TIME DILATION. Is time absolute??

Special theory of relativity was a revolution in science. Sir Einstein with his theory connected the link between space and time. He said a couple of simple things. The laws of physics are the same in all frame of reference and the speed of light is constant. We all know that motion is relative and your state of motion depends on the frame of reference. But using his theoretical explanation Einstein drew a mind boggling conclusion which we could have never imagined. Moving clocks slows down. Or the time that we thought to be absolute is actually relative.

When I was a kid this particular observation made me intrigued and curious. So, with that feeling in mind let's go. We'll first mathematically prove Einstein's conclusions and see how exactly moving clocks slow down using lorentz equation. Then, we'll end our article with the twin paradox and how this phenomenon can potentially affect real humans.

If you want to skip the mathematics, feel free to do so. skip to the paragraph after the second written photograph. Anyways, even if you don't understand, I'll recommend you to read the full thing to maintain the continuity.

TIME DILATION

We will be using Lorentz transformation equation to derive the expression and to prove that time dilates for moving objects. Let's first define two frame of references one at rest (say S frame) and other moving with uniform velocity V along x axis (say S' frame) . We will see how space and time varies in both frames. Let x, y, z be the position of an object in s frame and x', y', z' be the position in s' frame. Let t be the time taken in s frame and t' in s' frame.

We know that the Lorentz equation says that 

       

First of all let's define some events. Let two events occur in the same place w.r.t S frame at time t1, t2 respectively. But in S' frame it'll seem to be happening at two different places x1' and x2' at t1' and t2' respectively. Think, you are sitting in a bus. In your observation, the passenger next to you will be at same position for two different times in the bus. Where as, for an observer outside the bus, the position of the passenger will be different at different points in time. Now, using Lorentz transformation we can relate the improper time interval or the time interval w.r.t the S' frame or the moving frame and the proper time interval or the time interval w.r.t the S frame or the rest frame. This will let us establish a relation as to how time varies with motion.

The above is the expression for time dilation. We know that V is always less than C. Hence, improper time is greater than proper time. TIME DILATES WHEN AN OBJECT IS IN MOTION. HENCE, MOVING CLOCKS SLOW DOWN.

Now you all will bang me hard in the head and say that, does it make me older than others if I stay at home instead of travelling in buses and trains all the time. Or, are the drivers of trains and buses who look like that of your age are actually as old as your grandpa. Well, the answer is simply no. As most of the speeds that we deal with in our daily lives are very very less in comparison to that of the speed of light. So, we can say from the formula that the proper time and the improper time will be equal or it will not have any effects on us.

TWIN PARADOX

Well if you have reached till this point and are still continuing to read. Hats off to you. But now we'll discuss something that may blow your mind apart even more.

So let's say Jay and Viru are twins. Jay leaves earth when both of them were of the age 10 in a spacecraft travelling with a speed of 0.6 times the speed of light. Now, 20 years have passed on earth. Using the formula we can say that for a hundred days in jay's life, viru will only get 80 days to live. Or if viru returns after 20 years have passed on earth, jay will be 30 years old where as viru will only be 26 years old. It sounds very complicated right. Well it kinda gets even worse. I would like to eat your last brain cell remaining.

Now, everything is clear but what's the paradox. Well, if we consider Viru's frame as rest frame or assume that we are in the spaceship. The earth will appear moving to us with a velocity of 0.8c. Now, Viru should age faster than Jay. But this generally doesn't happen. A possible reason can be that Viru had to change inertial frames to divert his direction back to earth, but Jay is constantly in the rest frame of earth. Hence, it is more accurate to consider Jay's rest frame rather than Viru's. 

But what if Viru gets very close to the speed of light, will he be immortal. The answer is no. His time is passing way slower than the ones that are relatively travelling slower than him. But he will exactly feel the same number of days as the one on earth. In Mr. Beiser's words, "longer life but it will not seem longer". Or ,if he is left disconnected from earth, he will never even realize. We'll discuss about this in detail some other time, giving references to popular movies like the "Avengers Endgame" and everyone's favorite "Interstellar".  See ya.

Source: Concept Of Modern Physics by Arthur Beiser