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The strange behaviour of the oobleck can now be predicted by researchers

The strange behavior of the Oobleck can now be predicted by researchers

Oobleck is a strange material that is also referred to as a non-Newtonian fluid. This weird substance behaves sometimes as a liquid and a solid the other times. It is made of water and corn-starch entertaining children for many hours. If it is punched it appears to be solid but if picked up it flows away. 

Scientists at MIT have studied the magic substance and published a 3D mathematical model that can predict when the oobleck can change from solid to a liquid and vice versa. The findings are published in the PNAS journal. 

The scientists explain that the fine particle suspensions demonstrate drastic changes in viscosity on shear which produces interesting behavior. This is captivating to both children and rheologists. In the model, researchers have introduced a 3D continuum model with the help of mixture theory coupling the particle and fluid phases. 

The term oobleck is derived from a green substance in the book Bartholomew and the Oobleck authored by Dr. Seuss. This has fascinated researchers for a long period of time as its behavior depends on the way it is interacted with. 

The size of the particles plays an important role in this ability of the non-Newtonian fluids. The particles of corn starch are a fraction of the size of a sand grain, so due to their small size, they can be influenced by the temperature and electric charges around them. On moving slowly through the oobleck, the grains repel each other however on hitting it fast, the particles touch giving the feel of a solid. According to Ken Kamrin, mechanical engineer, MIT although this can be created very easily the rules governing it are complex.

This research can be mostly considered as a recreational work, scientists think that this modeling can be used to test oobleck for several materials such as bulletproof vests. Although it is an important question if it can stop a bullet. 

Researchers had been working on a model for wet sand but had to change it to obtain the desired oobleck variables. They ran experiments to check if the model was perfect, such as squeezing it between plates and shooting a projectile to a tank having the substance. An X shaped wheel ran through the material at different speeds to help understand the behavior. The model was able to predict the change of oobleck from liquid to solid substance and vice versa as the wheel rolled back. 

Journal Reference: PNAS

 

Schrodinger equation

Schrodinger’s Equation – A key equation in Quantum Mechanics

Until the beginning of the 20th century, we have developed laws and equations which govern the behaviour of relatively larger objects. In the early 20th century, we started digging deeper and deeper into the matter and found out that the laws we have developed over centuries don’t work at atomic and sub-atomic levels. This was the beginning of Quantum Physics.

Quantum Mechanics was started by Max Planck who is known as the Father of Quantum Mechanics. Quantum Mechanics tells that matter also have wave-particle duality and it is significant at the atomic scale. Thus it was thought that a wave equation might explain the properties and thus the first such wave equation was developed by Erwin Schrodinger and is named as Schrodinger’s equation.

Schrodinger’s wave equation looks like:

schrodinger-equation-time-ind-laplacian

 is the reduced Planck constant,
m is the electron mass,
 is the Laplacian operator,
Ψ is the wave function,
V is the potential energy,
is the energy eigenvalue,
(r) denotes the quantities are functions of spherical polar coordinates (r, θ, φ)

As always, I am not going to bore you explaining those complex terms. Instead, let us know why is this equation so important. We all know about Newton’s laws of motion, they changed the course of physics as we could tell the destination of a moving body by knowing its initial conditions. Schrodinger’s role in Quantum mechanics is somewhat similar to that of Newton.

The Schrodinger equation is used to find the allowed energy levels of quantum mechanical systems (such as atoms, or transistors). The associated wavefunction gives the probability of finding the particle at a certain position. A particle whose position and momentum was completely unpredictable according to the uncertainty principle got at least boundaries by using Schrodinger’s equation. It really means a lot. Though there are many implications of this equation, the above one is the most important.

I hope you got a glimpse of Schrodinger’s equation.

