The Need for Quantum Theory

The Need for Quantum theory

Philosophically, we all might think that our universe is completely deterministic. This is exactly what scientists thought before the quantum model was hypothesised. A system that is deterministic can be classified as Classical Mechanics (a world where macroscopic objects moves under a set of forces) and since it predicts an object's future by knowing its present or past states with high accuracy, it is thereby, highly built up with strong applied mathematical tools that are really helpful in dealing with these complicated systems. And inevitably, it did a pretty good job in predicting everything other than microscopic objects. So, towards the end of the 19th century, physicists started trying to create classical models of microscopic objects. But its theoretical predictions did not agree with the experimental results. Since, the the theory didn't agree with the experiment, theoretical physicists had to come up with a new theory that agrees with the experiment. With numerous failures in the classical interpretation of microscopic objects, physicists came to a conclusion that there must be a new way of looking at the problem, that might actually help them define the microscopic system.

Quoting Dirac, "We have here a very striking and general example of the breakdown of classical mechanics- not merely an inaccuracy in its laws of motion, but an inadequacy of its concepts to supply us with a description of atomic events" 

The necessity to depart from the classical to the quantum model was inevitable. 

Observational Disturbance

Observation is certainly accompanied by some disturbance. It is impossible to observe an object without interacting with it. Therefore its clear that, there is some kind of universal limitation to our powers of observation. If you had to observe a microscopic object, you have no other way to observe it other than disturbing the object itself. The only reason as to why macroscopic objects can be predictable with high accuracy, is because the unavoidable disturbance is negligible when compared to the size of the object. Determinism applies only to a system that is left undisturbed. In classical mechanics, since the objects are macroscopic, the disturbance is negligible and therefore almost equivalent to the deterministic world. But, in a quantum (microscopic) scale, due to the disturbance, the quantum world becomes indeterministic. Therefore, the mathematics that will be used to formulate this quantum model, will be closely related to the mathematics of the classical model with a lot probability involved in it. And due to the disturbances, nature limits us by allowing the theory to compute only the probability of us obtaining a particular result when an observation is made. 


Classical Mechanics can be viewed as an approximation to quantum mechanics. In reality, the world is actually more bizarre than we thought. And the only reason as to why we find quantum mechanics really hard to believe, is because we human beings were evolved in a classical world. If we were microscopic objects just like the electrons, and other sub-atomic particles. Then we would understand quantum mechanics intuitively. 

"No one intuitively understands quantum mechanics because all of our experience involves a world of classical phenomena where, for example, a baseball thrown from pitcher to catcher seems to take just one path, the one described by Newton's laws of motion. Yet at a microscopic level, the universe behaves quite differently." - Lawrence Krauss

Skepticism is the key to reality

Understanding Skepticism

A skeptic is someone who is inclined to question and doubt any idea until he or she gets the proper evidence to believe in it. Skepticism is sub-divided into two groups -Philosophical Skepticism and Scientific Skepticism. 

Philosophical Skepticism (PS) is an approach that requires all philosophical views to be well supported by logical arguments. Whereas, Scientific Skepticism (SS) is an approach that requires the idea to be well supported by scientific facts. Both PS and SS is very important to a skeptic. Philosophical views give rise to Hypothesis (Proposed theory based on limited evidence) eventually the hypothesis must be proven or disproven through scientific techniques. If an hypothesis is proven through scientific methods then it is considered to be a fact. No one can be 100% sure about anything, in fact science just provides the likelihood of something being true. Every Scientist should be a skeptic, they should put scientific theories to test and check whether the theory holds to be true or not. 

"It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong." -Richard Feynman

Faith vs Science

I'm not going to explain the difference between faith and science. Let Tim Minchin's beautiful words speak for itself. 

"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved" -Tim Minchin

Faith is one's perspective of what they are willing to believe rather than what they should believe. Who do you think is more reasonable, a skeptic who is willing to change his beliefs based on evidence, even if its against what he used to believe or a person who is bounded by his faith and is not willing to change his beliefs even if evidence is provided?

"Water is two parts hydrogen and one part oxygen. What if someone says, "Well, that's not how I choose to think about water."? All we can do is appeal to scientific values. And if he doesn't share those values, the conversation is over. If someone doesn't value evidence, what evidence are you going to provide that they should value it? If someone doesn't value logic, what logical argument could you provide to show the importance of logic?" -Sam Harris

Skepticism is extremely significant for humanity to advance. We are looking for the answers to both deep scientific and philosophical questions and it won't be possible to find them if ignorance still holds us back.

