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

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Prisoners of Space and Time

Prisoners of Space and Time:

Prisoner of time:

Right from the dawn of ages, human beings have always been a prisoner of time. Time has kept on flowing uni-directionally, unconditionally, and above all uninterestingly without giving us any break at all. Probably it presents us with the best natural example of continuity. 

Sand clock showing the passage of time

Enormity of Time

Great men like Albert Einstein have pondered over the nature of time and tried to understand its fabric. But it is unfortunate that the mystery of time remains unsolved till date. Man has almost reconciled to his fate of not being able to gain control over the flow of time and use it to his advantage.

Einstein and Time

                                    

                                                 

There is no going forward or backward in time for man. Once a moment passes it will be lost forever in the infiniteness of time. All of us long for our childhood days and hope against hope that it would be great to be able to relive those days once more in a lifetime. 

Likewise a point of time in future cannot be lived before it actually arrives by the natural flow of time. We are the captives of time in a helpless situation. The invisible prison holds us tight and we have no way out. This victory of time over man is so comprehensive that it has compelled him to live within the vicious cycle of life and death.

Prisoner of Time

                                               

The much awaited time machine is just an item of fiction for the time being and probably for many years to come. Our knowledge of time is so constrained that even the thought of a time machine seems to be an utter luxury for the time being. Our ignorance has pushed us to such a point that time itself seems to be an illusion to us!!! The illusion of time keeps wielding its magic over us.

The illusion of Time Travel

                                          

Prisoner of Space:

Most of us will think that we are free to move around in space with unlimited freedom. Indeed we can move freely forward and backward, up and down, left and right. That allows us three dimensional motion through space. In that sense we are really free to move spatially. Here we will consider a different point of view of motion through space.

We know that we can move through space. No doubt about that. Now we ask the question how far can we move or how far have we moved till now?

We know that we have travelled to Moon whose distance is 384400 kilometres from Earth. May be we will travel to Mars in near future which is at a distance of 54.6 million kilometres from us. Thats all!!

Our Moon

                                                   

The Mars

                                                    

                                                  Which is our nearest star? 

Most of us know that it is the Proxima Centauri situated in the Alpha Centauri system. It is situated at a distance of 4.2 light years away from us. Now 1 light year is the distance that light travels in a year at an enormous speed of 300000 kilometre/second.  Now if we calculate we see that,

                                   1 light year=  9461,000,000,000 Kilometres.

Proxima Centauri

                                                  

Our Latest Technology:

Nasa’s Juno probe is currently the fastest spacecraft built by man. It was slipped into an orbit around Jupiter in July, 2016. It briefly clocked around 2,66,000 kilometres/hour (1,65,000 miles/hour) making it the fastest till date. This was certainly assisted by sun’s own gravity.

Nasa’s Juno probe 

Helios I and II, which started their journey way back in 1970’s reached speeds of around 2,41,000 kilometres/hour (1,50,000 miles/hour).

Nasa’s Parker Solar probe is set to beat all these records. By December, 2024 it will be at its peak speeding at around 6,92,000 kilometers/hour (4,30,000 miles/hour). With that speed we can travel from Washington DC to Tokyo under a minute. Now thats very fast!!

Nasa's Parker Solar probe

                                           

Other latest technology spacecrafts that we have built are Deep Space, New horizon, Voyager, etc. These have a maximum speed of around 60,000 kilometres/hour.

Our biggest Nightmare:

Even if we consider the highest speed attained or to be attained by our latest technology spacecraft (Parker solar probe in 2024) using repeated gravity assists the time taken to reach our nearest star (Proxima Centauri) will be around 6555 years. With an average human life span of 80 years, it will amount to more than 100 human generations. That’s ridiculous!!!!!

This means that an astronaut who decides to travel to Proxima Centauri or its exoplanet Proxima B, will never reach it in his lifetime or in a few lifetimes. He or she is defeated by his or her biological setup. In other words, the human life span seems to be totally inconducive to interstellar travel. These numbers are so staggering that space travel seems to be beyond the realm of practicality. Although we are free to move around at will our movement in space seems to be highly constrained when large distance travel is considered. In a sense, we are the prisoners of space as well.