Einstein's Field Equation

#5 Einstein’s Field Equation

Einstein, an absolute genius, has given a lot of groundbreaking theories and the one which completely changed our understanding was the Theory of Relativity. Both Special and the General theory of relativity being two of the most famous and fundamental scientific theories have a lot of revolutionary equations. In this article, we are going to talk about one such equation which is Einstein’s second most famous equation after E=Mc2. It is Einstein’s Field Equation

einstein field equation

where,

Einstein's Field Equation

– Einstein tensor

Einstein's Field Equation – Ricci curvature tensor

Einstein's Field Equation– Scalar curvature

g_{\mu\nu}– Metric Tensor

\Lambda– Cosmological constant

G– Newton’s gravitational constant

c – Speed of light

T_{\mu\nu}– Stress-energy tensor

Did not understand the terms? This equation looks pretty clean and simple but isn’t that simple, it involves many crazy Tensor calculations, matrices, etc. So, don’t get afraid, all these terms are pretty complex and need a lot of explanation which I won’t be doing here because it will be boring (Still want to read about these terms: Read here). Instead, let us know the importance of the equation and why is it so famous.

First of all, you have to know that this is not a single equation, this equation hides and summarizes 10 partial differential equations in it. This small equation that doesn’t look too complex, (at least not as complex as Schrodinger’s wave equation :-)) completely changed our understanding of the universe. It revolutionized the concept of gravity.

According to General Relativity, Gravity is because of mass curving space-time. Einstein’s field equation explains the mass, energy, momentum, pressure distribution across space-time and how does these curve space. The left side of the equation (which has Einstein tensor) is about the curving of space and the right side (which have stress-energy tensor) is about the distribution of energy and mass, so, it relates mass and energy to curvature of space-time.

'Space-time tells matter how to move; matter tells space-time how to curve'--John Wheeler Click To Tweet

This equation has been used to predict the existence of black holes and gravitational waves. It explains how black holes warp space-time. Einstein’s equation can tell us how our universe has changed over time and offers glimpses of the earliest moments of creation. This equation has been used to understand many processes of the universe.

So, that was a glimpse into Einstein’s Field Equation, Hope you liked it.

Read more: Famous Equations

Albert Einstein

Albert Einstein – The Godfather of Modern Physics

Albert Einstein was a German-born physicist who has developed the General and Special Theory of relativity and is one of the recipients of the Nobel Prize for Physics in the year 1921 for his understanding of the photoelectric effect. Einstein is generally perceived as the most influential physicist of the 20th century and is also known as the father of modern physics.

Content

  1. Personal life and Education
  2. The Journey from Graduation to Scientific Miracles
  3. Ignored To World-Renowned Physicist
  4. Einstein’s last days
  5. Conclusion

Personal life and Education:

Albert Einstein was born on 14th March 1879 in the city of Ulm, in the Kingdom of Württemberg of the German Empire. His parents were Hermann Einstein and Pauline Koch. Hermann was a salesman and engineer by profession. His parents were secular, middle-class Jews. His father was initially a featherbed salesman and later ran an electromechanical factory.

Want to read about General and Special Relativity, Here is a book for you:

  1. Relativity: The Special and the General Theory (General Press)
  2. Relativity: The Special and the General Theory – 100th Anniversary Edition

The family estate and the household was run by his mom, Pauline Koch. Albert had a sibling sister, Maria who went by the name Maja and she was born two years after him.

At the age of five young Einstein went to Catholic Elementary School in Munich and continued there for 3 years. At the age of 8, he was transferred to the Luitpold Gymnasium which is now known as the Albert Einstein Gymnasium where he got his primary and secondary education until he left the German empire almost seven years later. 

Albert Einstein at the age of three

Albert Einstein at the age of three(Wikipedia)

Einstein would write that his early years were profoundly influenced by two “wonders.” The first was an encounter with a compass and its needle when he was 5 years old. He was perplexed about the needle being distracted by unseen and invisible forces. Little did he know, that this would result in a lifetime fascination. The second wonder happened when he discovered a book of geometry, he called it a “sacred little geometry book”.

Einstein became profoundly religious at the age of 12 and even composed several pieces in honor of God and began chanting religious songs on his way to school. After reading various science books that contradicted his faiths, he started to alter his beliefs. This incident left a profound, enduring mark and a long-lasting impression for a lifetime.  Einstein often felt out of place at Luitpold Gymnasium and was the victim of a Prussian-style education system that appeared to suppress originality and creativity. There was even one teacher who informed him he’d never mean anything.