Debunking Astrology

Basic Introduction to Astrology

Astrology is a belief system made into an elaborate pseudoscience, that basically concentrates the humans as the focal point of the universe. It considers the movement of planets or any astronomical event and relates it to the events in the human world. Astrology consists of horoscopes (An astrological chart that contains the information about the positions of the planets and other astronomical events) that claim to predict a person's personality or their future events.

The need for Astrology

The foundations of Astrology were all debunked more than three hundred year ago, yet it is still taken seriously by a large number of people. The main reason as to why everyone feels the need to check their horoscopes everyday is because of their curiousness to know about their future. Humans always feel the need to be the focal point, they want to feel special and connected. But Science has thought us so much, including the fact that the universe really doesn't care about what humans think. Nature behaves the way she is, it doesn't care whether you like it or not.

People learnt that the earth must be special from religious teachings so they developed models that advocated it. One of these models were Geocentricism, an astronomical model in which Earth is the centre and all other planets including the sun revolved around it. We now know that the Sun is the centre of our solar system and all other planets revolve around it.

Predicting the future is impossible

No one can possibly predict the future. The barrier here is not incapability but a universal limitation that nature sets. The Uncertainty Principle clearly depicts that it is impossible to accurately predict the velocity of a particle if we know its position with high accuracy. It is easy to handle with Classical physics i.e the dynamics of the larger objects. By way of an example, when person throws a ball at you from a far distance, you can accurately predict the movement and catch the ball. It is as though you computed a set of complex differential equations of a system that governed the movement of the ball within few seconds. This seems easy because we were evolved with Classical physics. But Quantum physics (i.e the physics of tiny objects) is entirely different it seems intuitive and bizarre but it has been experimentally tested numerous times. If suppose we could break the Uncertainty Principle barrier and calculate both the velocity and the position of each and every electron of a person. Then it is possible to predict that person's future with high accuracy. But unfortunately, the barrier set by nature cannot be broken.

Why do we consider Astrology as a Pseudoscience?

There has been no evidence that proves the predictions of Astrology. People tend to think that astrology is true because they might have had few experiences in which the predictions were absolutely true. But do they really think they can start believing in something which seems to work only few times? The search for the truth is entirely based on skepticism and continuous experiments. Nature does not change physical constants. If continuous experiments yield to the same answer again and again, we deduce its dynamics, i.e the working behind it and conclude that it must be true.

The Uncertainty Principle is a fundamental limitation that cannot be broken and this is why the scientific community has always considered astrology as a pseudoscience.

"What can be asserted without evidence can also be dismissed without evidence" -Christopher Hitchens. 

Is Mathematics Invented or Discovered?

The Queen of Sciences

Gauss referred to mathematics as "The Queen of Sciences". Mathematics is an universal language that uses logic as its own base for further predictions. We could define any physical object with the help of mathematics. But math isn't just about defining events or objects. Its dynamic, it is as though the language reveals further predictions from the logical assumptions we have taken from the nature. For mathematicians, they think of it as a game. A game which can be assigned, controlled or played with different rules. Rules which aren't compatible with reality. But why does a mathematician have to understand something which isn't compatible with reality? Isn't that just like a child dreaming about Sasquatch? The answer to this is mathematicians really don't care about what relates to the reality, their interests in math is exclusively for their own happiness or the pleasure they get. Mathematicians, can create their own mathematical world. All they needed to do is kick start a world with odd rules or rules of their own interest and play around with them, to find out the governing dynamics. Its beautiful, sometimes messy. The more messy it gets, the more unpredictable the world becomes.

"Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true." -Bertrand Russell

Our universe too is unpredictable but not too messy because of the symmetries and constants. The only reason our world is unpredictable is because of quantum mechanics. If rules of quantum mechanics didn't interfere with our universe then it would be easy to predict ones future with incredibly high accuracy.

The Uncertainty Principle

It states that if we know the velocity of the particle with high accuracy then it is impossible to find the position of the particle with high accuracy. This might sound bizarre, because it conflicts with our everyday experience. If we know the velocity of a car moving, then using Newtonian dynamics we can compute the position of the car to high accuracy. The only difference here is Newtons laws (Classical World)  are applicable only to classical objects i.e objects that are large. The rules of Quantum Mechanics (QM) are only applicable to tiny objects like electrons, protons. QM seems strange only because we weren't evolved to understand it. If you were to shrink yourself to the atomic level, your everyday experience will seem to conflict most of the rules of the classical world.

