## Sunday, September 30, 2007

### Measuring Time

Is time immanent in the world - reducible, perhaps, to the ticking of an atomic clock - or transcendent, somehow beyond the physical universe? (One of my old Canterbury lecturers gave a great talk on this a couple of years back.) We seem pressed towards a kind of middle ground. No mere clock can be the ultimate standard of time, for a clock may slow down, and that does not mean that the rest of the universe has speed up! No, we take them to be measuring something beyond themselves. The same will be true of any local standard (e.g. the movement of the sun).

Markosian (1993) suggests:
[The change in the sun's position] is also meant to be a stand-in for a more important change, namely, the pure passage of time. Indeed, it seems that our assumption that the sun's position changes at a constant rate amounts to the assumption that the sun's position changes at the rate of fifteen degrees per hour, i.e., that every time the sun moves fifteen degrees across the sky, one hour of pure time passes. So it at least appears that what we are after in trying to determine the rates of various physical processes, such as Bikila's running of the marathon, are the rates at which those processes occur in comparison to the rate of the pure passage of time. (pp.840-1)

I hope we can come up with a better account of this appearance, since "the rate of the pure passage of time" is gibberish. But why should we interpret "fifteen degrees per hour" as relating two changes (the sun through space vs. the present through time)? It seems on the face of it to just be reporting a single change, i.e., that the sun moves fifteen degrees across the sky in the space of one hour. The hour doesn't have to move. Just the sun.

Perhaps the worry is that if time doesn't pass, then the standard of an 'hour' must be defined in terms of immanent physical changes (like the sun's movement, or a clock's ticking). But all measurement is like this. A clock is to time as a ruler is to space. Nobody takes this to mean that we need an objective 'here', extending over space at a rate of one meter per meter, to tell us how long a meter really is in case all our rulers suddenly shrink. Yet Markosian writes (p.841):
suppose that the pure passage of time thesis is false... if it should turn out one day that the motion of the sun in the sky appears to speed up drastically relative to other changes, then we should say, not that the motion of the sun has sped up drastically relative to the pure passage of time, while every other change has maintained its rate, but, rather, simply that the sun's motion has sped up relative to the other normal change.

Why can't we say that the sun has sped up drastically, not relative to any other rate, but just simpliciter? It is moving a greater distance in space for the same interval of time. Simple.

It seems like the real issue here is substantival vs. relational conceptions of space-time. If space-time is like a container, an objective thing in its own right, then universal shrinkage - or slowing - of its contents might be a coherent possibility (even if we couldn't recognize such an event from the inside). If they're merely relational, on the other hand, and so fundamentally about relative proportions, then the idea of all distances or durations universally increasing may make no sense, since to double each component is to leave the ratio the same. (Note that while this is a curious issue in its own right, it's nothing to do with the passage of time.)

In any case, if immanent relations are all that we have access to, we may wonder whether substantive, transcendent space-time could really matter. So it is worth seeking a plausible immanentist theory. We noted at the start that no local standard would do. But perhaps a global generalization would serve better. Plausibly, we seek a frame of reference that yields the greatest amount of stability in our general region. Relative to my heartbeat, the world is in a crazy flux. But my clock, and the sun's movement, and a whole cluster of other natural processes, can be interpreted as each holding a constant rate relative to each other. So we take this general cluster as our standard of time. Any one component may become out of sync with the rest, in which case we will judge it to have changed its pace. The stability of the cluster thus transcends each of its parts (considered individually), whilst remaining wholly immanent. That strikes me as providing as good a basis for measurement as one could hope for.

1. err - aren't we addressing a question that physicists have already largely solved and come to a provable conclusion that would be almost impossible for you to intuit?

2. Hi Richard,
You say:
"Why can't we say that the sun has sped up drastically, not relative to any other rate, but just simpliciter? It is moving a greater distance in space for the same interval of time. Simple."

Wouldn't we have the issue of what is this 'same interval of time'? We can imagine of course the case where the Sun *would* in the same time pass more space, but then we are comparing the actual and imagined movement of the Sun, so we have not moved beyond the relational conception of space-time.

Related to this I want to add another note about the 'universal shrinkage'. I don't think that it is just valueless pragmatically (or meaningless in empirical positivism sense of way - one can not state the circumstances under which universe would be smaller or greater simpliciter), but I take it that it is even *unthinkable* without getting into relativistic thinking (i.e. comparing this universe with an alternative universe). But how does one imagine greater or smaller universe simpliciter without such comparing?

That's why I buy the relativistic concept of time and space, though as I said in a previous comment, I don't think that those are self-subsistent at all, but are only abstractions from more complex things like change.

3. Genius - I don't know, what do physicists says about all this?

Tanasije - sure, I'm sympathetic to the relational conception. My point there is just that if we want to be substantivalists, we don't need the passage of time. Rather than comparing the rate of the sun's movement to the passage of pure time, we can compare it to the (non-passing) interval of pure time. Whether time passes or not is nothing to do with whether it is 'pure' in this sense.

4. Hmmm...it seems my first comment didn't take this morning. Sorry if this is a repeat. Feel free to delete if it is.

I'm no physicist, but I thought a la general and special relativity that there could be no "just simpliciter" about time. Is that relevant to this discussion, or am I missing something?

5. Given the theory of relativity:

1. Actually, yes, a clock is the standard of time: for the frame of reference of that clock, is is true to say that the rest of the universe has sped up. At least, there is, as an axiom, no possible test which can distinguish the states of a slowed clock or a speeded-up rest of the universe. The same is true of rulers in space: there not only is no test, but there can be no test, which allows me to distinguish whether ruler A is elongated, or whether ruler B is shrunk.

2. Relative and relational are not at all the same thing. Relativity, as the denial of any principle of absolute simultaneity, forbids not just time as an absolute, but also time as a set of relationships: because those relationships shift depending on where they are viewed from, without the possibility of some privileged frame of reference which may be trusted more than any other. That is: by shifting frame of reference we get a corresponding shift in perceptions of simultaneity, but there is no simple description of relationships of simultaneity behind all these shifts.

Or: if A takes 5 minutes and B, under time dilation, takes 10 minutes, it is _not true_ that there is an Absolute Time in which A is twice as slow as B. This is obvious if you consider that the extremity of time dilation—as in a singularity—means that time stops, or becomes infinite. An Absolute Time, then, would have to elapse an infinite amount of time in relation to any other finite duration—an absurdity.

6. I haven't studied relativity but here's my take.
We have a set of mathematical relationships that are known to describe observations well. A variable appears in these relationships and we call it 'time'. We call it time because when we apply these mathematical relationships to things for which we also have reliable intutition this variable maps well onto our intuitive concept of time. It is this mathemetical object that I would call the true time. It is not an absolute time but is a well-defined one.
From a practical perspective we want a way to measure time. Clocks are nice, because we can have several of them, and compare them to each other to get an idea of their accuracy. It is unlikely that if we keep them in different places, make them in different ways, etc, that they will all have the same error. This makes them nicer than the position of the sun in the sky. Also the behavior of ceasium atom resonance frequencies (used in atomic clocks) is simpler than planetary dynamics (nasty multi-body effects).

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