In physics matter there is a theory about time dilation. If we understand well about it, we will find some of events will happened faster while the others will happened slower. We probably wonder how could that happened? To answer this problem, here Cool Knowledge presents you a story. The twins paradox is a story which is describing the time dilation theory.
Einstein said “if we placed a living organism in a box. One could arrange that the organism, after an arbitrary lengthy flight, could be returned to its original spot in a scarcely altered condition, while corresponding organisms which had remained in their original positions has long since given way to new generations”.
An intriguing consequence of time dilation is the so-called clock or twins paradox. Consider an experiment involving a set of identical 20-year-old twins named Miko and Miki. The twins carry with them identical clocks that have been synchronized. Miko, the more adventuresome of the two, sets out on an epic journey to planet X, 10 light years from Earth. (Note that 1 light year (ly) is the distance light travels through free space in 1 year.) Furthermore, his spaceship is capable of a speed of 0.500c relative to the inertial frame of his twin brother. After reaching planet X, Miko becomes homesick and impetuously sets out on a return trip to Earth at the same high speed of the outbound journey. On his return, Miko is shocked to discover that many things have changed during his absence. To Miko, the most significant change is that his twin brother Miki has aged more than he and is now 60 years of age. Miko, on the other hand, has aged by only 34.6 years.
At this point, it is fair to raise the following question—Which twin is the traveler and which twin would really be the younger of the two? If motion is relative, the twins are in a symmetric situation and either’s point of view is equally valid. From Miko’s perspective, it is he who is at rest while Miki is on a high-speed space journey. To Miko, it is Miki and the Earth that have raced away on a 17.3-year journey and then headed back for another 17.3 years. This leads to the paradox: Which twin will have developed the signs of excess aging?
To resolve this apparent paradox, recall that special relativity deals with inertial frames of reference moving with respect to one another at uniform speed. However, the trip situation is not symmetric. Miko, the space traveler, must experience acceleration during his journey. As a result, his state of motion is not always uniform, and consequently Miko is not in an inertial frame. He cannot regard himself to always be at rest and Miki to be in uniform motion. Hence Miko cannot apply simple time dilation to Miki’s motion, because to do so would be an incorrect application of special relativity. Therefore there is no paradox and Miko will really be the younger twin at the end of the trip.
The conclusion that Miko is not in a single inertial frame is inescapable. We may diminish the length of time needed to accelerate and decelerate Miko’s spaceship to an insignificant interval by using very large and expensive rockets and claim that he spends all but a negligible amount of time coasting to planet X at 0.500c in an inertial frame. However, to return to Earth, Miko must slow down, reverse his motion, and return in a different inertial frame, one which is moving uniformly toward the Earth. At the very best, Miko is in two different inertial frames. The important point is that even when we idealize Miko’s trip, it consists of motion in two different inertial frames and a very real lurch as he hops from the outbound ship to the returning Earth shuttle. Only Miki remains in a single inertial frame, and so only he can correctly apply the simple time dilation formula of special relativity to Miko’s trip. Thus, Miki finds that instead of aging 40 years (20 ly/0.500c), Miko actually ages only (√(1-v^2⁄c^2 )) (40 yr), or 34.6 yr. Clearly, Miko spends 17.3 years going to planet X and 17.3 years returning in agreement with our earlier statement.
The result that Miko ages 34.6 yr while Miki ages 40 yr can be confirmed in a very direct experimental way from Miko’s frame if we use the special theory of relativity but take into account the fact that Miko’s idealized trip takes place in two different inertial frames. In yet another flight of fancy, suppose that Miki celebrates his birthday each year in a flashy way, sending a powerful laser pulse to inform his twin that Miki is another year older and wiser. Because Miko is in an inertial frame on the outbound trip in which the Earth appears to be receding at 0.500c, the flashes occur at a rate of one every
This occurs because moving clocks run slower. Also, because the Earth is receding, each successive flash must travel an additional distance of (0.500c)(1.15 yr) between flashes. Consequently, Miko observes flashes to arrive with a total time between flashes of 1.15 yr + (0.500c)(1.15 yr)/c = 1.73 yr. The total number of flashes seen by Miko on his outbound voyage is therefore (1 flash/1.73 yr)(17.3 yr) = 10 flashes. This means that Miko views the Earth clocks to run more slowly than his own on the outbound trip because he observes 17.3 years to have passed for him while only 10 years have passed on Earth.
On the return voyage, because the Earth is racing toward Miko with speed 0.500c, successive flashes have less distance to travel, and the total time Miko sees between the arrival of flashes is drastically shortened: 1.15 yr - (0.500)(1.15 yr) = 0.577 yr/flash. Thus, during the return trip, Miko sees (1 flash/0.577 yr)(17.3 yr) = 30 flashes in total. In sum, during his 34.6 years of travel, Miko receives (10 + 30) flashes, indicating that his twin has aged 40 years. Notice that there has been no failure of special relativity for Miko as long as we take his two inertial frames into account and assume negligible acceleration and deceleration times. On both the outbound and inbound trips Miko correctly judges the Earth clocks to run slower than his own, but on the return trip his rapid movement toward the light flashes more than compensates for the slower rate of flashing.
Now, you can understand how the theory of time dilation. That’s all from Cool Knowledge today.