Gravitational Bending of Light: Quantum Mechanics of light

Wave-Particle Duality

Wave-Particle duality is the rudimentary introduction to Quantum Mechanics. Quantum mechanics is the study of microscopic part of our nature or the study of the actions taking place at sub-atomic level. This is a total contrast to Classical Mechanics in which the study involves only macroscopic level.

Wave-Particle Duality is something like split personality. Electrons sometimes behave as waves and sometimes as particles. It all depends on the situation. In 1905, Einstein published a paper that revolutionized physics, it was known as the photoelectric effect, i.e Electrons are ejected out from metals, when they absorb light in the form of photons in quantized packets. This  proved that light acts as particles and comes in the form of photons in tiny packets as Planck deduced. Einstein was rewarded with a Nobel Prize for his work on photoelectric effect, because it helped physicists understand the true reality of light. Light being both wave and particles how can that be? If this didn't sound bizarre to you, then you haven't actually understand what I just told.

For those who are not shocked when they first come across quantum theory cannot possibly have understood it -Richard Feynman

These actions should sound bizarre because these type of duality never happens in our classical world. Obviously, you don't see homo-sapiens often change into canis (Latin word for dog). We live in a world which is entirely different from the quantum world, If suppose you and your friends shrink yourselves to a tiny electron or a photon you would totally understand how the quantum world works, in fact you would be a part of that world, moving around randomly, obeying wave-particle duality and other quantum postulates.

Now that I've given you an example of a particle situation. I would like to demonstrate a situation in which wave is considered. Imaging a slit that has two slits (holes) and there is another sheet behind it in order to capture the paths of light. If suppose you shoot one particle on the left side of the whole you would get a pattern only on the left side. Similarly, if you shoot another particle on the right side, you would an interference pattern on the right side only. But what happens when you shoot a particle on both sides? Well, obviously according to our classical world throwing a ball on both the slits would result in imprinting both sides of the sheet i.e is the left and the right one.

But unfortunately this doesn't happen in the quantum world. You see we are talking about particles not tennis balls. So, here you see a complete interference pattern that looks like this.

This interference pattern looks this way because in this particular situation light acts as a wave. Just like how when you cause a disturbance to the water it starts creating waves. Now allow water instead of light through those slits, guess what? You will certainly see the same interference pattern. Because water too travels as waves too. The dark spots are the paths of light waves. The white parts occurs due the cancellation of light waves. Now that you know a basic property of light I would like to introduce special relativity in order to explain the gravitational bending of light phenomena. For more information on dual slit experiment I suggest you to check out the lectures given by Richard Feynman in Caltech.

Special Relativity

In order to understand the depth of this topic you will have to read the basics of Special Relativity.
Since I've already introduced you to the basics of special relativity, I will be talking about special relativity from the notion of photons.

Anything that has mass, is incapable of traveling at the speed of light. -Albert Einstein.

Light that is made up of photons. How could photons travel at the speed of light?
You see, according to the postulate, if you moved at the speed of light it would take infinite amount of energy to push you to reach the speed of light, which is impossible.
But if you had no mass. i.e mass is equal to 0. Then you would certainly be possible to move at the speed of light. Photons are mass-less particles and that's the reason why it travels at the speed of light.

The Equation,

was derived from special relativity. This 1 inch equation explains numerous things. An important and famous equation.  According to Einstein, a small mass has enormous amount of energy (Postulate). In fact, this is solution for atom bombs. Scientists used Einstein equations to produce atom bombs.

Lets do some elementary math to confirm this postulate,

From a small amount of mass we get enormous amount of energy.

I haven't still explained the answer to the gravitational bending of light, because this requires a bit of mathematics. I will conclude this with an answer to the topic in the next article.  

Gravitational bending of Light

Bending of light? How is that possible? We all know that light always travels in straight line. In fact light is an electromagnetic radiation that is responsible for the sense of our sight. Without light we would blinded forever.