The uncertainty principle is a well defined mathematical model. Quantum physicists who study the world of QM find it extremely hard to grasp the concepts. In fact Feynman once said "If you think you understand QM, you don't understand QM" The only hope quantum physicists get is from mathematics. They put their theories for tests and gives the exactly the same result as what was predicted using the mathematics of quantum mechanics.

"The mathematical framework of quantum theory has passed countless successful tests and is now universally accepted as a consistent and accurate description of all atomic phenomena." -Erwin Schrodinger

Is Mathematics Invented or Discovered?

I'll be honest with you. No one actually knows the answer to that. But I think it is more likely to be discovered than to be invented. As a skeptic, I have no problem with mathematics being invented. If mathematics was invented then I would be astonished by the fact that the humans were so imaginative in inventing something that happens to work very well with the nature. Math is everywhere and the fact that we can relate/ define to at least some extent and predict its outcomes satisfies me. If mathematics was invented then there must be something or the other that cannot be fully explained by math. But we have no evidence to conclude that, since we still do not have all the mathematics needed for its explanation.

I haven't covered any of these topics in depth but I'll soon post a PDF on the nature of mathematics. 

Gravitational Bending of Light: Energy of Photons

Article Series 3. Continuation of Gravitational Bending of Light and a sequel to Quantum Mechanics of Light.

Mass-Energy Equivalence

This principle revolutionized physics over a century, But unfortunately people now are still unaware of this beautiful equation. The Equation,
                                           
                                                                

signifies that anything that has mass has an energy associated with itself. And the speed of light is a proportionality constant that helps us to calculate their energies.

Special Relativity was the basis for formulating this equation. Even though there are many mathematical foundations to understand this better, I will try to explain it in the simplest language.

According to Einstein, if we travel faster, the heavier we get. This might seem impossible, but it is true and it is happening everywhere. A family traveling in their car, puts on more weight while traveling.
If you haven't inferred it yet, then I would explain it in simple terms. Firstly, what do you need to move a ball from one place to another? Most people will say 'Work'. And they are correct, but what is work? By definition, Energy is the ability to do work. No Energy no work. By way of example, if you kick they ball by giving a specific amount of force, the force given by to the ball, is a direct way of passing your energy to the ball. Now assume that it is an isolated system, and there is no friction. The energy passed on to the ball is its kinetic energy. Since this ball has its own kinetic energy now, it will travel in a straight line forever. Now that Einstein has showed us the relation ship b/w Energy and mass we can understand that this ball's mass should be increased since energy level is raised. Ergo, velocity and mass are also related. This is why the faster you travel, the heavier you get.

Unfortunately, this is the reason why nothing can travel faster than light. Mathematically speaking, if you reach the speed of light, your mass will tend to infinity and you will need infinite amount of energy to keep pushing you to keep you at that particular speed. Therefore, anything that mass is incapable of achieving the speed of light.

You see, that is also the solution of how photons that are mass-less particles are capable of traveling at the speed of light.

Energy of photons

According to Mass-Energy Equivalence, photons who are mass-less are supposed to be energy less. But they aren't and you know it, because you know that plants get their energy from sun's light. If photons do have energy, then does that mean Einstein's equations are wrong? Certainly not.

Quantum Physics gives us the solution for this question. It says that light is an electromagnetic wave that is a form of energy. And its Energy is dependent on its frequency not with mass.

This is one of the famous equations in Quantum physics, in fact this too was formulated by Einstein. He found this relationship when he was working on photoelectric effect. He used Planck's idea. The 'h' in the equations stands for Planck's constant which is a physical quantity that is extremely small and is used mostly in the field of Quantum Mechanics, since it deals with microscopic things.

Deriving the Energy of a photon from Mass-Energy Equivalence.

This video clearly illustrates the notion of Energy of light.
Prerequisites: Introduction to Special Relativity and a bit of elementary mathematics.

Rephrasing the postulate of General Relativity: Anything that has mass, energy/momentum follows the geodesics( Straight line in a curved geometric surface) path of the curvature made by another object.

Ergo, light is can be bent due to any strong gravitational field. Einstein gave this solution to Arthur Eddington, a famous British astronomer to test this theory. He said the stars behind the sun would be seen some where else due to the bending of light. The Theory of Relativity was confirmed by Eddington in 1919 during a solar eclipse. Eddington observed from the images that light from stars passing close to the Sun was slightly bend, so the stars were out of their positions. This discovery made Einstein popular. And finally Newtons theory of Gravitation was thrown out and General Relativity was its fine replacement. 

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.