Quantum Physics for Beginners PDF

Quantum Physics for Beginners Discover the Most Mind-Blowing Quantum Physics Theories by Analyzing the Greatest Physics Experiments of All Time. A Real Eye- Opener to Understand How Everything Works Gary Carroll © Copyright 2020 Gary Carroll - All rights reserved. The content...

Quantum Physics for Beginners Discover the Most Mind-Blowing Quantum Physics Theories by Analyzing the Greatest Physics Experiments of All Time. A Real Eye- Opener to Understand How Everything Works Gary Carroll © Copyright 2020 Gary Carroll - All rights reserved. The content contained within this book may not be reproduced, duplicated or transmitted without direct written permission from the author or the publisher. Under no circumstances will any blame or legal responsibility be held against the publisher, or author, for any damages, reparation, or monetary loss due to the information contained within this book. Either directly or indirectly. Legal Notice: This book is copyright protected. This book is only for personal use. You cannot amend, distribute, sell, use, quote or paraphrase any part, or the content within this book, without the consent of the author or publisher. Disclaimer Notice: Please note the information contained within this document is for educational and entertainment purposes only. All effort has been executed to present accurate, up to date, and reliable, complete information. No warranties of any kind are declared or implied. Readers acknowledge that the author is not engaging in the rendering of legal, financial, medical or professional advice. The content within this book has been derived from various sources. Please consult a licensed professional before attempting any techniques outlined in this book. By reading this document, the reader agrees that under no circumstances is the author responsible for any losses, direct or indirect, which are incurred as a result of the use of information contained within this document, including, but not limited to, — errors, omissions, or inaccuracies.  Table of Contents Introduction Chapter 1: What is Quantum Physics Chapter 2: The Fundamental Blocks of our Universe Chapter 3: Black Body Radiation (A Planckian Revolution) Chapter 4: The Photoelectric Effect: Is Everything Quantized? Chapter 5: The Franck-Hertz Experiment Chapter 6: Atomic Model of Bohr Chapter 7: Confirming The Quantum Theory Of Light: Compton Effect Chapter 8: The Wave-Particle Duality Dilemma Chapter 9: The Double-Slit Experiment Chapter 10: De Broglie Hypothesis Chapter 11: Heisenberg’s Uncertainty Principle Chapter 12: Introduction To Quantum Superposition: Schrödinger’s Cat Chapter 13: The Quantum Fields And How Empty Space Doesn’t Exist Chapter 14: Riding The Wave Function Chapter 15: Quantum Tunneling Is the First Step Towards Teleportation Chapter 16: Welcome to Copenhagen: Solving The Bohr- Einstein Debate Chapter 17: The Copenhagen Interpretation  Chapter 18: Many Interpretations of Quantum Physics Chapter 19: The Epr Paradox Chapter 20: The Revolutionary Discoveries in Quantum Mechanics Of Bohr, De Broglie, Einstein, Heisenberg, And Many Others Chapter 21: The Strange and Fascinating Rules of the Law of Attraction Chapter 22: Introduction to Symmetries and Conservation Laws Chapter 23: Basic Principles of Quantum Mechanics Chapter 24: Applied Disciplines Chapter 25: The Quantum Dimension Chapter 26: About the Mathematics of Microcosm Behavior Conclusion  Introduction Through experiments in quantum physics, we have come to the seemingly unavoidable conclusion that the act of observation is a creative act. In other words, through observation, we help to create, recreate, perpetuate, increase, lessen, and end that which we perceive and observe. Observation equals influence. Observation equals creation. It means that we have not been merely discovering what is so through our comments of it. We have been helping to make what is so what it is through our words. Let that concept sink in and settle. Begin to feel your power. So, in which ways do we affect those things and circumstances we observe? We influence them in an infinite number of ways. And by what means do we affect those things and events we keep? Our power is in our thoughts, feelings, beliefs, expectations, opinions, attitudes, and assumptions; our prejudices, desires, fears, intentions, understanding, and confusion are in our knowledge. We affect all we perceive in countless ways. By how we observe, we affect people, objects, events, and circumstances. We make things more desirable or less desirable, larger or smaller, stronger or weaker, better or worse. We make things stop or continue. For most, of course, this ongoing process of modifying all they observe is unconscious. This process is knowing what is going on, but people have no concept of how specific ways the act of their observation affects what they are observing, and they have no conscious control over the process. We can all hope our words will have a constructive and destructive effect on that which we keep. But hope is not knowing; hope is not doing. We could ask this: How is my observing affecting what is going on out there? Just as important a question is this: How am I affecting what is going on out there affecting me? By learning how to manifest in the advanced and easy way, you will not only be helping yourself in countless, meaningful ways, but you will be supporting all people on the planet in numerous, meaningful ways. In light of this encouraging fact, consciously and intelligently manifesting in the advanced and easy way sit could be viewed as a humanitarian effort. Improve your life to whatever degree, and to that degree, you improve the whole world. Increase your happiness to whatever degree, and to that degree, you increase the satisfaction of the world as a whole. Regarding people who understand this, we can argue that it is their great blessing to improve their lives and themselves by manifesting in the advanced and easy way and their great responsibility. A single individual has the potential to save the world; a single individual has the potential to destroy the world. We can help the world be happy, not so much by fighting