K^2

In either case, our data doesn't show any deviation from fair coin. At 125 tosses, expectation is at 62.5 ± 5.6 heads. We're at 59, which is slightly over half sigma off. p > 0.62 is not what I'd call suspect. Maybe with more data.

It might be worth pointing out that this isn't an exact answer. It's a good starting point, and might be all you need for a sim, but it won't be quite right. For starters, reduced mass is giong to be a factor here. Even if the star is taken to be stationary, planet is clearly being simulated. So planet's-to-moon's mass ratio is going to be important. But even outside of that, you're firmly in the 3-body world here. Even with a stationary star, the planet-moon system experiences a periodic perturbation. If they are close to resonance, big trouble. If not, it will still cause a slight change in moon's period. So even with reduced masses in place, the orbital velocity will be slightly off. And that's likely to keep happening. a) I'm pretty sure your simulation will have significant errors. At that scale, there is going to be significant interaction between the two orbits. Either one of these might have been alright, but toghether, you're pretty much guaranteed an ejected moon.

And you don't think it's a problem? I'm yet to see a paper that backs up your claims.

I'm going to say it's closer to 100-300 times, allowing normal life on Mars' surface. Proof by fabrication. It's fun for everyone! Also, completely useless. Available hypogravity research is very limited, but what we have points to even small amount of persistent gravity making a huge difference. We will know a lot more once the centrifuge module is built on ISS, but right now, there is no reason to think that Mars' gravity is insufficient. It might be. But it's total speculation.

The actual ISP and power/thrust are well within the parameters of an ion drive. These are the absolute physical limitations. The fact that actual power transfer is way more efficient than in any existing ion drive could be within the realm of Quantum Weirdnessâ„¢. There are number of effects that work along this line. Laser is a good example. Mossbauer Effect is another one. Certainly, if there are no measurement errors in thrust output or energy input, something very weird is going on. But it is far, far easier to believe that what we are seeing is interaction with macroscopic quantum state explained by some nuance of condensed matter physics, then that it is a reaction-free drive. One is a Nobel Prize discovery, the other is finding that all of our physics is wrong, and we've been getting correct results from a totally wrong system of assumptions by pure chance. Smart money is doubling down on ion propulsion. Such a configuration does not conserve charges, so it's impossible to achieve. A lot of the problems in GR appear to be paradoxical, until you introduce actual matter fields and see that configuration in question is simply impossible.

Well, yes. 1) is also wrong. The rocket formula is not strictly correct, once you take relativity into account. Your actual dV will be slightly less than you expect. But at "normal" speeds, the deficiency is negligible. When you get close to light speed, discrepancy becomes huge. But the reason it's wrong still goes back to the velocity addition formula. The correct formula is kind of ugly. But the key to derivation is recognizing that proper acceleration is frame-independent. Which allows you to integrate proper velocity over time. Once you correct for the fact that fuel is expended at a rate proportional to proper time, you can integrate for total velocity gained as function of classical dV. And yes, you always end up with less than dV. Edit: Special Relativity tends to be pretty straight forward, but once accelerations get involved, some formulae get ugly and derivations tedious. Rocket formula is definitely one of these.

Ditto. And we'll have it that much faster if funding is focused on looking for exhaust, rather than "quantum foam" nonsense. Now, mind, I don't exclude possibility that there is a quantum plasma/foam intermediate, which would be kind of cool. But it's irrelevant until we track down what actually carries away momentum.

All of which is equivalent to unicorn-in-a-box. EM Drive is reported to produce a force. That means there has to be a stress-energy current leaving the thing. That means either a) Massive exhaust, or Environment to push from. Why can't vacuum be suitable environment to push from? Because it'd need to have quite a bit of mass. Now, vacuum might be massive, but we'd detect that much mass long time ago. Why can't it be virtual particle exhaust? Because somewhere down stream you must have massive particles carrying away the current. Virtual particles can't propagate out to infinity. Energy required to create massive particles downstream would be enormous. Far greater than energy consumption of EM Drive. Every other "explanation" falls onto some combination of the above. This leaves us with just two possibilities. a) There is massive environment besides vacuum, such as residual atmosphere, that the craft pushes from. and/or It's leaking something. In other words, it acts either like a normal rocket or a normal jet engine in terms of how it interacts with reaction mass. Either one can still be useful, because everything points to it being damn efficient. But it still uses reaction mass. So it will either need a supply that it can run out of, or it can only operate in LEO. Making it just an efficient ion drive.

