5 Applications of Dimensional Analysis

The concept of dimensional analysis was introduced by French mathematician Joseph Fourier in 1822. It is a useful method in physics and engineering to identify the relationships between various physical quantities by analyzing their base quantities.

There are seven base or fundamental quantities of primary importance in physics. The rest of all the physical quantities are derived, that is, written in terms of the following base quantities:

1. Mass (M)
2. Length (L)
3. Time (T)
4. Temperature (K)
5. Electric current (A)
6. Amount of substance (Mol)
7. Luminous intensity (Cd)

Others are derived quantities, for example: Speed is distance upon time, where distance is a type of length. So, the dimension of speed in terms of base quantities is [L][T]^-1

1. Find dimension of unknown quantity

Example: To increase the temperature of a substance by ΔT, heat required is given by Q=mSΔT where m is mass and S is specific heat capacity of the substance. We can find the dimension of S by doing simple algebra.

S=Q/mΔT

S=[M L² T^-2]/[M][K]

S=[L² T^-2 K^-1]

Since heat (Q) is a type of energy we have used the dimension of energy [M L² T^-2]. Knowing the dimensional dependence is useful while performing experiment in laboratory.

2. Find unit of physical quantity

Example: The dimension of force is [M L T^-2]. Therefore, the unit of force in the standard MKS system is kg.m.s^-2 corresponding to the base quantities used. Likewise, the unit of force in the French CGS system is g.cm.s^-2

3. To check correctness of formula

In an equation, the left hand side should match the dimensions on the right hand side. That's because, you can't have apples on one side and oranges on the other. This is useful in multiple choice questions as it helps in eliminating the wrong options.

Example: Is force F=mv²/r correct? where m is mass, v is velocity and r is radius. To find out, we start by writing the dimensions on both sides.

[M L T^-2] = [M][LT^-1]²/[L]

[M L T^-2] = [M][L²T^-2][L^-1]

∴ [M L T^-2] = [M][L][T^-2]

The formula is correct. In fact, it is the centripetal force if you might recall, which acts upon a body directed towards a fixed center, thus keeping it in orbit.

4. To roughly derive formula

Example: Suppose that the time period of a simple pendulum is dependent on mass of the bob, length of the string and gravitational acceleration due to earth.

Let's assume that the time period is proportional to some powers of mass, length and gravity: t∝m^al^bg^c

To find the formula of time period, we must obtain values for a, b and c. We start by writing the dimensions on both sides.

[M]⁰[L]⁰[T] = (constant)[M]^a[L]^b[LT^-2]^c

The dimension of constant is 1. So,

[M]⁰[L]⁰[T] = [M]^a[L]^b[LT^-2]^c

Comparing the exponents on both sides, we get:

a=0, b+c=0 and -2c=1

On solving we obtain values of a=0, b=1/2 and c=-1/2. Now, putting back in the original equation t∝m^al^bg^c  gives:

t ∝ m⁰l^1/2g^-1/2

t=(constant) l^1/2g^-1/2

Thus, time period of a simple pendulum is independent of mass of the bob. This is because, physically speaking, mass is both the cause of swinging motion and the resistance to swinging motion, so it cancels out.

5. To express in new base quantities

This type of questions can come up in competitive exams like the JEE-Main. Example: If pressure, velocity and time are taken as base quantities, then what would be the dimension of force?

Let's start by assuming powers

Force = P^av^bt^c

And write dimensions on both sides

[M L T^-2] = [ML^-1T^-2]^a[LT^-1]^b[T]^c

[M L T^-2] = [M]^a[L]^-a+b[T]^-2a-b+c

Comparing powers on both sides

a=1, -a+b=1 ⇒ b=2 and -2a-b+c=-2 ⇒ c=2

∴ Force = Pv²t²

How Antimatter Was Discovered By Carl Anderson

British physicist Paul Dirac showed in 1928 that every particle in the universe should have an antiparticle with the same mass as its twin, but with the opposite electrical charge. Across the pond, an American physicist would detect the first such particle, four years later.

Carl Anderson, inspired by the work of his Caltech classmate, Chung-Yao Chao, set up an experiment to investigate cosmic rays under the supervision of physicist Robert Millikan. In 1932, he won the Nobel Prize in physics at the age of 31, becoming one of the youngest recipients.

Discovering the positron was no easy feat but the mechanism he employed to do so was fairly simple and ingenious enough to overcome the limited budget. He found the mysterious particle almost by accident with the help of his own improved version of the cloud chamber.

