Relativity for All !!! (The Special theory of Relativity)

We are fast approaching the birthday of Albert Einstein on 14th March, the most celebrated physicist of the 20^th century. Although he was awarded the Nobel prize for the discovery of Photoelectric effect (a pivotal step towards the development of the Quantum mechanics), yet his best scientific work considered by many scientists is the theory of Relativity. Here we revisit the theory in simple terms. So sit back and contemplate the genius of the man and enjoy the beauty of his masterpiece.

Albert Einstein

Background

In 1905, while working in the capacity of a clerk in a patent office in Bern, Switzerland, Einstein had an insight that was going to change the path of science forever. This year is called Einstein’s miraculous year (annus mirabilis) during which he published four ground breaking research papers in the prestigious journal Annalen der Physik (Annals of Physics). Special theory of Relativity was one of them.

Einstein's paper on Relativity in Annals of Physics

Special Theory of Relativity

Einstein always thought that Newtonian mechanics was not enough to reconcile the laws of classical mechanics with the then newly developed Electromagnetism. He developed Special theory of Relativity to address this issue. His fascination with light from his early childhood played a big role in the development of the theory.

Some technical details

The Problem

Newtonian mechanics used the Galilean transformation for the change of reference frames. Due to this the speed of light (c) varied with the transformation of frames of references. This was the weak link which created doubt in Einstein’s mind since he always thought light to be an universal entity which should be invariant to transformation of frames of reference.  So we needed a transformation that will keep the speed of light invariant with the transformation of frames of reference.

Moreover at the turn of the 19^th century Michelson-Morley experiments showed that the speed of light is an universal constant and cannot vary under any circumstance. Keeping these in mind Einstein stated the postulates of special theory of relativity.

Postulate 1:  Speed of light is an universal constant and it is the universal speed limit.

Postulate 2:  All the laws of nature remain invariant under transformation of reference frames (inertial or non-accelerated systems).

Using these, Einstein went on to derive Lorentz transformation that became an alternative for the unacceptable Galilean transformation of Newtonian mechanics.

Note: The basic idea behind the transformation was to preserve the constancy of the speed of light with the transformations of reference frames.

However from the mathematics of the theory it is seen that a deviation from the Newtonian mechanics is obtained only when the speed of a particle is comparable to the speed of light. For low speed particles special theory of relativity coincides with Newtonian mechanics.

It must also be noted that special theory of relativity is only valid for inertial (non-accelerated) frames of reference.

Consequences of the Theory

The consequences of the theory are numerous and far reaching. Here we discuss two important consequences:

       

        1.  Length Contraction

  2.  Time Dilation

Length Contraction

A body travelling with a speed comparable to the speed of light will have its length shortened by a certain amount determined from the Lorentz transformations. This phenomenon is known as length contraction.

An Example: 

Suppose there is a spaceship moving at a speed 0.8c (say) i.e. at 80% of the speed of light  which is close to the speed of light. There is a rod of length 100cm (say) inside the spaceship. For the astronaut on board everything will seem to be normal and the length of the rod will be 100cm.

But consider a stationary observer outside the spaceship. For him the observed length of the rod inside the spaceship thus moving with it will not be the actual length, but a length shorter than it. The length of the rod observed by the observer outside the spaceship will be 60cm.

Thus 100 cm for the astronaut inside a spaceship moving with a speed of 0.8 times the speed of light is equivalent to 60cm for us on Earth. For us the length seems to have shortened compared to the actual length. Hence length decreases as the speed approaches the speed of light. That’s Length contraction for you.

Time Dilation

Time for an observer stationed inside a body travelling with a speed comparable to the speed of light will run slower compared to the time for a stationary observer outside the body as observed by the latter. This is the phenomenon of time dilation.

An Example: 

Suppose a spaceship is moving at a speed of 0.6c (say) i.e. at 60% of the speed of light which is comparable to the speed of light. Now suppose a particular event occurs inside the spaceship which takes a time of 80 seconds (say) as measured by a clock inside the spaceship thus moving with it.

Now consider a stationary observer outside the spaceship with a clock in hand measuring time. The time recorded by him for the same event that occurred inside the spaceship will 100 seconds as calculated from the special theory of relativity.

This means that 80 seconds for an astronaut inside a spaceship moving with a speed of 0.6 times the speed of light is equivalent to 100 seconds for us on Earth. Time has run slow for the astronaut as compared to time on Earth. That’s what we called dilation of time.

Note: Both the above phenomenon are true and practically observed

Twin Paradox

This is a scenario that evolves as a result of time dilation. Suppose we have an identical twin. Lets name them X and Y. We send X for a space travel for some years, say 50 years (time passed on Earth, i.e. time on Y’s clock who stayed on Earth) at speed of 0.8 times the speed of light.

Then from our calculations of special theory we see that for X the corresponding time spent in space will be just 35 years (time on X’s clock who went for the space travel). So when X returns to Earth after his space journey then X and Y are no longer twins. X is younger than Y by 15 years. 

35 years in space was equivalent to 50 years on Earth.

Now isn’t that difficult to digest!!! But it is true. Practically it has been verified for astronauts who go for space expeditions. On their return they look younger than expected. This is in fact regarded as time travel in future.

Now this difference in time elapsed on Earth and in space can be regulated. It can be increased by increasing the speed of the spaceship. 

An unbelievable scenario that defies human imagination

Suppose we consider a scenario when the spaceship carrying X is passing by a black hole or any gigantic body which has immense gravitational pull. It will be gain a speed almost equal to the speed of light.

In that case our calculations will give terrifying results. A few hours on the spaceship can amount to a few years on Earth. Difference between the ages of X and Y will increase more and more.

So it is quite possible that the timeline of human relations that we generally know can get defied. For example a son or daughter staying on Earth can become older than his or her father who has gone for a space travel and met that black hole. The father has actually performed a time travel in future and met his daughter who is quite old by that time. Now isn’t that mind blowing!!! That’s special theory of relativity for you.

"When you are courting a nice girl an hour seems like a second. When you sit on a red-hot cinder a second seems like an hour. That's relativity."

......Albert Einstein

Note:   We will discuss the General theory of Relativity in our next article.

By Prabir Rudra