Theory of Relativity
Maybe travelling in time is an interesting topic. Also the idea of the flow of time at high speeds is a difficult idea to understand. But did you know that in 1905, someone dared to think differently. He is Albert Einstein. Questions such as, what will you see if you are moving at the speed of light? Well, it is argued that light speed is the maximum speed that is available in the entire universe. The speed of light was calculated by Maxwell using the equations of Electromagnetic wave.
c=√(1/(ε_o μ_o ))
We were able to understand that anything that has speed travels a certain distance in space in amount of time.
Einstein argued that measurements done on physically observable quantity must be uniform in all inertial reference frame. The problem is there is no such as universal reference frame. This gives rise to the assumption that everyone is moving relative to one another. This would give rise to another claim that is, “measurements taken from one reference frame, will be different from measurements taken from other frame of reference”. This argument is absurd because it will mean that laws of physics were different for different reference frames. The theory of relativity holds to the fact that the laws of physics were the same for all inertial reference frames.
This will be eminent when we apply the concept of the Doppler Effect to sound. We know that whenever the source of the sound moves with a velocity V_s, with respect to the observer there will be a change in the measured frequency. Furthermore there will be more measurements that can be made depending on the observer. So how do we determine the real frequency of the sound emitted by the source?
Another instance is when we are on board a plane with some velocity Vplane and we fire a bullet the relative velocity of the bullet on an stationary observer will be;
V=Vbullet+Vplane
Which is correct in Galilean transformation. Now what if we turn on the headlight of a plane? Would it mean that the speed of light will be the velocity of the plane + the speed of light? (v=c) ?. Absolutely not, because this will violate the premise that, “the speed of light is constant in a vacuum”.
Clearly from the two instances there must be a different formula that will unify measurements made on different reference frame. This method is called transformation.
So let us create two equation that will unify measurements in these two instances. The first instance is at the plane, the observer at the plane will have (x,y,z,t). and the observer from the earth will us the coordinates (x^',y^',z^',t^'). So which is it the spaceship is moving away from the earth or the earth is moving away from the spaceship. To fix this, we assume that the origin O and O^'coincide and are parallel to one another at all times. Further more we let t and t^' be equal that is t= t^'.
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