What is Time Dilation?
Earlier in the study of special relativity, students understand about the occurrence of time dilation, which further explains the “moving clocks run slowly”. Those who have properly encouraged the fact that all motion is relative and who have properly appreciated that the tendency of clocks to measure the passage of physical (in biological) time, ought necessarily to experience some mental discomfort at this result.
Because when you see any two observers passing each other on street, the prediction is that both will find the other person’s clocks to run slower than their own. This might as well seem impossible, to invalidate the entire theory. Nevertheless, there is a detailed analysis that rightly takes into consideration two other equally peculiar relativistic effects such as the Lorentz contraction and the relativity of simultaneity. And that shows that one can build a perfectly sensible relativistic world in which all observers form an agreement on the only things that they must agree on including such as the detailed information of local events (For instance, what everybody’s watches and the temporal order of causal sequences (For instance, which of the two came first, the lightning or the thunder?)
And those questions created confusion along with the phenomenon of time dilation that has long been abbreviated in the so-called “twin paradox” stated as below:
On the 20th birthday of the identical twin, the astronauts volunteer for an experiment. Out of these twins, Terra remained on Earth whereas, Stella, Terra’s sister boarded on a spaceship. Stella’s ship travelled at the speed of light 86.6% in order to visit a star which was 10 light-years away and then she returned to the Earth at the same speed. As both of the sisters decided to go on their separate ways, they wondered what would happen when they stay together. As long as, the light year was exactly the distance light can travel in a year, Stella’s journey should take 23 years at the least. But because she was well aware of the special relativity, the twins already had an idea about its complexity.
The “Twin Paradox”
Firstly, the faster an object moves through space, the slower it moves through time when compared to an unmoving observer. And this relationship can be evaluated well with the help of something called the Lorentz factor, which is defined by the equation:
γ=1√1−v2/c2 γ = 1 1 − v 2 / c 2
And second of all, the length of a moving object can be measured using an observer who is at rest and who would contract by the same factor. At 86.6% of the speed of light, the Lorentz factor is 2, which means that the time will pass twice as slowly aboard the spaceship.
Of course, it will not come in Stella’s notice that the time is slowing down. That’s because all time-based processes in the ship will slow down as well such as clocks, electrical devices and all the biological activities of Stella including her rate of ageing and her perception of time itself. The only people who could actually notice time on the moving spaceship passing slower for Stella would be the observers who remain in the state of passivity, non-accelerating, reference frame just like Terra. But that is just one way at looking at things as all the movement is relative. Here, Stella brings up with an argument that it would be just as valid to say her spaceship will stand still while Terra along with the rest of the universe, moves around her.
Therefore, Terra concludes to the argument by stating that when they meet back on Earth, Terra will be older than Stella. And if that is the case, time will pass two times slower for Terra, making Stella the older twin in the end. As they both can’t each be older than the other, so which one of them is right? This apparent contradiction is known as the “Twin Paradox”.
So, let’s understand how the relative paradox can be easily understood. And to test the theories, both Terra and Stella agreed to send a burst of light to the other every time a year was passed for them. And unlike other objects, the speed of light is always constant regardless of the observer’s reference frame.
A burst of light which is sent from Earth will be measured at the same speed as that of the burst of light sent from the spaceship, irrespective of whether it is on its outbound or return trip. So, when one of the twins observes a burst of light, they start to evaluate how long it took the other twin to experience the passing of a year. Also how long it took for light to travel between them. To bring more clarity to the theory, let’s keep a track on what is happening using the graphical representation.
Let’s say for example, X axis marks distance from Earth, whereas the Y axis tracks the passage of time. So, from Terra’s perspective, her path will simply be a vertical line, with distance equal to zero and each tick on the line equivalent to a year as she grasps it.
Now, the path of Stella will stretch from the same origin to a point 11.5 years in time and 10 light-years in distance from Terra before intersecting again at zero distance and 23 year’s time. After her first one-year mark, Terra will send a burst of light from Earth towards Stella’s spaceship. And because the light year takes around a year to travel one light-year, its path will be a 45-degree diagonal line. And by the time Stella plans to travel away from it, the time light catches up to her, over 7 total years will have passed for Terra, and over 4 for Stella. And by the time Stella observes Terra’s second burst, she will already be on her return journey.
However, she will now move towards the source of the light, which will take less amount time to reach her, and then she will be able to experience the bursts even more customarily. This means that Stella observes Terra ageing slowly for the first of her journey, but ageing rapidly during the return half.
Meanwhile for Stella, it would seem as if her sister Terra, the destination star, along with the whole universe is moving around her. And due of the contraction of light, Stella observes the distance between them diminishing by a factor of 2. This means each leg of the trip will only take about six years from Stella’s perspective. This means that when she sends her first signal to Earth, two years will have passed for her sister. Stella will send four more light bursts during her outbound journey, each one from farther away. And by the time Terra observes the first pulse of light from Stella’s inbound journey; over 21 years will have passed for her.
For the rest of Stella’s home return journey, Terra receives multiple pulses of lights each year. Therefore, Terra notices Stella ageing slowly for about 90% of their 23 years apart, and ageing rapidly during the last 10%. This asymmetry accounts for why the paradox is not really a paradox. Although each twin witnesses time both speeding and slowing down for the other, Stella sees an even split, while Terra sees Stella aging slowly for most of the time they are apart. So, when they get back together, Terra will be 43 years old, while Stella will be 31.
So, as twins who are eleven years apart in age, they are a perfect example of special relativity.
Also the physicists who confirmed a prediction of Albert Einstein’s special theory of relativity discovered of the unprecedented accuracy. Experiments at a particle accelerator in Germany, verifies that time moves slower for a moving clock than for a stationary one.
Conclusion
Time dilation is therefore a theory of special relativity, the “slowing down” of a clock as determined by an observer who is in relative motion with respect to that clock. So, the conclusion of Einstein’s work comes from the realisation that time moves relative to the observer and that an object always in motion experiences time dilation, meaning that time moves more slowly when one is moving, than when one is standing still. Therefore, a person moving ages more slowly than a person at rest.
