Big Bang: The beginning of the Universe

The Big Bang theory is the prevailing cosmological model for the observable universe's earliest known periods and its subsequent large-scale evolution. It proposes that the universe began as a hot, dense state approximately 13.8 billion years ago and has been expanding and cooling ever since.

Here's a brief overview:

1. Initial Singularity: The Big Bang theory proposes that the universe began as a hot, dense point known as a singularity. At this moment, all the matter, energy, space, and time were contained within this infinitesimally small point. As a result, certain qualities became infinite or undefined at the Big Bang, hence the name singularity.

2. Rapid Expansion: Approximately 13.8 billion years ago, the singularity underwent a rapid expansion known as cosmic inflation. This expansion caused the universe to cool down and expand, leading to the formation of subatomic particles and eventually atoms.

3. Formation of Elements: As the universe expanded and cooled, subatomic particles such as protons, neutrons, and electrons combined to form the first hydrogen and helium nuclei. This process, known as Big Bang nucleosynthesis, occurred within the first few minutes after the Big Bang.

4. Formation of Stars and Galaxies: Over millions to billions of years, gravity caused regions of higher density in the early universe to collapse, forming stars and galaxies. Within galaxies, stars formed from clouds of gas and dust, and many stars went on to form planetary systems.

5. Cosmic Microwave Background Radiation (CMB): About 380,000 years after the Big Bang, the universe cooled enough for neutral atoms to form. This event, known as recombination, led to the release of photons that continue to travel through the universe today as the cosmic microwave background radiation. The CMB provides a snapshot of the universe at that early stage.

6. Observable Universe: The expansion of the universe continues to this day. The observable universe, the part of the universe we can see, includes galaxies, clusters of galaxies, and cosmic structures, all moving away from each other due to the ongoing expansion.

The Big Bang theory is supported by a wealth of observational evidence, including the cosmic microwave background radiation, the observed distribution of galaxies, the abundance of light elements, and the large-scale structure of the universe. However, it's important to note that there are still unanswered questions and areas of active research within cosmology, such as the nature of dark matter and dark energy, and the conditions of the universe before the Big Bang. This is probably the reason why various competing theories like the steady state theory, cyclic universe model, multiverse hypothesis, quantum cosmology, etc. find their place in the literature.

Prabir Rudra

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Wormhole: The missing link between us and our future home

 

The term "wormhole" usually describes a theoretical spacetime tunnel-like structure that may link two different points in space or time, possibly enabling instantaneous or faster-than-light travel between far-off places. The idea comes from theoretical physics, specifically from the perspective of general relativity.

Wormholes are frequently discussed as solutions to Einstein's field equations in astrophysics and cosmology. These equations control the gravitational effects of matter and energy on the curvature of spacetime. Although the equations of general relativity make wormholes theoretically viable, they have not been detected or verified to exist in reality, hence they are still considered speculative.

Scientists, authors, and filmmakers have all been captivated by wormholes, which are often depicted in science fiction as a way to travel through space or journey back in time. Wormhole stability, traversability, and the exotic stuff needed to stabilize them are only a few of the many unresolved concerns in the nascent scientific field of wormhole research.

More recently, the word "wormhole" has been used metaphorically to refer to systems or procedures that allow for unusually fast data transfer, financial transactions, or communication between distant sites or systems in domains like computer science and finance. A "wormhole" in the context of blockchain technology, for instance, might be a bridge that permits token transfers between several blockchain networks.

Given the challenges and uncertainties like existence, stability, need for exotic matter, traversability, time dilation, and paradoxes, interstellar travel via wormholes remains highly speculative at this point. While it's an intriguing concept that has captured the imagination of scientists and science fiction enthusiasts alike, practical implementation would require significant advancements in our understanding of fundamental physics and the development of technologies far beyond our current capabilities. But if this turns out to be a success then humanity can seriously think in terms of colonizing other habitable planets in the future, when the resources of our planet get completely depleted. 

It is said that the future of humanity lies in space and wormholes might just be the missing link between us and our destination (future home). But we have a long way to go!!

