Monday, October 29, 2012

Relatively relative

Most of you might know einstein as being synonymous with genius. Yes he is the epitome of creative science and is still regarded as idols by some of the finest scientists of the world. Even the top most scientists considered him as being a revolutionary as his out of the box thinking. Today we are going to touch upon his theory of special relativity.

Right so first we shall discuss a bit about relative speeds.
Let us suppose that there be a system of two bodies named a and b respectively which were moving with velocities va and vb respectively towards the left. Now if you were standing on the ground at rest you would notice that both moved towards the left with velocity va and vb respectively. However if you were on the object a you would notice that the velocity of b looks to you like va-vb towards you(towards a) (here we are considering that va>vb)however if you were on b you would notice that b is moving towards you with velocity vb-va. Now if one of the objects were to be accelerated and supposing you were on the accelerating body you would feel as if a pseudo force was acting upon you which caused you (the object ) to move towards the other object with a greater speed. Hence to find out the real force acting upon you you would need to have an observer in the inertial frame of reference. However where is this frame of reference?
If you think about it you yourself are not in an inertial frame of reference  are you?
You are rotating on the earth and a rotating body is certainly not an inertial frame of reference as there is a pseudo force acting here as well called the centrifugal force.
So is there any point in the universe which can be called an inertial frame of reference? Scientists began looking for this stationary frame of reference and they were fixed upon ether. Ether was supposed to be a hypothetical jelly like fluid medium through which light propagates. However the michelson-morley experiment disproved the existence of ether. Hence scientists were now worried as without any fixed frame of reference they could not work out the electromagnetic theory as proposed by Maxwell for maxwell’s theory of electromagnetic waves were absolutely perfect in their description.
Now this is where einstein comes into the picture. He had been continuously thinking of how to make the electromagnetic theory work without the need of an inertial frame of reference. And then while looking at a big clock tower he finally found his eureka moment. He had been thinking if the speed of light was the same in all inertial frames and didn’t know how to make that work. That’s when it hit him that maybe time was affected in the overall process. And then he postulated his special theory of relativity.
The two postulates of his special theory of relativity are:
1) the laws of physics are the same in all inertial frames of reference.
2) the speed of light is constant in all frames of reference.
These two postulates worked perfectly as it has been measured to be found that the speed of light was truly constant in all inertial frames of reference.
Here is what this means. In our previous example we used the objects a and b. Now let us suppose that a shone a torch light towards b. Let the speed of light to an inertial frame of reference be c. Then the light beam is supposed to have reached b at a speed of c-(va-vb).
However it will be found that the speed with which the light beam still reached b is still c.
It discarded the need of an absolute inertial frame of reference and hence the notion of ether.

However it had certain consequences as well like time dilation and space contraction!
What are they?
Well here is a brief example of what it might look like.
Supposing there was an observer in the S frame which is relatively at rest to another frame and suppose there was another frame S’ which moved with a velocity v with reference to the stationary frame S.
Velocities (and speeds) do not simply add. If the observer in S measures an object moving along the x axis at velocity u, then the observer in the S′ system, a frame of reference moving at velocity v in the x direction with respect to S, will measure the object moving with velocity u' where (from the Lorentz transformations above):
The other frame S will measure:
Notice that if the object were moving at the speed of light in the S system (i.e. u = c), then it would also be moving at the speed of light in the S′ system. Also, if both u and v are small with respect to the speed of light, we will recover the intuitive Galilean transformation of velocities


While the equations do look big and scary i will try to make it look fascinating instead. If you look at the equations a bit more carefully you will see that at speeds close to the speed of light.
From these equations you will find that even the speeds of both the frame and the object cannot exceed the speed of light.
C+C is not equal to 2C!!

Also here are some more scary equations...Bear with me!
Consider two observers O and O' , each using their own Cartesian coordinate system to measure space and time intervals. O uses (t, x, y, z) and O ' uses (t' , x' , y' , z' ). Assume further that the coordinate systems are oriented so that, in 3 dimensions, the x-axis and the x' -axis are collinear, the y-axis is parallel to the y' -axis, and the z-axis parallel to the z' -axis. The relative velocity between the two observers is v along the common x-axis. Also assume that the origins of both coordinate systems are the same, that is, coincident times and positions. Then?

  • v is the relative velocity between frames in the x-direction,

  • c is the speed of light, is the Lorentz factor,  again for the x-direction.


Here is what these equations tell you. They tell you that if you were moving towards an object which is stationary with reference to a stationary frame of reference with a speed close to that of the speed of light, the moving object would find  takes greater time  to travel a certain distance than if it were measured by an observer on the fixed reference frame. Meaning?
Time slowed down for the fast moving object.
Also in the frame of reference of the moving object itself. It would find that the moving object had to travel a lesser distance than what it would have to travel as measured from the frame of reference of the stationary observer.

I have not explained the works to my readers as it would go on for pages. However I hope you understood how relativity opens up the doors to slowing down time or contracting space! Einstein wasn’t a genius for nothing! He literally opened up the door for turning something as fictional as star wars into a living reality!!

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