Look deep into nature, and then you will understand everything better. --Albert Einstein Click To Tweet

Young Einstein was also influenced by a medical student name Max Talmud who introduced Einstein to many higher concepts. But, Einstein’s training and education had been disrupted by his father’s frequent business failures. 

In 1894, Hermann Einstein relocated to Milan to operate with a friend after his business failed to get a signed agreement to electrify the town of Munich. Einstein was then left at a boarding house in Munich and was supposed to complete his studies. Alone and miserable, deterred by the looming military duty when he was 16, he ran away 6 months later and landed at his parents’ doorstep. 

Einstein at Patent office

Young Einstein at patent office

Einstein then applied to the Swiss Federal Polytechnic School in Zurich. He proved that he was excellent in mathematics and physics, but failed in French, Chemistry and Biology subjects. He was permitted to study polytechnic due to his outstanding scores in Mathematics, provided that he completed his official training and schooling first. 

In the following years, he moved to Aarau, Switzerland and took admission in a special high school which was run by Jost Winteler. He graduated in 1896. At that moment he also gave up his German citizenship. He became lifelong buddies with the Winteler family, with whom he was staying.

Einstein would mention that his Zurich years were some of his happiest years. He found many learners, like Marcel Grossmann, a mathematician, and Besso, with whom he had a long conversation about time and space. His future spouse, Mileva Maric was a fellow student of physics from Serbia at that time. 

The Journey from Graduation to Scientific Miracles :

After graduation in 1900, Einstein faced one of the greatest crises in his life. Because he studied advanced subjects on his own, he often skipped his classes and this, in turn, earned him the animosity of some of his professors, especially Heinrich Weber. Unfortunately, Einstein asked Weber for a letter of recommendation. Einstein was subsequently turned down for every academic position that he applied to.

Einstein reached the lowest point of his life in 1902. He was unable to marry Maric and support his family without a stable job and at the same time, his father’s business went bankrupt. Desperate and unemployed, Einstein took to low tutoring jobs for children but was later fired from them as well. 

The turning point came later that year when his lifelong friend Marcel Grossmann’s father was able to recommend him as a clerk at the Swiss patent office in Bern. With a small and steady income for the first time, Einstein felt confident enough to marry Maric, and he did so on January 6, 1903. Their children, Hans Albert and Eduard, were born in Bern in 1904 and 1910, respectively.

Einstein’s work at the patent office was a blessing. He would rapidly complete examining patent requests, giving him enough time to think about the dream that had fascinated him since he was 16: what would occur if you run alongside a light beam? While studying Maxwell’s equations at the polytechnic school, which describe the nature of light, he discovered a fact unknown to James Clerk Maxwell himself namely, the speed of light remains the same no matter how fast one moves. 

However, this violates Newton’s laws of motion, however, because there is no absolute velocity in Isaac Newton’s principle. This knowledge prompted Einstein to formulate the concept and Theory of relativity

Albert Einstein in his Berlin office in 1919.

Albert Einstein in his Berlin office in 1919 (Credit: Wikimedia Commons)

There were other scientists who were actively working towards the theory of relativity, but Einstein was the first one to assemble the whole theory of relativity and to identify that it was a universal law of nature and not merely a curious figment of motion. 

There were two pillars of physics in the 19th century: Newton’s rules of movement and Maxwell’s theory of light. Einstein was certain in knowing that they were in contradiction and that one of them had to collapse.

