Universe: A Dream reigning in the veins

Lyrid meteor shower is happening now

2024-04-21T18:42:00.001+05:30

Yes, the Lyrid meteor shower is indeed happening today! The Lyrids are an annual meteor shower that occurs from about April 16 to April 25 each year, with the peak usually around April 22 or 23. The best time to observe them is typically during the predawn hours, when the sky is darkest and the shower's radiant point, the constellation Lyra, is high in the sky.

These meteors are caused by the Earth passing through the debris left behind by the comet C/1861 G1 Thatcher. If you have clear skies and minimal light pollution, it's a wonderful celestial event to witness. Under a perfectly dark sky, you may be lucky enough to catch a glimpse of 10 to 15 Lyrids per hour.

So why wait!! Just go outside and look upwards. You might just get lucky and witness a heavenly show.

All the best!!

Prabir Rudra

Fermi Paradox: Where are all the Aliens!??

2024-04-17T03:43:00.003+05:30

The intriguing idea known as the Fermi Paradox poses the question of why, despite the likelihood that there is extraterrestrial life out there, we have not yet found any proof of these civilizations. The paradox draws attention to the apparent contradiction between the likelihood that extraterrestrial civilizations exist and the paucity of evidence or communication with them. It is named after the Nobel prize-winning physicist Enrico Fermi, who famously raised the question during a discussion about the viability of space travel and the existence of intelligent alien life.

The Fermi Paradox has several proposed solutions and explanations.

The rare earth hypothesis lowers the possibility of the existence of additional intelligent civilizations by suggesting that the conditions required for complex life to arise are exceedingly rare.

The Great Filter Hypothesis postulates that life, whether it be microbiological, complex multicellular, or technological civilizations, may be stuck at some point in its evolutionary process due to an impenetrable barrier.

The theory of technological singularity postulates that sophisticated civilizations will ultimately reach a point at which their technology advances to the point that they are undetectable and uninterested in communicating with other civilizations.

Self-destruction: The theory suggests that civilizations may eventually wipe themselves out through conflict, deterioration of the environment, or other ways before they have an opportunity to colonize other planets or extend into space.

Transcendence: This theory postulates that advanced civilizations may evolve into entities that live outside the realm of human comprehension, such as energy- or digital-based beings, rendering conventional means of communication obsolete.

The Zoo Hypothesis postulates that extraterrestrial civilizations exist and are aware of us, but they have decided not to contact us, either so they may observe us in peace or so they can let us evolve naturally.

Though each of these theories provides a unique viewpoint on why we haven't yet found any evidence of extraterrestrial intelligence, the real reason is still one of the greatest mysteries of science. These days, several studies from various research groups are published annually on the subject of extraterrestrial intelligence. The current exoplanet revolution has bolstered the hypothesis that advanced civilizations might exist outside of Earth.

More instruments are available for researchers to use in this kind of investigation. In April 2018, for instance, NASA's Transiting Exoplanet Survey Satellite (TESS) successfully launched and quickly took over from Kepler, which was retired later that year. Among many other things, the highly anticipated $10 billion James Webb Space Telescope of the agency was launched in December 2021 and is currently searching for possible biosignature chemicals in the atmosphere of neighboring exoplanets. The PLATO (Planetary Transits and Oscillations of Stars) mission of the European Space Agency is scheduled to launch in 2026. Later this decade, three massive ground-based observatories with adequate power to detect exoplanet air are expected to go online: the Extremely Large Telescope, the Giant Magellan Telescope, and the Thirty-Meter Telescope. Furthermore, a very ambitious initiative called Breakthrough Starshot intends to use swarms of small, laser-sailing nanoprobes to conduct up-close studies of Proxima b (The exoplanet Proxima Centauri b, also known as Alpha Centauri Cb, is a member of the larger triple star system Alpha Centauri and is circling the red dwarf star Proxima Centauri, which is the nearest star to the Sun.) and other adjacent worlds. Around 2050, if technology development proceeds as planned, the first of these robotic interplanetary vehicles may take off.

These kinds of missions and tools will aid scientists in expanding their knowledge of astrobiology, which is still in its infancy. For example, we have no idea whether our backyard contains worlds that support life. Since bacteria can endure in harsh conditions, studies conducted on Earth have led to the possibility that microbial life exists on Mars, Europa, Enceladus, and/or Titan, the massive satellite of Saturn. However, none of those planets have been investigated quite well enough for us to be certain.

But the Fermi Paradox is thinking much beyond microorganisms. In order to find a solution, we must ascertain the frequency with which extraterrestrial life emerges as well as the frequency with which it acquires the capacity and inclination to interact with other sentient beings or travel among the stars.

Perhaps the most prevalent life-supporting habitats in the Milky Way galaxy are subterranean waters, like those found on Europa and Enceladus. It appears improbable that organisms evolving in such environments will create spacecraft; in fact, a large number of them might not even be aware that there are other planets to discover.

Another possibility is alien psychology. Perhaps there are many advanced extraterrestrial civilizations, but the majority don't seem to want to interact with humans or come to Earth. Maybe Earth and its people are just too boring for them to play around with, and they won't until mankind proves intelligent and deserving enough to be accepted into the "galactic club."

Or perhaps the majority of sentient aliens generally remain silent out of fear that communicating with their galactic neighbors will result in their own captivity or destruction. Such possibilities have been mentioned by some researchers, including the late Stephen Hawking, to support their contention that mankind shouldn't actively promote itself.

Then there are the practical challenges associated with the search for sentient aliens. The cosmos is vast and extraordinarily old. Only 200,000 years have passed since the beginning of human history, and only since 1960 have we been searching for potential E.T. radio transmissions. Thus, the likelihood that we coincide with a detectable alien civilization in space and time doesn't appear very high.

Most academics believe that there is most likely no single answer to the Fermi Paradox. The "great silence" that faces us now is probably the result of several circumstances, some of which may have been mentioned above. And it could not be too long until the characteristics of those things become more apparent.

Prabir Rudra

Will Pluto ever regain its status as a planet? Does it matter?

2024-04-11T20:30:00.001+05:30

The general public was furious. Textbooks needed revision. On August 24, 2006, scientists at the International Astronomical Union (IAU) decided to reclassify Pluto, reducing its status from a planet to a dwarf planet. This decision was widely viewed as a demotion and has had a lasting impact on our understanding of the solar system.

The whole Pluto controversy is based on the problems with the definition of a "planet." According to the International Astronomical Union, a planet is a celestial entity that

1) orbits the sun,

2) appears almost spherical

3) has largely cleared its orbital vicinity of debris.

However, opinions on even this collection of measures differ. Despite their massive size, few asteroids have been removed from Earth's and even Jupiter's orbits. Ceres is one example of a small, circular globe that orbits the sun but is not regarded as a planet.

A lot of confusion indeed

The purported downgrade of Pluto from planetary classification presents more significant questions regarding the definition of any object in the solar system, or perhaps in space in general. It demonstrates how science isn't always able to classify objects into neat categories. Because it is not clear how to evaluate the many non-circular objects that round our sun if the definition of a planet is expanded once more. This might potentially cast doubt on the asteroid belt—the vast swath of tiny asteroids that lies between Mars and Jupiter. Or what would happen if a planet were to mysteriously fragment?

Nevertheless, many people are still confused about the controversy surrounding Pluto and the reasons behind its removal from the planetary orbit, even after the argument began nearly 20 years ago. However, the evolution of the solar system from nine planets to eight (at least according to the IAU definition) took a long time and illustrates one of science's greatest assets: the capacity to modify concepts that appear unchanging in the face of new information.

Peculiarity of Pluto

When astronomer Clyde Tombaugh of the Lowell Observatory in Arizona studied photographic plates of the sky on several nights, he saw a tiny dot that floated back and forth against the backdrop of stars. This led to the discovery and classification of Pluto as a planet in 1930 (note the IAU was created in 1919). However, the newest possibility in the solar system was immediately seen as a peculiarity. For 20 of its 248-year journey, it actually approaches the sun closer than Neptune due to its extremely eccentric, or non-circular, orbit. In addition, it is inclined toward the ecliptic, the plane that the other planets in the solar system revolve.

The first object in the Kuiper Belt was identified by scientists in 1992 as 1992 QB1, a small body orbiting beyond Neptune's orbit and out in Pluto's neighborhood. Soon, a large number of these objects were discovered, and they revealed a belt of tiny, frozen worlds like the asteroid belt between Mars and Jupiter. Though first believed to be even larger than Pluto, the faraway body Eris was discovered by astronomers in July 2005, upending Pluto's reign as the ruler of this region.