A cloud chamber is a sealed box with water vapor. When a charged particle goes through it, the vapour is ionized and leaves behind a trail. Thus, the trajectory of the particle can be seen virtually. Carl used a mixture of water and alcohol to get clearer photographs.

Carl included a Lead plate in the middle to slow down the particles and surrounded the chamber with a large electromagnet, which caused the paths of ionizing particles to curve under the influence of magnetic field.

As can be seen in the picture, the radius of curvature of the track above the plate is smaller than that below. Thus, the particle entered from the bottom, hit the Lead plate and came to a halt above it due to loss of energy. This and the direction in which the path curved helped in identifying that the charge was positive.

That it was antielectron and not proton was determined by the observation that the upper track was much longer in length than predicted for proton. A proton would have come to rest in a much shorter distance, since it is heavier. The trajectory observed was that of a particle much much lighter than the proton.

So, that's how the first antimatter was found and Dirac was proven right within a matter of few years. Furthermore, antiproton and antineutron were discovered in 1955 and 1956 respectively. The first antiatom was produced by CERN in 1996.

Why antimatter is important? Because, studies related to antimatter will help in our understanding of the early universe. Also, Positron emission tomography or PET scan is used to detect early signs of cancer. Scientists hope that some day, antimatter may be used for the treatment of cancer. Who knows!?

10 Roger Penrose Facts That You Didn't Know

Nobel – British mathematician and physicist Sir Roger Penrose is popularly known for black hole singularity theorems which later on inspired Stephen Hawking's singularity theorem for the entire universe. In 2020, Penrose won the physics Nobel Prize for work done in the 1960s. Yes, it took that long.

Childhood – Penrose spent his early childhood during the second World War in Canada. It is quite surprising to know that Penrose was not always the brilliant man he is today. After winning the Nobel prize, in an interview, he revealed: "I was always very slow. I was good at maths, yes, but I didn't necessarily do very well in my tests."

Genius family – There also was added pressure due to the fact that he was born in the Penrose family, a family of artists, scientists and chess players.

Penrose's paternal grandfather was a famous portrait artist while his maternal grandfather was a physiologist and an early biochemist.

His father Lionel was a geneticist whose interests extended well beyond his profession and included such fields as geometry and chess, which he often shared with his children.

No surprise that Penrose's older brother went on to become a distinguished physicist himself. The younger brother and sister became Chess grandmaster and geneticist respectively.

Love of geometry – As a student, Penrose used to create illusory objects like the Penrose Triangle and the Penrose stairs. Several artworks by the renowned Dutch artist M.C. Escher were in part inspired by Penrose's impossible figures.

PhD – Post graduation, Penrose came under the supervision of mathematician W. V. D. Hodge. Though after one year, he was "thrown out" of the class for not being able to find solution to the problem assigned to him. "I decided that the problem Hodge suggested had no solution but he didn't believe me."

For the next two years, Penrose worked under geometer John Todd and in 1958 finished his doctorate degree with a thesis on tensor methods in algebraic geometry.

Inspiration – Roger Penrose was encouraged by his cosmologist friend Dennis Sciama to work alongside Stephen Hawking on the problems in astrophysics. "What are you doing with this pure mathematics nonsense? Come and work on physics and cosmology."

Lectures on quantum theory by Paul Dirac and on general relativity by Hermann Bondi influenced Penrose further. In the 1960s, he joined Sciama and Hawking to derive the Penrose–Hawking singularity theorems using Indian physicist Amal Kumar Raychaudhuri's namesake equation.

Consciousness – Apart from the problems in physics, Penrose has also explored the nature of consciousness, especially in his 1989 book: The Emperor's New Mind.

He was partly motivated to write the book after hearing computer scientist Marvin Minsky, one of the fathers of artificial intelligence, say: Human brain is just a computer made up of meat.

Minsky was of the belief that human intelligence could be mimicked artificially in accordance with a learning program. Roger Penrose argued against that viewpoint, saying: Human thought and intelligence cannot be simulated artificially.

In 1997, Penrose devised a theory of consciousness based upon quantum gravity. However, it failed to garner critical or experimental support. Hawking commented: Penrose's argument seemed to be that consciousness is a mystery and quantum gravity is another mystery so they must be related.

Religion – Roger Penrose regards himself as an agnostic. During an interview with the BBC in 2010, he stated: "I'm not a believer myself. I don't believe in established religions of any kind." Penrose is also a well-known supporter of Humanists UK organization.

