Gravitophoton Field Propulsion:

This primer is currently in development, if you see any errors or need me to expand on something, feel free to send me an email.

When Heim first developed his propulsion system he envisioned two possible configurations, a vehicle with one propulsion ring that would remain in real space and a vehicle with two propulsion rings that would be able to enter into n^th parallel space. As discussed in the development section, when all the theoretical conditions are met, gravitophoton pair production will begin. The cross section of absorption of the protons and neutrons in the propulsion ring and ship will interact with the gravitophotons in such a way that the vehicle is accelerated by the Heim-Lorentz Force.

I suspect a vehicle with one ring would be able to accelerate in real space only. The rate of acceleration would be limited by the structural integrity of the ring and vehicle as well as the energy required to generate the magnetic field and rotate the torus. As the vehicle acceleration is increased the concentration of gravitophotons would increase proportionally. Eventually the concentration of gravitophotons will be high enough that the positive gravitophotons will interact in force with the vehicle's gravitons to produce quintessence particles, which will reduce the gravitational potential of the vehicle. A reduction in the gravitational potential would require either a reduction of mass or a reduction of the gravitational constant, both of which would result in violating the conservation of energy and momentum in real space. So, with an ideal single stage drive you could increase you acceleration up to a point where the ship naturally transitions into n^th parallel space. Although this would most likely happen at an extremely high velocity, the vehicle would transition well before it reaches the speed of light, thus maintaining the speed limit in real space. Of course this natural transition would occur at some high velocity that would require a long acceleration time, an extreme amount of energy to produce the required theoretical conditions, and a vehicle made of materials that will be able to withstand the dynamic loads without disintegrating. So, a real vehicle would not be able to reach its natural transition point with only one propulsion ring, this is where the second ring comes into play.

A vehicle using a two propulsion ring system would use one propulsion ring to accelerate in real space and the other propulsion ring to make the transition into n^th parallel space. As the vehicle accelerates, low concentrations of gravitophotons are produced in the vicinity. The concentration is only enough to maintain a prescribed acceleration, say 1g. The vehicle will be accelerated to a specific velocity, at which the second ring will be initiated. The second ring works the same as the first ring, but is designed to rapidly increase the gravitophoton pair production, thus increasing the concentration of quintessence particles and reducing the gravitation potential of the vehicle. Although the vehicle will experience some acceleration from the second ring, soon after it is engaged it will have entered into n^th parallel space. So, turning on the second drive will essentially cause you to immediately enter into n^th parallel space and once you shutdown the drive you will immediately return to real space. The vehicle velocity in n^th parallel space is determined by the velocity of the vehicle at the point of entry and the scale factor n, determined from the formula below. The point at which you enter n^th parallel is determined on the desired travel time, taking into consideration the time required to accelerate and decelerate the spacecraft in real space. According to the papers:

The existence of n^th parallel space is entirely theoretical and mathematical. It is the result of the assumption that the vehicle's gravitational potential could be reduced by the production of quintessence particles. The transition into n^th parallel space was derived to avoid any conflicts with the theory of relativity. In deriving the equations for parallel space, Heim found that the physical laws in real space take on covariant forms that are characterized by n, the previously mentioned scaling factor; the covariant equations are listed below.

This stems from the assumption that spacetime is quantized and that the Lorentz transformation is invariant in regards to the equations. When a vehicle enters into n^th parallel space the speed of light is now scaled by n, thus real space superluminal velocities are now attainable without running into violations. Although n is an integer due to the quantized nature of spacetime and could have any integer value, some sites claim that claim the maximum value of n is 6.6x10¹⁰; so that and the natural transition velocity of the spacecraft would limit the velocity in n^th parallel space. Heim also noted that the transformation from real space to n^thparallel space and back to real space are not symmetrical. Thus, when the vehicle re-enters into real space, it will have traveled some distance in real space. Taking advantage of this and the superluminal velocities in parallel space, Heim postulated that this would finally make long distance space travel more feasible.