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Supersymmetry predicts that elementary fermions and bosons exist in pairs. None of the discovered particles are such a pair to any other known particle. LHC has effectively raised the energy scale at which superpartners might exist, and that's a problem for the theory. Wikipedia article on the topic goes into a bit more detail. I don't know enough about string theory to say anything for sure, but there seem to be similar problems there. Some of the effects predicted at high energies are yet to be observed. Again, you can get the general gist of it from the Wikipedia article.

Coke and Mentos. To sponsor a propulsion system, obviously.

You are applying equations from Special Relativity to an accelerated frame of reference. That's a big no-no. If you turn around in transit, you have to use GR equations, or you have to treat everything from an external inertial frame. In either case, you'll end up showing that your FTL ship could not deliver information about consequences of event before it happens. You really do need at least two FTL ships on different trajectories communicating in transit. Like I said, I can prepare some diagrams if you think this will help. I just don't want to waste time on that if nobody is going to care. As for imaginary time, etc. Yes, at face value, using SR equations, you end up with ship heading in an imaginary direction, which should be a warning sign. Fortunately, warp drive resolves this issue. The ship itself is actually at rest with respect to the space in the bubble, so there are no issues with time doing anything weird. However, the really cool thing about the warp drive is that so long as there are no other sources of significant curvature*, we can forget all that. From perspective of exterior observer, the ship behave as an object traveling faster than light. The only difference is that time aboard the ship isn't governed by SR time dilation equations. In other words, all of the concepts about two FTL ships above can be applied to a pair of ships under Alcubierre warp metric. When we talk about the way the FTL ship under warp drive perceives the rest of the world, on the other hand, warp bubble cannot be ignored. Crew aboard such a ship cannot see a portion of the universe immediately behind the ship, and they cannot send messages to anyone directly ahead of the ship. Since two FTL ships required to set up time travel have to be moving in roughly opposite directions, they actually cannot communicate with each other as required to set up time travel. So Alcubierre Drive preserves global causal structure of asymptotically flat space-time, which is a really neat feature. * In this case, "significant curvature" means in comparison to warp bubble's own curvature. So if you are flying a warp ship through an event horizon of a "small" black hole, you'd have to do some very hairy math to figure out what's going to happen. However, even with a black hole, if it's big enough to have gentle enough curvature at the event horizon, you can basically predict how the ship will behave just by assuming it can go FTL.

We could also launch some cubesats. Nothing fancy. Just boot them out of the rear door.

The heavenly bodies themselves are on rails. I haven't checked if orbits make sense with gravitational parameters of the parent bodies. But yeah, if you use period of the Mun to get gravitational parameter of Kerbin, it doesn't necessarily have to make sense. For ships, however, gravitational constant is consistent. So if you have a ship in orbit, you should be able to compute gravitational parameter to within the precision with which you can get the values for period and semi-major axis. Keep in mind that apses are given with respect to mean sea level, so you have to add planet's radius. Alternatively, you can make measurements at different orbits and estimate that as well. Math is going to be a bit more complex for that, though.

"We have an orbital bus that we'd like to make sub-orbital, so naturally, we thought of you." But I don't think their stuff is quite in the right thrust range. The reason I thought of Virgin is that SpaceShipTwo is about 20,000lb. Engine from one of these is going to be just right.

Well, the navs can be built on the cheap. Electronics wouldn't have to live long, and I doubt it requires better radiation protection than the pilot. So you could probably just use a laptop with a GPS receiver. Just needs to be one of these unlocked receivers that can operate at 200km+ of altitude and 8km/s. Software is easy enough to write. Ditto communications. The only parts that I can't think of how to do cheap are power production and propulsion. For the later, maybe talk to Virgin? See if they'd be willing to part with one of their hybrids from SST. It has sufficient kick, and it'd be a hell of a way to test it, as well as great promotion. For power, it'd have to be solar panels. Regular solar panels are cheap enough, but something tells me these won't cut it.

