K^2

Sangam seems to be using Cartesian and simply integrating the forces. It kinds of sounds like he (or she) is forgetting to include force from the primary into the integration. Foce between two satellites alone would be insufficient to maintain orbit, so it would be consistent with distance constantly increasing. More Boosters is right, though. Distance between two satellites in co-planar circular orbits is perfectly described by law of cosines, with period given by abs(T1-T2)/(T1T2)

This is in reply to a comment from another thread. I've figured it's worth a proper response for the sake of anyone who is likewise misinformed or just curious about quantum transitions, and it has taken me a bit longer to put this together than I anticipated, so I am posting this as a new thread. Hopefully, a discussion to follow will be worth a thread. To keep things simple, let us consider a harmonic oscilaltor, rather than an atom, since oscillator can be described with just one dimension. The spectrum of a quantum harmonic oscillator is descrete, same as that of an atom, but unlike an atom, all of its energies are separated by an equal spacing of ћÉ between levels. Nonetheless, it serves as a simpler analog fo the purposes of this discussion. What's going to follow is a bunch of math describing the system. If you don't care or end up giving up on following the math, skip to the pictures! Dynamics of any quantum system is governed by Hamiltonian. In classical analog, it's the energy of the system. Given a Hamiltonian H, any physical state |È> of the system must satisfy H|È> = iћ∂t|È>, which is known as time-dependent Shrodinger equation. Just like classical oscillator, the total energy is sum of kinetic and potential, which gives rise to the Hamiltonian. H = p²/2m + kx²/2 There is a set of time-independent solutions to this equation that satisfies H|Èn> = (n+1/2)ћÉ |Èn>. Energy of each of these state is precisely (n+1/2)ћÉ, which is the eigen value of the Hamiltonian operator. Any other physical solution is a superposition of these states, and can be written as |È> = Σ bn|Èn> for some set of complex numbers bn that satisfy Σ |bn|² = 1. In other words, any solution is a superposition of eigen states of the system, such that total probability of finding system in one of the eigen states is 1. We wish to describe system in terms of these eigen states, for which there is a much more convenient formalism of rasing and lowering operators. (See Quantum Harmonic Oscillator for more details.) H|È> = ћÉ(a†a + 1/2)|È> We can also write down interaction with external field using these operators. Specifically, we wish to hit this oscillator with an electromagnetic field of frequency ν. I am going to demonstrate that so long as ν = É, the energy of incoming photon is absorbed. Otherwise, energy cannot be absorbed, and there is no transition to higher levels. Because position is proportional to a†+ a, we can describe the interaction with the electromagnetic field of incoming photon as follows. H|È> = [ћÉ(a†a + 1/2) + (a†+ a)qE cos(νt)]|È> (There is a constant in there, dependent on É, which I absorbed into charge, q for simplicity.) Finally, while there is no clean way to solve this algebraically, we have everything we need to solve it numerically. ∂/∂t |È> = -i/Ñ› H|È> While one could solve this in coordinate space, it is far easier to use the fact that we have a convenient basis and re-write the equation in the following way. ∂bi/∂t = Hij bj Where bi are the aforementioned complex numbers describing the system in term of its superposition of eigen states of the non-interacting Hamiltonain, and Hij is the matrix representation of the interacting Hamiltonian. At this point, we might as well just plug these matrix representations into computer and make it do the hard work. The following are the results. First, we hit the sytem with a resonant wave. ν = É The top part of the image shows probability distribution for the charged particle. It's clear that under influence of the incoming energy, particle begins to oscillate. Which is what we expect. It's also clear that it does so in continuous fashion. Gradually building up the sing. The bottom part shows corresponding energy levels in multiples of ћÉ. They are discrete. Energy is not a gradual distribution. Particle starts out at precisely (1/2) ћÉ and then starts gaining higher energy elevels with no states anywhere in between. This leaves just one more things to consider. What happens if energies don't match? Here is the simulation with ν = 1.5 É Note that while there is some effect, oscillations finally die down. (The electromagnetic wave keeps hitting the system, it does not go away.) Once oscillations die down, process repeats. There is slight and brief excitation of second energy level, but it quickly vanishes. The net transfer of energy from photon to the particle is zero. However, the fact that particle did move a little has an effect. And this happens with atomic excitations as well. The fact that glass has no transitions invisible light means that it does not absorb light. But there are transitions close to visible light, which is what gives glass an optical density. This interaction "slows down" the electromagnetic wave without ever absorbing it. The conclusion is pretty straight forward. The description in Chemistry texts and some popular science articles about electrons "jumping" orbitals in atoms is a gross oversimplification. Electron never jumps. The electron cloud transitions gradually from one orbit to another over time. Likewise, probability of finding electron in ground or excited state transitions gradually. The only thing that "jumps" is the actual energy. It never matches an intermediate value between the two states. The main difference between atom and simulations above is that in an atom, all energy levels are different. That's what allows a transition from one state to another, rather than to a distribution of states in the simulation. Otherwise, results are very similar, and the atomic orbital does look llike it's forced into rotation by the oscillating EM field. Maybe one day I'll actually have time to put together some animations for these as well.