things that make people unhappy by becoming glad ourselves. We can help the world to live more abundantly, not so much by fighting things that breed lack as we can by living ourselves abundantly. And, of course, by sharing our abundance in whatever forms it may come. Know that what we resist persists and that we give might to what we fight. As individual conscious creators of material reality at large and our material existence, we should strive to move toward what we want more than we move away from what we don’t want. We should strive to increase what we view as desirable things for the world, and us more than we aim to decrease what we view as undesirable things for the world and us. We should be for what we deem as good, right, and just more than we are against what we think is immoral, wrong, and unjust. This material should not mean we cannot and take actions that may make us appear to be fighting or resisting something. It means we should take all such steps from a fundamentally different philosophical point of view. For example, it’s OK for you to give money to homeless people. But you should not give homeless people money in an attempt to compensate for their lack. Instead, you should give homeless people money with the explicit intention of adding to their abundance. Don’t see that an individual homeless person has little or no money. Instead, notice that the homeless person in question is in the process of receiving all the money they need, and see the act of you giving that person money as evidence of that fact. In other words, don’t feed people’s poverty. Instead, provide their prosperity. Yes, you can give a homeless person money, and it is an admirable thing to do, but there are a harmful way and a helpful way to do it. In one way, you observe the situation in a manner that helps to push the homeless person further down into their prison of lack and despair. On the other way, you watch the case in a form that allows you to lift the homeless person into the freedom of abundance and hope. Though the act itself is essential, of most significant importance is the consciousness behind the action. Thought and feeling are the forces that create and recreate material reality for good or bad. Remember that it is how you view what you observe that determines your effect on what you watch. Observing is creating. Think about how you usually look at things such as war and violence, illness and disease, and so- called injustice. How have you been viewing such things? How have you been observing them? Have you been watching them help strengthen and perpetuate them or in ways that help weaken and lessen them? It’s one or the other. The gift of the power to observe carries a significant obligation to monitor responsibly. The advantage of our ability to transform our lives by following them is our gift of the power to change the world by observing it. And just what is it at the bottom of all that determines how we keep a given thing? It comes down to the primary factors of individual will and personal choice in the final analysis. We can choose, and by how we view things, we will make things what they are and what they will be. Can you grasp the significance of what you are reading here? Do you have any idea? At all of how powerful you are? Do you know that your life will be what you choose it to be? Do you understand that you have thus far realized only the tiniest fraction of your potential? Can you fathom how much more is possible for you? Do you see that what you see will be what it is following how you see it? Can you accept the fact that you can see things in any light you decide to? It’s time to wake up. You need to know yourself. You need to stop hiding from yourself. You need to stop denying yourself. You need to allow yourself to be. Perhaps you want more money or more success or more influence. Maybe you desire more fulfillment in your life or better relationships or greater peace of mind. The point is there are things you want to attain that you think will give you other things you are seeking. For instance, perhaps you think that finding the love of your life will bring you happiness or that establishing yourself in a lucrative profession or amassing a great fortune will give you security. On the surface, perhaps, you may be able to find some of what you are seeking in this way—at least in the short term. But you will never truly gain inherently inner qualities—such as the emotion of happiness and the feeling of security—from temporary outer things such as relationships, objects, and circumstances. All that stands in your way is a decision. Do you want to be happy? Then be satisfied right now. Do you want to feel secure? Then feel safe right now. Have you done it yet? Are you comfortable and safe now? You may think you can never be happy until you find your ideal mate. You may think you will never feel secure until certain financial conditions. But what if that’s not how it works? What if you first need to be happy before you can find your ideal mate? What if you must first feel secure before you can bring about certain financial conditions you desire? What if you have it backward? Entertain the following concepts. The perfect mate may not be the cause of your happiness but an effect of your satisfaction. Having the financial resources, you desire may not be the cause of your feelings of security but the impact of your feelings of security. The universe doesn’t bring you what you want or what you need as much as it brings you what you are. Everything you become aware of and experience is you being reflected in yourself. All you can ever see and know is you.  