Confusion all around

The following queries required to be posed to researchers: Did this imply that Eris was a planet as well if Pluto was? What about the smaller things in the asteroid belt or all those other icy objects out in the Kuiper belt? What was the precise threshold for designating a body as a planet? A phrase that had appeared clear-cut and uncomplicated was now revealed to be strangely equivocal.

Following a heated discussion, numerous new definitions for planets were put forth.

Astronomers were no closer to finding a solution a year later, and the problem cast a shadowy pall over the 2006 IAU General Assembly meeting in Prague. Four proposals were put forth throughout the eight days of intense debate that the researchers had to sit through at the meeting. A contentious proposition proposed increasing the number of planets in the solar system to 12, incorporating the largest asteroid, Ceres, and Pluto's moon, Charon.

By the end of the Prague conference, three new categories for solar system objects were decided upon by the 424 astronomers. Only the planets Mercury through Neptune would be regarded as planets after that. From then on, Pluto and its relatives, which were spherical objects that orbited alongside other objects, were referred regarded as dwarf planets. Small solar system bodies would be the name given to all other objects in orbit around the sun.

The planet discussion underwent a major sea change as the New Horizon spacecraft flew across Pluto, revealing a world far more active than anyone had previously thought. Big mountains, beaten craters, and evidence of liquid moving across the surface all indicate that the world has experienced significant geological change since it formed. Based solely on this, some, like Stern, have argued that Pluto ought to be classified as a planet because it is a dynamic location that is not so static that the only things that perturb its surface are micrometeorites.

Observations of Charon, the moon of Pluto, reveal a very dynamic planet with a red cap on its pole that seems to change color in response to the gradual seasonal changes that occur so far out in the solar system. Notably, Mercury and Venus, two well-known planets, do not have as many moons as Pluto. (Most asteroids and dwarf planets have moons as well, which further complicates the definition of a planet.)

There are always new classification schemes emerging. As per a suggestion from 2017, a planet is characterized as "a round object in space that's smaller than a star." This would reclassify Pluto as a planet, but it would also reclassify the moon of Earth and many other moons in the solar system, bringing the total number of planets recognized by the scientific community to 110. A year later, Alan Stern, a leader of NASA's New Horizons mission coauthored an editorial piece in The Washington Post with planetary scientist David Grinspoon, claiming that astronomers ought to reevaluate their theories since the IAU's definition was "flawed" and "hurriedly drawn."

Will Pluto ever regain its planetary status?

So far, these requests have been ignored, and it doesn't appear probable that the IAU will take up the issue again anytime soon. As of now, it is thought that Pluto was misclassified when it was first discovered; it was never on the same footing as the other eight worlds. So Pluto is still not a planet. It was never, in fact. Scientists think that we have misinterpreted it for fifty years. Maybe we are wiser now. Nostalgia for Pluto indeed makes for a weak planet argument, but that's all there is to it. Probably we should move on to reality now.

Does it really matter?

This abundance of planet-forming possibilities suggests that every solar system might be a different ecosystem. Although it is generally true that stars can create planets through the collapse of gas and dust in their surroundings, the specific dynamics involved in planet formation are much more intricate. Are several stars involved, for instance? What is the amount of dust that is available? Is a supernova or a black hole stealing the essential gas and dust that planets require to expand?

All of this suggests that in order to account for the variety of ways that a globe could emerge, our definition of a planet might need to change. Planets might be associated with specific zones or creation conditions. It appears that the only certainty is that planethood and the controversy surrounding Pluto will remain hotly contested for some time to come as data continue to be gathered.

But when modern-day kids (who were not born when Pluto was a planet) raise a question about the necessity of the definition of a planet, it is very difficult to give an answer, and one generally avoids such a situation by saying that it's complicated!!

Prabir Rudra

Theoretical Physicist Peter Higgs, Who Discovered 'God Particle', Dies At 94

2024-04-10T18:35:00.002+05:30

Peter Higgs, born on May 29, 1929, committed his life to deciphering the secrets of the universe. His 1964 proposal that space is filled with a field that would eventually be called the Higgs field was his groundbreaking contribution to science. Fundamental particles get mass through interactions with this field. A major validation of his pioneering work came in 2012 with the finding of the Higgs boson, the predicted particle associated with the field, at CERN's Large Hadron Collider. Peter Higgs and François Englert split the 2013 Nobel Prize in Physics. The man after whom the particle is named died on Monday, April 8, 2024, at the age of 94.

In order to find the Higgs boson in 2012, the largest and most sophisticated machine in the world had to work for about 50 years. Every other particle is known to acquire mass from an elementary particle, such as an electron, quark, photon, or neutrino, or the Higgs boson. Although its existence was anticipated in the 1960s, it wasn't discovered until 2012 thanks to complex research conducted at the Large Hadron Collider, the largest and priciest machine in the world at the time, which is situated on the French-Swiss border.

Peter Higgs favored a solitary existence filled with study and introspection. He admitted that he had never used a cell phone, written or received emails, or even viewed the internet. Despite his acute shyness, Higgs had chosen to leave his Edinburgh home on the day of the 2013 Nobel Prize in Physics announcement, confident that his discovery of the Higgs particle the year before would get him the honor. Higgs, who was 82 at the time, continued to stroll the streets, stopped for lunch at a restaurant, and went to an art exhibition in an apparent attempt to avoid the spotlight and the attention that would follow. Eventually, he ran across a former neighbour who delivered the news to him. He said that the discovery of the Higgs particle had ruined his life in a later interview.

The fact that the Higgs boson (mass-giving particle) has been nicknamed the "God particle" is largely responsible for the public's fascination with it. Nobel Prize-winning physicist Leon Lederman coined the phrase when he wrote a book with the same name on the ongoing hunt for the Higgs boson in the 1990s. Lederman was convinced by the publishers to choose the term "God particle," which stuck, instead of calling his book "The Goddamn Particle," which he had intended to use to depict the enigmatic character of the Higgs boson. That phrase is hated by many scientists, primarily because it gave the particle religious undertones in certain quarters.

The Higgs boson is a particle that is intended to explain the mass of all other fundamental particles, which makes it extremely significant. Through the efforts of multiple physicists, it was revealed in the 1950s and 60s that mass is not a fundamental property of matter. Particles such as protons and electrons, despite their apparent similarity, lack mass. Similar to how there is an electric field, magnetic field, or gravitational field, Higgs and other scientists proposed the concept of an all-pervasive field, which they called the Higgs field.

However, Higgs' influence is felt far and wide, cutting across national boundaries and age groups. A tremendously great scientist, and a wonderful person whose imagination and vision have expanded our understanding of the world around us. His groundbreaking work has inspired hundreds of scientists, and for many more generations to come, his legacy will do the same.

Peter Higgs, rest in peace. Your brilliance will endure forever.

Prabir Rudra

If Earth suddenly has the atmosphere of Venus

2024-04-07T18:15:00.000+05:30

At a distance of 108 million kilometers (67 million miles) from the Sun, Venus is the second closest planet to the Sun in our solar system. So it is expected that the planet of love is a broiling hot inferno.

The conditions on Earth would drastically change if it had the atmosphere of Venus, making it incredibly inhospitable to life as we know it. Once the clear blue sky would now be a thick oppressive canvas of yellow with massive clouds of sulfuric acid. Though they would block out most of the Sun, this would not be enough to mitigate the extremely hot temperatures on the ground. How would that transform the Earth? Will that ring the death bell for all life on Earth? This is what would probably occur:

Extreme Heat: Venus has a thick atmosphere primarily made up of carbon dioxide, with some clouds containing sulfuric acid. The runaway greenhouse effect produced by this dense atmosphere traps heat and raises temperatures to extremely high levels. Earth's average temperature would soar to around 460°C (860°F), hot enough to melt lead.

Crushing Pressure: The pressure in Venus's atmosphere is roughly 92 times higher than that of Earth. It is like living approximately 900 meters underwater. Human beings would be crushed and structures would be flattened by this pressure.

Toxic Atmosphere: Venus's atmosphere would be incredibly corrosive due to the sulfuric acid clouds. When they combine with water vapor in the Earth's atmosphere, they would produce acid rain, which is deadly to living things and capable of dissolving most materials.

No Oxygen: In the atmosphere of Venus, oxygen is scarce. Breathing would be impossible for most species, including humans, as a result. Asphyxia and death would result from a shortage of oxygen.

No Liquid Water: Any water on the surface of the Earth would either boil away or exist as vapor high in the atmosphere due to the extremely high temperatures and pressure. There wouldn't be any liquid water left on the planet's surface, which is necessary for life as it exists now.