Absolutely wrong. Orbital transition is a gradual process that takes finite time. Electron, at no point, jumps from one orbital to another. The energy states are discrete, and during transition, the electron goes through a superposition between the two energy states. However, wave function is simply a linear combination of the two eigen states at every point in between, giving a smooth evolution of the probability distribution function from one state to another. Likewise, all of your "conclusions" on this misunderstanding of how basic QM works are completely wrong.

Sure. Slightly negative pitch can reduce the stall section during vertical auto-rotation. But you need to understand that a) it's not critical, and the angle of attack remains positive. Outer section is the one that generates all the lift for you during auto-rotation. Sure, you can reduce pitch there to cut the drag. It will also reduce lift, and you'll be coming down like a rock. That does not seem like a sound plan. The reason heli blades have higher pitch near the hub is because it makes sense during powered flight. The relative wind points down, so as the horizontal speed of the blade is lower near the hub, the pitch needs to be higher to get good angle of attack. Unfortunately, that leads to significant stall section on a prop during auto-rotation. Autogyro blades tend not to have that twist, because for them, the airstream is always from bellow. That allows autogyro rotor to operate with no stall section. It goes from driving to driven. Still, I can't say I've ever seen an autogyro with an opposite twist on the blade, to have a slightly negative pitch near the hub. They might exist, though. It would make perfect sense for an autogyro. But again, the critical part here is that you don't have to have that negative pitch near the hub or anywhere else on the prop. Auto-rotation relies on blades "gliding" down to generate rotation, not on turbine effect. The reason is that with auto-rotation you want to generate as much lift as possible, while with a turbine, you want to generate as much torque as possible. Hence one has positive angle of attack, the other negative. Hm. Maybe they filter by IP. I'm going to change it to http from https. Maybe it will help. Try again. Yeah, source is about FAA regs on the matter, not on aerodynamics of it. I've intentionally avoided making any specific claims in that sentence. Just took away the part about negative pitch, which was absolutely not true for helicopters (even if they are neg-pitch capable, pitch is higher near the hub), and might only be true for some autogyros. I doubt this will cause a discussion, but if it is, it'll get resolved in a talk page. Yes, both vertical and horizontal auto-rotation work the same way. Although, your typical general aviation helicopters tend to settle much faster in vertical auto-rotation, so coming in at an angle is highly recommended when possible. The reason is the aforementioned stall region on a general aviation heli. It's still there even if you come down at an angle, but you get more lift from the driven section, so you are still better off. Autogyros tend to be designed for horizontal flight, so it's very difficult to get them to settle vertically. But some lighter ones are capable of almost vertical, zero-roll landings.

The contract/expand analogy is a very bad one for warp-drive, both because it isn't exactly what happens, and because it leads to some bad intuition. Such as the statement that we can contract, but can't expand. Alcubierre Drive ONLY has negative energy density, which does both "contracting" and "expanding". And it's possible to come up with positive-definite stress-energy densities that do both as well. For example, consider Schwarzschild in moving reverence frame. But the crux of it is that FTL and FTL-capable warp metrics allow for CTCs, which appears to require negative energy densities. A sub-light warp doesn't have to. But sub-light warp doesn't have the simplicity of Alcubierre Drive, which makes it extremely difficult to come up with a warp scheme which conserves currents and has positive-definite stress-energy density.

Limiting factor is likely to be power, not capacity. Cellphone battery would give you about 1HP if it gave up all of its charge in 1 minute. I don't think any cellphone battery could survive that.

