OMG, that’s an interesting discussion, how I’ve missed it so far?

Well, lets speculate for a moment. I’ll try to be as clear in my thoughts as possible, trying to explain everything instead of making it “magic, antigravity blabla, q-bits, super effect”.

We know from the general theory of relativity that the gist of gravity is acceleration. And to make a “Standard” gravity of 1G you just need to pull your station/ship constantly with the acceleration of about 10 meters per second squared. In the age of antimatter reactors, it doesn’t seem like impossible energy consumption per second. The main question comes how to pump that energy into the gravity/acceleration without pushing the whole ship and make zones of anomal controllable gravity.

As it was mentioned in the discussion already, developers gave us a hint: gravitons. So, lets make some weird graviton physics! It is a hypothetical particle with Compton’s wavelength of about 10^13 km. If it flies with speed of light (about 3x10^8 m/s), it gives us the frequency of about 3x10^(-8)Hz. Which relates to one vibration in a year. Not really something we can work with.

Lets then make an assumption of graviton field (as opposed to gravity field) and assume that it is a standing wave. Its frequency can be found out from well known equation E=hv. What is an energy of a graviton field though? The first idea that came to me was that it is an spherical intergral of potential energy. Of course, we can’t take potential energy as simple E=mgh, as it doesn’t show the dependency of g from h and clearly will not converge. We then can take potential energy as integral from r=infinity to r=x from gravitational force (lets take Newtonian physics for a start), F=GmM/r^2, where G is gravity constant, M and m are masses of attracting bodies. That gives us simple integral from infinity to X of (1/r^2) multiplied by constant GmM. And integral of 1/r^2 is just -1/r. Then we get potential energy E=-GmM/r.

Unfortunately, spherical integral from 1/r does not converge (it gives ln( r ) that is not 0 on infinity).

Quite lucrative it seems to take as energy simple E=mc^2, as it directly binds energy to the mass, but, unfortunately, that gives too large overestimate for graviton field, because gravitational force is quite weak compared to energy that we can get if we “turn” mass into “pure energy” in form of photons and kinetic energy of fragments.

Lets return back to classical potential energy, but slightly modify the way we obtained it. We can take from the start that full energy of graviton field is a spherical integral of gravitational force. We already got that integral of (1/r^2) is just -(1/r), so we have only add the spherical part of it, which will be integrals on angles from 0 to Pi and 0 to 2Pi, which will give us as a result -2Pi^2/R, and the energy of a graviton field can be estimated thus as E=-2GmMPi^2/R. The main issue here is m/R, which doesn’t let us define energy of such field without defining and object it interacts with. And we can’t integrate from 0 just because of 1/R^2 or 1/R function, that has limit with R->0 at infinity.

And still we need to find the energy of the gravity well. Unfortunately, arising 1/R turns energy into infinity for infinite amount of space. There is, however, one more trick we can pull out: since we need to create gravity inside our ship or station, we simply don’t need gravity outside of it, and now we can integrate the function on the limited volume. There is one more thing we shall mention. The gravity formula was giving us attraction of two points, but if we are inside the body - we need to integrate over the whole volume.

To approach this we need to get rid of the second mass from our gravity equation, and the best way to do this is to use gravity potential, which is defined as potential energy divided by mass. If we call energy E, lets call potential U = E/m = -GmM/mr = -GM/r, or more precisely U( r ) - it will be a function of r. In fact, lets call this vector x, because ( r ) gives symbol ® (thank you, forum software!). U(x) = -GM/x. (And please, don’t divide our game masters! It’s just mass multiplied by gravity constant, okay?)

But we can’t use M anymore, because we don’t consider our ship as a point. So, instead of that we will introduce function of mass density p(x), (I don’t want to use ‘d’, because it will be a differential), and r now will be a vector (not just distance). But I am really not going to integrate over a volume of random ship with random mass distribution. So, lets make another assumption: our ship is a sphere. And then mass can be shown as M=4Pi S(x^2)p(x)dx|(0-R). where S is symbol for integrating and |(O-R) means from 0 to radius. And this p(x) mass distribution can be used both for finding the potential, and then for finding the energy! (As we have defined potential as E/m).

I won’t be torturing you with math and will just say that it will give us E=-3GM^2/5R, where R is radius of our sphere and M its mass (assuming mass is distributed evenly). Finally, we can make some estimations! Lets make them for the marvel on New Eden engineering, the best industrial freighter in our cluster - the mighty Charon (also, Glory to the State!). It has a mass of 960 000 000 kg, approximately 10^9 kg. Its signature radius is 10.66km, approximately 10^4m. And we can take G as 9.7x10^-11 m^3/kg*s^2. That will give us energy of 4x10^3 kg*m^2/s^2 (or J).

That’s not a lot! But it’s just because our freighter is tiiinyyyy compared to a planet that gives us 10m/s^2. We needed that energy for that frequency that we have started from. And now we can estimate that by formula v=E/h. h is Plank’s constant, approx. 1x10^-34 J/s. And we now have frequency of our so-called “graviton field”, 4x10^37 Hz. And that’s something we can work with!

I think most of us already heard about the gravity waves. But what the real science deals with is a perturbation of gravity field by fast moving/changing systems. Our hypothetical graviton field wave is something completely different, it is an intrinsic property of graviton field, that characterizes its strength, just like frequency of a photon characterizes its energy.

And here comes the most fun part - actually creating gravity (antigravity). We know already that fast changing systems create gravity waves, it means we can create gravity waves as well. Also we know that a graviton is a quadrupole. The solution is simple and elegant: QUADRUPOLE MECHANICAL MASS RESONATOR!

So, how does this animal look like? First we need to imagine quadrupole. Monopole is a single charge, imagine it as a charged sphere, or electron, or something like that. Dipole - is a system of two charge. But you can imagine a magnet, that exists only as dipole (there are no magnet monopoles possible). And quadrupole is a system of four charges, where equal charges sit on diagonals (otherwise it would be just a dipole).

But like magnets, gravity doesn’t have charges. It has only mass. But there can be more or less mass. What we need to do, is a system of four lead beams, arranged together in form of letter X (imagine it as a cross section of all 4 beams, one in top, one on bottom, and two more left and right, each of them shaped as |>). Now we make it vibrate, pulling at the same time horizontal beams apart and vertical - together. Then we do counterwise, pull vertical apart and horizontal together. Ta-daam! We have a quadrupole mechanical vibrator!

But for it to do actual work (and not just **BRRRRRrRRRRrrRRRRrrRR** sound), we need to make it vibrate fast… extremely fast. Faster than pistons of any known car. 10^37 vibrations per second is an astronomical value, but in the future, with all that high-temperature superconductivity technologies they might find a way to achieve it. It will vibrate so fast, that it won’t even produce sound. *But it will produce gravity.*

Well, not exactly gravity, but quadropole gravity wave. We still need to make that vibration into gravity. For this we will use another physical effect: resonance! (That’s why I called the device “resonator” in the first place). By matching gravity wave frequency with frequency of the graviton fields you can start actually “pumping” your energy into gravity. You can interfere waves and nullify gravity (for antigrav engines), you can shape them, direct them, or make gravity field as strong as your energy source will allow (and you need to keep pumping into your resonator as much energy as you will need to keep accelerating to 10m/s^2 to keep earth level of gravity stable).

All hail Graviton Physics!