No Protection from Radiation: Right now, the atmosphere of Earth acts as a barrier to keep dangerous solar radiation from reaching humans. This shield would be compromised in the presence of an atmosphere like Venus, leaving life on Earth vulnerable to hazardous solar radiation levels.

But astronomers suggest that things were not always so drastic as it is today in Venus. A long time ago Venus might have had a climate similar to that of Earth. There might even have been oceans of water. But those times are long gone. With time the planet's atmosphere built up an excessive amount of carbon dioxide and other gases trapping heat from the Sun paving the way for a runaway greenhouse effect. Now the planet is basically an apocalyptic wasteland.

If Earth today had a similar atmosphere, all the gardens, trees, and forests would burn out leaving out their blackened skeletons. Birds will fall out of the sky. Animals would gasp their last breaths and even the fishes would bubble out of the sea. Water bodies across the planet will be at their boiling point. With time all the water will boil out and the surface of the Earth will become absolutely dry leaving behind the skeletons of the marine life. With enough time even the things that used to symbolize humanity's achievements would become grotesque sculptures of what they once were. Due to the extreme pressure, the buildings would collapse, and so would the bridges. Roads will develop cracks and become completely undrivable. This will present a devastating image. Overall, if Earth had the atmosphere of Venus, it would become an uninhabitable, hellish world devoid of life as we know it.

The only way to survive these extreme conditions is probably to take shelter underground. Subterranean shelters in the planet's crust will protect us from the extreme heat and pressure. With the right design, these shelters can recreate the favorable atmosphere that we need to stay alive. Geothermal energy can be harnessed and used in these shelters to power them. Another way of survival is to leave Earth and inhabit another planet that has favorable conditions for life.

Maybe this transformation of Earth as we know it today into a Venus-like planet will not happen overnight as we tried to imagine in the above note, but conditions show that probably we are on course towards reaching such a situation. Global warming, melting of polar caps, pollution, and deforestation are all pointing towards such a catastrophic end to life on Earth.

It's a stark reminder of how delicate and crucial Earth's atmosphere is to sustaining life and preservation of this atmosphere should be our priority.

Prabir Rudra

Total Solar Eclipse in April 2024

2024-03-30T19:20:00.005+05:30

The total solar eclipse that will occur on Monday, April 8, 2024, will cross North America, going over Canada, the United States, and Mexico. When the moon moves between the sun and the Earth and briefly obscures the sun's face, this is known as a total solar eclipse. The term "path of totality" refers to the lunar shadow's trajectory across the surface of Earth. Thirty-one million Americans already reside inside the path of totality, making the celestial marvel accessible to them. The South Pacific Ocean will be the starting point of the total solar eclipse. The Pacific coast of Mexico will witness totality first in continental North America, weather permitting, at approximately 11:07 a.m. PDT.

Following its journey from Mexico, the eclipse will pass across Oklahoma, Arkansas, Missouri, Illinois, Kentucky, Indiana, Ohio, Pennsylvania, New York, Vermont, New Hampshire, and Maine before entering the United States in Texas. The complete solar eclipse will also be visible in a few isolated areas of Tennessee and Michigan. After crossing Southern Ontario into Canada, the eclipse will pass over Quebec, New Brunswick, Prince Edward Island, and Cape Breton. At 5:16 p.m. NDT, the eclipse will leave continental North America and cross the Atlantic coast of Newfoundland, Canada.

The total solar eclipse on April 8 is expected to be the largest mass travel event in U.S. history, drawing together eclipse professionals and amateur skywatchers alike.

Various things should be avoided during a solar eclipse. Following is a list of such things:

1) Do not look directly at the sun.

2) Avoid using optical devices.

3) Don't drive wearing eclipse glasses.

4) It is better to avoid travel.

5) Do not drive while trying to watch the eclipse.

6) Use proper eye protection.

7) Don't use optical devices without proper filters.

8) Supervise children while watching the event.

Prabir Rudra

The Devil Comet is approaching us

2024-03-28T20:42:00.004+05:30

Over the next few days, skywatchers will be able to see more than just the bright planet Mercury and April's total solar eclipse. Comet 12P/Pons-Brooks, sometimes known as the "devil comet," will be visible in the night sky for the next few days and might emerge during the April 8th total solar eclipse. Since Pons-Brooks only completes one orbit around the sun every 71 years, observing it is usually an opportunity that comes only once in a lifetime.

Pons-Brooks is a ball of ice and rock that is 10.5 miles wide. In comparison, it will be twice as large as the Mount Everest. It is currently traveling towards our sun with an extremely elliptical or stretched-out orbit. It features a frozen shell, or nucleus, encircling a core composed of solid ice, gas, and dust. A coma, or a cloud of frozen material, progressively seeps out of the comet's center and covers the nucleus.

Pons-Brooks is cryovolcanic, unlike most other comets. It frequently erupts when the nucleus's fractures are opened by sun radiation. As a result, frozen cryomagma under extreme pressure erupts into space. The surrounding cloud of frozen particles enlarges and seems brighter than usual when this happens.

For the first time in 69 years, Pons-Brooks erupted violently in July 2023, leaving behind two separate gas and ice trails that resemble a pair of devil horns. It has persisted in erupting rather regularly.

When will it be visible?

Pons-Brooks may become visible to the unaided eye during the next few weeks as it passes through the inner solar system. It will stay that way until April 2 when it moves closer to the sun and disappears from view in the pitch-black night sky. The evenings of 30th and 31st March are considered to be the best time to see the comet as it will be nearest to the Earth at that time. On June 2, when it moves away from the sun, it will be at its closest to Earth. It will be roughly 139.4 million miles away and presents no known hazard to Earth.

It is expected to become even more active in the upcoming weeks and be visible to the unaided eye with a maximum brightness magnitude of about 4.0, according to SETI Institute postdoctoral scholar Ariel Graykowski. The appearance appears brighter the lower the magnitude. It won't be very noticeable in the sky because "the limit for naked eye objects in dark, moonless skies is around 6 magnitudes," according to Graykowski.

Where should we look?

It is most seen in the early evening in the Northern Hemisphere toward the west-northwest horizon. Pons-Brooks is located low in the northwest sky, close to the Pisces constellation. It should look like a blazing ball of ice, trailed by the forks of its horns.

An hour or so after sunset, the comet should be visible to the unaided eye low in the west. As it approaches the sun, it will become somewhat brighter. You want to find a place where you can see the western horizon unhindered and where there are no city lights. Using binoculars might be a good idea as the comet might be difficult to find without them.

The brightest planet Venus will become visible on one side of the sun as the sky grows darker. Jupiter, the second-brightest planet in the solar system, is located on the other side. Furthermore, you should be able to see Comet Pons-Brooks closer to Jupiter but between Jupiter and the sun if it is sufficiently bright.

Remember this is your only chance to see it because it won't be seen again until 2097.

Prabir Rudra

Big Bang: The beginning of the Universe

2024-03-26T02:58:00.000+05:30

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

Emmy Noether: Probably the best female Mathematician in the history

2024-03-23T19:13:00.001+05:30

Consider that you are launching a ball into the air. The skill of juggling involves a dance between motion and rest, with the ball's speed decreasing as it rises and increasing as it descends. One of the fundamental ideas of physics is revealed in this dance: conservation laws. Earth, or juggling for that matter, is not the only place where conservation principles apply. These are general laws of physics that hold true in many branches of the subject. However, they aren't always clear-cut. Here's where the woman from Germany enters the scene. Her discovery revealed an incredibly straightforward relationship between these conservation rules and the symmetries of the world.

Emmy Noether, the woman who developed one of the most beautiful theorems in physics. Today (March 23) is her birthday.

Emmy Noether was a German mathematician who made significant contributions to abstract algebra and theoretical physics. She was born on March 23, 1882, in Erlangen, Germany, and died on April 14, 1935, in Bryn Mawr, Pennsylvania, United States.

She developed what is now known as Noether's theorem, which is fundamental in the study of symmetries in physics. This theorem relates symmetries and conservation laws, showing that for every continuous symmetry in a physical system, there is a corresponding conserved quantity.

Despite facing discrimination as a woman in academia during her time, Noether made significant contributions to mathematics and physics. She worked at the University of Göttingen, where she collaborated with prominent mathematicians and physicists such as David Hilbert and Albert Einstein. Her work laid the foundation for modern algebra and had a profound impact on theoretical physics, particularly in the development of quantum mechanics and general relativity.

Noether thought about the issue raised by Hilbert and Einstein, namely that the General Relativity Theory appeared to violate the law of conservation of energy. This led to the development of her well-known theorem, which fundamentally altered the path of physics.

