The Concept of Relativity
Our understanding of physical universe comprises certain key aspects namely space, time, matter, energy, electricity and magnetism. Physical universe consists, in another sense, also of observer and the observed. The importance of relativity lies in understanding the manner in which these key aspects of physical universe are affected by the relative motion between observer and observed. Relativity demonstrates that these aspects are dependent on such relative motion and are not absolute. I will be writing only on Special Relativity.
Special Relativity works on two basic principles:-
i) The laws of Physics are same in all inertial frames of reference (i.e. frames with no acceleration).
ii) The speed of light in free space has the same value of 3×108 m/s in all inertial frames of references.
The second principle, though a statement of fact, defies common logic. It implies that a person sitting in a spacecraft moving with a speed 2×108 m/s will also find the speed of light to be 3×108 m/s only. A natural corollary of these principles is the limitation of speed of any object to 3×108 m/s.
One of the fundamental outcomes of Relativity is the phenomenon of time dilation. It states that a moving clock ticks slower than a clock at rest. It basically conveys that measurement of time intervals are affected by the relative motion between observer and observed. Let us understand it in this manner. Say ‘A’ and ‘B’ are two human beings. ‘A’ measures the time interval between the heartbeats of ‘B’ when both are at rest with each other and finds it to be t0. ‘B’ goes in a relative motion of speed ‘v’ w.r.t. ‘A’. ‘A’ again measures the time interval between the heartbeats of ‘B’. He now finds it to be t1. Relativity says that t1 shall be longer than t0 by a factor of ϒ where ϒ = 1/(1-v2/c2)0.5. That is, t1 = ϒ t0. The phenomenon of heartbeats is also true for spring controlled clocks.
Similar phenomenon is found in the field of space. The measurement of length is also found to be affected by the relative motion. Length is found to have contracted if there is relative motion between observer and observed. In short, L1 = L0 / ϒ.
We can refer to t1 and L1 as relativistic time and relativistic length. It is found that mass and therefore momentum are not left alone by relativity either. Relativistic mass is found to have increased by a factor of ϒ and is equal to ϒm0. Similarly, momentum also increases by a factor of ϒ.
The twin paradox, in this regard, can be studied for better understanding. One will find it to be not a paradox at all as it violates the basic premise of having an inertial frame of reference.