Prabir Rudra

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The amazing journey of E=mc2: The most famous equation of the world (Meme)

 

Read the article at:  https://www.spacetimerecipe.com/2019/04/the-amazing-journey-of-emc2-most-famous.html

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Prabir Rudra

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General Theory of Relativity (Meme)

 

Read the article at:  https://www.spacetimerecipe.com/2019/03/relativity-for-all-contd-general-theory.html

by

Prabir Rudra

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Special Theory of Relativity (Meme)

Read the article at:   https://www.spacetimerecipe.com/2019/03/relativity-for-all.html

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Prabir Rudra

 

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Black Hole: The monster of the Universe

 

A black hole is a region in spacetime where the gravitational pull is so strong, that no matter can escape from it. The gravity in such a region is of such magnitude that not even electromagnetic radiation (light) can escape from it. Theoretically, black holes were predicted from the solutions of the field equations of general relativity, as regions in spacetime with infinite curvature, such that gravity in the region becomes extremely large.

The boundary of a black hole is called the event horizon, which has great significance for a particle falling into the black hole. The event horizon is basically a point of no return for the infalling bodies, because once a particle crosses the event horizon it does not have any possibility of making it back, and is destined to be engulfed by the black hole. For an external observer, the infalling body will appear to fall into the black hole for eternity due to time dilation near the black hole. Time dilation is caused by the extreme gravity of the black hole and the flow of time is slowed down drastically. The object that is falling into the black hole will appear to fall very slowly to an external observer and the event of falling will seem to occur for eternity.

Using quantum field theory in curved spacetime famous cosmologist Stephen Hawking predicted that a particular type of radiation is emitted from the event horizon of a black hole. This radiation is called the Hawking radiation, whose temperature is inversely proportional to the mass. This temperature is of the order of a billionth of a kelvin for stellar black holes due to which it is almost impossible to detect it directly.

Black hole as a Mathematical entity

In 1916,  Karl Schwarzschild derived the first solution of the Einstein's equations of general relativity which directly showed the presence of a black hole theoretically. For a long time black holes just remained a mathematical curiosity with no physical reality associated with it. With the discovery of neutron stars by Jocelyn Bell Burnell in 1967, new interest was generated in the field of gravitationally collapsing bodies. 

Formation of a black hole

A star at the end of its lifetime undergoes gravitational collapse and forms a white dwarf which is a compact astronomical object. Further collapse from this state will occur if the mass of the white dwarf exceeds 1.4 solar mass (Chandrasekhar limit) and the resulting object will be a highly compact neutron star. If this state is not in equilibrium, then further collapse is a possibility, which will result in a singularity. If the singularity is shrouded by an event horizon, then it is a black hole. The first black hole known to us was Cygnus X-1 identified in 1971.

After the formation of a black hole

After a black hole is formed it can grow by absorbing the surrounding mass due to its immense gravitational pull. Supermassive black holes (millions of solar masses) can absorb stars or even other black holes. The presence of a black hole is generally inferred by the way it interacts with the surrounding matter and electromagnetic radiation. Any infalling matter in the black hole forms an accretion disk which is enormously heated due to friction. Stars which are in the close vicinity of a black hole will be shredded and engulfed by it, whereas stars which are at a considerable distance will orbit the black hole. The mass of the black hole and its location can be inferred from the orbit of these stars. It is believed that supermassive black holes exists at the centres of most galaxies. There is a radio source at the heart of our galaxy Milky Way known as the Sagittarius A*. It is believed that it houses a supermassive black hole of 4.3 million solar masses.

Recent Advancement

On February 11, 2016 gravitational waves due to a black hole merger was recorded by the LIGO and Virgo scientific collaboration. On April 10, 2019 the first direct image of a black hole was recorded by the Event Horizon telescope. It was situated in the M87 galaxy around 50 million lightyears away from us. Till date gravitational lensing is possibly the best method to infer the presence of a black hole. Although only around 20 black holes have been detected so far, it is expected that there are hundreds of millions of such monsters roaming in the universe. Having an encounter with such a thing is not going to be a pleasant experience at all!!

By

Prabir Rudra

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Relativity for All Contd.!! (The General theory of Relativity)

On the 140^th birth anniversary of Albert Einstein it is our great pleasure to revisit one of his greatest masterpiece, the General theory of Relativity (GR) (arguably the best theory of Einstein). Today we discuss GR in his memory and ponder over the extraordinary genius of the man who redefined Physics in the 20^th century.

