All movement exists in relation to the idea of stillness. Bodies in motion move in relation to bodies at rest with respect to their local coordinate systems (citation). This is how we know they are moving. It could even be imagined that this imaginary quality called stillness is the medium within which movement happens. Still, stillness, like movement, is only relative to a particular situation (a coordinate system, ibid.) being considered. An elevator can be be said to be at rest on the 3rd floor of a building, and yet the planet on which the building itself resides is itself speeding through space, in rotation around both the sun, and about its own axis. Our galaxy, further, is in rotation about its center as well, and in fact, according to Edwin Hubble's slowly (from our coordinate system) stretching "constant" the entire universe is moving, expanding, as evidenced by the the fact that galaxies both distant and local to our own appear red-shifted with respect to us. Everything appears to be in motion, spreading apart, away from us, as the fabric of space itself expands.
Despite the fact that everything else is red-shifted, this does not imply that we are in the center, and are motionless, instead such red-shifted galaxies would be seen from any point in our isometric universe, and thus our own galaxy would appear red-shifted if seen from another, or so goes the theory.
Thus, nothing can really be said to be at rest. Even molecules super-cooled to absolute zero would retain the inertial mass of the coordinate system they exist in, the planet they are on. Yet typically human beings measure time as though we ourselves are at rest, and who can blame us? Our common sense idea of time, and thus of rest, as applied to our utilitarian exploitation of time works just fine.
So then, people characterize time in terms of direction. Tomorrow is in the future. Yet, the systems in place for quantifying and measuring time operates with reference to the three spacial dimensions, in terms of volumes of time, durations. We play out actions in three-dimensional space in terms of these time volumes, and without the implied but not quantified sense of directionality, which is caused by the movement of the expansion of the universe, the movement of space through itself, there would be no before or after. Everything would happen at a point, at once.
So what is time? Time, and the perceived quality of non-repeatability in our universe are analogous and inseparable. What we call time is a perceived vector quality. Time is a direction and a movement within our environment. The strange part is that really, the entire three-dimensional environment is moving, it moves, itself, though time. Everything exists, as it where, in time.
One curious side effect is that although the spacial quantities are reversible, at least to the zero point, time is irreversible. This is curious, because simply put, this is what time is, a principle of irreversibility. We can break time into units, and measure it out quantitatively (this is done despite the lack of any absolute zero state of rest to refer to), but unlike the spacial dimensions, in which reversibility is possible, at least down to zero and further in some cases), in time this simply isn't possible. It goes in one direction, and that maybe is its only attribute. You can lose weight but you can't go back in time.
In fact, when one tries to prove time's existence, the mind finds an irreducible barrier within the concept of non-repeatability. Time has direction, it is direction, in which space and everything in it, everything in our experience and seemingly outside of it, moves. The whole universe is doing it, and that is it, and really all we know about it. Time simply goes. As a certain natural scientist put it "evolution is just one damn thing after another" (citation), and maybe that could be said for time itself, if it wasn't for the fact that the things themselves seem to exist in the medium of time rather than the other way around.
Another curious experience is apparent fluidity of the movement of time. We have all experienced, certainly, at one time or another, the feeling of that time is "flowing" at different rates. This can at times be quite extreme. Waking, for example, from what one thought to be a short rest only to realize that one has slept for hours (if not years in the case of Rip Van Winkle mythologies). To compare such experiences with our imposed regular quantitative divisions of time, that is, clock time, are a source of wonder and amazement, but still all we can say about time is that it moves. It is MOVING. It IS moving. IT is moving. But where is it going? It is going towards Later.
We know this based on one thing: that we cannot go back. Repetition, in a very strict sense, is impossible. Every repetition, in a strict sense, is a new event against the axis of time. It is, at most, a similar shape, in the geometrical sense, if we where to imagine a four dimensional coordinate system with the three spacial axes and time as a fourth axis. The same three dimensional form at two points on the fourth dimensional axis creates a similar form but not the same one.
Perhaps, as present in science fiction and in certain Fenneyman (citation) -esque branches of particle physics (about which, this author admittedly knows almost nothing) retrograde temporal movement is possible. When one finds theories regarding this, they usually are framed in orders of magnitude much smaller or much greater than ours. Some theories about anti-matter particles imply a retrograde temporal movement to account for the existence of these particles but this is on an order of magnitude so much smaller than our own everyday world that very little in fact behaves in similar ways, even though we are made of that world. It seems impossible to experience such a transformation here and, with your pardon, now. No anti-author will appear to annihilate this author. Traveling the other direction, upwards to agreater orders of magnitude of spacetime, should the universe end in a big crunch in which time reverses backwards into an inverse big bang, the experience of this is still quite beyond the scope of our present discussion.
Time has every appearance, and in fact, we find our utility of it in the firm directionality of its development in relation to spacial forms. This directionality is time itself. Although some mathematical models, referred to earlier, describe time and space on a four dimensional coordinate system, and as such, more or less mathematically equivalent to one another, it seems that in some ways they are not equivalent. Spacial events happen in time. Time is, in this sense, the media in which spacial events happen. This idea is very commonly encountered in everyday speech. One doesn't say that time exists inside of an object. Yet an object, like a block of wood, clearly exists in time. The usage illustrates important aspects of how we use time itself, and these are formed by and indeed form our conceptions of what time is itself.
This is why, when in need of quantitative reference for time, we place a grid over it. This grid consists of assigned, regular units marked off according to a reference point, as we do with spacial coordinates. Throughout history, humanity has relied on myriad reference points such as the behavior or the sun and moon, tides, decaying isotopes, and so forth for such reference points, but what are we trying to do with our grid once established? We are trying to see the progression of three-dimensional events. For example, a baby book, in which parents collect photos of their child at regular intervals displays the three dimensional development (two dimensionally, of course, using photos) with reference to a time grid, here a calender. We make such grids to see change more clearly.
To put the problem another way, imagine an object in an environment. The object's environment (set A) is simply the collection of all other objects not object A (our initial object) inside set A. The development of object A (the changes which this object goes through while remaining, for the purposes of a perceiver, object A)in relation to the other objects in set A represents object A's path through time, if not the path of set A itself. All of this can then be set against time grid T, which is based on a regular division of time (which as stated before is simply this quality of irreversible movement in our universe). The relationships between object A within set A (the development discussed earlier), in reference to grid T, and set A's relationship to grid T can be described as a "rate of change", and units from time grid T can be used to describe it. This quantification thus describes both time and space, and both space and time coordinates are necessary to catch a particular bus or arrange a meeting with a person in the center of a crowded city.
Interestingly, this relationship of interdependence between time and space shows up in the tools of calculus, where rate of change is measured and often expressed graphically. Curves have attributes of being analyzable graphs of functions, and in this way share a behavior with other curves, such as those found in nature or in nature as designed by humans - architecture. Curves turn out to be curves whether they represent data about spacetime, or whether they are stone monuments. Still, this conceptual flattening of spacial and linear curves is something of a game. The effect of negating the function of such curves is unfortunately similar to the flattening effect of treating the three spacial values and the time dimension as mere numerical values or variables in a coordinate system when in fact their behavior seems to be very different.
Consider this final point: if time is taken to be a medium of sorts, in which spacial events happen, and irreversible a paradox emerges. Time described as the concept of movement cannot be quantified. When one tries, the best that emerges is the idea of a field. That is not problematic as certainly spacial events can develop against, or better, in, such a field, but that field itself exists in relation to something, since it itself describes a development. What then, is the field of time in development in, what is its medium, given that nothing could exist without or before it? After all, we have never known stillness.