Thinking over the second Newton's law and Einstein's GR, we must come to the question what the reference frames or, what background are to be considered, in relation to which
the acceleration of a respective accelerated mass object should be taken.
That is to say not only from mathematical, but also from physical point of view. Located far from the respective mass object, we will of course believe, that the best object to connect the reference frames system with it, will be some stable cosmic object (like a star), since it gives us chance to define exactly the object's trajectory (mathematical standpoint).
In case however, we were located somewhere in a free space, closely to the object, we would prefer to connect the
reference frames system with our position (we can of course define our position with the relation to the stable
cosmic objects). Besides, located closely to the object, we are much more aware of the fact that the force we need to accelerate the object serves not to overcome the resistance of the remote cosmic objects, but to overcome the accelerating resistance of the space (spacetime structure) itself. That is, the accelerating force is not required to increase the object's speed with respect to the remote objects, but to increase its speed with respect to the spacetime structure (substance) in that it is immersed and, of that is created (physical standpoint).
The space itself therefore must be understood as an entity that really exists. Not only as the background, but also as the substance responsible for all space-time phenomena (we shall see later, that the mass must be considered as one of them). Under these circumstances, although we do not see it, the space becomes the natural place, where we may locate the systems of the reference frames, to study the motion of the objects. In some cases (for instance inside gravitational fields) the motion of the mass objects cannot be detected if the reference frame will be connected with the cosmic objects, but it will have to be connected with the space.
At that time already, when the Special relativity was acknowledged, admitting the time dilation and length contraction, even long before, when the theories admitting various space geometries (or the space curvature) were accepted by scientists, the fact that the spacetime continuum has its own structure was accepted. We can hardly imagine the curvatured spacetime without the idea that the things deformed in a curvatured spacetime are firmly bound up with it.
We can conceive the space as the continuum created by the standing undulation of the primary substance. It would look like a collection of the oscillating wave packets (spacetime cells). The number of space-time cells in a predefined distance (space density) and the frequency of the cells (time density) are the quantities responsible not only for the space-time curvature, but for the whole physics. The following three works are based on such quantized conception of the space (space flow theory):
THE SPACETIME PHENOMENA part one Relativity
interpretation of the length contraction (or dilation) as a consequence of the change of the density of the spacetime
interpretation of the time dilation (contraction) as a consequence of the change of the frequency of the standing waves
of the spacetime cells,
interpretation of mass by means of the flowing spacetime structure,
interpretation of the mass particles by means of a very dense spacetime structure flowing into singularity.