Potato, potato. ... Wow, that just doesn't work on a forum. What I mean is, there isn't a difference. One will lead to the other eventually. The only question is whether it will be an evolution or revolution. Our cybernetics are severely lagging our tech, but fortunately, so does our robotic. So there is still a chance for a smooth transition, where we won't really notice how we became the machines replacing the human workforce.

Velocities don't add like that in relativity. See this link.

Lets see, does Warp Drive violate local Poincare symmetry? No. Actually, it's the consequence of it. So Warp Drive works because momentum is conserved. If you'd actually studied field theory and relativity, you'd know these things. And you'd be able to tell what is and is not a violation. This isn't something people just make up. There are firm, mathematical definitions for absolutely all of it. Of course, it's much easier for you just to use your ignorance as cover and pretend that everyone else is just as ignorant. How's that working out?

That barrier will resolve itself once robots replace customers.

Again, same argument. Do you know the history behind the "game changers"? Do you understand why conservation laws are different? Do you know why they are fundamental? Any of this? Then what in the world gives you the idea that you have a better idea about how likely it is than somebody who has spent a decade or longer actually studying these things? We have knowledge necessary to gauge how unlikely this is. It's absurdly unlikely. It would be a waste of time trying to verify these things. Not to mention that it's practically a problem of proving the negative. Any hypothesis of EM Drive's operation that assumes violation of the conservation laws is false by any practical measure. We do not need to investigate these. And if you'd like to spend a decade of your life and actually learn some field theory, we can have a discussion about the specific reasons. But by then, you'll probably already understand.

That would change pretty fast once it starts raining.

Tail wags the dog. Critical thinkers tend to be atheists. Critical thinkers don't expect miracles. They know what the odds are that this is new physics, vs just a very weird application of well-known science. And to be clear, a lot of people criticizing this thing are very far from being laymen. I have over a decade of academia to back me up. And what actually annoys me is not whether or not this thing works, but how people with absolutely zero knowledge in any relevant field jump in and start arguing the "you can't possibly know," angle.

Well, you need something to sustain the field. I'm guessing, it would involve a planet-wide network of superconductors. But you will still need that energy to energize the magnets.

Ayup. Photon drive is the most effective a reaction drive can be, giving you effective ISP of c. But relativistic rocket formula is tricky if your velocity changes significantly. In general geometry, sure. But Earth results in almost perfect Schwarzschild geometry, which isn't usable for this. And while there are gradients you could probably grab onto, they are absolutely miniscule. You'd need a much larger system to produce far less thrust than is reported. In the end, momentum still needs to be transferred to something. If you are using space-time curvature to push from, you are effectively using gravity of the planet bellow you to transfer momentum to it. You don't need General Relativity to understand how it works or how weak the effect is going to be for Earth. You only other options are to have propellant. If you don't bring any mass with you, or don't have medium to push from, best you can do is aforementioned photon drive. A warp drive still can't produce thrust in vacuum. It can move an object, but not generate a force against it. This goes back to conservation of momentum and the notion above about propellant. Now, could the system be generating a weak warp field that simply deflects nearby matter? Sure. But it's very unlikely that we are generating a strong enough warp field here to account for that much thrust. It would be very obvious. So it still leaves us with two plausible explanations. Either the drive produces exhaust, or it interacts with medium. I'm still betting on the former, because it's been reported that resonance chambers with perfect vacuum did not work as well. A piece of polymer in the chamber, which is known to evaporate under test conditions, gives much higher "thrust". So it's still very likely that the thing simply manages to work like an ion drive. If it's managing to produce thrust from interaction with environment, on the other hand, there might be some interesting applications to the system. It's worth looking into. You have absolutely no idea what you are talking about. The words "negative energy" can be replaced with "pixie dust" in your sentence with no change to the meaning.

