Time dilation

Time dilation:-

In the year 1686, Sir Isaac Newton gives three laws of motion which are world famous laws in the era of physics.

Sir Isaac Newton

These laws gives true and better results when applied to the daily life objects which are travelling with speed. But these laws doesn't gives satisfactory result when applied to the high speed approx the speed of light. But only few people conclude this but only Elbert Einstein proved this. In the year 1905, he gives "special theory of relativity", he introduced every one to the new world of physics.

Elbert Einstein

His theory has three main consequences-

1- Time dilation

2- Length contraction 

3- Relativistic mass

But in this discussion I talk only about the time dilation, in brief if any person who is sitting in plane which is travelling with a high speed observe that there time spent is slow then the observer who observe from the outside. 

Time dilation

Einstein used two assumptions in his theory of relativity:-

1- physics special laws are applied similarly in every corner of universe.

2- in fixed medium speed of light is constant for all observer.

Time dilation:- 

If we consider a simple light clock in which there are two mirrors are attached (as shown in fig 1) one mirror at its upward and another downward and a sensor is attached to downward mirror. The sensor record the reading at the time when light is reflected by upward mirror and hit the downward mirror.

Fig 1. A simple light clock

Fig 2.

Let us assume that the distance between the two mirror is 'h' and light take some time to travel this distance if that time is 't' then we have h = ct.

Now if we assume that light clock is in a plane (fig 3.)which travelling with high speed i.e approximately to the speed of light. For the person who is sitting in the plane observe that there is no change in the initial condition of light clock which is light travel in straight path and hit the both the mirror.

Fig 3.  Case 1 when the observer inside the plane

But the observer who is outside observe that something different because plane in motion which means light clock in motion then light seems travel in diagonal path instead of straight path to travel upward and downward.

Fig 4. Case 2 when the observer outside the plane

 It has to travel large distance we know that speed of light is constant in every frame of reference we have also to increase the time to make speed of light is constant which 3×10^8 m/sec but for the simplification we take v = 3m/sec and observe the result in both the case-

 Case 1:- 

In first case (fig 3.)if we assume that h=6m which is the straight path travelled by light and we assume v=3m/sec then we know that time = distance/speed 

t=6m/3m/sec we get t= 2 sec.

Case 2:- 

In second case light travel diagonal path (fig 2.)which is a large distance if we take distance=12m and also we know that speed of light is remain constant then 

t=12m/3m/sec we get t= 4 sec

it means that the person who is sitting in plane observe the time spent 2sec which is slow in comparison to person who is observing from the outside which observe time spent as 4 sec this is called "time dilation".

So we conclude that there is a slowing of time in accordance with the relativity.