## Is the Metric the Reality?

December 30th, 2103

One of the most important insights that led Albert Einstein to the theory of General Relativity was the realization that a straight line is defined by the path taken by a ray of light. Consider: we check the straightness of a board by holding it up and sighting along its length — checking that the edge of the board follows the same path taken by a ray of light. We line up three objects by squinting and placing our eye directly on the path between two of them. Thus, light defines straightness. Einstein used this idea to declare that light defines the shape of the universe. If light follows a curved path, then space itself is curved.

That was a brilliant insight, and I’d like to extend it in two ways. First, consider how we measure distance: we place a marker — an object — at one point, then we use a marker — another object — at the other end. Those two objects might well be marks on a ruler. But one thing is absolute: those markers must have mass. At the very least, we must place a single particle to mark a position in space. Imagine utterly empty space: you could not measure the distance between any two points without having some bit of mass at each point. In utter emptiness, spatial distance is unmeasurable.

Thus, matter is fundamental to measuring spatial position in exactly the same way that light is fundamental to measure the shape of space. In a universe with zero mass, space could not exist; after all, if you can’t measure something, it cannot be said to exist, can it?

This leads to another realization: events are the markers we use to measure time. Physicists describing special relativity always talk about clocks moving at speeds close to the speed of light. But it’s not really the clock that measures time: it’s the ticks. Each tick is an event. The only way to mark time is to use an event. We define time in terms of two events: one second is defined to be 9,192,631,770 multiple by the difference in time between two peaks of the electromagnetic radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. Those two peaks are events. Therefore, events define time, just as particles define space.

Now let’s get really weird. Perhaps we should not perceive the universe in terms of space and time; perhaps we should perceive the universe in terms of particles and events. After all, they’re the basis of measuring space and time — does that not make them more fundamental?

Lastly, I’ll note that this lines up neatly with my emphasis on the fundamental role played in the universe by the two fundamental elements “things” and “processes”. Interestingly, I’ve never written an essay on the topic, so that shall be one of my next priorities.