Life support is pretty straight forward. Pressurizing the whole thing is just not practical. The best on-the-budget solution is a simple space-suit tied by umbilical to the life support system. Since the odds of a spark are now absolutely minimal, you can feed pure ox to the suit, requiring it to maintain only 1/5th bar. And all the "life support" is going to consist of is an air circulation system with some CO2 scrubbers and a bunch of oxygen tanks connected to it via pressure regulator valve. I can get most of the supplies at a diving store. The downside is that pilot is going to be limited to liquid food, but that's probably not an issue for a short mission. This leaves radiation protection and thermal regulation. Radiation shouldn't be too problematic. Might be worth it to look into which types of glass provide better protection, and maybe do metal coating like they do on space suit visors. Other than that, since it doesn't have to hold pressure, it doesn't have to be anything fancy. The metal body of the bus should provide adequate protection elsewhere. This leaves temperature. Again, I vote for simple solutions. Make all of the top and side coating reflective. Underneath, attach some panels reflective on one side and black on the other. Between the panels, paint alternating black and reflective stripes. Flipping panels from one position to another switches between reflective and black coat, basically. Between that and adjusting orientation of the bus, it should be possible to maintain comfortable temperature of the frame. And since there is no air, the suit is going to be in radiation equilibrium with the walls of the bus. Still leaves a lot of sub-systems. The thing will need propulsion, at least enough to re-enter. Maneuvering system. Navigation. Communication. Power. The total is going to be in millions, easy. Oh, and like I said, there needs to be a return vehicle stored on board. There is no way in hell this thing is landing in one piece. Pilot would have to bail out during re-entry procedure. Return vehicle would need to have a heat shield, parachutes, life support, communication equipment, and probably a raft, since the only sane place to re-enter would be over an ocean. It's not much, but it's still a whole separate vehicle to build and test, and this one would have to be from scratch and 100% reliable. Not cheap. P.S. And yes, I'd also vote short bus if it's meant to actually do anything up there. It would make it easier to re-enforce the frame and add all the necessary equipment. Would be easier to maneuver as well. And somehow, if you are launching a school bus into space, short bus just seems appropriate. If it's compact enough, it might fit through the back door. Or maybe, the door should be made wider. Would make things easier. Man, that'd be a wild ride. Edit: Actually, now that I think about it, does it really need to be more than a heat shield with an oxygen tank? I mean, we've already seen a person jump down from 30km. All you should really need is a heat shield.

Clearly, this would be art.

No. The most funded ones were still in a few $M ranges. But if you can fund just a few percent, it can get enough publicity going to get other sources involved. Media rights on this ought to be worth a few $M as well. Maybe Red Bull would chip in. They tend to like this sort of publicity.

Well, it'd be up to whoever fronts the cash, surely. Besides, the rocket is going to be automated anyways. It's only once the bus is in orbit that it'd need a pilot. Not entirely sure what for, though. This mission needs an appropriately insane objective. Oh, and not to sound too demanding, but I would need a return vehicle. Nothing fancy. Something similar to a Mercury capsule would do. I can push it out the back once the bus is on the re-entry trajectory. Just needs to not burn up in atmosphere and not go splat on the landing.

Precisely. It's either already in an orbit around the planet, in which case there is nothing to capture, or it's on an escape trajectory, and it's not going to be captured.

If you need a volunteer to pilot it, sign me up. I have a bit of experience with moving trucks and light planes, not to mention lots of experience playing KSP, so I figure I can drive a space bus.

If you can measure angle between your current direction of motion and a line from center of the body to your ship, yeah. Call that angle θ. It's also more convenient to use distance from center, which you can compute as r = h + R, where h is the height above the body and R is the body's radius. For KSP, you can look up the radius in the wiki. Then your specific angular momentum is L = v r sinθ. Here, v is your ship's speed. Also, you know the specific energy, which is E = v²/2 - MG/r, where M is planet's mass and G is the gravitational constant. In wiki, you can look up the value μ = GM, called gravitational parameter, directly. At the periapsis and apoapsis, θ = 90°. And values of L and E remain constant through the orbit. So you can solve the following system of equations. vaps raps = L vaps²/2 - μ/raps = E The first equation can be written 1/raps = vaps/L. Which I can now substitute into second equation. vaps²/2 - μ vaps/L - E = 0. That's a quadratic equation, which has two solutions. vaps = μ/L ± Sqrt(μ²/L² + 2E) And, of course, you can obtain raps = L/vaps now, which will give you two solutions corresponding to apoapsis and periapsis. You can use these together to determine semi-major axis and eccentricity based on equations from Sternface's link.

Which is impossible, because from far enough away, that speed is zero. Good luck finding an asteroid going with negative speed. Yeah, there have to be more than two bodies involved, because in two-body interaction energy of each body is conserved. Well, there can be some perturbations due to masses not being perfectly spherical, which can be just enough to take an object from just above escape velocity to just below, but this is extremely unlikely to happen. In practice, any real capture is going to be an n-body interaction.

Corona is easily visible because it has peak luminocity in visible band. By the time solar wind reaches Mercury, peak wavelength from thermal radiation should be in the 2-5μm range. I can't imagine it being luminous enough in visible band to be picked up by detector. I can be wrong about that, but I would need to see a source. I would be more willing to believe that it's a scattering or even refractive effect.

Based on what information?