Prisoner of Space

                                                  

Very little time in hand:

With the expansion of the Universe, the stars, the planets, the moons, the galaxies are all moving away from us every second. With the passage of time it becomes more and more difficult for research and for any realistic chance for an interstellar travel. We have to act very fast otherwise it might be too late. Everything might go beyond our reach and we will be left contemplating in despair.

                        

                                What if we fail!!

The result of our incapability will be terrifying. It will have far reaching consequences than it seems. Probably our future generations are going to see a dark starless sky only to live and die believing that they are alone in this universe with nowhere to go. What a boring life that would be deprived from the beauties of heavens!! The stories of stars, planets, galaxies will only become fantasy tales for them which they will pass on from generation to generation as legends. Slowly and silently time is leading us towards such a terrible situation.

Space Travel: A choice or a compulsion for us?

With the advent of science and technology human civilization have reached new heights. But every success has its disadvantages as well. Pollution, deforestation, ozone layer deflation, use of nuclear weapons, etc. have led to global warming on large scale. This has eventually led to the melting of polar ice cap and rise in sea level all over the planet.

Effect of Global warming

Rise of Sea Levels is threatening life on Earth

The effect on life is already visible. Already a lot of species of animals have become extinct and the number is on the rise as the days go by.

Slowly but surely this will catch up with the humans in near future. The end of days is not very far away! Earth will not be a suitable place to sustain life for a long time unless we take serious steps to preserve it.

 The End of Days (The catastrophe leading to human extinction)

                   

In such a situation we have to think of an alternative home for us. We should attempt more and more space travel in the quest of some other planet that can sustain life and think of colonizing it. Some exoplanets have shown promising signs and are already on the list. So space travel will no longer be a choice but soon a compulsion for the human race in order to save it from extinction.

Our dream of Colonizing some other planet

We know that we have already thought of warp drives, worm holes, etc that can assist in our venture. But unfortunately, they are still mere theories and are considered as objects of science fiction pictured in Hollywood movies. We need to get practical results from our theories very soon.

Let us hope that we will soon understand the secrets of the fabrics of space and time and reveal the mysteries of nature. This along with our technological advances will help us realize our dream of interstellar travel and liberate us from the invisible prison of space.

By Prabir Rudra

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Life is just an accident !!!

One explanation for the development of the universe is that life on Earth is just an accident. From this angle, life didn't originate from a conscious plan or purpose; rather, it developed as a consequence of a sequence of probabilistic events and natural processes. This opinion is supported by several ideas.

Chemical Evolution of life

One theory holds that life emerged from non-living elements via a process known as abiogenesis. This process entails the progressive transformation of simpler chemical compounds found in the early Earth's environment into complex organic molecules. Although scientists are currently investigating the precise processes that led to abiogenesis, there is evidence that shows natural chemical reactions and environmental factors may have had a role.

Biological Evolution

Following its emergence, life experienced biological evolution, giving rise to the wide variety of species that exist today. The evolution theory of natural selection postulates that features better adapted to an organism's surroundings increase its chances of survival and procreation, which in turn transfers those traits to offspring. This process has resulted in the extraordinary diversity of life on Earth over millions of years.

Cosmic and Planetary Conditions

There is a limited set of physical factors that are required for life as we know it, including liquid water, a stable climate, and a protective atmosphere. Earth just happens to have these attributes. We go into further depth about these requirements below.

We know that the Earth’s axis is tilted at an angle of  23.5 degrees to the vertical. This is a phenomenon that makes Earth a favorable place to harbor life. A little disturbance here and there and the whole balance gets destroyed. This will result in a doomsday for living organisms including us.

                                     Why is it so important? 

Seasonal variations that we experience throughout the year are a result of this precise angular tilt of the axis. If the axial tilt changes to some different value due to some reasons then we will experience strange phenomena on Earth. It would be a totally new place to live in. 

Some places will be shrouded in darkness for six months while others will be roasted in the sun’s heat for the same amount of time. The known picture of ice-capped poles and hot equatorial regions will no longer be a reality. We may even get the opposite scenario depending on the angular tilt.

Ice capped polar regions

Hot Equatorial Regions

The familiar patterns of the ocean currents will cease to exist and we will be left with no mechanism for temperature control. Daytime temperatures will rise up beyond expectations and may be as high as 90-100 degrees centigrade. Similarly, nights will be unbearably cold.

Extremely heated up Earth will make it uninhabitable

                                   

    What are the chances that life forms will survive? 