Albert Einstein

Background

After his miraculous year in 1905, when he laid the foundation of 4 groundbreaking theories of nature (Photoelectric effect, Brownian motion, special theory of relativity and “the world’s most famous equation, E= mc2”), Einstein came to the limelight. 

World’s most famous equation

From a patent clerk in Bern, Switzerland Einstein became a lecturer in the University of Bern in 1908. The following year he was appointed as an associate professor of theoretical physics in the university of Zurich. Einstein became a full professor in the Charles-Ferdinand university in Prague in April, 1911. In 1912 he returned to Zurich as a professor of theoretical physics in ETH, Zurich. He decided to move to Germany and on 1^st April, 1914, he joined the Berlin University.

During all these switch overs from one institute to the other Einstein kept nourishing his original idea of generalizing the theory of relativity that he proposed back in 1905. It was as situation of crisis to humanity. First world war was about to break out. But all these seemed to have minimal effect on the genius. A sense of incompleteness kept haunting him through days and nights.

General theory of Relativity

                                       The Problem 

If we recall our last discussion of Special theory of Relativity we will note that the theory was valid only for inertial (non-accelerated) frames of references. But in reality almost all frames are accelerated . A moving car needs to accelerate or de-accelerate. Similarly a cyclist has to use brakes while cycling. A football rolling on the ground de-accelerates due to friction. All these are non-inertial (accelerated) frames of references where special theory of relativity is not applicable. 

So we need a general theory of relativity that will be applicable to all frames of references (both inertial and non-inertial frames).

Why a theory of Gravity?

In the attempt to generalize his theory of relativity, Einstein knew that he has to incorporate acceleration in his theory. Now acceleration comes from force. In a great insight Einstein understood two things which he stated as the Principle of Equivalence.

1)  The equivalence of inertial and gravitational mass.    

2)  The gravitational force experienced locally while standing on a massive body like Earth is the same as the pseudo force experienced by an observer in a non-inertial frame of reference.

He had the feeling that this can really be a theory of gravity. He started to consider the problem of gravity seriously. He consulted Max Planck (who laid the foundations of Quantum mechanics in 1900) and told him about his intentions to work out the gravity problem. 

The legend says that Planck told him “There are two possibilities: (1) The gravity problem is so difficult that probably you will never succeed.  (2) Even if you are able to find a solution to the problem nobody will believe you.”

Max Planck

The weak link of the prevailing Newton’s theory of Gravitation

The first comprehensive theory of gravitation was stated by Isaac Newton in the 17^th century. It stated that:

Any two masses separated by a certain distance will attract each other by a force directly proportional to the product of the masses and inversely proportional to the square of the distance between them.

The theory seemed to be fine at that time with no flaws and was universally accepted. Newton became the God and very few people had the guts to question his intellect. Moreover the problem of gravity was very difficult to address and so only a few showed any further interest and believed in Newton.

Isaac Newton

But some natural questions arise:

What is the source or the origin of the force?

What is creating it?

Why is it present at all?

Newton was silent to these questions. He did not have any logical answer to it. 

The Theory that answered the above questions

Einstein’s theory of General Relativity is a geometric theory of gravitation that answered the prevailing questions of the critics.

Einstein argued that space-time (space and time together) is like a stretched fabric.  Now when we put a mass on such a fabric naturally it will create a curvature around itself. This is warping (curving, bending or twisting) of space-time that gives rise to a gravity well around the mass. Now when a second mass comes within the curvature quite naturally it moves towards the first body due to the gravity well produced. 

Curvature in space-time

Einstein argued this is what gravitation is!! It is not a force at all as Newton had proposed almost 250 years back. It is a phenomenon that is created by the geometry or curvature of the space-time.

Greater the mass greater the curvature on the space-time fabric

What a masterstroke indeed!! What a beautiful insight!! The common mind can only bewilder and get lost in its aura!! Such was the extraordinary genius of a curious mind.   

The Race to Glory

Einstein had developed the physics of the theory back in 1912, but he did not have any clue about the Mathematics. He needed sufficient knowledge about the geometry of curved space-time (Non-Euclidean geometry) before he could proceed towards developing any meaningful mathematics of the theory. 

