It is commonly believed that time is a uniform entity throughout the universe. Newtonian mechanics is based on the paradigm that time is same for whole of universe and moves at a constant speed in forward direction, one of the entrenched belief that was proved wrong by Einstein in his seminal paper on special relativity which was so controversial for it's time that he was not awarded for his work on relativity.
The story begins with the curious situation that came to fore by the incompatibility of Maxwell law of electromagnetism and Newton's law of mechanics. There was an effort to bridge this gap by proposing ether theory which hold sway for close to a century before being proved wrong by MichelsonMorley experiment. The idea behind ether theory was that earth like any other celestial body was moving in an ether medium, a medium which help light waves to propagate like water allows transverse mechanical waves to propagate. The falsifiable aspect of this theory was that , if ether existed it would cause difference vis-a-vis speed of light when measured from different directions. This aspect was tested and proved wrong by MichelsonMorley in his experiment. Work over coming decades would lead to substantial revision of Newtonian mechanics which come to be known as Lorenz transformations of Galilian equation of motion.
And here comes the contribution of Einstein. Even though Lorenz transformations have existed for sometime, they were not given much importance as their theoretical underpinning was weak.They could not explain the results that they gave by application of mathematics.Einstein provided a theoretical framework and above all had a revolutionizing impact as it uprooted the very paradigm that time is same for every point in universe.For this he gave forth two postulates
1. The laws of physics are the same in all inertial frames of reference
2. The speed of light in free space has the same value c in all inertial frames of reference.
The results of Einstein theory of relativity were tested in an experiment conducted using atomic clocks over Chesapeake bay and were found to be true.
The basic derivation that explains the time dilation concept is as follows.
Imagine a large array of clocks on all three dimensions with you standing at origin. The time in your clock is 0:00. Now you want to synchronize all clocks wrt to your position so you emit a light signal in all directions. The observer at some clock receives the signal and since light signal can't travel at infinite speed, he adds the time that light has taken to travel to his station to get a proper value of time at his co-ordinate.
Now conduct a small experiment.
Imagine you are in a train moving forward with a velocity u. You conduct an experiment in which a photon is emitted by a photon emitter (whatever) and it goes up till a mirror after which it is reflected back. The height is h
now since photon travel at speed of light, time as measured by someone inside the train t' is 2h/c.
Now consider an observer who is standing on stationary platform.
To him the photon would appear to travel in a triangular path. let the total distance travelled by train during this whole event is 2l and the time measured by a fellow on ground be t.
so 2l= u.t
also by Pythagoras theorem, distance travelled by photon wrt to an stationary observer is 2.[ l[SUP]2[/SUP] + h[SUP]2[/SUP]][SUP]1/2[/SUP]
Also since speed of light is constant, distance travelled by photon would be c.t
putting the values of l and h in equation 1 and equating both equations we get
ct = 2 [ (ut/2)[SUP]2[/SUP] + (ct'/2)[SUP]2[/SUP]][SUP]1/2[/SUP]
c[SUP]2[/SUP]t[SUP]2[/SUP]= u[SUP]2[/SUP]t[SUP]2[/SUP] + c[SUP]2[/SUP]t'[SUP]2[/SUP]
t[SUP]2[/SUP]( 1- v[SUP]2[/SUP]/c[SUP]2[/SUP])= t'[SUP]2[/SUP]
t= t' / ( 1 - v[SUP]2[/SUP]/c[SUP]2[/SUP])[SUP]1/2[/SUP]
Above derivation is one of the easiest one of theory of relativity and gives some curious results
Suppose you hop in an space craft travelling at 99.8% of the speed of light ant take a tour on 10 years and then decide to return to earth retracing your path.Though only 20 years have passed on your spaceship,but how many years have passed on earth? Calculations show that 488 years would have passed on the earth during same time.
And this is not a fluke mind experiment. Time dilation is observed in atomic clock whenever they are moved from one point to another and also on GPS satellited which are nothing but miniaturized atomic clocks.
There is and another method of time travel. Parking yourself next to event horizon of a black hole after finding one massive enough to rip you apart by gravity waves. due to time and space being weaved together, time itself stops at even horizon of black hole.and if are able to return back to earth in future you would find that everything on earth has aged more than you.