It is quite obvious that complex life forms like humans and other animals will cease to exist in such unfavourable conditions. The reason is the lack of oxygen. Quite obviously green plants will have a tough time surviving such harsh conditions. This will result in a drop in oxygen levels in the Earth’s atmosphere. 

Earth without plants

                                                       

Earth without oxygen

                           Then who will be around? 

It is only a few bacteria (which are relatively simpler forms of life) that may stick around, with a very bleak chance of developing into complex organisms that need greater quantity of oxygen to develop.

 Bacteria

            How did Earth’s axis get this precise tilt? 

Now that we know what will happen without the tilt, the vital question that arises is what created it. The answer can be found in the idea of the Giant-impact hypothesis (Read  https://www.space.com/19275-moon-formation.html). This is the theory that explains the formation of the moon.

According to this theory, around 4.5 billion years ago our Earth collided with an astronomical body of the size of Mars which is known by the name of Theia. An enormous amount of debris was projected in the space due to the collision. 

With the passage of time, this debris collected around the Earth due to gravity to form the Moon. 

                                                 

 Collision of Earth with Theia   

                                                   

This collision is not only responsible for the precise angular tilt that sustains life on Earth but also for the extra large core of Earth compared to its size. It is believed that Theia’s core and mantle mixed with Earth’s during the collision to give it a larger core than expected.

Placed in the Goldilocks Zone

The area surrounding a star that could support liquid water on an orbiting planet and, thus, potentially support life is known as the habitable zone.

The planets orbiting at that "just right" distance from a star are neither too hot nor too cold to support liquid water, hence the term "Goldilocks zone" for the habitable zone. When a planet gets closer to its star, the water turns into steam; when it gets farther away, it freezes.

When Earth was formed 4.5 billion years ago, there was some fine-tuning in the dynamics of the solar system that resulted in its position in this perfect place that supports life.

Magnetic field of Earth

Earth's magnetic field plays a crucial role in supporting life by providing several key functions:

 

Earth's magnetic field acts as a shield, deflecting the solar wind—a stream of charged particles emitted by the Sun—away from the planet. Without this protective magnetic field, solar wind particles could strip away Earth's atmosphere over time, making it inhospitable for life as we know it. The magnetic field also helps protect Earth from harmful cosmic radiation, such as high-energy particles from outer space. These particles can be damaging to living organisms and DNA, so the magnetic field helps reduce their impact on the planet's surface.

 

Earth's magnetic field is used by many animals, such as birds and certain marine species, for navigation during migration. Additionally, humans have used Earth's magnetic field for navigation for centuries, with compasses being one of the earliest tools to utilize this feature.

 

Overall, Earth's magnetic field is an essential component of the planet's habitability, protecting it from the harsh environment of space and helping to create the conditions necessary for life to thrive.

  Is there a supernatural influence or just a mere coincidence? 

Since the collision produced the precise axial tilt, it would naturally lead us to the question who or what did the fine-tuning? A different impact would have resulted in a completely different scenario. A little alteration in speed or point of impact may have resulted in a different angular tilt. The same argument goes for the position of the Earth in the habitable zone of the Sun and also for the existence of the magnetic field of Earth.

We may have never come into existence. I may not have been around to write this story, you may not have been there to read it. Then why did we get the precise impact that supported life!!! 

Is everything planned!! Are we being monitored by something or someone!!! Is it God!! Or is it just a mere coincidence!! 

Doubts and speculations will always be there. But of now it seems that we are really lucky to be living. The odds are heavily loaded in favour of our non-existence. 

Think about how big the cosmos is and how many circumstances had to come together perfectly for life to emerge on Earth: the correct combination of components in the appropriate amounts, the right kind of climate, and a series of random events spread over billions of years. In this way, one may contend that life as we know it is a result of pure coincidence. Probably it’s just an accident, that we live.

But that doesn't lessen the importance or worth of life itself—even though it may have arisen from what appears to be a series of accidents. The fact that we are here and can think about ourselves and the cosmos around us in spite of all odds is a source of awe and significance for a lot of individuals.

 Whether one believes that life is the product of chance or that it is a part of a greater cosmic plan, the fact that we are here and have the capacity to experience and enjoy the world around us does not change. In the end, the philosophical topic of why life exists and what its potential purpose may be is a very personal one that frequently reflects personal opinions and ideas.

By Prabir Rudra

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