Time by Jenann Ismael

Author:Jenann Ismael [Ismael, Jenann]
Language: eng
Format: epub
ISBN: 9780192568953
Publisher: Oxford University Press
Published: 2021-08-10T00:00:00+00:00

Chapter 3

Philosophical implications of relativity

In this chapter, we look at some of the counterintuitive implications of the special theory of relativity. We start with the phenomena known as time dilation and length contraction: the fact that measurements of spatial distances and temporal intervals vary with the motion of the observer. We already saw a glimmer of this in Chapter 2 when I spoke of the ships trying to coordinate events along their own timelines. The intrinsic structure of spacetime is fixed and is given by spatiotemporal distances between points. Nothing is actually varying; time is not speeding up or slowing down. Clocks are not running fast or slow. Measuring rods are not shrinking or expanding. What is actually happening is that people at motion with respect to one another and using a certain convention to assign times to events end up disagreeing with one another about which sets of events are happening at the same time, rather like people on opposite sides of the Earth using the same convention (up = in the direction of the sky) are going to end up disagreeing which direction is up. Disagreements in which events are happening at the same time will translate into disagreements about temporal intervals and spatial distances; everything gets roundly messed up. We can get rid of these weird and artificial effects by sticking to the intrinsic geometry. That means talking about the spatiotemporal distances between events and not carving them up artificially into distances and durations.

Let’s see how this works more precisely. Suppose that I have a watch and you have a watch. If you and I employ what seems like the most natural way for assigning temporal coordinates, it will turn out that if we are moving at a constant velocity (speed + direction) relative to one another, we are going to assign different times to distant events. Here is how we assign times to events. I have a team of people, each with their own watches and at rest relative to me, distributed at convenient locations around space: some close by, some far away. I synchronize my watch with theirs by dividing the time it takes for a light signal to travel to them and back by two. You do the same. You have your own watch and your own team. Your team is spread out evenly across space and at rest relative to you. You synchronize your watch with the watches of your team members by dividing the time it takes for a signal to travel back and forth between you by two. I trust my team, you trust yours, and we each carve spacetime up into spatial slices corresponding to events that happen at the same time. If we were moving at the same velocity, our paths would be parallel and this convention would yield the same carving into same-time slices. But if you are moving at some constant velocity relative to me, when you apply this convention, you will end up carving spacetime into spatial slices that are tilted with respect to mine.

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