On the Dynamics of Time, Space and Quanta

Space flights are very important for navigation, communication, as well as for the exploration of weather, climate, geophysics, celestial bodies, time and space.
Space navigation requires synchronized clocks. Clocks are subject to relativistic time dilation. However, relativity theory does not predict adequate frames, which are essential for the prediction of time dilation. As a provisional solution of that frame problem, the International Astronomical Union (IAU) recommends celestial reference systems: a geocentric and a heliocentric or barycentric reference system.

In order to solve the problem of predicting adequate frames, we propose new tools: a three clock device, a ballistic device, a levitating device, and a new symmetry.

With the above tools, we show that each clock onboard every spacecraft has an adequate frame, so that the clock has a uniquely and correctly determined velocity and time dilation. Since, these adequate frames determine the propagation of time, they are physically essential, and must be identified:

Near an isolated celestial body, a frame at rest in the local gravitational field is adequate. Near several celestial bodies, their fields and frames move relative to each other. Therefore, the space that determines the propagation of time separates into moving parts, and their fields exhibit linear superposition. The above derived separation of space is additionally confirmed by a new space paradox. Due to the linear superposition of fields, the celestial reference systems recommended by the IAU are approximately adequate near their celestial bodies.

A systematic investigation of the above derived separate parts of space, spacetime or volume in nature provides an indivisible description of curvature of spacetime, gravity and quanta. Based on that, the linear superposition of moving fields is solved with help of quantum expectation values of velocity that exactly predict the time of clocks onboard spacecrafts. Summarizing, we see that celestial reference systems are approximate solutions of the above frame problem, whereas expectation values provide an exact solution.

We use data from former space flights as tests, and we propose further space flights to areas between celestial reference frames, as well as additional measurements on Earth.
We elaborate a universal reference system and derive its universal time dilation. We use the Hubble tension as a first test.
We identify idealized and realistic principles in general relativity and quantum physics.
Our results are in precise accordance with observation. Thereby, no fit has been executed, and no additional hypothesis has been introduced.
We derive our findings in a systematic, clear and smooth manner. We summarize our results by definitions, propositions and theorems. Our results are adequate for classes from grade 10 or higher, courses, research clubs, enthusiasts, observers, experimentalists, mathematicians, scientists, researchers .