It's likely true that Emmy Noether is the best female mathematician in history. Noether's theorem fundamentally changed our view of the cosmos. Her pioneering work in abstract algebra also revolutionized mathematics.

Contributions

Emmy Noether made several significant contributions to mathematics and theoretical physics during her career. Some of her most notable contributions include:

1. Noether's Theorem: This is arguably her most famous contribution. Noether's theorem states that for every continuous symmetry in a physical system, there is a corresponding conserved quantity. This theorem has profound implications in theoretical physics, particularly in the conservation laws of energy, momentum, and angular momentum.

2. Abstract Algebra: Noether made significant contributions to abstract algebra, particularly in the development of ring theory and group theory. She introduced the concept of "ideals" in ring theory, which has become a fundamental concept in modern algebra. Her work provided important insights into the structure of algebraic systems.

3. Invariant Theory: Noether worked on invariant theory, a branch of mathematics concerned with properties that remain unchanged under a group of transformations. Her work in this area helped to clarify and extend the understanding of the relationships between symmetry and invariance.

4. Algebraic Geometry: Noether made contributions to algebraic geometry, particularly in the study of algebraic curves and surfaces. She developed the theory of "Noetherian rings" and made significant advances in understanding the properties of algebraic varieties.

5. Physics: While primarily a mathematician, Noether's work had a profound impact on theoretical physics. Her theorem has applications in various areas of physics, including classical mechanics, quantum mechanics, and general relativity. She collaborated with notable physicists such as Albert Einstein and David Hilbert, contributing to the development of their theories.

6. Teaching and Mentorship: Noether was also known for her exceptional teaching skills and mentorship of students. Despite facing discrimination as a woman in academia, she mentored several prominent mathematicians and physicists, inspiring future generations of researchers.

Emmy Noether's contributions to mathematics and theoretical physics have had a lasting impact on these fields, and she is widely regarded as one of the most influential mathematicians of the 20th century. She has left a lasting legacy, with her work continuing to influence research in various fields of science and mathematics.

Prabir Rudra

Abel Prize for 2024 goes to Michel Talagrand

2024-03-22T20:54:00.001+05:30

The 2024 Abel Prize has been awarded to Michel Talagrand of the French National Center for Scientific Research (CNRS), Paris, France for his ground-breaking work in functional analysis and probability theory, which has excellent applications in statistics and mathematical physics.

Michel Talagrand is recognized for his contributions to stochastic processes and probability theory. Problems arising in the context of gambling or risk assessment served as the first impetus for the creation of probability theory. An overarching theme throughout Michel Talagrand's seminal discoveries is interacting with and comprehending the stochastic processes surrounding us. It is now evident that in the modern world, a deep comprehension of random events is crucial. For instance, our huge language models and weather forecasts are based on random methods.

Random events are constantly at work in the modern world and have far-reaching implications for everything from condensed matter physics to business logistics. Talagrand's work mostly focuses on comprehending and applying the "Gaussian distribution," which is often referred to as the "Normal distribution" or, because of its form, the "bell curve". The Gaussian distribution governs every aspect of our lives. Weight at birth, grades at school, and retirement ages of athletes are all seemingly random phenomena that nicely fit into the Gaussian distribution.

Specific areas of research

The prize has been awarded for the following three basic areas:

Suprema of stochastic processes:

The greatest value that can be anticipated from a group of random values is known as the "supremum" of stochastic processes. A stochastic process generates a series of random values. Knowing the expected height of the biggest wave that will hit the beach the following year is helpful if the height of waves that smash onto a beach is determined by a stochastic process.

Concentration of measures:

It may seem counterintuitive, but when a process relies on a variety of random sources, rather than becoming more complex, the various random components may be able to balance each other out and yield more predictable outcomes. For this, Talagrand has provided accurate quantitative estimations.

Spin glass:

Leaving abstract probability theory behind, physicists were first surprised to learn that atoms may arrange themselves in a unique form of matter called a "spin glass". Talagrand finished the proof of Giorgio Parisi's work, which won him the Nobel Prize in 2021, by using his understanding of statistics and probability to establish bounds on the behavior of spin glass matter.

Talagrand is a strong problem solver in addition to being an outstanding mathematician. He has significantly advanced our knowledge of random processes, particularly Gaussian processes. His contributions have changed probability theory in several ways. Professor Helge Holden, chair of the Abel Prize Committee, adds, "His proof of the renowned Parisi formula for the free energy of spin glasses is an amazing accomplishment."

Life

Michel Talagrand was born in France in 1952 and graduated from the University of Paris VI with a Ph.D. in mathematics in 1977. He studied for a while at Ohio State University in the United States. He is married and has two sons. He is a member of the French Academy of Sciences and has won various honors and awards. One of the amazing things that he runs on his website is that he challenges mathematicians to solve riddles under the banner "Become rich with my prizes."

Prabir Rudra

The explosion of Corona Borealis: Once in a lifetime sight in the sky

2024-03-22T01:42:00.001+05:30

According to NASA, astronomers anticipate that a "new star" will emerge in the night sky at any moment between now and September, 2024. This celestial spectacle is expected to be once in a lifetime.

The Milky Way's Corona Borealis, or Northern Crown constellation, which is situated between the Boötes and Hercules constellations, is where the anticipated brightening event, known as a nova, will occur.

A nova is the quick, brief explosion from a collapsing star known as a white dwarf, whereas a supernova is the catastrophic death of a large star.

The "Blaze Star," or T Coronae Borealis, is a binary system in the Corona Borealis that consists of an aged red giant star and a dead white dwarf star. When stars run out of hydrogen for nuclear fusion and start to fade, red giants are created. NASA estimates that in roughly 5 or 6 billion years, our sun will turn into a red giant, sputtering and growing as it releases layers of material and probably vaporizing the inner planets of the solar system. In this context, Earth's future is yet unknown.

An explosive event occurs in T Coronae Borealis approximately every 79 years.

Because of their close proximity, the stars in the orbital pair interact furiously with one another. As the red giant heats up, it becomes more unstable, shedding its outer layers that fall as matter onto the white dwarf star.

According to the space agency, the interchange of stuff leads the white dwarf's atmosphere to steadily heat up until it undergoes a "runaway thermonuclear reaction," which results in a nova.

How to keep an eye on the event?

Astronomers are closely monitoring T Coronae Borealis once more after it last had a spectacular outburst in 1946.

In an email, NASA Meteoroid Environments Office lead William J. Cooke stated that "most novae happen unexpectedly, without warning." Nonetheless, T Coronae Borealis is among the galaxy's ten recurrent novae. From the last eruption in 1946, we know that the star will darken for a little more than a year before brightening up quickly. T Coronae Borealis started to dim in March of last year, and between now and September, some researchers anticipate that it may go nova. We are unable to predict with greater accuracy than the few months it will take for this to occur, given the current state of knowledge.

It is anticipated that the star system, which is 3,000 light-years away from Earth and usually too faint to be seen with the unaided eye, would become as bright as Polaris, or the North Star.

When the nova reaches its maximum brightness, it will appear as if a new star has emerged. It can be seen with binoculars for a little over a week and without any equipment for a few days, after which it will fade and be lost from view for another 80 years or more.

The nova will be visible from the Northern Hemisphere, appearing in a little arc between the constellations Hercules and Boötes.

The Neil Gehrels Swift Observatory, located in space, will be used by astronomers to analyze the celestial event through ultraviolet and X-ray light, while the Hubble Space Telescope will be used to observe the nova.

Cooke stated, "Repeated novae like T Coronae Borealis provide us insights into the thermonuclear runaway that occurs on the surface of the white dwarf when the star goes nova and help us understand the mass transfer between the stars in these systems."

Updates regarding the eruption and its appearance will be available from the NASAUniverse account on X, formerly known as Twitter.

Cooke remarked that the brightness of Nova Cygni, which he saw last in 1975, was comparable to that of T Coronae Borealis. It is not anticipated that Nova Cygni will encounter another explosion.

"On August 29, I was outside as a teenage astronomy geek who was about to start college," Cooke recalled. "Looking up at the sky, I saw that there was a star that shouldn't have been there in the Cygnus constellation. We discovered that we were staring at a nova after I persuaded some pals who thought I was insane to look at it! It was a really memorable event that confirmed my professional decision to pursue astronomy. I used to make jokes about how undergraduate physics had to blow out a star for me to have to endure it.