If suppose light was able to bend in one particular medium, then we all would be seeing each other in different places which results in a messed up optical illusion. This optical illusion doesn't occur to anyone of us because light always travels in straight lines in a particular medium. Obviously the degree of bending of light differs in various mediums. Say if suppose you half dip a pencil inside a Water (Another Medium) you will notice that the pencil would look slightly bent inside the water than in air. This is because due to the deflection of light in that medium it makes it look like its bent inside the water. But what is it that it has to do with gravity? Honestly nothing. I've introduced you to one of the properties of light to prove that the relative index( i.e the number that describe how light propagates through a medium; in this case: how the light bends in different medium.) of air and vacuum are approximately similar i.e The Reflective Index of vacuum is 1 and the reflective index of air is 1.000293 approx. 1. So in Space (Vacuum) light behaves the same as how it behaves in earth i.e it travels at straight lines. Now if there is no bending of light in vacuum then why would I mention the topic as Gravitational bending of light?

You see, from the title itself  you would have guessed that the bending of light is somehow related to gravitational field of an object. In order to elaborate this idea with simplicity I have to introduce you to another abstract concept called General Relativity.

General Relativity

General Relativity is  the curved geometric theory of gravity. As I've already mentioned it before in few articles, Newton's gravitational theory explained everything from the falling of an apple to the earth and other planets revolving around the sun in their own orbit. But it failed in one major thing, it couldn't explain how this gravitational force worked or what it is? Newton himself knew that he couldn't understand it but he left it to god. He said that some mystical force was responsible for gravity. Newton's laws was helpful in various fields but it failed to explain Mercury.
It always failed when computed, many physicists even tried to solve it by introducing many mathematical methods but it didn't work for mercury. But Einstein's General Relativity theory worked really well for it. In fact Newton's Theory of Gravitation is just an approximate theory. General Relativity is known to be the accurate account for gravity. Even though the mathematics of General Relativity are too complicated, its equations are elegant and this one inch equations explains almost everything in our universe. Einstein knew that this theory was correct before even they tested it. Avoiding all the mathematical concepts I'll try to explain it to you in short terms in order to explain how the light bends due to gravity.

Space-Time

Space as we all know has three dimensions, the one everything lies. Up-down, right-left, front-back.
These three dimensions are all familiar to us. But Einstein thought of another dimension he called it the time dimension. Special Relativity his earlier theory published in 1905 tells us that time is not the same for everyone. Unlike Newton who thought of time as absolute, Einstein knew that time is another dimension. The faster you go, the slower your clock ticks. That is why when you move at the speed of light your time relativity ticks even more slower, than the person who is standing still, and after few hours of your trip you will notice that you are much younger than your friend who was standing still. This might be complicated, take a look at this article Special Relativity for more information on it.

You know what? Lets just forget about the notion of this abstract Special Relativity all you need to know is that time is another dimension. Extract from The Elegant Universe - Brian Greene

You would have to know four things in order to meet your friend.
First: Which street?
Second: Which Building?
Third: Which floor?
fourth: What time?

The first three all are three spatial dimensions and the fourth one is the time dimension.
With this idea bare with me for a few moments. Now that you are aware that there are four dimensions. Space-Time is a four dimensional mathematical representation of our reality.
This Space-time is like a fabric, it can be bent, curved, twisted, flexible and many other properties that are almost similar to a bed cloth.

Thought Experiment:

Call your four of your friends and tell them to hold a bed cloth stretched wide. Now take a football and place it in the center of the cloth. You will notice that the mass of the ball creates a curvature around it. Now roll a tennis ball with an initial speed you will notice that the ball will try to take the circular path around the curvature of the football. This what exactly happens in space. Our earth revolves around the sun because of the curvature made by the mass of the sun in the fabric of space-time.

The main idea here is that: Anything that has mass and energy will distort space-time. Since light has energy it is certainly possible for light to bend due to the curvature of a massive object, just like how the moon takes the path of the earth's curvature.

Wait, we haven't actually come to the problem yet? But the main problem here is that how can a light(collection of photons) have no mass at all but still have energy?
In order to understand this we need to indulge into a bit of Special Relativity and Quantum Mechanics. I will continue this in the next Article series.

Wormholes and Multiverse Theory

Einstein-Rosen Bridge

Einstein-Rosen Bridge aka. Wormholes are theoretically developed feature of Space-Time it was theorized on the basis of Einstein's General Relativity solutions. Wormholes is just a hypothetical feature and there are no evidences of its existences. But surely General Relativity predicts it mathematically, and there are chances of its existence but it has been found that it can exist only at the Planck Scale (Energy Scale). 

