in most real life scenarios. Anyway, that was just an addendum, the main argument is still that you don't shoot them down at all for the reasons given above.

No. Not even a single (almost) elliptical round around a black hole is possible if too close. Again: this has absolutely nothing to do with tidal forces, Roche limit, some very long term effects like gravitational wave based energy extraction or other "imperfections", but is solely a effect of the geometry of spacetime.

I follow him till he runs out of gas or lands for other reasons. It's completely the same in many car hijackings: they follow it until there is either a safe way to stop the car without too much danger or untill the driver stops for whatever reason. What they don't do is shooting rocket launchers at the car, despite this definitely being a "working" solution. And in the car I described above, there is _only_ auto control. No stiring wheel. No manual overide. Just a play "get me to X"-interface and maybe some gimicks like air-conditioning.

If your technike is nuking a city because someone stole a dollar, then your people are gonna die out. Also, protests (leading to more nuking). A bit more seriously, would you want it to rain cars every time some guy steals one¿ And now in full seriosity, what makes you think that all of them escape¿ It's not like they magically are safe when they leave the city. Still no reason to shoot them down there. Also, you probably have lots of relevant data to track him down later. And if that veficle is fully automatic, police could have a way to take over.

No, that is not what K^2 was talking about. Close enough to a black hole there is no possible orbit, not even for particles like photons or electrons. That has nothing to do we the Roche limit.

Better not than that way.

Terrorism is different, as this is one of the very few cases where shooting them down may reduce the harm caused. But like with other kinds of terrorism, this is a job for the military, not for the police. So you would suggest stopping theft by killing the thief, destroying the stolen vehicle in the process and possible causing more damage and fatalities on the ground¿ Sorry, but I don't understand the morality behind that. I would already be against shooting him down even if there will be no damage on the ground; there is no gain for anyone involved.

Even if hijacked, the one(s) responsible will probably not be too keen on dying, so at some point they will have to land or leave the city. At worst, they run out of fuel and come down that way, which sounds still more controlled than shooting it down. If we want these in cities, we probably want them to be autopilot only anyway. Humans are probably neither capable nor responsible enough to this themselves. So don't even add a stiring wheel/joystick/whatever that would use. A simple terminal to enter destinations and such is enough.

What for¿ There is not much anti-car weaponry either (the only thing that comes to mind are the different types of spikes) and I am pretty sure we don't want to shoot down flying vehicles unless they pose an even greater threat than that. If your carplane breaks some law, then you can follow it (secretly landing and hiding is much more difficult than just taking an unexpected turn to escape a police car on the ground).

I think you are making up unrealistic scenarios ("strawmen") on purpose to search flaws in those instead of adressing the general manner. First Biosphere 2 and now this. And to answer it: who would be so stupid and not have spare parts¿ If we have this supposedly easy metallurgy we would not even need to bring them with us. And obviously we would aim for some overproduction allt he time to have some food in storage in case of problems. Yeah, because a geodome would _obviously_ face the same reasons like weather and unexpected import of parasites, right¿ /sarcasm Yeah, single ones. Take 10000 fish and this is just a statistic. I would claim we can do the latter. But regardless, we would then aim for the 30t to be enough, everything else is bonus and allows an easier second year. What "needs" are you talking about¿ Obviousy, living on mars/moon is no luxury in the beginning. It will be corn products every second day, cheap bread every other day, and some potato mash in between or something like that. All minor vitamin problems could easily be dealt with using stuff from earth, the mass would be insignificant. There obviously is at least one stable ecosystem called "earth" (for pragmatic nitpickers: add the moon and sun into the system). Thus your argument is invalid as it did nowhere adress why or how size should matter. Because there are reasons we want them to be clean for the next use. This is not caused by the remainder being worthless waste that could not be recycled. They won't be lost in a _closed_ biosphere. That's the definition of that word. We can easily build that. What we currently lack is to get them into a biologically stable state. And we don't need such filters. Counterexample "earth" again. Sorry, but it's really annoying if your arguments are contradicted with such ease. Try making ones that actually consider the given paramters (mass, size, limited species, whatever), but your current ones are just "I don't think closed ecosystems are possible", which is obviously wrong. Yes, you adress that later and I will now get to why that's ridiculous: That's idiotic as a counterargument to biospheres. We want one that works for a couple of years. Earth obviously is and was stable for that time and even much longer. Are you now starting to use entropy as an argument against doing anything because it will be irrelevant 10^100 years from now anyway¿ And please go to everyone talking about "regenerative energy" and tell them they are so wrong for the sun being finite; please put up videos^^ I would also doubt that 10% energy increase would turn earth into venus, but that's just the smaller and completely irrelevant flaw in there. The only reason that CO2 is even relevant is because plants are allowed to store carbon as coal for almost forever. Not a relevant problem in anything like a biodome. This is not a short-term effect nd we could even prevent it from happening should we ever plan a million-year-dome. It is more generally not appropriate for anything short-term having enough of each species.