Cycle of time – According to Penrose, the universe keeps dying and being reborn. In 2010, he reported possible evidence based on the data from cosmic microwave background, of an earlier universe existing before the Big Bang.

His conformal cyclic cosmology model although derives inspiration from Hindu-Buddhist philosophies is built within the framework of general relativity. Penrose has popularized the theory in his 2010 book Cycles of Time: An Extraordinary New View of the Universe.

Architecture – Believe it or not but Roger Penrose has made a remarkable contribution to architecture as well. Penrose tiling, a covering of the plane by non-overlapping polygons, is quite a popular choice for floor designs.

According to one alumnus, the campus of Indian Institute of Information Technology, Allahabad was inspired by Penrose architecture. "The domes and the corridors were the nodes and connections respectively of the Penrose architecture."

Similarly, Miami University in Ohio, Andrew Wiles Building at the University of Oxford and Mitchell Institute for Fundamental Physics and Astronomy (as seen in the picture) make use of Penrose Tiling.

Steven Weinberg's four tips for aspiring scientists

Steven Weinberg (1933-2021) was an American physicist who worked alongside Pakistani physicist Abdus Salam to unify electromagnetic and weak interactions in 1967. He shared the Nobel Prize in physics for the same work later on.

Weinberg was not only famous as a scientist but also for his outspokenness and elegant writings outside of science. He thus made important contributions to history as well as to politics. Following are his 4 advices for aspiring scientists.

1. You don't have to know everything

Weinberg's first golden lesson is specialization. He wrote for Nature in 2003: When I received my undergraduate degree, the physics still seemed to me a vast, unexplored ocean.

How could I begin any research of my own without knowing everything that had already been done? Weinberg recalled.

A lot of the times students are so overwhelmed or even excited by that vastness that they fail to go forward. Weinberg says: You don't have to know everything because I didn't when I got my PhD.

2. Aim for rough water

When Weinberg was a professor, a student came up to him and said that he would pick general relativity rather than the area Weinberg was working on - particle physics.

Obviously as the teacher Weinberg was disappointed. When asked to explain, the student replied: The principles of general relativity are well known, while the particle physics is an incoherent mess.

Weinberg quipped: That makes it all the more worthwhile because in particle physics creative work can still be done.

So, according to Professor Steven Weinberg, it would be a lot better to aim for the rough water especially while you are able to swim in that vast, unknown ocean. For who knows what might be out there?

3. Forgive yourself for wasting time

This is his most beautiful advice: Forgive yourself for your failures. Forgive yourself for wasting time on the wrong problems. Whatever can go wrong will go wrong, but there will always be silver lining in the end.

Weinberg cites an example in history... When scientists were trying to prove existence of the Ether they didn't know that they were working on the wrong problem. It nonetheless helped Albert Einstein in 1905 to realize the right problem to work upon.

Weinberg adds: You will never be sure which are the right problems most of the time that you spend in the laboratory or at your desk. But if you want to be creative, then you will have to get used to wasting your time.

4. History of science

Final tip to aspiring scientists: Study the history of science as it will make your work seem more worthwhile to you. Because, a work in science may not yield immediate results, but to realize that it would be a part of history is a wondeful feeling.

As you will learn its rich history, you will come to see how time and time again - from Galileo through Newton and Darwin to Einstein - science has weakened the hold of religious dogmatism: Weinberg adds.

In one interview, when asked whether he believed in God, Weinberg replied... If by God you mean a personality who is concerned about human beings, who did all this out of love for human beings, who watches us and who intervenes, then I would have to say in the first place how do you know, what makes you think so?

Science is either physics or stamp collecting?

What is science? In one simple sentence, science is the study of nature. However, different sciences like: astronomy, chemistry, biology, geology, etc. have different approaches to do so. Thus, not all sciences are equal.

The quote 'All science is either physics or stamp collecting' by New Zealand physicist Ernest Rutherford perfectly reflects that inequality. According to him, physics is the king of sciences because it is fundamental to all other fields of study.

But why exactly did Rutherford think in that manner? Despite himself being the recipient of Nobel Prize in chemistry, what made him consider physics the most noble of sciences?

The answer lies in stamp collecting - a hobby in which people collect and classify stamps as objects of interest or value.

Stamps are available in many varieties - big and small, square and round, stamps with famous human faces, stamps with animals and birds, stamps commemorating anniversaries, etc.

 Rutherford's stamp 

Similarly, some branches of science, such as zoology or botany for example, are mostly concerned with collection and classification of species - animals and plants, respectively.

