One of Einstein's old tutors, a man by the name of Minkowski showed that the special theory of relativity could be expressed in an interesting way.
The world we live in consists of four dimensions, the three space dimensions and one that is not exactly time but is related to time (it is in fact time multiplied by the square root of -1). This is not at all easy to understand but it means that space-time as we call it has some rather weird properties. In particular, when you move through one of the space dimensions you also travel, unwittingly, through time. You do not notice this, indeed as far as you are concerned nothing happens to you at all, but someone observing you would say that you have travelled through time. Of course, we are always travelling through time, but when you travel through space you travel through time by less that you expect. The most famous example of this effect is the "Twins Paradox".
All the effects of special relativity, such as the slowing down of clocks and the shrinking of rods follow from the above. In fact, it is often better to think of some things, such as electromagnetic fields as being four-dimensional objects. However, the important thing to remember for the moment, is: when you move through space you are compelled to move through time but, when you move through time (which of course you are always doing) you do not have to move through space.
So, what does this have to do with gravity? It is quite simple! When a mass is present in the above space-time it distorts it so that whilst it remains true that travelling through space causes you to travel through time, travelling through time now causes you to move (accelerate) through space. In other words just by existing, you are compelled to move through space - this is gravity.
The particular advantage of this theory of gravity (General Relativity) is that it explains, at a stroke, all the observed properties of gravity. For example the fact that it acts equally on all objects and substances becomes obvious when you thing of gravity as a distortion of space-time rather than a force.
Imagine that you are in free space, away from any planets or stars, when suddenly a planet is created quite close to you. You would not be aware that anything is happening to you, you would feel no force, but you would find that you started to accelerate towards the planet. This is just like the case where you travel through space, you are not aware that you have also travelled through time but people observing you are.
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