When considering the Special Theory of Relativity we concluded that the state of motion of an observer with respect to, say, a laboratory, determines the rate at which his/her clocks tick with respect to the lab's clocks (see Sect. 6.2.3). Thus, in this sense, time and space mingle: the position of the observer (with respect to the lab's measuring devices) determines, as time evolves, his/her state of motion, and this in turn determines the rate at which his/her clocks tick with respect to the lab's.
Now consider what happens to objects moving under the influence of a gravitational force: if initially the objects set out at the same spot with the same speed they will follow the same path (as required by the principle of equivalence). So what!? To see what conclusions can be obtain let me draw a parallel, using another murder mystery.
Suppose there is a closed room and a line of people waiting to go in. The first person goes in and precisely two minutes afterward, is expelled through a back door, dead; it is determined that he died of a blow to the head. The police concedes that the room is worth investigating, but procrastinates, alleging that the person was probably careless and his death was accidental. Soon after, however, a second victim enters the room with precisely the same results, she also dies of an identical blow to the head; the police claims an astounding coincidence: two accidental deaths. This goes on for many hours, each time the victim dies of the same thing irrespective of his/her age, occupation, habits, color, political persuasion or taste in Pepsi vs. Coke; animals suffer the same fate, being insects of whales. If a rock is sent flying in, it comes out with a dent of the same characteristics as the ones suffered by the people and animals.
The police finally shrewdly concludes that there is something in the room that is killing people, they go in and... But the result is not important, what is important for this course is the following. We have a room containing something which inflicts a certain kind of blow to everything going through the room, I can then say that this inflicting of blows is a property of the room.
Consider now a region of empty space relatively near some stars. Assume that the only force felt in this region is the gravitational pull of these stars, hence all objects, people, animals, etc. going into this region will accelerate in precisely the same way. Then I can state that the region in space has a property which generates this acceleration .
Remember however that the region considered was in empty space (it only contains the objects we send into it), yet some property of this region determines the motion of anything that goes through it; moreover this property is a result of the gravitational pull of nearby heavy objects. The conclusion is then that gravity alters the properties of space, we also saw that the rates of clocks are altered under the influence of a gravitational force, it follows that gravity alters the properties of space and time. Space and time is in fact very far from the unchanging arena envisaged by Newton, they are dynamical objects whose properties are affected by matter and energy. These changes or deformations of space and time in turn determine the subsequent motion of the bodies in space time: matter tells space-time how to curve and space-time tells matter how to move (Fig. 7.13).