What are Wormholes? How does it look like? 

Wormholes are basically is passage through two different space-time that could create shortcuts for long journeys across the universe. To picturize this Try folding an A-4 size paper and make a hole at the center with the help of a pencil. Now unfold it and see the point of holes. For instance name the first hole A and the second hole B. If you are living in A and want to meet you friend who is living in B, you will have to walk quite a distance. But if you were to create this Wormhole (i.e fold the paper again) you would have reached B. i.e The point A and B will interest. And those two points are linked with a help of a wormhole. Its just like a long tube but allows you to travel much faster than the usual route. Science Fiction writers are fascinated with this theory and they almost frequently use them in their stories. In fact you can actually link this to the great novel Alice in the Wonderland written by Lewis Carroll ; The Rabbit Hole that Alice can actually be thought as a wormhole which led to another universe (Multiverse).

Multiverse Theory

Multiverse theory is also an hypothetical set that compresses infinite or maybe possible set of universes similar to a huge hamburger stuffed with infinite or maybe finite cheese layers. These type of universes are also called the parallel universe. And strangely according the quantum theory there might be a possibility in which Elvis might be still living and rocking out, or maybe time much be running backwards i.e Entropy( Degree of Disorderness) might decrease with time. Constants might differ in different universe due to that there might not be life forms in some universes. Strangely in our Universe the constants are perfectly tuned in a way that life could form that doesn't mean we are lucky its just an accident that happened and if it didn't we wouldn't have been able to evolve and ask questions about the universe. 

I know that these theories are strange and hypothetical but it has the mathematical proof behind it , as far as that holds experimental researches and theoretical development on that particular theory will continue. In fact the most strange theory ever known to mankind is the Quantum Theory in which strange things happen. For example: Wave-Particle Duality; Light being an electromagnetic wave acts both as wave and particle. This particular theory is certainly strange and different from what we perceive in our world. How could something act both at the same time. Check out Dual-split experiment for more information on Wave-Particle Duality. 

These bizarre things happen almost every time  in the quantum world and it seems strange to us because we are part of the macroscopic world. Surely if we could shrink ourselves with a cosmic quantum crusher (Made-up name) we could  turn into a size of an electron and experience all this by ourselves. 

In fact even-though Quantum theory seems strange it has be tested over and over again and has not been proved wrong even once. All the technologies which we use in our world: From the TV's / Computers to Microchips everything works under the workings of Quantum Mechanics. 
Mathematics is the only language which helps physicists to understand the universe. Without the help of math, it would be impossible for any scientist to deduce the nature. Math is logic. Even-though these theories might seem bizarre it will certainly might become a fact one day. Just like how Nicolas Copernicus theory (The Earth and the other planets are orbiting the sun and not the other way around) is an obvious fact now.

"Pure Mathematics is, in its way, the poetry of logical ideas." - Albert Einstein

"Everything is becoming science fiction. From the margins of an almost invisible literature has sprung the intact reality of the 20th century." - J.G. Ballard

Introduction to Black Holes

Brief History of Black Holes

It is called the black hole because light itself is not capable of escaping its gravity pull. It is formed when a star collapses with a mass of more than 3 times the Sun’s. When it reaches the end of its life, it gets crushed under its own gravity, leaving behind a compact black hole. The first prediction was in 1783, John Michell a geologist, conjectured that there must be a massive body in the universe that has an escape velocity greater than the speed of light. And when Einstein published his general relativity paper in 1915; A German astrophysicist Karl Schwarzchild defined gravitational radius of black holes by using Einstein's general relativity equation in 1916 later known as the Schwarzchild Radius. During that period all these were just theoretical predictions without evidence and many other scientists opposed this black hole theory including Sir Arthur Eddington a famous astronomer who helped Einstein prove his Relativity theory by detecting the Gravitational lens. Later in 1935 an Indian astrophysicist, Chandrasekhar pioneered in the theory of white dwarfs that led him to understand the mass limits of the stars and soon he was able to deduce and tell which star would turn out to be a black hole or a neutron star. This particular limit which he deduced was later known as the Chandrasekhar Limit. After his discovery, John Wheeler coined the term "Black Hole" and since it is black it was unable for the astronomers to find it. But it is certainly possible to detect one because each and every black hole converts its energy to radiation and this radiation can be detected by gamma ray detectors. And the first evidence of an existing black hole candidate was Cygnus X-1. Later in 1994 the best evidence of black holes was provided by the Hubble Space Telescope which captured a picture of a Super-massive Black Hole (Largest type of Black Hole) at the center of our Milky way Galaxy.

