Time Dilation Example

Position and time were once thought to be absolute. Newton's laws of motion discredit absolute position in space. Einstein's theory of relativity discredits absolute time. The time dilation effect comes from the nature of spacetime.

"Time and space are now seen as dynamic quantities with each individual particle, or planet, having its own unique measure of time depending on where and how each is moving."
- The Illustrated A Brief History of Time, Stephen Hawking, Page 45

Observer 1 has two accurate clocks on the surface of the earth. Observer 1 is on a small island in the North Atlantic Ocean.



Observer 1 reports that time appears to be absolute since the clocks stay synchronized over long periods of time.

Observer 1 concludes the time on the surface of the earth is 12:25.

Astronaut 1 is in a space shuttle floating in space high above the earth. The shuttle is (1) travelling the same speed as the surface clock relative to the speed of light and (2) is far from the earth's surface, affected by a much lower level of earth's gravity than the surface clocks.

Prior to the trip, Astronaut 1 had a personal clock synchronized with the Observer 1 earth surface clock. After the mission, the clocks are compared. The surface clock has a different time than the astronaut's clock. Compared to the people on earth, the astronaut has travelled through the space-time continuum at a different rate. The difference in time is caused by gravitational time dilation.

Earth surface clock is 12:25.
Astronaut 1's clock is 12:28.




"Another prediction of general relativity is that time should appear to run slower near a massive body like the earth. This is because there is a relation between the energy of light and its frequency (that is, the number of waves of light per second): the greater the energy, the higher the frequency. As light travels upward in the earth's gravitational field, it loses energy, and so its frequency goes down.
...
This prediction was tested in 1962, using a pair of very accurate clocks mounted at the top and bottom of a water tower. The clock at the bottom, which was nearer the earth, was found to run slower, in exact agreement with general relativity. The difference in the speed of clocks at different heights above the earth is now of considerable practical importance, with the advent of very accurate navigation systems based on signals from satellites. If one ignored the predictions of general relativity, the position that one calculated would be wrong by several miles!"
- The Illustrated A Brief History of Time, Stephen Hawking, Page 43

Astronaut 2 is in a space shuttle returning from a high-speed trip around the solar system. Prior to the trip, Astronaut 2 also had a personal clock synchronized with the Observer 1 earth surface clock. During the mission, the shuttle travelled at a very high speed by approaching the speed of light while Observer 1 and Astronaut 1 remained at a much, much lower relative velocity. After the mission, the clocks are compared.

Observer 1 surface clock is 12:25. (O1)
Astronaut 1 clock is 12:28. (A1)
Astronaut 2 clock is 12:21. (A2)

Astronaut 2 has returned with a different time completely! The difference in Astronaut 2's time is caused by relative velocity time dilation. The faster the velocity, the greater the time dilation.



Expanding on the differences with the clocks - what if Observer 1, Astronaut 1, and Astronaut 2 were triplets? What if the clock differences were in months and years instead of minutes and seconds? Though all 3 individuals have the same age prior to space travel, the triplets might record different ages when regrouping.

Astronaut 1 is the oldest (perhaps 28) as a result of gravitational time dilation.

Observer 1 is the middle (perhaps 25) as a result of aging on the surface of the earth.

Astronaut 2 is the youngest (perhaps 21) as a result of relative velocity time dilation.

For each person, time appears to pass at the same constant speed. Once regrouped, time differences can be recorded.

In the example above, time discrepancies are exaggerated.
In an actual experiment, the discrepancy is observed in nanoseconds. During the Hafele and Keating experiment, airplanes carrying atomic clocks flew around the world. The resulting discrepancy between ground clocks and plane clocks was reported in nanoseconds.