A fly-by-wire hybrid drive quadcopter is a bit different than the way they originally presented the concept. But I suppose, there's nothing wrong with ideas evolving. This is all quite sensible. In this case, they'll probably have to put a governor to limit air speed to 55 KIAS for the ultralight package, and they can have a pro version with no such restriction, which actually requires a rotor PPL. That version can come with a larger gas tank as well. Perhaps even additional instrumentation for IFR flight, etc. A rider seat? So many possibilities! Speaking of possibilities, if they go with hybrid drive, they can absolutely add a battery to cover main engine failure, and even deduct it from total weight limit, since it'd count as safety equipment. As for landing on motor failure, that's trickier. But yeah, going to two motors, using third for steering actually sounds reasonable. I don't see why it couldn't run an electric motor in reverse to help balance the thing. Actual auto-rotation is out of the question, though. There is absolutely no reason to make props variable pitch, and something that's built to work as an efficient ducted fan simply cannot auto-rotate. I guess they'll have to go with parachutes, same as Martin's, to cover these requirements. And have hover-to-land as a low altitude failure mode. Yeah, it's an optional piece of equipment that makes takeoff way easier. Before these became standard, you had to have people on the ground actually spin the rotor manually to get it going. PitA that is. So modern autogyros do tend to have a drive from the main engine that lets you pre-spin the rotor during takeoff. As you've said, though, it doesn't have nearly enough power for actual flight.

Blargh. Sorry. Substitute "Lepton" everywhere I wrote fermion in that post. It was late.

It's all about the lift. And the picture I gave you shows why this doesn't happen. Note that on all 3 sections relative wind points up. The flow is same as on your picture. Note that on middle section the net aerodynamic force points FORWARD, which keeps the blade turning. It does not stall, despite all three section having positive pitch and wind going up. That's the most fundamental thing they teach about auto-rotation. Know what? Lets go for some hard quotes. Here is my copy of Rotorcraft Flying Handbook, published by U.S. Department of Transportation for Federal Aviation Administration, publication number FAA-H-8083-21. Chapter 3 - Aerodynamics of Flight. (This is actually where images on Wiki were taken from.) I added the emphasis on the critical part of this statement. Pitch is more positive near the center, in the driving region. It is NEVER negative. (Edit: As with most FAA publications, this one is available on-line as well. Here is a link: Rotorcraft Flying Handbook. Please, take a look at section 3-10, and in particular, figure 3-22.) That section was written by a complete idiot. I will fix it with a reference to the flight manual. Thank you for bringing it o my attention. (Edit: The article has now been corrected. The actual aerodynamics of auto-rotation is better explained in the external link at the bottom of the page. Aerodynamics of Autorotation) They are discussing body pitch. You do point the helicopter down, towards the ground. But this is also the case in forward flight, see your own image. If anything, body pitch is less negative in auto-rotation. Again, see your own image. What we are talking about is blade pitch. Also known as collective. That always remains positive. There are VERY few aircraft that are even capable of generating negative pitch on collective. These are usually military and high performance stunt choppers that are designed to be capable of brief inverted flight. They can actually benefit from negative pitch. In virtually all commercial aircraft, pitch remains positive. In many autogyros, not only is the pitch positive, but it's fixed and cannot be changed. If you are still confused about how the blade can keep turning forward despite positive pitch, I can try and help with that. But we first need to establish that this is the case. If you need to go out and see a real helicopter, and convince yourself that inner part of the blade has higher pitch, then do so.

Why are you making all these threads for things you don't understand, then get offended when it's pointed out that you don't understand them? Fine, I'll go through it once more. The conservation laws are tested far more precisely by indirect means. Every single computation on self-interaction includes innumerable delta functions for 4-momentum conservation at each vertex. These produce computations that are verified to up to 12 decimal places. Similarly, DIS events test these conservation laws at far higher energy ranges. While precision there isn't quite as high, all of them fall within predicted ranges. Main advantage of wake field accelerators is in how simple a device can be that achieves high energy scales. We have plenty of facilities that specialize in fermion acceleration. I've done summer work at one, namely, Jefferson National Laboratory. If that's all you're interested in, there is plenty of data on fermion-fermion and fermion-nucleon collisions.

Cool story. Show me an article that claims that Higgs is responsible for inertia. Not a news article about one, or a citation from someone in a news paper. An actual, published scientific paper.

No, no, no. Pitch always remains positive. Now, a helicopter can perform a collective flare, where pitch is dramatically increased right before hitting the ground, which does allow for softer landing. But even on aircraft with fixed pitch, such as majority of autogyros, it always remains positive for the duration of auto-rotation. It might seem counter-intuitive that propeller keeps rotating in the same direction despite air flow direction changing and pitch remaining positive, but it is indeed so. Here is an image that illustrates how it works. The three sections correspond to stalled, driving, and driven regions from Wiki respectively. The w vector shows relative wind. It's more vertical in stalled region because blade moves slower close to the hub. The actual pitch of the blade is roughly constant throughout, but the angle of attack changes because angle of relative wind changes. In the driving region, drag is very small, and relative wind is pretty vertical. Lift is much higher than drag here, so the net force on the blade actually forces it to rotate forward. This is similar to how the glider keeps going forward despite maintaining positive angle of attack. In contrast, while driven portion actually generates more lift, it also generates significantly more drag, and because the relative wind is more horizontal here, the net force ends up against motion of the blade. Torque on driving and driven portions of the blade ends up balancing each other out, providing constant rate of revolution of the main rotor during descent.