We all know that the Luna (Earth's Moon) orbits around the earth. And the Earth and the other planets in our solar system revolve around the sun. But have you ever pondered about the Sun? What does the sun revolve around? Is it just static there or is it moving around something?
The answer is that our Sun and other billions of star in our Milky Way Galaxy revolve around a Super-massive Black hole. The reason behind is similar to the reason behind why the earth revolves around the sun; its because of the Gravitational pull. A Super-massive black Holes gravitational pull is extremely intense; and that is why even the fastest (speed of light) itself is not capable of overcoming the gravitation pull of a Black Hole.

Event Horizon

It is a horizon surrounding a black hole most commonly known as "Point of no return" If you were to go close to the event horizon of a black hole its literally impossible for you to get out from there because the gravitational pull is extremely intense and it is impossible to get out from there because even if you tried to get out at the speed of light it wouldn't work; At that point the gravitational pull will be just too intense and you would experience intense gravity acting on your legs than on your head; there is the vertical stretching and horizontal compression due to which you will turn into spaghetti like shapes this particular phenomena is actually known as the Spaghettification in Black hole physics.


Schwarzchild Radius

What if I told you that if you were to compress Earth to a radius of 8mm it would turn out to be a Black Hole! This might be ridiculous but it is certainly true and there is no physical reason why it couldn't be possible. Obviously it isn't possible to compress the earth to that radius you would need a huge compressor and plus humans aren't dumb enough to turn their home into a sucking black hole!
But this particular way to create a black hole out of earth is certainly possible theoretically. As I've already mentioned before Karl Schwarzchild used Einstein's General Relativity equations to deduce his equations. And the formula which he derived was this:

M- Mass of the object
G- Gravitational Constant
c - Speed of Light

Substituting the Mass of Earth and everything you will get radius as 8mm and this by definition is known as the Schwarzchild radius of the Earth a point at which the earth itself will collapse into itself and form a Black Hole.

The Universe is full of mysteries we should try to understand our level best of these mysteries there is always a solution to everything.

"If you want to see a black hole tonight, tonight just look in the direction of Sagittarius, the constellation. That's the center of the Milky Way Galaxy and there's a raging black hole at the very center of the constellation that holds the galaxy together"- Michio Kaku, Theoretical Physicist.

Introduction to Special Relativity

Relativity

The concept of Relativity is well familiar and quite old. We all are familiar with relativistic events, and we do know that different events occur in different frame of reference. If suppose I was sitting in a moving bus and look outside I would notice the trees passing by rapidly; Similarly if I was standing beside the trees, I would notice the bus passing by rapidly. Everyone is free of accusing the other person in relativity; and obviously the judge would support the person who has his similar frame of reference. We use concept of relativity in our everyday life: "What is the speed of the car? How long will I reach my destination?" The speed of the car to what? Obviously when we talk about its speed we wouldn't say relative to the sun, moon or any other planet. Its a common relative conception that we are referring to the speed of the car relative to the ground. If we were to use more complex relative comparisons then our languages would all be a mess and no one would ever be able to make up anything at right time. The idea of this notion has been discovered long before Newton and its just as simple as arithmetic addiction.

• If your car was moving at 20 m/s at positive x-axis and your friend's car was moving at 10 m/s at positive x-axis then the relative velocity with respect to your car would be 20-10=10 m/s. 

• If your car was moving at 20 m/s at positive x-axis and your friend's car was moving at 10 m/s at negative x-axis then the relative velocity with respect to your car would be 20-(-10)=20+10=30 m/s. The reason why I considered 10 to be -10 is because it was in the negative x direction.

This concept of relativity is too old and it can be noticed in our day to day life. But the problem arises only when we start to introduce light here.

