Abstract

In this paper, I have broken down the core aspects of Einstein’s theory of General Relativity, time dilation, into its smallest parts. This description is as far removed from the mathematical and technical aspects as possible, while still holding true to the theory itself. Only 2 relevant equations are given, and a figure is used to show the very basis of the theory. In this paper, you will find examples and thought experiments in Layman’s terms, guiding you through time dilation as a concept and its uses in the real world. 

Time Dilation due to Relative Velocity

In astronomy and physics, one of Albert Einstein’s most renowned theories is the theory of special relativity. Within this theory, he found that time dilation using the Lorentz factor 1/(1-√(v²/c²)) (v representing velocity and c representing the speed of light)  impacted the very nature of time as a concept. To find the time dilation experienced with any given time and velocity, Einstein came up with the equation Δt’=Δt/(1/(1-√(v²/c²)), where Δt’ is the experienced time, Δt is the proper time (the time an observer from a stationary position), v is the velocity the object is moving at, and c is the speed of light. Putting the math aside, time dilation is, in its simplest form, the difference of time that passes between two objects or people which are moving at different velocities. The faster something moves, relative to the speed of light, the slower time passes for that object, and Einstein proved it to be fundamental to the nature of space-time. 

Other physicists had predicted and observed the phenomenon before Albert Einstein; in 1887, physicist Joseph Lamor found that time dilation seemed to have an effect on electrons as they orbited in their atoms. Citing the Lorentz factor, he wrote “…individual electrons describe corresponding parts of their orbits in times shorter for the latter system in the ratio” (Larmor). This means that he observed electrons moving at different paces due to a change in velocity of the overall system. Seven years later, the Lorentz equation was used by Emil Cohn to study and observe the rate of clocks. 

Only one year later, Albert Einstein came to his conclusion that the Lorentz factor didn’t only have to do with our observation of time; it impacted the fabric of time itself, which he knew to be synonymous with space. However, until humanity is able to travel near light speed, there are only a select few ways time dilation impacts the real world. The average person will never run into anything noticeably impacted by time dilation, but with some research, the extent of its impacts can be seen. And, without the research already done and corrections made daily, time dilation would change everybody’s daily lives. 

After months in space, astronauts return home with clocks and watches that are only a fraction of a millisecond off from atomic clocks on Earth. However, GPS satellites in the atmosphere experience daily time dilation effects of 38 microseconds (Boogaard), and they rely on these clocks to precisely position themselves. With precision in the nanometers necessary for accurate GPS satellite calibration, 38 microseconds translates to an error of 10 kilometers every day if adjustments are not made to the clocks (Boogaard). Without corrections, this would have disastrous consequences for everybody who relies on GPS signals or digital maps of any kind to navigate. 

The effect of time dilation on travel is negligible until the velocity reaches near the speed of light, but we are able to observe it in the real world. When an astronaut goes to the International Space Station, they travel at 7,700 m/s, or .0025% of light speed. Imagine one astronaut brings an atomic watch to the station with them. If this astronaut remains in space for 6 months, the clock will be .005 seconds behind the clocks that remained on Earth. If we were to increase the astronaut’s velocity to 10% of light speed, the clock would be 22 hours behind its Earth-bound counterparts. As we can see, it begins to add up to noticeable amounts by the time we reach 10% of light speed. Changing the astronaut’s velocity to 50% of light speed, the exponential growth becomes clearer: the clock is now 28 days behind the clocks on Earth. This also means that the astronaut has experienced 28 fewer days than everybody who remained on Earth. 

The reason this happens is fundamental to understanding the concept. As previously mentioned, time moves slower for a fast object or person than it does for a slow, or average speed, object and person. Relative to a clock that is stationary, it takes more time for 1 second to pass for a moving clock. The faster the clock moves, the longer it takes for 1 second to pass from the perspective of the stationary clock. This can be observed in Figure 1, where each party involved in the scenario has an atomic clock ticking each second. From a stationary perspective, the atoms are moving in a straight line. According to basic trigonometry, this is the shortest possible path. As the observers watch the falling man and his atomic clock, it appears that his atom is moving diagonally, which means that the path taken by his atom to take one second is actually longer than the paths taken by the observers’ clocks – it is comparable to the hypotenuse of a triangle.

