# Is time the property of an object?

I don't know if the title makes much sense, but hopefully it will become clear with the text.

Temperature is not a property of a point in the three dimensions, but actually of the object occupying that point. Similarly, is time the property of the point in three dimensions or of the object occupying it?

If time is the property of an object, take the example of the twin's prardox in relativity. The twins have different ages, but it seems to me that they share the same time after they both stop at earth.

EDIT:In case we say that time is an independent dimension, (just like z on a graph is independent of x and y), then the question is how does age relate to time? If time is not the property of an object, then age seems to be one. But then what is age? Can it be compared to distance/displacement?

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An object moving through spacetime will exist at many different events over the course of its history. The string of all the events an object visits is called its worldline. The age of an object is a function of the "length" of its world line. This age is called proper time; it is a natural parameter for the world line. Inside a given reference frame, the square of the differential of the proper time, $\textrm{d}\tau^2$ is some quadratic function of the differentials of coordinates, meaning $$\textrm{d}\tau^2 = g_{00}\textrm{d}t^2 + g_{01}\textrm{d}t\textrm{d}x + \ldots + g_{33}\textrm{d}z^2$$ Once we know all the coordinates of the worldline and all the coefficients $g_{\mu\nu}$, we can find the proper time $\tau$ by integrating over the entire worldline. (It is not always possible to cover all of spacetime with one coordinate system, so we may need to do more than one integration.) The coefficients $g_{\mu\nu}$ depend on the reference frame used as well as the underlying geometry of spacetime. Once we know them, we can find the proper time, and therefore the age, of an object. So proper time is a property of an object's history. Time, as a coordinate, is not.