I agree about gravitational charge, since that's stress-energy, anyways. In fact, I'd simply avoid thinking of mass as ever being the gravitational charge. But inertia? Relativistic mass completely agrees with concept of inertia. A particle moving at relativistic velocities requires disproportionately higher impulse to deflect it. That happens to scale precisely with relativistic mass, and precisely because p = mrelv. I agree that one should be very careful with the concept, but it's not "useless" if you know what it really means. Relativistic mass provides some neat algebraic shortcuts for these who know what they are doing. Frame-dependent quantities aren't bad. They are still important. You just have to be aware of how they transform from a frame to frame. When you are dealing with relativity, keeping track of your frames is important anyhow. There is no added complexity here.

Energy density of Earth's magnetic field is about 0.5-1 mPa. So on the order of 1016J to re-magnetize Mars. That's a "few" years of Earth's total energy consumption. Keeping in mind that I did a very rough estimate for total energy which could be more than an order of magnitude off. So we can be talking weeks or decades instead of years. But these are comprehensible amounts of energy even now.

We might be able to increase pressure by using heavier buffer gases. Since oxygen's partial pressure would still be just enough for breathing, it wouldn't escape any faster than without a buffer gas, but total pressure would be higher, and oxygen would be diluted. Both are very good things. Unfortunately, it's hard to come up with a good, heavy buffer that is easy to get in planet-wide quantities. And I mean even in comparison to such a gargantuan task as simply dumping enough CO2 or water vapor into atmo to offset the pressure. As for gravity itself, I don't think it's going to be a huge problem. It's low, but it's within adaptable range. With the right exercise regimen, it should be possible to live on Mars long-term without ill effects to health. This leaves the next big problem. Lack of the mag-field. Re-magnetizing Mars is going to be one of the pre-requisites to making it livable. Not only is it bad enough that it's going to be irradiated, but radiation is going to be breaking down water vapor, and the planet will keep losing hydrogen, like it did in the past.

Do you happen to know how precisely our velocity relative to CMB has been measured? It'd be a very curious number to know.

Science is about systematic building of knowledge. Using existing knowledge is not bias. It's what science is all about. It never assumes existing knowledge to be infallible, but every observation reduced the odds of an error. We cannot possibly explore every possibility. The only way to move forward is discounting the unlikely ones. You cannot prove beyond shadow of a doubt that water that's been sent in a vial made of pure sapphire to Mars and back when Earth and Mars are at their closest approach is not a cure for all known disease. Should we actually fund such an endeavor? Absolutely not. Looking for ways that EM Drive might be violating conservation of momentum is a waste of time. It's like spending your entire pay check on lottery tickets. Sure, if you win, it's going to be all kinds of beneficial. But you aren't going to. Not in any likely scenario.

No, I'm talking about the term that goes with (t')². That's the term that acts as gravity on a static object. (To clarify, I'm using primes to denote derivatives with respect to proper time.) Starting with u' = -Γuu, I get the following for r' in natural units and rs = 1. r'' = - (r - r²)(r')² / (2 (1-1/r)² r4) + (r - r²)(t')² / (2 r4) - (r - r²)(θ')² / r The first term is relevant to GR only. Second term is gravity. Third term is centrifugal. In the classical limit of the r >> 1, the above reduces to r'' = -1/(2r²) + r(θ')², which is precisely the classical result for M = 1/2. Now, the only context in which I can even imagine the words "effective potential" to apply to this problem is finding V, such that Hamilton's Equations for H = x'p/2 + V give the above EQMs. I don't see how you can get that (r - r²)/r4 out of a cubic term in V. Edit: And it does look consistent with equations from the paper you've linked, with the right choice of λ(Ä).

Sure. But I don't think people appreciate the sort of odds we are talking about here. Conservation of charges, including momentum, is the most fundamental thing we have. Absolutely every branch of modern science, in one way or another, takes these as root assumptions. The odds of there being a way to violate these isn't a matter of one in a thousand, or a million. It's the sort of thing with so many zeroes that it makes chances of finding an atom you lost on the other side of the universe to be reasonable in comparison. This could be a new reactionless drive that violates known laws of physics. And I could run into a T-Rex on my drive to work. Yet I am not planning to keep an elephant gun in my trunk for that event. Keeping priorities straight is important here. We are looking for either an error in measurement or a reaction mass the drive uses. Finding either one could be important. But looking for ways this thing violates conservation of momentum isn't even on the table.

If you want environment that can only be briefly visited, sure. But what's the point of converting an entire planet to that, then? Just put up an inflatable dome where you need it. And for long-term teraforming, a CO2 environment is probably a better starting point.