Relativistic Clocks
Posted by on Friday, April 30, 2021
When people are first exposed to the predictions and properties of Einstein's theory of relativity, one of the most difficult concepts for them to understand and accept is the nature of time. For our entire lives, we are taught that there is a single time that everyone experiences. We have standard times and time zones, and our society and our technology are based on all clocks displaying the same time. The internet and the GPS satellites would not work if two machines were not set to the exact same time.
And yet the idea of a single measure of time is just an illusion.
According to the special theory of relativity (which has been extensively tested for over a century, and has been confirmed many times to be true) everyone experiences their own unique time, and the more that they move the slower their own personal clock will run. In fact if a person or an object were able to travel fast enough, they would observe everyone around them aging by centuries in the span of just a few moments. And the fastest objects in the Universe, photons of light, actually do not experience time at all - their internal clock has stopped completely.
This often leads students or curious members of the public to wonder how this can happen, and often raise variations of the following thought experiment. Suppose that an astronaut is sent into space on a rocket ship, and travels to a nearby planet and then returns to the Earth. Before they leave, they shake hands with a scientist at mission control, and when they return the shake hands again. According to the astronaut, there is one hour between the two hand shakes. According to the scientist there is ten years between the hand shakes. And yet clearly these two observers were in the same place at the same time for both events, so clearly one of them is mistaken.
The solution to this puzzle is actually quite simple, but it does require you to think in four dimensions - and some people have trouble with that. So permit me to create an entirely different thought experiment that works in just two dimensions.
Suppose that there are two students taking the same physics class at university, and after the lecture one day they shake hands and both go back home. One students lives in the dorms beside the lecture hall, the other lives many kilometers away on the other side of town, and as they are both into fitness they both wear pedometers. The next day when they arrive at class, they shake hands again and then compare their pedometers. One student says that he has only traveled one hundred meters between the two hand shakes. The other says that she has traveled twenty kilometers between hand shakes. And yet they were in the exact same location for both hand shaking events.
Would you claim that one of them is mistake, or that the difference in distance in merely an illusion? Of course not, because we are quite used to the idea that two points can be joined by paths of different lengths. That is obvious.
And it turns out that that is how time operates as well. Two points in space and time (aka spacetime) can be joined by paths that have different lengths, except in four dimensional spacetime, the distance that you travel is experienced as the passage of time*. And therefore the astronaut and the scientist can both be correct - they were in the same time and place for both hand shakes, and yet because they traveled different paths through spacetime they experienced a different amount of time passing between the two events.
Time dilation is really just that simple.
* This explanation is a beautiful way to introduce the concept of spacetime and how different observers experience time in different ways, but it is a bit dangerous for students starting out in relativity because of one strange aspect of the spacetime that we are living in. In our Universe, longer distances in spacetime are experienced as shorter periods of time, and shorter distances seem to be longer periods of time. The reason for this inverse relationship is beyond the level of this brief introduction, but students must be aware of it. Longer paths create shorter intervals of time, because the Universe is bizarre.
And yet the idea of a single measure of time is just an illusion.
According to the special theory of relativity (which has been extensively tested for over a century, and has been confirmed many times to be true) everyone experiences their own unique time, and the more that they move the slower their own personal clock will run. In fact if a person or an object were able to travel fast enough, they would observe everyone around them aging by centuries in the span of just a few moments. And the fastest objects in the Universe, photons of light, actually do not experience time at all - their internal clock has stopped completely.
This often leads students or curious members of the public to wonder how this can happen, and often raise variations of the following thought experiment. Suppose that an astronaut is sent into space on a rocket ship, and travels to a nearby planet and then returns to the Earth. Before they leave, they shake hands with a scientist at mission control, and when they return the shake hands again. According to the astronaut, there is one hour between the two hand shakes. According to the scientist there is ten years between the hand shakes. And yet clearly these two observers were in the same place at the same time for both events, so clearly one of them is mistaken.
The solution to this puzzle is actually quite simple, but it does require you to think in four dimensions - and some people have trouble with that. So permit me to create an entirely different thought experiment that works in just two dimensions.
Suppose that there are two students taking the same physics class at university, and after the lecture one day they shake hands and both go back home. One students lives in the dorms beside the lecture hall, the other lives many kilometers away on the other side of town, and as they are both into fitness they both wear pedometers. The next day when they arrive at class, they shake hands again and then compare their pedometers. One student says that he has only traveled one hundred meters between the two hand shakes. The other says that she has traveled twenty kilometers between hand shakes. And yet they were in the exact same location for both hand shaking events.
Would you claim that one of them is mistake, or that the difference in distance in merely an illusion? Of course not, because we are quite used to the idea that two points can be joined by paths of different lengths. That is obvious.
And it turns out that that is how time operates as well. Two points in space and time (aka spacetime) can be joined by paths that have different lengths, except in four dimensional spacetime, the distance that you travel is experienced as the passage of time*. And therefore the astronaut and the scientist can both be correct - they were in the same time and place for both hand shakes, and yet because they traveled different paths through spacetime they experienced a different amount of time passing between the two events.
Time dilation is really just that simple.
* This explanation is a beautiful way to introduce the concept of spacetime and how different observers experience time in different ways, but it is a bit dangerous for students starting out in relativity because of one strange aspect of the spacetime that we are living in. In our Universe, longer distances in spacetime are experienced as shorter periods of time, and shorter distances seem to be longer periods of time. The reason for this inverse relationship is beyond the level of this brief introduction, but students must be aware of it. Longer paths create shorter intervals of time, because the Universe is bizarre.