Special Theory of Relativity

 

SPECIAL THEORY OF RELATIVITY

 

   TWINKLE GURUNG (PHYSICS DEPARTMENT)

In physics ,the special theory of relativity ,is a scientific theory regarding the relationship between space and time. In Albert Einstein’s original treatment ,the theory is based on two postulates:

1.The laws of physics are invariant in all inertial frames of reference .

2.The speed of light in vacuum is the same for all observers , regardless of the motion of the light source or observer.

Special relativity was originally proposed by Albert Einstein on 26 September 1905. The incompatibility of Newtonian mechanics with Maxwells’s equations of electromagnetism and experimentally the Michelson-Morley null result demonstrated that the historically hypothesized luminiferous aether did not exist.This led to Einsteins’s development of special relativity ,which corrects mechanics to handle situations involving all motions and especially those at a speed close to that of light (known as relativistic velocities).

Special relativity has a wide range of consequences that have been experimentally verified. They include the relativity of simultaneity, length contraction ,time dilation, the relativistic velocity addition formula , the relativistic doppler effect, relativistic mass, a universal speed limit, mass-energy equivalence, the speed of causality and twin paradox.

It has replaced the conventional notion of an absolute universal time with the notion of a time that is dependent on reference frame and spatial position. Rather than an invariant time interval between two events, there is an invariant spacetime interval. Combined with other laws of physics, the two postulates of special relativity predict the equivalence of mass and energy , as expressed in the mass-energy equivalence formula e=mc^2 , where c is the speed of light in vacuum. It also explains how the phenomena of electricity and magnetism are related.

A defining feature of special relativity is the replacement of the Galilean transformations of Newtonian mechanics with the Lorentz transformations. Time and space cannot be defined separately from each other (as was previously thought to be the case). Rather space and time are interwoven into a single continuum known as “spacetime”. Events that occur at the same time for one observer can occur at different times for another.

 

TWIN PARADOX

Many of the predictions of special relativity such as length contraction, time dilation, mass-variation with velocity, mass-energy equivalence appeared somewhat paradoxical because the concepts were baffling to our daily experience. However, experiments indicated their truth and they are now webbed to be the very fabric of physics.

But the ‘twin paradox’ is one of the most controversial predictions of special relativity. It is this :

Let A and B be identical twins at rest somewhere on the earth(assumed an inertial frame) with their respective clocks. Let both set their clocks to zero time and then B begins his journey in a spaceship to a distant star. If the velocity of spaceship be uniform and comparable to c, the light velocity, he reaches the destination in a few years. He then returns to the earth with his spaceship propelled with the same velocity and meets the earth-bound twin brother A. Since according to relativity ,time slows with velocity, B finds A much older than himself!

Let  v=bc (b=beta) be the velocity of the spaceship relative to the earth. A measures the time t for B reaching the star as t=d/v, where d is the distance of the star. According to A’s clock the return trip also takes the same time t. So, B’s round trip takes, according to A’s clock , a time 2t. But, according to A, B’s clock runs slow . So the total trip of B takes a time 2t’, as measued by B’s clock, which will appear less to A by the factor sqrt(1-b^2). Hence

2t’=2t sqrt(1-b^2)=2t sqrt(1-v^2/c^2).

So on return to the earth, B finds that his round trip time ,as recorded in his clock (2t’) is less than what was recorded by A on earth (2t). So to B, A appears much older and this is also the conclusion drawn by A!

The paradox is rooted to the one-sidedness of the event . For the return journey ,B had a sudden reversal in the direction of the velocity , magnitude remaining the same. This implies an acceleration and a change from one inertial frame to another. Nothing like this occurred to A. The momentary acceleration of B’s reference frame is contrary to the equivalence of the frames of A and B ---- the basic postulate of special relativity. Hence the one-sidedness(that is non – symmetrical) of the result is real and the so called ‘paradox’ gets resolved.

The ‘twin paradox’ is also called as the ‘clock paradox’.