You are aware that K^2 essentially said that it should not exist for theoretical reasons¿ Anyway, all your answers follow from Newton's laws as already discussed in this thread.

Then you need to learn basic algebra. It is not that hard, especially if you work with examples and a motivation in mind. But closing your mind off by deciding "I can't do algebra" won't help.

For a start, try to understand logarithm to base 2 and 10, and their relations to 2^x and 10^x. After that try to understand natural logarithm "ln" and e^x. And stop doing this with pencil and paper; it' wont work well.

There is ongoing and partially successful research on making self-sustaining biodomes including several humans. One of them would suffice. You would need to make them somehow transportable, i.e. minimizing materials needed for walls, ground (including earth/dirt) and initialisation (you probably can't start with seeds only; but if you can, that sounds optimal). After that, fertilizer will come from the humans and possibly some smaller animals we need to stabilize the ecosystem; and maybe a small amount form chemical machines.

You may not need them for oxygen, but you need some source of food, and growing vegetables is one of the easier ways to get a sustainable food source. And if you do that you can take the oxygen that comes with it for free. It may even be necessary to use the human CO2 at places where there is no other viable source of CO2 (the moon, space).

Yes, but it also cannot tell the difference between m and -m. Any solution to it should give us another solution with negative m (and p). So how do you get that conclusion¿ No, K^2 is only talking about energy there, not momentum.

The whole idea should work. Essentially, yours is just one of many ways to generate energy and negative energy from nothing; and there is no reason why this should not be possible: E+(-E)=0 surely is correct. But I have some nitpicky engineering detail for you: You would also need to somehow disperse the momentum of the negative mass. To make things worse, friction won't work as it would accelerate it even more, just as about anything else with normal matter. You need to another magnet or something like that.

That's why I explicitely talked about gravitational mass. Negative inertial mass would not only wreck Newton's laws, but also come necessarily with negative energy and whatever other strangenesses.

That's not an answer. If it's only the gravitational mass that is negative there will definitely no problems with Newtonian physics and no infinite energy. Also having negative inert mass might have weirder effects.

There is no "2-dimensional boundary region" as you describe. For example, the version I gave does not have one, the space where the portals are looks exactly like every other part of spacetime. The only exception is the one-dimensional boundary of the portals, but that's not the effect you describe. I am reading "I have concluded" or "for obvious reasons" and such way too often in your post. Please give an actual argument instead of repeatedly claming that. There is an error: you are assuming that everything that passes through a portal has to be at some point completely contained in the portal. The example I gave does not do that, for example. As another example, you could use the same faulty reasoning to argue that all universe is motionless and there is no light: consider any frame of reference and in that a single moment in time; both matter and photons are at some time in exactly that slice of spacetime; but as you said, photons and matter cannot exist in such a lower-dimensional thing alone. While all of this being technically existing terms, this usage sounds a lot like technobabble. At least it is missing any arguments. You are aware that any soccer ball is an example of a 3-ball in 3-dimensional space¿ I simply don't get what you want to contradict here when there obviously exist such mappings. No, they are n-dimensional tunnels in n-dimensional spacetime. The (probably ill-defined) boundary would be (n-1)-dimensional. Sorry of the above sounds harsh. But I have serious troubles to understand what you want to convey, the above is the result from trying to guess.

It's indeed quite difficult to properly put it down, unless you just want to give it its own class. Mathematicians make predictions and try to check of they are true or false [or undecidable]. Yet it all happens in the mind, apart from that there is no direct relation to reality. Thus it satisfies half of each, being some hybrid.