Erm... My understanding of expansion is rather rudimentary. I can write down a very simple metric which would have expansion consistent with Hubble law, and yeah, such a metric would have a horizon - a distance from beyond which information will never reach you, and which you can never reach. So it'd be like an effective end to the universe you know or could ever know, while the universe can actually be much bigger or infinite. As far as I understand, something like that is expected to exist in our universe. But I'm a little sketchy on the details. Does that answer it somewhat?

Could you be a bit more specific? What do you want to compute based on what information? It is relatively easy to do things like compute the necessary delta-V for a transfer from one orbit to another. Or to compute amount of time it would take you to go from periapsis to apoapsis. Your question doesn't make it clear what exactly you want to know.

Inertial/relativistic mass diverges as v->c. In old convention, which you'll find in early relativity books, the symbol m and the term "mass" was reserved for such, which is why many old articles and books on relativity will say that the mass increases. Modern convention is for the term to mean invariant/rest mass, which is always the same. In the old books, you would frequently see it denoted as m0, but now we just use m. The conversion factor should look familiar. mrel = γm. And since Lorentz factor, γ, goes to infinity as v does, so does relativistic mass.

I have to ask a potentially stupid question. Are we actually seeing solar wind on this image? Looks too persistent to be just noise, and direction matches, but does it really have sufficient density to be visible? Or does the choice of spectrum have something to do with it?

You do realize it's been nearly a century since General Relativity got published and more than a century since Special Relativity, right? You do realize we've been probing the hell out of both in the mean time. Not only have we not found any problems with GR, but it's now the most precisely tested theory. Furthermore, it packs neatly into our understanding of field theories in general. Yes, we now have many more, stemming from both relativity and quantum mechanics. We now understand the relationship between geometrical properties of space-time and the fundamental symmetry groups. And while precise mathematical formulation of Grand Unified theory still remains problematic, we do know how General Relativity fits into it and that speed of light is built in as one of its fundamental properties. As for your misconception of what constitutes theories and laws, it could not be further from the truth. Laws are just observational rules of thumb. Like Newton's Laws. They are not derived from any deeper principles, but rather stem from empirical observation directly. A proper scientific theory is an entire construct which based on some postulates derives a model with mathematical precision. The fact that we call General Relativity a scientific theory puts it on the highest pedestal of reliability. We already know how to break the global light barrier. There is warp drive and there are wormholes. You are not satisfied with that, for some reason, even though that's the practical way of "bending" the laws. Instead, you want to break the local light barrier which serves absolutely no purpose and only leads to a complete and total breakdown of all known physics. Even if it's possible beyond all measurable bounds we've established, why? What in the world would be the point of that?

A single FTL traveler does not break causality. The reason is that FTL travel is between space-like separated events by definition. So if in some reference frame event A causes event B, meaning they are time-like separated, a FTL traveler can observe event B occur before event A takes place. However, he cannot send a signal to location of A to reach it before A happens, so he still cannot cause any paradoxes. It takes two FTL travelers going in different directions and communicating in transit. So the first traveler, having observed B take place, can send a message to second traveler saying, "I saw B happen because of A." The second traveler can now arrive at location of A before A takes place and avert it, causing a paradox. (Edit: I can draw some space-time diagrams, if anyone thinks it would help.) The reason a single traveler cannot just turn around and head back to A is that acceleration will cause enough time dilation to prevent arrival in time. Take a look at twin paradox for a sub-light version of that. The cool thing about the communication requirement? Two ships under Alcubierre Drive cannot communicate in such a manner without having their warp bubbles cross. Bubbles crossing would be very bad mojo, however, so we can exclude this possibility, meaning that we can have FTL Alcubierre-like warp ships without worrying about breaking causality. There are other situations when FTL ship can act as a time machine, and there the Alcubierre Drive actually works, but it requires a space-time that's very far from flat.

That's the cool thing about Hafnium-178. Its m2 nuclear isomer has a half-life of about 30 years. In other words, it stores relatively well. Furthermore, the transition is entirely into electromagnetic radiation, so in theory, you can get it to lase, making it give up its energy in short time. And there is a lot of energy there. About 2MeV per nucleus, which gives you about 100 thousand times better energy density than any chemical fuel. Huge amount of energy, releases on demand, no neutron radiation, and it only loses half of the "charge" in three decades. Comparisons to Californium or any other fission fuel are absolutely useless. The DARPA TRIP document, which was finally declassified a few years ago, suggests that it would cost about 1$/J of energy stored, however. So with current technologies, we can't make good use of 178Hf, but as we get better understanding of the nucleus, we might be able to improve on that. In fact, there are already better techniques available for production than were around during DARPA's TRIP project.

This is kind of up to interpretation, but if you describe strong interaction between nucleons as virtual gluon exchange, then the nucleons can be non-color-neutral during the exchange. So a green proton is easy. I know that's not what you meant, but I found it humorous. No ideas on the "dirty" part, though. Sorry.