During 1905, often called Einstein’s “miracle year,” he published four papers in the Annalen der Physik, each of which would alter the course of modern physics:

  1. “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt” (“On a Heuristic Viewpoint Concerning the Production and Transformation of Light”), in which Einstein applied the quantum theory to light in order to explain the photoelectric effect. If light occurs in tiny packets (later called photons), then it should knock out electrons in a metal in a precise way.
  2. “Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen” (“On the Movement of Small Particles Suspended in Stationary Liquids Required by the Molecular-Kinetic Theory of Heat”), in which Einstein offered the first experimental proof of the existence of atoms. By analyzing the motion of tiny particles suspended in still water, called Brownian motion, he could calculate the size of the jostling atoms and Avogadro’s number 
  3. “Zur Elektrodynamik bewegter Körper” (“On the Electrodynamics of Moving Bodies”), in which Einstein laid out the mathematical Theory of Special Relativity.
  4. “Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?” (“Does the Inertia of a Body Depend Upon Its Energy Content?”), submitted almost as an afterthought, which showed that relativity theory led to the equation E = mc2. This provided the first mechanism to explain the energy source of the Sun and other stars.

Albert Einstein had a massive influence on the subject of contemporary physics. His equation, E = mc2, which explained how stars produce energy for the first time is still considered one of the most popular equations. This equation also foreshadowed the creation of the atomic bomb giving some negative fame to this equation. Einstein’s understanding of light as something which can function both as a wave and as a stream of particles became the basis for what is today known as quantum mechanics.

Ignored To World-Renowned Physicist

Einstein’s 1905 papers were so revolutionary that no one was ready to believe and they just ignored Einstein. Einstein’s work then caught the attention of Max Planck, probably the most influential physicist of that time and the founder of Quantum theory. After Max Planck’s appreciating comments and experiments proving Einstein right, things started changing. Soon, Einstein got invites from Universities for lectures and he started gaining fame.

Albert Einstein

Credit: Wikimedia Commons

One of the deep thoughts that consumed Einstein from 1905 to 1915 was a crucial flaw in his own theory: it made no mention of gravitation or acceleration. To Einstein, Newton’s gravitational force was actually a by-product of a deeper reality: the bending of the fabric of space and time.

In November 1915 Einstein finally completed the general theory of relativity, which he considered to be his masterpiece. In the summer of 1915, Einstein had given six two-hour lectures at the University of Göttingen that thoroughly explained an incomplete version of general relativity that lacked a few necessary mathematical details.

Much to Einstein’s consternation, the mathematician David Hilbert, who had organized the lectures at his university and had been corresponding with Einstein, then completed these details and submitted a paper in November on general relativity just five days before Einstein, as if the theory were his own. Later they patched up their differences and remained friends. Today physicists refer to the action from which the equations are derived as the Einstein-Hilbert action, but the theory itself is attributed solely to Einstein.

To prove his theories, Einstein would need to get some observations of a solar eclipse. With the images of the solar eclipse, Einstein could prove that the sun bends the light coming from other stars to earth which would prove his “bending of the fabric of space and time” theory.

Albert Einstein Eclipse

Two expeditions had been sent to sample Einstein’s forecast of deflected starlight closes the Sun. One set sail to Principe Island off the West African coast and the other to Sobral in northern Brazil to observe the solar eclipse on May 29, 1919.  The results were announced at a joint meeting of the Royal Society and the Royal Astronomical Society in London on November 6. This led to Einstein becoming a world-renowned physicist and he soon became the successor to Isaac Newton. 

In the year 1921, Einstein received the Nobel Prize for Physics, for his services and contributions to theoretical physics and the discovery of the law of the photoelectric effect. But this award was only for the photoelectric effect and not the theory of relativity. During his acceptance speech at the awards, he startled the audience by telling them about the theory of relativity instead of the photoelectric effect. 

Einstein’s last days: 

Einstein continued to pioneer and contribute to many key developments in the theory of relativity, the existence of time travel, the existence of black holes and the creation of the universe. It is rather quite sad to know that he was isolated from the rest of the members of the physics community. Einstein was isolated because of his strong opposition to Quantum Theory.

The other reason for Einstein’s increasing detachment from his colleagues was his obsession, beginning in 1925, with discovering a unified field theory—an all-embracing theory that would unify the forces of the universe, and thereby the laws of physics, into one framework. 