For the purpose of this mental experiment, imagine the man is falling at 90% of the speed of light. Plugging the velocity as well as time (which is 1 second in this instance) into the Lorentz equation, we find that the observers will see 2.3 seconds pass on their clocks before 1 second passes on the falling man’s clock. However, it is important to note that this is all relative; the falling man experiences 1 second exactly as he normally would. To him, the observers are moving at 90% of light speed in the opposite direction of him, and the ground is also moving at 90% of light speed straight towards him. This is because movement itself is relative; when somebody is sitting on a moving train and passes through a station, the walls of the station appear to be moving to them. Adults don’t tend to think of it that way, as it is known to them that they are the ones moving, but the relative appearance of movement remains the same.

When considering time dilation as a side effect of near light-speed travel, there are multiple other factors that must be taken into account. The biggest of these is length contraction, which goes hand-in-hand with time dilation as they can’t occur separate from one another. Whenever time dilation happens, length contraction also happens simultaneously. It is quite similar to time dilation; just as time is relative based on the velocity of the observer, length is as well. Even the equations are practically identical. The equation to find length dilation is ΔL = ΔL0√(1-(v²/c²)), where ΔL represents the observed length from within the moving object, ΔL0 represents the proper time observed from a stationary point, v represents velocity, and c represents the speed of light.  If a spaceship is traveling near light speed and an observer watches from Earth, not only will time appear to move slower but the ship itself will appear smaller. This, in part, also helps to explain why the journey appears to take longer from an observer on Earth than from the spaceship. 

A simple thought experiment can help describe why these concepts are intertwined. There is a crew of astronauts on Earth planning their round trip to a planet that is 5 light years away from Earth, from the perspective of the astronauts on Earth. This is considered the ‘proper length.’  They expect to be traveling at approximately 90% of the speed of light. A simple calculation will show how long the journey will take from Earth’s perspective: 5/0.9 gives the answer 5 years, 6 months, and 18 days. 

As the astronauts make it to light speed, they use the Lorentz formula to discover how long their journey will take from their perspective. They come to the conclusion that they should experience 2 years and 5 months before they reach their destination. Next, they can calculate their perceived distance between the two planets using the Lorentz equation in relation to length. This comes out to 2.18 light years, which is significantly different from the proper length of 5 light years. When these astronauts return to Earth, they will have only aged 4 years and 10 months, but everybody who remained on Earth aged 11 years, 1 month, and 6 days. This is time dilation at a very extreme level, and it isn’t something humanity is likely to see any time in the near future. Still, as technology advances closer to the world of science fiction, it is possible that travel like this will exist.

One theoretical method for applying the concept of time dilation in the real world would be time travel. The ratio of velocity to the speed of light defines how strong of an effect time dilation has, and the closer that ratio gets to 1, the slower time moves for those in the moving object. The last example given is a small-scale version of how humans could traverse time with minimal aging, but it is important to note that this method is only feasible for time travel to the ‘future’. Time dilation has no way to reverse time back, because we experience time in a linear manner. Time travel through time dilation is a way to bend the rules of space-time as we know them and experience a future in a one way trip. No feasible scientific possibilities currently exist for time travel to the past. 

While it is possible to observe the effects of time dilation in the real world, humanity lacks the advancements necessary to utilize its full potential. With the problems the Earth is facing, it will be a long time before we may see the science or funds in the sciences advance to this level. It may never even happen. For the foreseeable future, time dilation and length contraction will both remain primarily theoretical concepts. Researchers have spent decades figuring out the intricacies and understanding the existence of such a phenomenon, and it has paid off in massive ways. Without that research, GPS would be a far cry from what it is today, and science fiction would be lacking many fascinating but realistic storylines. Intense as the subject may be, it’s quite simple at its core, when most of the math and all the technical flare is stripped away.

Citations

Larmor, Joseph. “A Dynamical Theory of the Electric and Luminiferous Medium. Part Iii. Relations with Material Media.” Proceedings of the Royal Society of London, vol. 61, no. 369-377, 1897, pp. 272–285., doi:10.1098/rspl.1897.0036. 

Science ABC. Time Dilation – Einstein’s Theory Of Relativity Explained! YouTube, YouTube, 13 Apr. 2018, www.youtube.com/watch?v=yuD34tEpRFw. 

Boogaard, Chenoa van den. “Time Travel Is Possible, but It’s a One-Way Ticket.” ScienceBorealis.ca Blog, Science Borealis, 23 Nov. 2020, blog.scienceborealis.ca/time-travel-is-possible-but-its-a-one-way-ticket/.