Although this would be dumbing down those sciences but that is more or less the purpose, isn't it? In other words, those sciences are not fundamental sciences and their scope is limited only to Earth.

Physics, according to Rutherford, is the only science that has an elaborate structure consisting of observation, experiment and mathematics. Physics captures our imagination from mysterious atoms to supermassive galaxies. It truly is the universal embodiment of the scientific method.

By this definition, the science which is closest to physics is astronomy. You observe and measure the effects of, say a black hole on its surroundings, with the help of a telescope and basic knowledge of mathematics. In this way, like engineering, astronomy is an application of physics and mathematics.

Chemistry is a unique science because it has the 2nd most direct impact on day to day life after physics. The objects we use, such as plastic, glass, steel, etc. are all obtained by chemical processes.

Our body is a chemical engine and the food we eat are organic molecules. But just like biology, there is a lot of nomenclature and classification rules in chemistry to deal with. Chemistry is also not universally the same, like on different planets, but the laws of physics governing those chemistries are the same.

Likewise, sciences like computer science and psychology are neither fundamental nor universal. They are narrowed specializations and are heavily dependent on logic, mathematics and observation.

All the sciences, however, must ultimately be experimental because that is how they progress. That is how the hypotheses are tested and verified and accepted. So it is worth pointing out that no amount of belief can make something true. Sciences keep evolving with time as new evidence is uncovered.

Finally, it is equally important to mention that the statement "all science is either physics or stamp collecting" had more truth to it back in Rutherford’s time than today.

As you know, for example: With Darwin's theory of evolution, biological sciences have too become observational rather than just being classification sciences.

So, over time, sciences evolve and become more and more physics-like. They are no longer merely observe and classify but start using mathematical models. Still, Rutherford's point is intact, physics will be the king of sciences.

What Motivated Them To Become Physicists?

While several physicists like James Clerk Maxwell, John von Neumann and Lev Landau were child prodigies, most of the scientific greats developed an interest in science thanks to the environment they were brought up in.

A study conducted by Pew Research found that 27% scientists were motivated by their school teachers, 17% were inspired by childhood trips to science fairs and 12% became scientists thanks to family encouragement.

In this post, let us learn what motivated Geniuses like Einstein, Tesla, Feynman, Hawking and others to become scientists.

Richard Feynman

Feynman's father, Melville was an immigrant from Minsk, who although a uniform salesman by profession, had always wanted to become a scientist.

In one interview, Feynman recalled: When I was a child, my father would often let me sit on his lap and read to me from Encyclopedia Britannica.

Melville also encouraged his daughter Joan, nine years younger than Richard, to take up an interest in astronomy. She became a distinguished astrophysicist later on.

Albert Einstein

On Einstein's fifth birthday, his father gifted him a compass which left a deep and lasting impression upon the five year old. He noticed that the needle always pointed in the same direction no matter which way he turned the compass.

Einstein wrote years later: "It made me wonder why this needle behaved in such a determined way. Something deeply hidden had to be behind things." Thus, the compass was his introduction to scientific enquiry.

Stephen Hawking

Hawking was born in a family of intellectuals – Both his parents attended the University of Oxford, where his father studied medicine and his mother read philosophy.

He was enrolled at St. Albans school where he was nicknamed Einstein, despite his grades being below average. But of course, there was a reason why his friends called him that...

Hawking used to build model boats and aeroplanes at his home. In 1958, with help from his maths teacher, Dikran Tahta, Hawking and friends built a computer from clock parts, telephone switchboard and other recycled parts.

Carl Sagan

In 1993, Carl wrote: My parents knew almost nothing about science. But in introducing me to skepticism and to wonder, they taught me the two uneasily cohabiting modes of thought that are central to the scientific method.

His love for science was aroused at only 4 years old when his parents took him to the 1939 New York World's Fair where he witnessed the America of tomorrow – spiraling buildings, flying cars and smartphones.

Nikola Tesla

Tesla's mother had a talent for making mechanical appliances at home. She could also recite Serbian epic poems by heart. Nikola thus credited his eidetic memory and creative abilities to his mother's genes and influence.

He attended junior high school in Karlovac, central Croatia where he became interested in demonstrations of electricity by his physics professor. Tesla later wrote that these demonstrations made him want to know more of this wonderful force.

Jocelyn Bell Burnell

She is an astrophysicist who found the first radio pulsar in 1967. Her discovery was recognized by the Nobel Committee with a physics Prize, but despite being the one to identify the pulsar, she wasn't among the recipients.

