Time Dilation

56By Prof. Antonio Paris

What Is Time Dilation?

An accurate clock for one observer may be measured as ticking at a different rate when compared to a second observer’s own equally accurate clock. This effect is not a result of the clocks’ technical properties but of the nature of spacetime itself.[i] Clocks on the International Space Station (ISS), for example, run marginally more slowly than reference clocks back on Earth. This explains why astronauts on the ISS age more slowly, being 0.007 seconds behind for every six months. This is known as time dilation, and it has been frequently confirmed and validated by slight differences between atomic clocks in space and those on Earth, even though all were functioning flawlessly. The laws of nature are such that time itself will bend because of differences in either gravity or velocity, each of which affects time in distinctive ways. This phenomenon will have significant implications for interstellar or intergalactic travel.

What Causes Time Dilation?

Time dilation is triggered by disparities in both gravity and relative velocity. Together these two factors are at constant play in the case of a spacecraft’s crew. When two observers are in relatively uniform motion and not influenced by any gravitational mass, the point of view of each observer will be that the other’s clock is ticking at a slower rate than his or her own. Furthermore, the faster the relative velocity, the larger will be the magnitude of time dilation. This case is occasionally termed special relativistic time dilation.

The Spacecraft Scenario

Two spacecraft moving past each other in space would experience time dilation. If the crew inside each one could somehow have an unobstructed view into the other’s spacecraft, it would see the other craft’s clocks as ticking more slowly than its own. In other words, from Spacecraft A’s frame of reference its clocks are ticking normally, while Spacecraft B’s clocks appear to be ticking more slowly (and vice versa). From a local standpoint, time registered by clocks that are at rest with respect to the local frame of reference always seems to pass at the same rate. For example, if a new spacecraft, Spacecraft C, travels next to Spacecraft A, it is “at rest” relative to Spacecraft A. From Spacecraft A’s point of view, Spacecraft C’s time would also appear normal. Here arises a thought-provoking question. If both Spacecraft A and Spacecraft B think that each other’s clocks are ticking more slowly than the other’s, who’s time is correct, and who would have aged more?

Time Dilation and Interstellar Space Flight

Time dilation would make it conceivable for the crew of a fast-moving interstellar spacecraft to travel further into the future while aging much more slowly, because enormous speed significantly slows down the rate of on-board time’s passage.[ii] That is, the spacecraft’s clock would display less elapsed time than the clocks back on Earth. For extremely high speeds during a journey, the effect would be more dramatic. For example, one year of interstellar travel might correspond to ten years back on Earth. Therefore, constant acceleration at one G would theoretically allow a human crew to travel through the entire known universe in one lifetime. Unfortunately, the crew could return to Earth billions of years in the future. Interstellar travel at high speeds thus would have huge implications from both an anthropological and sociological perspective. The crew volunteering for a mission of this magnitude and speed would have to accept the fact that their loved ones, and perhaps even their home planet or star system, would have died long ago.[iii] Because of this effect, humans might wish to travel to nearby stars without spending their entire lives aboard an interstellar spacecraft.


The Twins Paradox

In this paradox one twin makes an interstellar trip in a fast-moving spacecraft but upon return to Earth finds that the other twin who remained there passed away hundreds or thousands of years ago.[iv] This result appears bewildering because each twin sees the other twin as traveling; therefore, each should find the other to have aged more slowly. The paradox can be resolved, however, within the framework of special relativity. The siblings are not equivalent because the twin on the interstellar trip experienced additional acceleration when switching direction to return back to Earth.

Consider by way of illustration an interstellar spacecraft traveling from Earth to Proxima Centauri, the nearest star system outside our solar system and four light years away. At a speed of 80% of the speed of light, the twins will observe the situation as described in the following paragraphs. To make the math less complicated, the spacecraft is assumed to have reached its full speed instantly upon departure from Earth.

The twin on the interstellar spacecraft would see low-frequency (red-shifted) images for three years. During that portion of the trip he would see his counterpart on Earth in the images grow older by 3/3 = 1 year. On the return trip to Earth, he then sees high-frequency (blue-shifted) images for another three years. During that time he would see his twin on Earth in the images grow older by 3 × 3 = 9 years. When the interstellar trip is completed, the image of the twin on Earth will seem to have aged by 1 + 9 = 10 years.

On the other hand, for nine years the twin back on Earth sees slow (red-shifted) images of the spacecraft twin, during which time the spacecraft twin ages in the images by 9/3 = 3 years. The twin on Earth then sees fast (blue-shifted) images for the remaining one year until the spacecraft returns. In the fast images the spacecraft twin ages by 1 × 3 = 3 years. The total aging of the spacecraft twin in the images received by Earth is 3 + 3 = 6 years, so the spacecraft twin returns a bit younger.

To avoid misunderstanding, note the difference between what each twin actually sees versus what he actually calculates. Each sees an image of his twin that he knows originated at an earlier time and that he knows is Doppler-shifted. He does not take the elapsed time in the image as the age of his twin now. If he wants to estimate when his twin was the age shown in the image, he has to determine how far away his twin was when the signal was emitted. In other words, he has to consider simultaneity for a distant event. If he wants to calculate how fast his twin was aging when the image was transmitted, he tweaks for the Doppler shift.[v]

Time Dilation and Communications with Earth

In theory, time dilation will also affect scheduled meetings between the crew on an interstellar mission and the mission managers back on Earth. For example, the crew would have to set their clocks to count the precise number of years time has passed for them, whereas mission control back on Earth would need to count several years more to allow for time dilation. At the velocities currently possible, however, time dilation is too trivial to be a factor in communications between the ISS and Earth.

Implications for Interstellar Travel

Time dilation will have huge implications for both the crew of a spacecraft and mission managers back on Earth. We must consider, for example, the age of the mission managers for the crew returning to Earth (or for alleged extraterrestrials returning to their home planets) and whether or not an interstellar mission would be sociologically accepted. Consider, for example, a spacecraft traveling at 99% of the speed of light to the center of the Milky Way. If everything goes right, the crew would have aged about 21 years. However, back on Earth over 50,000 years would have passed (as observed from Earth).[vi] Obviously all those involved in the initial planning of the mission, as well as generations thereafter, would have died long ago.

[i] Ashby, Neil (2003). “Relativity in the Global Positioning System.” Living Reviews in Relativity. http://relativity.livingreviews.org/Articles/lrr-2003-1/download/lrr-2003-1Color.pdf.

[ii] Toothman, Jessika (2012). “How Do Humans Age in Space?” HowStuffWorks. Retrieved 2012-04-24.

[iii] Calder, Nigel (2006). Magic Universe: A Grand Tour of Modern Science. Oxford University Press.

[iv] Miller, Arthur I. (1981). “Albert Einstein’s Special Theory of Relativity: Emergence (1905) and Early Interpretation (1905–1911).” SOURCE?

[v] Wheeler, J.; and Taylor, E. (1992). Spacetime Physics. 2nd ed. New York: W. H. Freeman.

[vi] Interstellar Travel Calculator. http://spacetravel.nathangeffen.webfactional.com/spacetravel.php.

Leave a Reply