Again, you are jumping to discussion of serious science without understanding the basics. Hadron scattering is a process that only becomes perturbative at absurd energy scales. Relevant regions are dominated by non-perturbative QCD, which is where people make careers in particle physics currently. Until you can understand scattering in classical QM, which you've made no indication of having any grasp of, there is no point in even discussing this with you.

Autogyro is always auto-rotating. There is no power to the main rotor. That's the whole point. And no, you don't invert the pitch for the auto-rotation. Merely reduce it, so that the driving section does not stall. You might benefit from reading Wikipedia's article on auto-rotation. I seem to recall that it was pretty detailed.

Ugh. If we do this, we'll never go anywhere. We'll just keep sending better and better robots until they don't need us anymore. Call me a Luddite, but I wholeselfishly object to that course of progress.

Ground-effect aircraft will "auto-rotate" on inertia of the blades alone long enough to settle down, even without variable collective pitch. (Yes, I realize that this isn't technically auto-rotation, but it serves the same purpose.) And I have no idea what you mean about speed limits. The 55 knots is more than generous enough. I doubt that Malloy's could top that. Or do you mean the power-off stall speed? That, indeed, does not apply to rotorcraft. The aforementioned auto-rotation condition applies instead. The bottom line, from perspective of FAA, is whether the aircraft can be landed safely in case of engine failure. So long as there is a way to do so, they are happy to grant you an exemption even if you don't fit the exact letter of the regs. Martin's Jetpack is a good example. They've substituted an emergency parachute for glide/auto-rotate capability. And as I've indicated above, there is no reason why Malloy's wouldn't be capable of safe landing on engine failure, unless you're doing something stupid. Now, it'd be pretty easy to crash on power failure, by simply fighting natural descent and trying to keep going at full speed. You'll still descend gently enough, but that won't help you much if your stands catch on the ground going 40 knots. On the other hand, that's not terribly different from any rotorcraft. Just because they can auto-rotate, doesn't mean they'll do that without pilot's help. In case of quad-like ground-effect craft, proper procedure in event of engine failure will be hard pitch away from direction of travel. That will rapidly kill the ground speed while also supplementing lift, allowing gentle landing. You'd have less than a second to react, but since pitching "back" when you start dropping should be normal thing to do even during normal operation, as it recovers altitude faster than throttling up, I don't expect it will be particularly difficult to land safely.

That's because you don't know any physics and keep extrapolating from computations carried out by third parties under irrelevant constraints. One of the key restrictions of FTL warp is bubble wall thickness. That simply isn't an issue for sub-light, since there are no causality concerns. Taking sigma = 1, even Alcubierre metric yields -5x1020J, or about 6 metric tons worth of exotic energy for a bubble 20m in diameter traveling at 100km/s. Other than the negative sign, this is an entirely reasonable amount. In fact, we are getting close to energy densities we can achieve with plasma in magnetic confinement. I couldn't tell you precisely what that plasma needs to be doing or what sort of mag fields it will take to keep it there without knowing the correct metric for a sub-light warp, but absolutely everything indicates that these are going to be reasonable quantities. Not your everyday amounts, but achievable by an organized effort. Will it be practical compared to ion drives? Hard to tell. One of the potential advantages is "regenerative braking" ability of a warp drive. For example, a cycler ship can transition to warp to complete the long part of its journey, and drop out of warp near each of its destination planets to pick up cargo and passengers, while spending very little energy to switch between warp and normal orbit. Even if ion drives end up way more efficient for a single leg, a sub-light warp cycler might be just the sort of thing that makes travel around Solar system actually economically viable. Finally, comparison of warp and EMDrive is just silly. One is a prediction of a well-established theory, the other is a mistake that nobody has invested enough effort into correcting.

It's not just violation of known principles. It's violation of the most fundamental principles that have been tested in most precise experiments we have. Some specifically designed to test these principles. We've gotten to multi-TeV levels with these. You are not going to violate these principles with a cheaply-built microwave cavity. This is the same level of absurd as expecting one of the perpetual mobile devices on YouTube to work.