Young Jocelyn discovered her father's books on astronomy and developed an early interest. However, at school, the girls' curriculum only included cooking and stitching classes, rather than science.

Her parents protested against the school policy, but to no avail. So they sent her to another school where she was permitted to study science. Jocelyn was impressed by her physics teacher, Mr. Tillott. She recalled: He was a really good teacher and showed me, actually, how easy physics was.

Marie Curie

Her father, Władysław Skłodowski was a mathematics and physics teacher. After Russian authorities banned laboratory instruction from Polish schools, Skłodowski brought much of the lab equipment home and instructed Maria in its use, at a young age.

Ed Witten

Mathematician and physicist Edward Witten, winner of the Fields Medal, grew up hearing about physics from his father, Louis Witten, who himself was a gravitational physicist. "I would talk to Ed about science the way I would talk with adults." Louis told The Guardian.

Summing up:

It can be concluded that parents and teachers who nurture the curiosity of children often help them towards a career in science. Whether it be book reading, gifts like model train, compass or general encouragement; early guidance is always ideal in making of a great scientist.

8 times when Nikola Tesla was wrong about physics

Nikola Tesla was a great Serbian-American engineer who played the major role in perfecting and promoting alternate current. He was also a visionary who predicted smartphones, renewable energy and creation of artificial Suns, much before time permitted.

However, it is surprising that Tesla sometimes took anti-science as well as anti-mathematics positions. Several of his views about the world were particularly pseudoscientific. So in this post, let us look at 8 instances when even the Genius Nikola Tesla was wrong.

On electrons

Tesla did not agree with the theory of atoms being composed of smaller subatomic particles. He thought that there was no such thing as an electron creating an electric charge and that it had nothing to do with electricity.

However, not only did the electron get discovered but also its properties and effects were measured by physicist J.J. Thomson at the start of the twentieth century. Without electron, technologies like the television couldn't exist.

On relativity

According to Nikola Tesla, Einstein's 1915 theory of general relativity was wrong. He commented in 1932: "I hold that space cannot be curved, for the simple reason that it can have no properties. It might as well be said that God has properties. He has not."

In 1935, Tesla told The New York times: "Einstein's relativity work is a magnificent mathematical garb which fascinates, dazzles and makes people blind to the underlying errors. The theory is like a beggar clothed in purple whom ignorant people take for a king."

In 2004, the gravity probe-b satellite was launched to measure the curvature due to Earth. Its data was analyzed by the Stanford University and it indeed confirmed Einstein's theory to a high degree of accuracy in 2011.

Furthermore, without relativity, the GPS would fail in its navigational functions and Google maps couldn't work to pinpoint precision.

On mathematics

Nikola Tesla said in 1934: "Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation and eventually build a structure which has no relation to reality."

That may be true, although mathematics and experiments are both fundamental to scientific progress. There cannot be one without the other, especially in the field of physics.

At the same time in Europe, Dirac was trying to find an equation to unify quantum mechanics and special relativity. He predicted the existence of antimatter in doing so, which was discovered in 1932.

Even 16th century Galileo Galilei had a high regard for mathematics, when he said: Philosophy is written in mathematical language; without it one wanders in vain through a dark labyrinth.

On atomic energy

Tesla told The New York Times in 1931: "The idea of atomic energy is illusionary. I have preached against it for twenty-five years but there are still some who believe it to be realizable."

Because, as mentioned before, he did not trust the theory of subatomic particles. So according to Tesla, atoms were immutable – meaning that they could not be split or changed in any way.

Two years after Tesla's death in 1943, not only did the humankind split the atom, they also used it to end the World War II. Although it began a nuclear arms race and a call for disarmament – well that is another story in itself.

Today, atomic energy is a source of nuclear power – as predicted by physicist Lise Meitner – which is in turn used to generate heat and electricity. Moreover, scientists are also working on a large-scale fusion project called ITER for future electricity generation.

On EM waves

German physicist Henrich Hertz demonstrated the accuracy of Maxwell's equations when he successfully generated electromagnetic waves in laboratory.

Because Tesla did not have the mathematical advantage, he relied completely on experiments and his own experiments led him to erroneously believe that Hertz and Maxwell were wrong.

In one 1891 lecture, Tesla expressed openly his disagreements with Hertz – which is anyway healthy for the sake of scientific progress.

But over the next few years, several groundbreaking evidences were collected in the favor of Maxwellian electromagnetism.

