iSoul In the beginning is reality

# Time defined anew

“Time is that which is measured by a clock” wrote Hermann Bondi in Relativity and Common Sense (p.65), though the idea goes back to Albert Einstein, and ultimately to Aristotle.

“A space is that which is measured by a ruler; time is that which is measured by a clock.” (George Lundberg, quoted in Abrahamson, 1981: p.256)

I think the truth of the matter is somewhere between a ruler and a clock. Let’s start with what a clock is.

“Almost any clock consists of three main parts: (1) a pendulum or other nearly periodic device, which determines the rate of the clock; (2) a counting mechanism, which accumulates the number of cycles of the periodic phenomenon; and (3) a display mechanism do indicate the accumulated count (i.e., time).” (Clocks, Atomic and Molecular)

The key component is a periodic movement, that is, a cycle. What is measured is a number of these cycles but notice that our clock nomenclature includes part of a cycle, too. The standard clock cycle is one hour, subdivided into minutes and seconds. These parts of a cycle are naturally associated with angles; they are angular divisions of a cycle. A clock is essentially a way of measuring a constant angular velocity.

Consider a vehicle; it travels on wheels and the turning of the wheels (or the axle mechanism) allows it to measure its distance traveled. If the wheels are turning at a constant angular velocity, they are a kind of clock — with this important difference: it is the movement of the circumference that is significant for the distance, not the angular movement.

A ruler is a tool to measure length. We do not associate movement with a ruler but in fact a ruler must be moved into position to measure anything. A measuring wheel shows that a ruler need not be a linear object, though length is a linear measure. It is the circumference of the measuring wheel that is significant; its angular movement is a means to linear movement. The odometer on a vehicle uses the circular movement of the wheels, but the result is a linear measure because the vehicle is moving linearly.

All this shows that movement is required for measuring length and time. The only difference is that we associate time with a continually moving system, a clock; whereas we associate length (and space) with a temporarily moving system. When the measuring wheel stops, the length ends; but time goes on, so we say.

This is so confused! The measuring wheel that measures length can also measure time (duration) if it is going at a constant rate. Where the wheel ends, the length ends; when the wheel ends, the duration (time) ends. The length (space) and the duration (time) go together.

If we wanted to have devices that measure length, and keep on going without stopping, we could do that. We could use a vehicle moving at constant speed around a racetrack. “What length is it?” would mean how far has the vehicle traveled. It would be exactly like “what time is it?” The only difference is whether the linear measure or the angular measure is taken.

The conclusion is that time (duration) is just like length: a device with constant cyclic movement is related to what is being measured; for the length, take the circumferential movement and for the duration, take the angular movement. After the measure is taken the device may be turned off or it may be left running. If it is left running, it is called a clock; otherwise not.

What’s the difference between a stopwatch and a clock? One stops and the other doesn’t. What’s the difference between an express train and a local train? One stops (more) and the other doesn’t. Movement can be measured by angular devices or linear devices. Either way, it’s still movement but we distinguish between them.

There are various reasons for a standard reference movement, as clocks provide. But the standard movement could be linear; it could be measured in units of length. It could be like a satellite circling the earth: its position over the earth could be taken as a measure of its movement; or if it were in a polar orbit, the corresponding longitude could be the measure. It doesn’t stop so it’s like a clock but it could just as well measure distance as an angle.

I could go around and around about this but the bottom line is that time is a difference in angular movement and space is a difference in linear movement. In the case of length, we’re only concerned with the difference; with time we’re more concerned with the movement. But it could just as well be the other way around. Clocks could cease and constant linear movements could be kept going. Time is that which is measured by a constant angular movement that stops when the measurement is complete.

When a measuring wheel stops, does space stop? No. When a clock stops, does time stop? No. Is it possible to have a zero length while a stopwatch is going? Yes, it’s called stationary. Is it possible to have a zero time (duration) while a measuring wheel is going? Yes, and that is also stationary.

We see both linear and angular movement with light. Frequency and wavelength, and the distance it travels and the time it takes to travel are proportional. The special properties of light make it an ideal standard for relating angular and linear movement, space and time.