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Wednesday, February 5, 2014

Special Theory of Relativity

The Special  Theory of Relativity was given by Albert Einstein in which he showed how our ideas of space and time are but special cases and that with increase in velocity of an object up to a level when it approaches the speed of light the closer it gets to the velocity of light its mass increases , how a rod would contract in the direction of motion as its velocity approaches the speed of light and how time passes differently in two different reference frame depending on their relative speeds.

             First of all the Special Theory of Relativity is based on Two postulates 1) Physical processes are same in all inertial reference frames and 2) The velocity of light in vacuum is same in all inertial reference frames. The second postulate that there is limit to the velocity levels that anything in the universe can attain is a crucial factor, the speed of light is supposed to be the maximum velocity that can be attained in the universe.

           Now in this blog I am not going in to the mathematical details of deducing the equations but will give the equations directly and show you the essence and effect of it . Now the equations deduced from this two postulates making various assumptions are as follows.

       if Mo=the mass of an object at rest, M=mass of the object, c=velocity of light in vacuum, v=velocity of the body.

 

Which implies that as the velocity of a body increases the mass of the body also increases in normal cases as we see on earth as the velocity of a body goes up the mass of the body seems to be constant , because normally we don't see bodies attaining so much velocity to cause any significant difference , a body moving a even 1000 km per hour speed would hardly make any difference to the mass of the body since c the velocity of light is a very big number.

         Now if the velocity of a body is increased to a level so that it is 80% of the velocity of light in that situation the mass of the body would be 1.67times more than the velocity of of the body at rest , if the velocity of the body is increased to 99% of the velocity of light in vacuum the mass of the body goes up by 7.08 times and as the value of c increases it gets heavier and heavier if you are somehow able to equal the velocity of light , LOOK at the equation , what will happen? the mass of the body is infinite.

          Now consider a rod  moving in a horizontal direction,now from the Theory of Relativity we deduce an equation for length of a rod as follows.

Here l= length of the rod, lo=length of the rod at rest, v= velocity of the rod, c=velocity of light in vacuum




This implies as the velocity of the rod increases the rod contracts of course it is not visible in normal circumstances since the velocities achieved are too low for any visible changes to happen but at velocities close to the speed of light the change is apparent if the velocity of the body is 80% of the velocity of light in vacuum the length of the rod contract to 60% of the original length. 

Now the most exiting part ,Consider the equation of time where T=time in a reference frame whose velocity is v, Tr=time with respect to an inertial  reference frame at rest ,v= velocity of the reference frame and c=velocity of light in vacuum.


     Now again the same thing applies here for small values of v the change in time in two reference frames is is very very small however as the the speed approaches the velocity of light the changes become more apparent one can consider one observer in space and another observer in a spaceship. The spaceship is moving at 90% of the speed of light with respect to the first observer from this equation we deduce that the time passes much more slowly in the spaceship. In fact 100 days for the first observer is less than 44 days for the observer in space.

               (To be continued............................)







     

         

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