In his later years, he stopped opposing the quantum theory and tried to incorporate it, along with theories of light and gravity, into larger unified field theory. Gradually Einstein became set in his ways. He rarely traveled far and confined himself to long walks around Princeton with close associates, whom he engaged in deep conversations about politics, religion, physics, and his unified field theory.

The true sign of intelligence is not knowledge but imagination.--Albert Einstein Click To Tweet

In the year 1950, he published an article on his theory in Scientific American, but because it neglected the still-mysterious strong force, it was necessarily incomplete. When he died five years later of an aortic aneurysm, it still remained unfinished.

Conclusion: 

Albert Einstein was indeed one of the greatest Physicists to walk the earth. His research was vast and well planned and spanned from the subject of quantum mechanics to theories relating to general relativity and those of gravity and motion. These theories of gravity and motion further expanded in itself and were just additions to physics theories that had been previously put forth almost 200 years back by Isaac Newton.

 

Maxwell's Equation

#4 Maxwell’s Equations – The equations behind major modern technologies

Maxwell’s set of four equations forming the basis for electromagnetism are as important as Newton’s laws in mechanics. Maxwell’s equations are applied in almost all modern technologies. The equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors, wireless communication, lenses, radar, etc. Firstly let us see these four sweet equations one by one and then discuss them as a whole.

1. Gauss’ Law or Maxwell’s first equation

Electric charges produce an electric field. The electric flux across a closed surface is proportional to the charge enclosed.

2. Gauss’ Law for Magnetism or Maxwell’s second equation

Maxwell's Second Equation

There are no magnetic monopoles. The magnetic flux-and-faradays-law-quantitative across a closed surface is zero.

3. Faraday’s Law or Maxwell’s third equation

Maxwell's third Equation

Time-varying magnetic fields produce an electric field.

4. Ampere’s Law or Maxwell’s fourth equation

Steady currents and time-varying electric fields (the latter due to Maxwell’s correction) produce a magnetic field.

Maxwell’s Equations as a Whole

As a whole, what do Maxwell’s Equations mean?

Maxwell’s equations describe how electric and magnetic fields are generated by charges, currents, and changes of the fields. One important consequence of the equations is that they demonstrate how fluctuating electric and magnetic fields propagate at a constant speed (c) in the vacuum, the “speed of light“. These electromagnetic waves have a wide variety of usage, they are used in small things like routers to big things like search for aliens using radio telescopes and all these devices involves the use of Maxwell’s equations. Maxwell understood the connection between electromagnetic waves and light with these equations in 1861, thereby unifying the theories of electromagnetism and optics.

Using these equations only we got a relation between the speed of light (an electromagnetic wave) and permeability and permittivity of free space. So now you know why the speed of light depends on the medium it is traveling in.

Speed of light

 

So, I hope you got the essence of Maxwell’s equation. So, if you want to know about these equations in-depth, then consider reading the references.

Reference:

  1. A Student’s Guide to Maxwell’s Equations (Student’s Guides)
  2. Maxwell’s Equations – Wikipedia
Famous Equations Einstein's mass energy relation

# 3 Einstein’s Mass Energy Relation

Einstein, an absolute genius, has given a lot of groundbreaking theories and the one which completely changed our understanding was the Theory of Relativity. Being one of the most famous and fundamental scientific theories, it has a lot of revolutionary equations. In this article, we are going to talk about one such equation which is one of the most well-known equation in Physics. It is the Mass-Energy Relation.

Einstein's Mass Energy Relation

Where,

  • E is energy
  • m is mass
  • c is the speed of light

I am sure that most of you might be knowing this equation. Did you ever think that why is this equation so important and groundbreaking? Let us know.

Before Einstein giving this equation, the world used to think that energy and mass are two very different things. Newtonian mechanics told that object at rest has no energy but this equation opened our eyes and told that even an object at rest has an energy of mc2. This equation has drastically changed our understanding and told us that mass and energy are the same and are interconvertible.

So, the equation tells that you can create mass out of pure energy and you can get energy from the mass. When you add one joule of energy to a system, you are adding 1.11×10−17 kg of mass to that system. In daily life this is negligible but we see its consequences when we travel at speeds close to that of light. Einstein has given a mass velocity relation which tells the increase in mass with an increase in velocity.

