This paper describes a novel space propulsion technique, based on an extension of a unified field theory in a quantized, higher-dimensional space, developed by the late B. Heim (1977) in the 50s and 60s of the last century, termed Heim Quantum Theory (HQT). As a consequence of the unification, HQT predicts six fundamental interactions. The two additional interactions should enable a completely different type of propulsion, denoted gravitophoton field propulsion. The fifth interaction, termed gravitophoton force, would accelerate a material body without the need of propellant. Gravitophoton interaction is a gravitational like force, mediated by gravitophoton particles that come in both types, attractive and repulsive. Gravitophoton particles are generated in pairs from the vacuum itself by the effect of vacuum polarization (virtual electrons), under the presence of a very strong magnetic field (photons). Due to gravitophoton pair production, the total energy extracted from the vacuum is zero. Attractive gravitophotons interact with matter, and thus can become real particles, exacting a force on a material body. Repulsive gravitophotons have a much smaller cross section and do not interact with matter. Consequently, the kinetic energy of the accelerated material body would come from the vacuum, satisfying the second condition, i.e., a low energy budget for space propulsion. The name gravitophoton has been chosen because a transformation of photons into gravitational energy should take place. The third condition for advanced spaceflight, superluminal speed, may be realized by transition into a parallel space, in which covariant laws of physics are valid, with a limiting speed of light nc, where n is an integer and c is the vacuum speed of light. In order to achieve such a transition, the sixth fundamental interaction would be needed, termed vacuum field (or quintessence), which is a weakly repulsive gravitational like force, mediated by the vacuum particle, being formed by the interaction of repulsive gravitophotons with the gravitons of the spacecraft. The paper discusses the source of the two predicted interactions, the concept of parallel space, and presents the physical model along with an experimental setup to measure and estimate the gravitophoton force. Estimates for the magnitude of magnetic fields are presented, and trip times for lunar and Mars missions are given.