Prabir Rudra

Wormhole: The missing link between us and our future home

2024-03-17T02:11:00.001+05:30

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

Pi Day 2024

2024-03-14T11:18:00.003+05:30

Pi Day is an annual celebration observed on March 14th (3/14) around the world. It's a day dedicated to the mathematical constant π (pi), which is approximately equal to 3.14159. Here are some key aspects and traditions associated with Pi Day:

Origin:

Pi Day was first celebrated in 1988 by Larry Shaw, a physicist at the Exploratorium, a museum of science, art, and human perception in San Francisco. Shaw organized various activities and celebrations to mark the day, including a circular parade and eating pie.

Significance of Pi:

Pi is a mathematical constant that represents the ratio of a circle's circumference to its diameter. It's an irrational number, meaning its decimal representation never ends or repeats. Pi has fascinated mathematicians, scientists, and enthusiasts for centuries due to its unique properties.

Activities and Events:

Pi Day is often celebrated in schools, universities, museums, and math clubs through various activities and events. These may include pi recitation competitions, pi-themed quizzes, math art contests, and hands-on activities related to circles and geometry.

Pie Eating:

One of the most popular traditions associated with Pi Day is indulging in pies, both savory and sweet. Whether it's apple pie, pumpkin pie, pizza pie, or any other kind, enjoying a slice of pie on Pi Day has become a widespread tradition.

Educational Outreach:

Pi Day provides an opportunity for educators to engage students in learning about mathematics and its applications in a fun and interactive way. Teachers often use the day to introduce concepts related to circles, geometry, and the history of mathematics.

Pi Memorization:

Some enthusiasts challenge themselves to memorize and recite as many digits of pi as possible. While memorizing pi to hundreds or even thousands of digits is impressive, it's important to note that the practical applications of pi typically require only a few decimal places.

Online Celebrations:

With the rise of social media and online communities, Pi Day celebrations have expanded to the digital realm. People share pi-related memes, jokes, artwork, and trivia on platforms like Twitter, Instagram, and Reddit, fostering a sense of camaraderie among math enthusiasts worldwide.

Overall, Pi Day is a fun and inclusive celebration of mathematics that encourages people of all ages to appreciate the beauty and ubiquity of numbers in our lives. Whether you're a seasoned mathematician or just someone who enjoys a good slice of pie, there's something for everyone to enjoy on Pi Day. Wish everyone a very happy Pi Day 2024!!

Prabir Rudra

Classical Mechanics: A journey from Newton to Lagrange and Hamilton

2024-03-12T15:46:00.003+05:30

Classical mechanics, as understood today, is largely attributed to the foundational contributions of Sir Isaac Newton, building upon the work of earlier thinkers like Galileo Galilei. Here is a brief overview of the contributions of Newton and Galileo to classical mechanics:

Galileo Galilei (1564-1642):

Experimental Approach:

Galileo is often considered the father of modern physics due to his emphasis on experimental methods. He conducted a series of experiments on inclined planes and falling bodies to study the fundamental principles of motion.

Law of Inertia:

Galileo formulated the principle of inertia, which states that an object at rest will remain at rest, and an object in motion will continue in motion with a constant velocity unless acted upon by an external force. This laid the groundwork for Newton's first law of motion.

Uniform Acceleration:

Galileo made significant progress in understanding uniformly accelerated motion. He developed mathematical descriptions of falling bodies, showing that the distance traveled is proportional to the square of the time elapsed.

Isaac Newton (1642-1727):

Three Laws of Motion:

Newton formulated three laws of motion, which are fundamental principles of classical mechanics.

First Law (Law of Inertia): An object at rest stays at rest, and an object in motion remains in motion with a constant velocity unless acted upon by a net external force.

Second Law: The force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma).

Third Law: For every action, there is an equal and opposite reaction.

Law of Universal Gravitation:

Newton proposed the law of universal gravitation, which states that every mass attracts every other mass in the universe with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Mathematical Formulation:

Newton's work was not only conceptual but also highly mathematical. He introduced calculus to describe motion and developed differential equations to express the relationship between force, mass, and acceleration.

Unified Theory:

Newton's laws of motion and the law of universal gravitation provided a unified framework for understanding a wide range of phenomena, from the motion of celestial bodies to the behavior of objects on Earth. This marked a significant departure from earlier fragmented approaches.

Together, the contributions of Galileo and Newton laid the foundation for classical mechanics, providing a systematic and mathematical framework for understanding the motion of objects and the forces acting upon them. Their work is essential for understanding the physical world and continues to be a fundamental part of the study of physics.

Development into an advanced form of mechanics

There was a lull following Newton, and it took until the end of the eighteenth century for classical mechanics to advance further. The development of classical mechanics from Newton to Lagrange and Hamilton represents a significant evolution in the understanding of physical systems. Here is a more detailed overview of this progression:

Newtonian Mechanics (17th century):

Isaac Newton (1642-1727):

Newton formulated the three laws of motion and the law of universal gravitation, establishing a comprehensive framework for classical mechanics. His work laid the groundwork for understanding the motion of objects and the force interactions between them. Newtonian mechanics was basically a force-based mechanics where all motions were considered to be directly associated with forces.

Principle of Least Action (18th century):

Pierre Louis Maupertuis (1698-1759):

Maupertuis introduced the principle of least action, suggesting that natural processes follow paths that minimize or maximize a certain quantity called action. The principle states that "the actual path taken by a physical system between two points in its configuration space is the one for which the action, defined as the integral of the Lagrangian over time, is stationary—either a minimum, maximum or a saddle point".

Analytical Mechanics and Euler-Lagrange Equations (18th century):

Leonhard Euler (1707-1783):

Euler made significant contributions to mechanics, formulating the Euler-Lagrange equations. These equations provided a mathematical framework for expressing the equations of motion using the principle of least action.

Lagrangian Mechanics (18th century):

Joseph-Louis Lagrange (1736-1813):

Lagrange further developed the analytical approach to mechanics, introducing the Lagrangian formulation. In his work "Mécanique Analytique" (1788), Lagrange employed generalized coordinates and the principle of least action to derive the equations of motion.

Hamiltonian Mechanics (19th century):

William Rowan Hamilton (1805-1865):

Hamilton built upon Lagrange's work and introduced Hamiltonian mechanics. He reformulated the principle of least action in terms of the Hamiltonian function (H= Kinetic Energy + Potential Energy) leading to Hamilton's principle. In 1833, he published "On a General Method in Dynamics," which introduced the Hamiltonian formulation of mechanics. This approach uses generalized coordinates and momenta to describe the dynamics of a system, and it is equivalent to the Lagrangian formulation. Hamiltonian mechanics provides an alternative perspective, particularly useful in certain physical problems and in the context of quantum mechanics.

In summary, the development of classical mechanics from Newton to Lagrange and Hamilton involved a transition from empirical laws to more abstract and general mathematical formulations. The most striking feature of this advanced form of classical mechanics is that it is no longer a force-based mechanics like its Newtonian counterpart, but it is now based on energy. Euler, Lagrange, and Hamilton each contributed significantly to the analytical and variational approaches that are foundational to classical mechanics today. The Lagrangian and Hamiltonian formulations provide powerful tools for solving complex problems and have applications in various branches of physics.

Prabir Rudra

Mysterious radio signals from space indicate that we may have contacted the Alien world

2022-10-01T12:16:00.008+05:30

China's five hundred meter aperture spherical radio telescope (FAST) has recorded some strange signals coming from a faraway galaxy (3 billion light-years from Earth). The cosmic source from which these signals are coming is identified as Fast radio burst (FRB) and the source is named FRB 20201124A.

This is in fact the second time that such repeated signals have been received after its discovery in 2019. FRBs are intense but brief flashes of radio frequency emissions. They last just a few milliseconds, and so detection of these signals requires high-end instruments and proper knowledge.

Chinese astronomers who have studied these signals say that the signals are coming from a magnetar or neutron star residing in that galaxy, having an extremely high magnetic field. The scientists continuously monitored these signals coming from the same direction for 91 hours. Out of these 91 hours, 1863 signals have been received for 82 hours.

Magnetar

Scientists from China and America are now collaborating in studying these strange signals and trying to derive meaning from them. They say that radio signals of different wavelengths have been received from time to time coming from this same direction. Moreover, the object is said to emit smaller and weaker radio bursts between the fast radio bursts. Observations from FAST, Guizhou, China have been localized by the US National Science Foundation's Karl G. Jansky Very Large Array (VLA).

Signals

They speculate that there is a hidden code in these signals and probably some alien species is trying to communicate with us via these signals. The trouble is however the decryption of this code and understanding the message hidden in it (if at all there is any).

