Copyright © 2015 jsd

Events and Signals in Spacetime
John Denker

1  Introduction

In physics, an event is something that happens at a particular place at a particular time. In other words, it is a single point in spacetime. This concept is heavily used in discussions of special relativity, e.g. reference 1.

The canonical example of an event is the explosion of a small firecracker. Two such firecrackers are shown in figure 1. We have arranged for these two events to be simultaneous in the lab frame.

Figure 1: Two Events that are Simultaneous in the Lab Frame

It is always important to distinguish events from whatever signals may come from the events. The event is a single, zero-sized point in four dimensions, whereas the signals spread out across space and time.

As a corollary, for reasons having nothing to do with relativity, it is important to distinguish the events from the local reception of whatever signals may come from the events.

Figure 2: Arrival of the First Signal

In our scenario, the signal from the eastern event arrives at the observation point relatively early, as shown in figure 2, and only somewhat later does the signal from the western event arrive, as shown in figure 3.

Figure 3: Arrival of the Second Signal

In science, there is a proverb that says the thing that is easy to observe may not be important, and the thing that is important may not be easy to observe. This has been well understood for 2400 years, and perhaps longer; see e.g. reference 2 and reference 3.

Therefore it does not suffice simply to take data; you also have to analyze the data. Also you must make sure to take enough data to permit proper analysis. In the situation portrayed by figure 2 and figure 3, suppose you want to determine whether the events are simultaneous. Then in addition to the timing of the received signals, it would be nice to know how far away the events are, and the speed of propagation of the signals. Then, starting from the signal-timing observations, you can apply a correction that tells you the event-timing. The correction requires using some physics you learned in elementary school: distance = rate × time.

The requirement to focus attention on the events themselves, and to compensate for signal propagation delays, has got nothing to do with relativity. This has been understood for centuries. For example, the first quantitative determination of the speed of light used this procedure in reverse. In 1676, Ole Rømer measured the timings and the distances, and used that to infer the speed of propagation.

2  References

John Denker,
“Welcome to Spacetime”

“The Allegory of the Cave”, in The Republic book VII

S. Marc Cohen
“The Allegory of the Cave”
Copyright © 2015 jsd