Collision cross-section has very little to do with size of the particle. This is real particle physics. If you actually want to understand something about it, start with Compton Scattering. But proton-proton cross-sections are actually a fairly complex topic.

Stop saying that nonsense. Higgs has NOTHING to do with inertia. Just stop. Warp drives come in two fundamental flavors: FTL and sub-light. There is a conjecture in General Relativity that states that any FTL travel requires negative energy density. (It's more complicated than that, but that's how it applies to warp.) All known warp configurations of space-time are FTL-capable, and so all require negative energy density. In fact, they are all variations on Alcubierre Drive. We're likely never be able to get around that limitation. I wouldn't give up on FTL warp completely, but there are still things we don't fully understand about vacuum to speculate about ways of achieving negative energy densities required. Let alone start talking about technical feasibility of it. On the other hand, there is absolutely nothing in modern physics that puts prohibitive limits on sub-light warp. So there is hope there. Sub-light warp would still be affected by relativistic effects, and must obey current conservation laws, most notably energy and momentum conservation. Which limits its use in a Solar System. But it should require dramatically less energy than FTL warp, has way fewer problems with radiation, and still lets you get around the tyranny of rocket formula. However, I am not aware of a single pure sub-light warp configuration. All we know at the moment is that there is no reason for one not to exist.

You've blown way past critical current. Keep in mind that it's current density, and not the absolute current in practice.

Of course you can't build from neutronium. That's what scrith is for.

It's not usually the mag field that kills superconductivity directly at high Amps. Though, obviously, that's one of the limiting factors. What you really end up with is a critical surface in the T-H-I space. So the closer you get to TC, for example, the less mag field and current the material can withstand before transitioning. Which is why vacuum pumps are a common feature of modern SC magnet. They help drop temperature to the 1K-2K ranges, allowing for higher critical fields and currents. Long story short, yeah, you won't be pushing amps through a grephene sc. In fact, I'm not quite clear on what the point is. We have great HTSCs, and way, way better conventional SCs as well. When I saw an article, I was expecting to see some absurdly high TC, maybe even room temp, but then I saw the 5.9K, and the only question I have is why anyone bothered reporting this?

None of the proposed systems have been able to generate thrust > drag at any speed that's sufficient for fusion, sorry. Angel, fact that ramming for matter for matter-antimatter drive is a bad idea is actually very easy to demonstrate. What might work way better is ramming for matter for an ion drive that you'll power with your matter-antimatter reactor. If you have no intention of going past 0.1c or so, that might actually work better than a pure matter-antimatter photon drive.

Well, here is the deal, more or less. At the base level, what we are talking about is not so much gravity or acceleration, but curvature. Each star within a galaxy or galaxy within a cluster is in free-fall. From perspective of differential geometry, it moves along the closest thing to a straight line in curved space-time - the geodesic. By watching these objects move we can plot out the geodesics and deduce the curvature. This is not how we actually compute these things, but it's easier to picture this way. So in effect, we are measuring curvature. This is where General Relativity comes in. We know how curvature corresponds to stress-energy density. The relation is given by Einstein Field Equation. We plug in our observations and obtain some sort of stress-energy distribution. It's a rank two tensor at every point. However, due to certain properties of GR, we can select a coordinate system, at least locally, that puts that tensor in diagonal form. Woot! So what do we get? We get two quantities. One that scales like energy and one that scales like pressure. Parts of energy and pressure density that we observe we can account for with luminous matter, which has both energy and pressure. However, majority of these, by far, is unaccounted for. And this is where things turn for the confusing, for you see, the Dark Energy is the unaccounted for portion of the pressure term. And Dark Matter is unaccounted for portion of the energy term, because this is the E = mc² situation. Tyson is absolutely correct in pointing out that we don't really know that Dark Matter is some sort of a particle. And really, the "Matter" here is just to indicate that it corresponds to the same part of stress-energy as normal matter does. Whereas Dark Energy corresponds to the part that you don't usually associate with matter. Not in these sort of quantities. Is the naming confusing? Yeah. I suppose, Dark Stress-Energy would have been better, but it's a mouthful. But I also don't like the idea of calling Dark Matter portion the Dark Gravity. It really doesn't reduce the confusion, since both attraction and repulsion are part of gravity here. Even though repulsion is not something we usually associate with classical gravity. Anyways, people who work in relevant fields are used to this, and people who don't will probably be confused regardless. I don't think it'd be worth changing.