Fast radio bursts are not new to us, in fact, they have been discovered 15 years ago. These radio bursts are associated with the energy release equal to millions of suns. Generally, most FRBs explode once and the corresponding radio signals are received once during a particular time. But there have been exceptions to this. Many FRBs have been found to emit signals continuously over a period of time which is quite baffling indeed. In 2020 a fast radio burst was discovered inside its galaxy, which is again a very rare and strange incident.

Since then the study of FRB has gained interest and scientists have continuously monitored FRB 20201124A. It has been found that the source is not only sending the signals but also polarizing them simultaneously. More polarization would mean stronger magnetic fields of the source.

Carefully studying these signals would help us to know more about the atmosphere of the source magnetar. The study has been published in the prestigious journal Nature. These signals are continuously reaching us for the past few years, but we are yet to derive any meaning from them. If we finally do succeed in doing that, probably it will be a new dawn in the scientific prowess of humans.

Prabir Rudra

The rings of Neptune captured by James Webb Space Telescope after three decades

2022-09-24T01:22:00.006+05:30

Rings of Neptune

Rings of Neptune!! Yes, you heard it correctly. We are all so familiar with the rings of Saturn, the countless small particles of different shapes and sizes that orbit around Saturn, giving a ring-like look. But very rarely do we find anybody speaking about the rings of Neptune. This is exactly what the James Webb space telescope has spotted.

But this is not the first time that these rings have been visible to us. We knew about these rings earlier, but this is the first time we have received such a clear and crisp image of the rings of Neptune and this spotting has been possible after 30 years.

James Webb Space Telescope

Neptune has always fascinated researchers since its discovery on 23rd September 1846 by Johann Galle. It is the only planet in the solar system which was discovered on the basis of mathematical prediction rather than by empirical observation.

Alexis Bouvard observed that there were unexpected changes in the orbit of Uranus. From this, he hypothesized that the orbit of Uranus was subject to gravitational perturbations of an unknown planet, which was later found to be Neptune.

In 1989 Nasa's Voyager II spacecraft did a flyby past Neptune and during this time it captured the planet's rings. After that Voyager II continued its journey in interstellar space beyond the solar system, so no more images of these rings could be captured.

The recent images captured by the Webb show Neptune's fainter dust bands in addition to several bright, narrow rings. It should be noted that Neptune is located 30 times farther from the Sun than Earth and its orbits are located in the remote darker regions of the solar system. Moreover, due to its chemical composition, it is generally referred to as an ice giant, in contrast to the gas giants like Jupiter and Saturn.

Hubble Space Telescope

The images of Neptune captured by the Hubble space telescope (images at visible wavelength) have a bluish tinge due to the presence of small amounts of gaseous methane. But the James Webb space telescope captured Neptune in its near-infrared range which gave the planet a purple tinge instead of blue.

Apart from these, Webb has also captured 7 out of 14 moons of Neptune. There is a very bright point seen in the image captured by the Webb, which is Neptune's large and unusual moon Triton (it orbits Neptune in a strange backward orbit). Triton reflects more than 70% of the sunlight that is incident on it. Moreover, due to methane absorption, the planet's atmosphere is darkened at near-infrared wavelengths. The combined effect is that Triton quite easily outshines Neptune in the image. The image from Webb has also revealed a continuous band of high-latitude clouds surrounding the planet, which was never seen before.

Prabir Rudra

TOI-1452b: An Earth-like planet with deeper oceans and two suns.

2022-09-06T16:53:00.006+05:30

Recently NASA discovered an exoplanet orbiting around two suns outside our solar system in the Draco constellation. It is named TOI-1452b and is 70% larger in size compared to Earth. The most striking feature of the planet is that it is covered with oceans considered to be deeper than those on Earth. But the feature that arouses the greatest interest is that the planet is situated in the habitable region of the parent stars and water on it remains in a liquid form unlike many moons in our solar system.

This super-earth was discovered two years ago by the TESS space telescope. The planet orbits a binary star system that has currently collapsed to its dwarf stage. So they are around four times smaller than the sun. The revolution speed of the planet is extremely high and so a year on this planet lasts for only 11 days. The orbit of the exoplanet is smaller compared to Earth separated by only 97 astronomical units. Moreover, it is cooler but receives enough light to sustain life.

Researchers have estimated a total ocean presence of around 30% of the total mass. This is huge compared to that of Earth because Earth's 70% water regions only make up about 1% of the total mass. The massiveness of the planet suggests that the depths of the oceans will be far greater than those on Earth. So from this, we can understand the huge reservoir of water that this planet holds. To add to this, all the water present on this planet is in liquid form, which is a real advantage. We know that Jupiter's two moons Ganymede and Callisto contain deep oceans, but they are buried deep beneath thick sheets of ice. The same applies to Saturn's moons Titan and Enceladus.

Jupiter and its moon Ganymede

Titan: Saturn's moon

To draw some concrete inferences, scientists need to get more observations from powerful telescopes like the James Webb. It is theorized that life originated under the oceans near the hydrothermal vents. Considering this, presence of such a huge amount of water are really positive signs for us. Although scientists are of the idea that the planet does not have an atmosphere, we know that the planet can be brimming with life. This is because some of the branches of the oldest bacteria can live in extreme environments. So in all, the exoplanet is of great interest to us and can be significant in shaping the future of humanity.

Bacteria

Prabir Rudra

Mathematical Theory of Probability: A historical perspective from Pascal to Laplace

2022-08-27T23:44:00.001+05:30

3 dice rolling problem

Terminology

The term 'Probability' literally means chance or odds or expectation or likelihood. The term originates from the medieval Latin word 'probabilis' meaning plausible. Probability is always utilized to study the behavior of stochastic (random) processes like tossing a coin or rolling a dice. Historically probability has always been closely associated with the term chance and used synonymously with it until we had a proper mathematical perspective in the 18th century. The early form of the theory was called the 'Doctrine of Chances'.

Origin

Probability finds its place in the ancient and medieval laws of evidence where they had to deal with proofs, credibility, and uncertainties of evidence in a court. Games of chance are believed to have existed as early as the Egyptian civilization. In the excavations of different tombs of the Pharaohs, they found a game called 'Hounds and Jackals' which matches closely with our modern-day game of 'Snakes and Ladders.' This must have been the early stage of the creation of dice. Throwing around a set of dice and betting on its outcome has been an ancient habit of humans and this has been passed on from one civilization to another. The first dice game found in the literature of the Christian era was known as 'Hazard', played with 2-3 dice. The game was thought to have been brought to Europe by the knights returning from the crusades. The pottery of the Greek civilization showed the existence of some games which involved various degrees of uncertainty. Present-day casinos all other the world have successfully carried on the legend to modern times.

During Renaissance, Europe was a center of gambling and other games of chance which involved a humongous amount of wealth put at stake. Maritime insurance plans were supposed to be estimated based on the risks involved. But during that time (17th century) there was no proper mathematical framework that could provide a logical basis to calculate or predict the degree of risks involved in these. People would always like to know an estimate of returns for the wealth they put at stake. These could only be provided by a sound mathematical theory that could take into account the randomness (unpredictability) of the systems and thoroughly perform a risk analysis. Under such situations, the stage was set for the mathematicians of that era to step forward and start developing a mathematical framework that would fulfill the needs of the prevailing society.

The early form of the theory

The early form of the mathematical theory of probability can be attributed to four mathematicians of that era, namely, the Italian polymath Gerolamo Cardano, the French mathematicians Pierre de Fermat and Blaise Pascal, and the Dutch mathematician Christiaan Huygens. Cardano began his investigations as early as 1560, but his work was unknown to society for 100 years. He basically put his thoughts into investigating the sum of the numbers obtained from the throws of three dice. The randomness involved amazed him and he tried to find a pattern in it. This was such a booming topic in those days that Galileo could not stay away from it. In the early 17th century he considered the problem of throwing 3 dice and declared that it is possible to throw some numbers more often than others because there are more ways to create that number. From the middle of the 17th century, there began a correspondence between Fermat and Pascal aiming to find a solution for the games of chance. This triggered a serious attempt towards the development of a mathematical basis of probability. In 1657 Huygens gave a comprehensive treatment to the concept.

Subsequent developments

In the 18th century, the subject was taken up by the Swiss mathematician Jacob Bernoulli and the French mathematician Abraham De Moivre. In his Arcs Conjectandi (1713), Bernoulli derived the first version of the Law of Large Numbers (LLN), which states that the average of the results obtained from a large number of trials of a random experiment should be close to the expected value and the gap gradually decreases as the number of trails are increased. De Moivre in his Doctrine of Chances (1718) showed the method of calculating a wide range of complex probabilities.