Einstein was far from being an expert in such a geometry. But one man by the name of David Hilbert was. He was a mathematical giant of that era. Hilbert took up the problem and started developing the mathematics, which came as a terror to Einstein. His theory was in danger of being credited to somebody else. He had to act and act fast.

David Hilbert

Einstein’s friend Marcel Grossmann (a great mathematician) came to his rescue. With his help Einstein learnt the concepts of Riemannian (Non-Euclidean) geometry and started developing the mathematics of his theory. Hilbert on the other hand continued his effort silently but swiftly. 

As the race to glory became more and more intense the scientific community watched the battle of the two scientific giants (one physicist, the other mathematician) and waited eagerly for a result.

By the grace of God, it so happened that both these great minds reached their destination independently and almost simultaneously. By 1915 both had their own versions of the mathematics of GR ready. On careful scrutiny it was found that both were correct.

Hilbert accepted that the contributions to the theory was far more loaded in favour of Einstein and the theory of general relativity must go by the name of Einstein. This ended all confusions if at all there was any. Finally in 1916, Einstein published his theory of general relativity in the Annals of Physics.

It is difficult to contemplate the feelings of the great man. During his quest, at some point he must have felt that he was losing the battle. After all Hilbert was a great mathematician and matching him was a herculean task. Therefore after the publication, it could have felt like winning a battle once thought to be lost. But it should be remembered that the physical basis of the theory was solely laid by Einstein and probably that’s enough to retain the credit. 

The Equations of General Relativity

This is a relation between mass and spacetime geometry.

Equation of GR

The Reaction from the scientific community

Accepting this theory was not at all easy for the scientific community. The theory will shake the very foundations of physics. Shock-waves were abundant and far reaching. Scientists had many years of scientific career jeopardized. Isaac Newton’s theory of gravitation was in danger. So it happened as Max Planck had predicted some years back. Everybody demanded a proof for the theory.

The radical nature of the theory was criticized by many great minds. Some even thought that GR is not a theory of physics, but the whims and fantasies of Einstein, who is living in a fantasy world.

Experimental physicists like Philipp Lenard (Nobel Laureate, 1905) went into direct confrontations with Einstein and mocked him publicly. He said that physics is a subject of experiments and observations. We believe what we see. There is no place for dreamers like Einstein in the scientific community. Science got really ugly!!

Einstein retaliated but he understood that he had to give a proof to save his theory from being demolished by the critics (specially nazi).

The Proof of General Relativity

The paper was published. The theory was complete. But it didn’t matter to anybody because nobody believed it. Now the genius of Einstein faced a bigger challenge. How will he provide a proof for the theory for which he fought for over a decade. Moreover he was not an expert in experimentation at all. It was an uphill task for him.

But again his extraordinary genius came out with an extraordinary idea. He proposed the bending of starlight around the solar limb (gravitational lensing) as a possible proof for general relativity. 

He argued that the light from the distant stars that pass by the sun before reaching us on Earth will bend while their journey near the sun. The sun being a massive mass will create a huge curvature in the space-time around it. The starlight while passing by the sun will follow this curvature and get bent. As a result multiple images of the star will be formed in the sky. This is in complete compliance with general relativity.

So if Einstein’s theory is correct starlight will bend around the sun and if it is not then the light will pass unaffected. Einstein requested the astronomers all over the world to go and check it.

Many astronomers including Arthur Eddington, a renowned British astronomer took up the challenge. Watching the faint starlight in the presence of powerful sunlight was always going to be difficult. So they chose total solar eclipse for their observations.

In 1919, Eddington’s observations of a total solar eclipse provided concrete proofs in favour of Einstein’s general theory of relativity. 

A British proof to a German theory provided a thrust towards world peace in the post first world war era. Einstein dreamt of a peaceful world without any wars. Even his greatest scientific theory advocated his humane feelings.

In 1921, Einstein was awarded the Nobel prize, not for his general theory of relativity, but for his discovery of the photoelectric effect (may be to his disappointment).

General theory of relativity has been termed as ‘the most beautiful theory of physics’ ever. Till date it remains arguably the best theory of nature not to win a Nobel prize.

I am not a genius. I am just curious...I ask many questions and when the answer is simple, then God is answering.     

         --Albert Einstein.

By Prabir Rudra

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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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