Now, If suppose your friends car is moving at the speed of light i.e (c= 3*10^8 m/s) in the negative x-axis direction and you are moving at 20 m/s in positive x-axis direction. What would be the Relative speed with respect to you?

According to the concept of Relativity, you would apply the rule and notice that 20-(-c) = 20+c m/s
where c is the speed of light.

Now the problem here is that when it was experimentally determined the answer was just c.

How could that be possible? Isn't it violating Newton's understanding of relativity? So does it mean that Newton is wrong?

No. He isn't wrong but he certainly made a mistake in believing in absolute time i.e Time is the same for everyone; It is relative like motion.

Before Einstein's period, physicists used believe in a medium known as the Ether. The medium through which light travels. So in order to find out the truth about the ether, they thought of an experiment that would allow them to calculate the precise relative speed of light, i.e if they noticed the speed of light decreasing, then there must be a medium that was acting relative to this and this medium should be the ether. As soon as this was suggested Michelson and Morley, the two scientists went out to explore for the truth and the result was just the speed of light. Since the speed of light wasn't changed they decided to abandon the idea of Ether.

Special Relativity

This idea of speed of light always being constant even when added or subtracted with other relative velocity annoyed all most all physicists. In fact, the main reason why they were really annoyed was because they didn't follow the symmetry between electromagnetic waves and Newton's relativity. (I'll talk about the symmetry of electromagnetism and Einstein's Relativity in the upcoming article).

Lorentz, an eminent physicists played a very vital role in the history of special relativity. He derived the appropriate formula for this situation. Even though the problem was quite solved it still had open wounds. To fully recover the idea of relativity, Einstein, a well known theoretical physicists came in and introduced an idea that was mind boggling. He called his new theory, the Special Relativity; the special thing about it is that it changed the way we understand the universe. In his new theory

• Time isn't Absolute; Its different for different person at different frame of reference. 

It is certainly important to understand the math behind it but I don't have the time to explain it here. But I'll surely attach a link to this post regarding deeper meaning of special relativity with mathematics involved.

Einstein basically used Lorentz equations known as the Lorentz Factor and used it make out his own understanding of light and it turned out that all the Newton's equations is just an approximation and the original equation was quite different. In order to theorize the new corrected Einstein formula; Einstein just plugged in the Lorentz Factor into Newton's equations and found that it satisfied everything and brought back the symmetry of  Electromagnetism. (Just FYI: Plugging equations wasn't all he did. He had to theorize his ideas with the help of complicated mathematics). All of physics was saved by a 26 year old German clerk working in a patent office. This elegant equations gave rise to different ideas and throws out our current common sense.

For instance: What if told you that you would age a lot slower when you reach the speed of light!

Einstein's equations tell us that if you were to travel close to the speed of light time will relatively start ticking slowly for you than the others who at rest. Its quite hard to wrap your head around this.
For instances, lets take a ride through Einstein's thought experiment:
                                                                                   

Suppose you are now travelling at the speed of light according to Einstein's Relativity equations your time will relatively slow down and you would age very slowly. But your friend on earth will be ageing normally. Since your ageing process has been slowed down when you come to a stop you will notice that your friend would have aged more and you less. Now what does that tell you? You have successfully traveled to the future. Time travel in the future has been proved by Einstein theoretically. But Time travel in the past isn't possible.

Why time travel to the past isn't possible? This is because there are too many paradoxes. The most famous paradox is known as the Grand Father Paradox; Its a thought experiment in which if suppose you were to travel back in time to your grand father's period and kill him; you wouldn't have been born and if you weren't born how could you have traveled back in time and killed your grand father?
Time travel in the future has been confirmed by numerous experiments but time travel to the past has too many paradoxes.

If you want to know more about Special relativity and how it works download the PDF here Introduction to theory of Relativity This books covers both Special Relativity and General Relativity.
And for Lectures on Special Relativity check the video tab of my blog.

Theory of Everything-3

Theory of Everything

Its the grand unification of all the forces known to mankind, from the Quantum level to the Macroscopic level. Its an abstract theory which describes almost everything in the universe in just one single mathematical equation. This mathematical equation might just look like E=mc^2 equation. An equation which is just 1 inch long but gives us vast information about the energy-mass relation. Physicists all around the world are contributing to this theory. And Just as our other physics theories, this one too has sub candidates. The main candidate that helps in constructing this extraordinary theory is the String theory. This theory states that everything in our universe is made of oscillating strings. Each and every vibration of a particular string corresponds to the behavior of a particle.