By the 19th century, it was almost evident that the mathematical theory of probability is a powerful mathematical tool having a wide range of real-life applications. The randomness or uncertainties in various activities of human life and natural phenomenon can be well addressed by a well-formulated theory of probability. To re-affirm this idea German mathematician and physicist Gauss used the theory in astronomical studies and the predictions were great. From a few observational data, he determined the orbit of Ceres (a dwarf planet in the asteroid belt between Mars and Jupiter). He used the method of least squares to perform an error analysis to correct the errors in the observations, which became a routine analysis in astronomy thereafter. To do this he used the normal distribution of errors in his calculations, which is a probabilistic tool. In 1812 French scholar and polymath Laplace further developed the theory by introducing fundamental concepts of mathematical expectations which include the moment generating function, the method of least squares, and the testing of hypothesis. From here the mathematical theory of probability took a turn and slowly started to develop a bonding with the mathematical theory of statistics. It was understood that the two concepts are related and one cannot do without the other.

Dwarf planet Ceres

Probability in Physics

By the end of the 19th century, physics was gaining ground and was the leading science of the era. Classical mechanics developed by Newton, Lagrange, Hamilton, etc were no longer valid for the sub-atomic worlds. Science needed new physical theories to describe the observations. Who knew that the mathematical theory of probability will form the cornerstone of the new theories to come? It was found that the properties of gases like the temperature could only be expressed in terms of the motions of a large number of particles. This could not be done without the help of statistics as the number of particles that we are talking about here is huge. Ludwig Boltzmann and J. Willard Gibbs developed the field of Statistical Mechanics to address the problem, which involved the concepts of probabilities and statistics.

Gas particles

The laws followed by the sub-atomic (micro) particles were queer and totally different from the classical world. To address this issue Quantum Mechanics was developed in the 20th century by people like Max Planck, Albert Einstein, Niels Bohr, Werner Heisenberg, Erwin Schrodinger, Paul Dirac, Wolfgang Pauli, Richard Feynman, etc. The basis of the modern quantum theory is the Uncertainty principle proposed by Heisenberg and it is built on the concepts of probability.

Probability in today's World

The twentieth century saw the mathematical theory of probability develop leaps and bounds. One of the basic problems of probability is finding a formal unambiguous definition of the mathematical origin. The theory is so realistic, obvious, and application-based that it was really tough to find a theoretical definition of probability. The classical definition was initially formed which was far from being sufficient and made way for the frequency definition. Finally, the frequency definition was replaced by the axiomatic definition given by the Russian mathematician Andrey Kolmogorov in 1933. The axiomatic definition is based on three axioms which are logical and accepted worldwide. It settled the long-standing disputes between mathematicians regarding the definition of probability.

Probability and Statistics found a link and came together through the concept of hypothesis testing introduced by the Polish mathematician Jerzy Neyman and the British polymath R.A. Fisher. In modern times the concept of hypothesis testing is applied in various fields like biological and psychological experiments. It is used in the clinical trial of drugs and also in economics. Nowadays the idea of probability is used in concepts like the Markov process, Brownian motion, and other places where we have to deal with an aggregate of entities. Random fluctuations of stock markets are studied using probabilistic mathematical models to provide predictions for investors. So Mathematical finance has emerged as a new area of mathematics.

The modern era is an era of computer simulations, artificial intelligence, quantum computing, data science, etc. In almost all these areas the mathematical theory of probability plays a significant role. It is understandable that there is still a lot of room for development. Mathematicians all over the world work on stochastic models with the aim of improving the theory and increasing its applicability. We hope that a theory that developed from within the human society out of utmost necessity, will continue to develop and help humanity reach new heights in science and technology.

Prabir Rudra

Quantum Mechanics: Are we a particle or a wave or both!!!?? Two contradictory pictures of reality!!

2022-08-24T17:30:00.021+05:30

I think I can safely say that nobody understands quantum mechanics-- Richard Feynman

The macro world that we know around us works on some simple set of rules and principles, that have been deeply inscribed in our intuition. When we push or pull an object, it tends to move. Throw a stone upwards and it returns to the Earth. Move towards a wall and try to walk through it and you cannot do it. These are familiar and accepted pictures of our day-to-day life. But as soon as we glance into the atomic and sub-atomic world (micro) the picture completely changes. As more and more observations were made it was clear that these microparticles followed some laws which were really very queer when compared to our accepted laws of the classical world. By the end of the 19th century, it was quite clear that classical mechanics will not work at micro levels.

Black body radiation

It began with the problem of black body radiation. A perfectly black body is one that absorbs all the electromagnetic radiation that falls on it. It is a perfectly idealized system. The radiation spectrum of such a body could not be explained by the classical law of Rayleigh-Jeans. Max Planck adopted a mathematical trick to get a solution for this problem. He assumed that light is not a continuous wave, but is made up of discrete packets of energy called quanta. This means that energy can only exist as integral multiples of some small units of energy (quanta) and not in any arbitrary amount.

Planck himself was very confused about this and did not believe it, calling it an act of sheer desperation. But with the assumption, the equations worked perfectly. With this adjustment, Planck proposed the basic form of quantum theory in 1900. It took some time for the people to get adjusted to such ideas but slowly it did happen. In 1905, Albert Einstein discovered the photoelectric effect where he considered the discrete quanta of light as discrete particles called photons. He was awarded the Nobel prize in physics for this contribution in 1921. Planck's theory coupled with Einstein's photoelectric effect is considered as the "old quantum theory".

Dawn of the era of quanta

With the advent of this concept of energy quanta, it seemed that since the building blocks of matter follow this strange law, there is an obligation to explain the entire physical world based on this conceptualization. Using the concept of energy quanta Niels Bohr finally pulled off his model of the atomic structure, which is the accepted model till date. He argued that the electrons revolving around the nucleus in different orbits can possess energy, which are integral multiples of the energy quanta, and transition from one orbit to another is associated with absorption or liberation of such energy quanta. As time went by the scientists looked for a quantum description of the fundamental forces of nature like the electromagnetic force. Richard Feynman played the most significant role in quantizing the electromagnetic force through his theory of Quantum Electrodynamics (QED). Till now we are searching for a proper quantum description of the gravitational force, which has been termed the theory of quantum gravity. String theory, Loop quantum gravity, gravity's rainbow, etc. are some of the leading contenders, but none have been able to provide a proper flawless quantum picture of gravity.

Wave-particle duality: How it really got bizarre!!

To describe the physical properties of sub-atomic particles it was seen that not only the accepted picture of classical mechanics failed but also our intuition regarding the very nature or identity of the particles needed a serious revision. This was evident when it was seen that in order to explain the physics of the micro world we needed to adopt a dual picture of wave and particle of all the matter present around us. It is actually a bizarre scenario where any matter can exist in both states depending on its state of being observed. To be more precise, a particle when not observed by the observer exists as a delocalized wave, but as soon as the observer lays his/her eyes on it, there is a complete collapse of the wave and it exhibits a pure particle nature. Equivalently it can be stated that when the properties of a particle are measured, there is a simultaneous collapse of the wave function. This is one of the fundamental features of the Copenhagen agreement of quantum mechanics between Niels Bohr and Werner Heisenberg. It was such an exotic and unbelievable concept, that Albert Einstein wrote, "It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality. Separately neither of them fully explains the phenomena of light, but together they do". He actually disliked the idea and said, "God does not play the dice with the universe". Although many scientists like Max Planck, Albert Einstein, Niels Bohr, Warner Heisenberg, Erwin Schrodinger, Arthur Compton, etc. were involved in the development of this concept, this idea is often attributed to the French physicist Louis De Broglie after he experimentally demonstrated the wave-like behavior of matter in 1927. De-Broglie was awarded the Nobel prize in physics for this effort in 1929.

Niels Bohr involved in a discussion with Albert Einstein

Further Developments

As the wave-particle duality of matter gained more and more acceptance, a picture of uncertainty at the micro level hovered in front of the eyes of physicists. This is evident when we consider the delocalization of the particle in the form of a wave. Such uncertainties will bring the mathematical theory of probability into the picture since we are no longer dwelling in our well-known deterministic world of classical objects. In order to set up a proper mathematical theory of this interpretation, we needed a wave function and a principle that well defines the uncertainty at the quantum level.

Werner Heisenberg, a young German theoretical physicist published his Uncertainty Principle in 1927, where he stated that the velocity and the position of a quantum particle cannot be measured simultaneously. He stated this mathematically through a set of inequalities asserting a fundamental limit to the accuracy with which certain pairs of physical quantities of a particle may be predicted from the initial conditions. Heisenberg also developed the matrix formulation of quantum mechanics. In 1932 he was awarded the Nobel prize in physics for "the creation of quantum mechanics".

