# Propulsion using 4-D momentum

4D momentum is another possibility which allows to travel near about the speed of light without violating laws of physics. This is based on 4D momentum that follows euclidean special relativity. The devices that generate electromagnetic fields in the particle accelerator should be moving themselves to reach a more efficient acceleration process. Alternatively photon could be used that are produced in a particle accelerator itself, observed as synchrotron radiation. Such radiation potentially could be used to further accelerate other particles. From ESR it follows that continuously accelerating the particle will not attain a speed beyond c but will ultimately decrease its speed again. The resulting particle will however have a negative momentum in proper time dimension. This acceleration principle if the interpretation from ESR is correct, allows the propulsion of any object without the use of propellent . The object must carry the device that produce photon with rotated momentum vector. The acceleration of an electron in rest of light speed theoretically requires only a single photon. The biggest gain in efficiency however comes from difference in magnitude of the resulting spatial momentum component of the particle according to Minkowski based relativity vs ESR. According to Minkowski relativity it violates the law of conservation of momentum . But according to ESR , the spatial component as item by the Minkowski 4-vector doesn’t represent the real physical momentum but mathematically represent an enlarged projection of 4D momentum towards 3D. You can find mathematical details here