Coming to the reverse process, the mass to energy conversion, 1 Kilogram of mass is equal to 9×1016 Joules which is really huge. If we could invent some method which can harness complete energy from mass then we wouldn’t need any other source for power. We know a process called Nuclear Fusion which can harness 0.7 times of this energy but sadly we don’t have the technology to do nuclear fusion on earth yet.

So, I hope that you got an essence of what this equation means and how did it change our understanding regarding mass and energy.

Read More: Famous Equations

 

Einstein's mass velocity relation

#2 Einstein’s Mass Velocity Relation

Albert Einstein, an absolute genius has given groundbreaking theories and one theory among them which was a revolution was the Theory of Relativity. It took 100 years to get strong proofs for this theory.

In 1905 Einstein proved that the laws of physics are the same for all non-accelerating observers and that the speed of light in a vacuum was independent of the motion of all observers. This was the Special Theory of Relativity. Einstein then spent 10 more years to include acceleration in his theory and published his General Theory of Relativity.

These theories had many revolutionary equations and relation. Let us see one such equation which is Einstein’s mass-velocity relation.

Einstein’s Mass-Velocity Equation

Where,

  • v is the magnitude of the velocity
  • c is the speed of light
  • m0 is the rest mass of the body
  • m is the relativistic mass

Now, what is so special about this mass-velocity relation. Let us understand what does this equation mean. This equation tells us that if we travel with speeds approaching the speed of light then our mass will increase with speed. So, do you really gain mass? Do you become fat? No, let me tell you that we take inertial mass into consideration here. Inertial mass measures an object’s resistance to being accelerated by a force. Now, every body has rest mass which is m0 here in the formula.    

If an object moves with some speed then the kinetic energy adds up to the rest mass and overall the inertial mass increases. This means that if an object approaches light speed then its inertial mass increases rapidly and accelerating it further becomes more and more difficult. If any object reaches light speed its inertial mass approaches infinite according to the above equation. Thus, Einstein stated that no object can travel faster than light speed.

I hope you got clarity about this equation and if you have any doubts please comment below, I will surely reply as quickly as possible.

Read about more such interesting relations and equations: Famous Equations

Euler's Identity

#1 Most Beautiful Equation in Mathematics – Euler’s Identity

Mathematics is a vast subject and is considered as the mother of all the science as it is a tool to solve problems in all other sciences. Mathematics is a subject with so many equations which can fill oceans.

Without mathematics, there's nothing you can do. Everything around you is mathematics. Everything around you is numbers. --Shakuntala Devi Click To Tweet

There are many wonderful equations in mathematics which really surprises us as to how can so many different things can be connected with a single equation.

One among such equation is the Euler’s identity, and it is considered as the most beautiful equation in mathematics especially Number theory. A poll of readers conducted by The Mathematical Intelligencer named Euler’s identity as the “most beautiful theorem in mathematics in 1990.

So, Euler’s identity is

euler identity

Where

  1. e is the Euler’s number
  2. Π is the ratio of circumference to diameter of a circle
  3. i is the imaginary unit satisfying   i2 = −1

Now, let us know why is this equation so special. We know that Mathematics has Real numbers and Complex numbers which are two different things. Then Real numbers have rational numbers and irrational numbers which are two different parts of real numbers.

To understand its beauty we also have to know about transcendental numbers. These numbers are real or complex numbers which are not a solution of a non-zero polynomial equation.

Now, as we have good background let us know the specialty of this equation.

In this equation, three of the basic arithmetic operations occur exactly once each: addition, multiplication, and exponentiation

The equation is considered as deep mathematical beauty because it connects very different things in mathematics and those are

  1. Two irrational and transcendental number that are e and Π
  2. The imaginary unit i
  3. Rational number 1 and 0

I hope you understand and feel the beauty of this mathematical equation.

Reference:

  1. Euler’s Identity(Wikipedia)