Heisenberg's Uncertainty Relation

Werner Heisenberg

Erwin Schrodinger was an Austrian-Irish physicist, who developed the wave mechanics of quantum mechanics. In 1926, Schrodinger published his famous wave equation that mathematically determines the wave function. He firstly derived it for time-independent systems and showed that it gave the correct energy eigenvalues for a hydrogen-like atom. He later published the dynamic solution characterizing the time dependence of the wave function. With complex solutions to Schrodinger's wave equation, quantum mechanics shifted from real numbers to complex numbers. Schrodinger was very disturbed by the probabilistic interpretation of quantum theory and the entire matrix mechanics. To ridicule the Copenhagen interpretation of quantum mechanics, he conceived the famous thought experiment known as Schrodinger's cat paradox. He kept himself completely aloof from the uncertainty principle and probabilistic aspects of quantum theory, as he did not believe in them. Regarding this, he said, "I don't like it and I am sorry I ever had anything to do with it". Nevertheless, his wave equation is universally celebrated as one of the most important achievements of the twentieth century and created a revolution in most areas of quantum mechanics. He won the Nobel prize in physics in 1933 for his extensive work on quantum mechanics.

Paul Dirac was an English theoretical physicist who had a profound impact on the development of quantum mechanics through his theory of relativistic quantum mechanics. His greatest contribution was the formulation of the Dirac equation which describes the behavior of fermions. This was the very equation that predicted the existence of antimatter. He shared the 1933 Nobel prize in physics with Schrodinger for his contributions to quantum mechanics. He also played a significant role in the reconciliation of quantum mechanics with general relativity, which was Albert Einstein's dream till death.

The development of quantum mechanics continued throughout the twentieth century and is even continuing today. Richard Feynman, an American physicist, through his development of quantum electrodynamics made a significant contribution. It reconciled quantum mechanics with electromagnetism. He received the Nobel prize in physics in 1965 jointly with Julian Schwinger and Shinichiro Tomonaga. Feynman was very famous for his Feynman diagrams which is a pictorial representation scheme for mathematical expression describing the behavior of sub-atomic particles.

The fifth Solvay conference on physics was held in 1927. The conference was dedicated to various aspects of quantum theory. Considered to be the image with the highest IQ in history.

Implications of the theory

It is believed that the bizarre nature of the theory is due to our lack of enough knowledge about it. Some of the implications of quantum theory like quantum entanglement are really baffling!! Quantum entanglement says that two particles separated by large spatial distances can interact with each other and link together to attain similar properties. It is as if we have two copies of the same particle separated by a large spatial distance. Just amazing!! This concept was addressed in a 1935 paper by Albert Einstein, Boris Podolsky, and Nathan Rosen, which came to be known as the EPR paradox. They considered this phenomenon to be an impossible event as it directly violated the causality principle.

Quantum teleportation is a procedure of transportation of quantum information from a sender to a receiver spatially separated from each other. Experimentally it has been seen that quantum teleportation is possible for quantum information in the form of photons, atoms, electrons, etc. But in the realm of teleportation, the actual challenge will be to transfer physical objects from one location to another location, which seems to be almost impossible at present.

Quantum computing is an area of study where we study computer-based technologies using the principles of quantum mechanics. In this realm, we actually use the intricacies of quantum laws to solve very complicated classical problems conveniently. To facilitate these quantum computers have been developed which are far more complex and completely different from their classical counterparts. Problems with a high degree of complexity are efficiently solved using these machines, which use quantum laws as the basic ingredient.

Quantum computer

Quantum mechanics is the theory of nature working at the most fundamental level and it is obvious that nature will not unfold its secrets so easily. The theory is still considered to be in its infancy and we do not know how long we will have to wait to know enough so that we have the complete picture at the quantum level. Over the years we have looked towards quantizing various theories of physics by reconciling them with quantum mechanics. This is felt necessary because a quantum theory works at the fundamental level and all the other theories must obey these laws at the quantum level. Currently, the biggest puzzle of modern physics is to reconcile quantum mechanics with gravitation giving a satisfactory theory of quantum gravity. Many stalwarts including Einstein have worked towards achieving it, but we are yet to get a satisfactory result. The singularity inside a black hole is believed to be the perfect laboratory for testing quantum gravity. There have been significant advances in the field of black hole physics and so we are hopeful of achieving something fruitful in near future. Perhaps we are waiting for the next Heisenberg or Schrodinger or Dirac to come along and show us the path.

Prabir Rudra

What if we can experience multiple sunrises and sunsets in a single day!!

2022-08-19T13:03:00.000+05:30

Prabir Rudra

The curious case of Pluto

2022-08-16T10:40:00.002+05:30

Prabir Rudra

How the stars and the planets influenced the date of India's Independence

2022-08-16T10:37:00.005+05:30

Prabir Rudra

White dwarf: The death bed of a star telling the story of its glorious past (Meme)

2022-08-07T16:18:00.003+05:30

Read the full article at: https://www.spacetimerecipe.com/2022/08/white-dwarf-death-bed-of-star.html

Prabir Rudra

White dwarf: The death-bed of a star telling the story of its glorious past

2022-08-06T23:16:00.002+05:30

A white dwarf is a compact stellar core remnant resulting from gravitational collapse. Dense electron degenerate matter fills up such astronomical objects. Since nuclear fusion ceases to take place in a white dwarf, it almost has no light of its own. But still, a white dwarf may appear faintly lit in the sky, due to the residual thermal energy that it carries forward from the fusion reaction during the star's lifetime. Sirius B at a distance of 8.6 lightyears is the nearest known white dwarf. Around 8 white dwarfs are known to us in the vicinity of our solar system.

Formation

When a star is on the verge of completing its life cycle, its thermonuclear fuel is completely depleted from the core. This results in the halt of the nuclear fusion occurring in its core and there is an imbalance of outward and inward forces in the star with the inward gravitational force dominating the outward thermonuclear force. So the star collapses due to its own mass, with its volume becoming smaller and smaller. This makes the inside material denser and denser. Now if the original star does not have enough mass (> 25 solar masses) to form a neutron star, the remnant generally goes on to form a white dwarf, which is the final evolutionary stage of such stars.

In the main sequence, a star fuses hydrogen to form helium, releasing an enormous amount of energy that counterbalances the inward gravitational attraction. But when all the hydrogen gets burned up, the star expands into a red giant phase, when it fuses helium into carbon and oxygen (true for low and medium mass stars). Now if the red giant cannot produce the necessary temperature (around 1 billion K) to fuse carbon, then the core will be filled with inert carbon and oxygen. After shedding off the outer layers, forming a planetary nebula, the final remnant core rich in inert carbon and oxygen will be the white dwarf. This is the most general scenario and most abundantly found in the universe. But in the case of some small stars, they are not able to fuse helium into carbon and oxygen, and so they form helium-rich white dwarfs.

Stellar Equilibrium

At the white dwarf stage, the further collapse of the star is hindered by the electron degeneracy pressure. But there is a maximum mass limit that can be supported by this degeneracy pressure. This limit is called the Chandrasekhar limit which is approximately equal to 1.44 solar masses. So if a white dwarf accumulates enough matter from its companion star to go past the Chandrasekhar limit, then the electron degeneracy pressure can no longer hinder further gravitational collapse. The resulting white dwarf explodes into a very violent and bright event known as a supernova and the core further collapses towards the formation of a neutron star.

Transformation into a black dwarf and the final fate

Since there is no nuclear fusion going on in a white dwarf, it slowly radiates out whatever remnant heat it has over time and cools down. So initially white dwarfs are bluish-white (hot) due to the radiations emanating from them, but with time they become redder due to cooling. Finally, these dwarf stars are supposed to totally stop radiating and turn into black dwarfs. But the time taken for a white dwarf to turn into a black dwarf is calculated to be greater than the age of the universe, and hence it is thought that there are no such black dwarfs existing in the universe today. The oldest white dwarfs exiting today still radiate out the heat of a few thousand kelvins, which is such a mind-blowing fact!! Even if a black dwarf forms, it will be a really challenging task to locate it due to its non-radiating nature.

No matter how dark, cool or insignificant they are, such entities will continue to roam around in the eternal space and tell the stories of their glorious past!! Such death beds of once fierce and powerful stars will keep whispering through the ages!!

Prabir Rudra

Prisoners of space and time!! (Meme)

2022-08-05T23:51:00.005+05:30

Read the full article at:

https://www.spacetimerecipe.com/2019/03/prisoner-of-space-and-time.html

Prabir Rudra