In 1898, Tesla himself developed a radio based remote-controlled boat and yet till 1919 he did not believe in the existence of EM waves and in the theories developed by Maxwell and Hertz.

On wireless electricity

Tesla was a great visionary but his vision was not always practical. After perfecting alternate current technologies, Tesla wanted to make a new revolutionary change - render wires useless!

At first, Tesla decided to transmit electricity through air but rejected the idea later on. In 1902, Tesla completed the Wardenclyffe Tower to tranfer electricity via ground.

However, engineers pointed out that currents once injected into the ground would spread in all the directions, quickly becoming too diffuse to be usable over long distances.

In addition to engineering and financial problems, the dangers of wireless electrical power to nearby wildlife was not taken into account by Tesla. Thus, the Wardenclyffe Tower project had to be abandoned.

During the same time, Italian engineer Guglielmo Marconi - who unlike Tesla, believed in and worked with electromagnetic waves, succeeded in the wireless transmission of information, rather than electricity.

On science

Although Nikola Tesla was a brilliant engineer and inventor, he sometimes delved into pseudoscientific ideas which had no basis in reality and lacked experimental data – a quality he admired.

For example, Tesla once said: A single ray of light from a distant star falling upon the eye of a tyrant in bygone times may have altered the course of his life, may have changed the destiny of nations.

That thought, although poetically is beautiful, has no scientific weight. Distant stars and planets and their motions have no measurable effects on people. What changes destiny of nations is politics and the king's advisor would have had far greater impact than light of a far away star.

On radioactivity

In 1903, Marie Curie, Pierre Curie and Henri Becquerel won the Nobel Prize in physics for discovering evidence for radioactivity.

However, Tesla was not convinced since he did not believe that the atom was divisible and that it had internal forces and subatomic particles.

According to him, the phenomena of radioactivity was not the result of forces within the radioactive substance but by the rays emitted by the Sun.

He told The New York Times in 1931: If radium could be screened effectively against this ray it would cease to be radioactive.

Summing up

Nikola Tesla was a genius inventor and explorer whose work ushered the electrical revolution that transformed daily life. Einstein wrote to Tesla: As an eminent pioneer in the realm of high frequency currents... I congratulate you on the great successes of your life's work.

But at the same time Nikola Tesla was also human – jealousy, denial and frustration, played a big role in his professional life.

His frustration with advanced mathematics led him to incorrectly conclude that Maxwell's equations and relativity were wrong.

His denial of modern science left him too far behind his contemporaries – Marconi, Braun, Bose – in his ability to contribute to the wireless communication.

Surely, Tesla did achieve what others could only dream of. But the point is, not to put Tesla on pedestal, or build conspiracy theories in his favor, as many fans would want to do. It does not do justice to Tesla's brilliance.

Hawking's black hole theorem confirmed by gravitational waves

A black hole has often been portrayed as the ultimate villain in sci-fi movies due to its mysterious nature. From the death of a large-enough star it emerges with such a strong gravitational field that not even light can escape from within its grasp.

However, in spite of its wildly mysterious behavior, the black hole obeys certain simple rules. One of those rules, first proposed in 1971 by English physicist Stephen Hawking, has been proven correct by the help of gravitational waves.

The area law, derived from Einstein's general relativity, states that it is impossible for a black hole to decrease in size, at least in the short term. Mathematically:

Recently, a team led by astrophysicist Maximiliano Isi from Massachusetts Institute of Technology studied the gravitational wave data released by the merger of two black holes.

Their calculations show that the total surface area of the resulting black hole is greater than the combined areas of the two smaller black holes. Therefore, Stephen Hawking was right.

However, while black holes cannot shrink according to Einstein's general relativity, they can do so as per the quantum mechanics.

Hawking worked that out too in 1974 – a concept known as Hawking radiation, which is predicted to emit because of strange quantum effects near the black hole's event horizon.

In his 1988 book A Brief History of Time, Hawking thus wrote: Black holes ain't so black. The release of these radiations would cause the black hole to shrink over longer time period and evaporate eventually.

Hence, theoretically speaking, both general relativity and quantum mechanics hold true. Maximiliano Isi said: "I am obsessed with these objects because of how paradoxical they are."

Now that the area law has been established for short to medium time frames, the researchers' next step would be to detect Hawking radiation by observing older black holes; no substantial evidence has been recorded so far.

Isi concludes: Black holes are those phenomena where gravity meets quantum mechanics, which makes them the perfect playgrounds for our understanding of reality.