"String Theory describes energy and matter as being composed of tiny, wiggling strands of energy that look like strings. And the pitch of a string's vibration determines the nature of its effect."-Roy Williams

Unfortunately, the problem with this theory is that it is not experimentally proven. Because of this, many physicists criticize this theory by calling it a pseudoscience. The reason why it is still not experimentally proven is because we are not yet capable of magnifying a particle to its lowest level; in other words we just don't have the technology to do so. But that doesn't mean that the theory is false and there should be an end to this quest. Maybe one day we might achieve the required technology that is capable enough to find the wiggly strings. String theory has been theoretically proven with the help  of mathematics. We should encourage these hardworking string theorists rather than demotivating them.

Mathematics has always been our language to describe our universe. I would describe Mathematics as an Universal language. A language which helps science to describe events occurring in our Universe. String theory should not been considered as a pseudoscience. People thought Einstein's General Relativity theory was crazy. Only few physicists that time who believed in mathematics could appreciate his works. He deduced it all with just a pen and a paper. He believed that math was the only key to unravel the mysteries of the universe. But It took approx. 100 years to prove his theories were experimentally right. Maybe String theory might also work the same way.Einstein's dream was to unify all the forces and understand the universe completely and this has been achieved by today's string theorists.

Soon after few decades we might be able to unlock the mysteries of big bang and the black hole with the help of this theory. And who knows Science fiction might one day turn out to be our reality.

"Science is the process that takes us from confusion to understanding.." -Brian Greene.

Theory of Everything -2

Sequel to Grand Unified Theory -1

Despite all his greatest achievements, Einstein wasn't satisfied. He was still looking for the ultimate answer. So he set on a goal to achieve this by relating his new picture of gravity ( General Relativity) with Electromagnetism(EM). During the early 19th century, Electricity and magnetism were scientists great interests. Both Electricity and magnetism played an important role together and was also helpful in further telecommunications systems. It was so important that it demanded a specific unification. For instance, if suppose you are in a hill station during a thunderstorm you will probably get the idea of how electricity and magnetism are closely related. i.e the thunder strike creates a magnetic field that will  show abnormal functions in your compass. This field was unified as the electromagnetic field and was developed using the language of mathematics. How fascinating is it to see just a four line mathematical expression showing the relation b/w electricity and magnetism. This equations were deduced by Maxwell. Just as how Newton revolutionized physics with Gravitation, Maxwell has equally helped in understanding our universe. Einstein believed that this unification of both his view of gravity and electromagnetism would give birth to the answer to everything. This step was the first try on understanding our universe completely. He was one of the physicists who wanted to know the mind of God(entire picture of our universe). In fact this is the goal of today's string theorists; To unify almost everything within one simple theory - From the big bang to the black holes.

As Einstein started working on his theory he found a major problem in unifying it, he noticed that there was a huge difference b/w the strength of the Electromagnetism and Gravitation. i.e the strength of EM force being far more stronger than the gravitational force. Wait! How is that even possible? Gravity is so strong that its even capable of bending light! Gravity probably should be the strongest force. Yes, that is partially right but it is a known fact that it is certainly not as much stronger than EMF(Electromagnetic Force). In fact EMF is billions time stronger than gravity. The reason behind this lies in the microscopic level and is also the reason why we don't fall right down into the center of the earth. It might seem quite strange but its the truth. Everything in our universe is made up small bits of atoms, in which the -ve electric charges are present in the outermost shell of the atom. Now remember, the force which keeps you on the earth's surface is EMF, because there is a strong repulsive force between the two -ve electric charges.(One being the electric charge of yourself and the other being the earth's surface's charge). Imagine the repulsive force created to sustain almost each and everything in our earth. In layman's language, we all know that gravity pulls you down to the earth. But guess what now you know that EMF creates a massive repulsive force which prevents the gravitation pull towards the earth. Now, do you think gravitational force is much stronger than EMF? No, certainly not. This was the underlying reason for the major problem in unifying them both.

To be continued in the next article-Importance of mathematics in physics and Quantum Mechanics.