Chapter 1: What is Quantum Physics For the vast majority of people, the term “quantum physics” is closer to “rocket science” than it is to “the wonders of the universe.” And that’s a real pity. Most of you might think of tedious formulae and explanations when thinking of physics - but the truth is that both “traditional” physics and quantum physics are pretty much the sciences that hold the secrets to the universe: The whys and the hows of how the entire cosmos works. No matter what you do are for a living, quantum physics will bring a whole new perspective into your life on so many things that it is impossible to ignore it. How could you, when you know that quantum physics is at the foundation of what you are, in the background of your fate spinning your life, and at the core of your very way of “functioning” as an intelligent being of the universe? Almost borderline between science and spirituality, quantum physics might finally be able to explain the unexplainable and help us transgress the borders of thinking that have been limiting us thus far and bring us closer to the essence of the world. What it is, where it comes from, and the fundamental theories that define this science. We invite you to discover the beauty of a study discipline that has been long considered a mystery and an impossible topic simultaneously, step by step. Let’s dive in and uncover the basics of quantum physics! What Is Quantum Physics? To understand what quantum physics is, you must first go to the “mothership,” i.e., physics. For many people, physics is that boring subject in school you have to be a real “nerd” to like: The one that is even worse than mathematics and even more difficult to understand than chemistry. For many other people, physics revolves around mechanics, or, in layman terms, “how cars work.” While it is true that physics deals, among many other things, with how cars work, that it also deals with a bit more than how cars work. It is also worth noting that mechanics is only one branch of physics, but lies at the very foundation of car-making, alongside electronics - another physics branch. The etymology of the word “physics” is pretty fascinating: It comes from the Greek word physique, which used to mean “knowledge of nature.” As such, the definition of physics is tightly connected to nature and getting to know it. Many define physics as a natural science that studies matter, how it behaves through space and time, and how it connects to energies and forces. Each of these deals with a different aspect of matter and other types of value (such as in nuclear physics, for example, which studies how atomic weight behaves in different contexts). In addition to this categorization, you may also find people talking about classical physics and modern physics, which is a way to look at this natural science from the perspective of its evolution in time. So, where does quantum physics lie in this entire paradigm, you may ask? Well, you see, quantum physics is a bit of an odd “animal” because it is sometimes used as a synonym to modern physics. So it only comes as both a continuation of traditional physics and as an antagonist as well. Although most modern physics revolves around quantum theory, it is worth noting that, at large, it is still considered to be only a direction of modern physics. To better understand the relationship between modern physics and quantum physics, consider the fact that two significant theories and theoreticians marked the beginning of modern physics : Planck’s Constant is the most famous one, and it entailed that the energy and frequency of light are proportional, which led Einstein to postulate that light exists in small quantities of energy called “photons.” Albert Einstein, whose major work was related to the theory of relativity and the photoelectric effect. The first postulates, in short, that massive objects can cause a distortion in space and time, which is felt as gravity. The latter says that light does not exist in waves, but in quanta (small pockets of energy), as mentioned above. If “big” physics deals with things, you can more or less see (or at least perceive, especially if you run experiments), quantum physics deals in the tiniest parts of matter. This is its actual definition: The science that deals with the atomic and subatomic levels of significance. That might not sound like much. However, quantum physics has gone so in- depth (and continues to do so) that it might be the one to explain everything in the universe finally. Everything we’ve never known. All the questions we always sought an answer to - the very essence of life. Can you think of quantum physics as a boring topic when you look at it through this perspective? When do you know that it is the science that will finally help us understand so much our place in the universe, more about ourselves, and where all of this is leading? Not only does it appear to hold the key to all the things we never managed to achieve (like teleportation, or understanding fate and destiny, for example), but it is also a contradiction to a lot of very well-established theories, including that of general relativity brought forward by Albert Einstein himself. There is a war for knowledge out there, and quantum physics just “happens” to lie at the very core of it. We bet we made you curious!  Chapter 2: The Fundamental Blocks of our Universe The expression “quantum mechanics” shows up in a 1924 paper by MAX BORN “Zur Quantenmechanik.” Outside of discourse talk, it recommends that particles are machine contraptions. From the perspective of quanta and Quantum-Geometry modules, this articulation obtains the pith of particles. Quanta modules are restricted estimation devices. The fundamental particle is described by a unique instrument that is comprised of the consistency of quanta modules. Fundamental proton articulation: The adaptability of quanta modules empowers the plan of different shells that address the particle’s resting and compact atoms. Live streaming is made into creative, exchangeable, with contraptions sorted out by quanta modules. Broadcasting is additionally accomplished by the inclusion of voids and apparent parts. A correspondence system was created to survey possible possibilities inside sub-proton sub-segments. The framework shows that the joined tetrahedron/octahedron can’t be sufficiently required to be depicted as a quantum-mechanical machine. There are similitudes among particles and standard machines. A proton has a rotor part like a stator. The shut Octet analyzes to the Rotor, and the incorporated tetrahedron/octahedron resembles a stator. A proton can be considered as a modifier of a close-by void capacity. The proton conceals portions of this compound. Hadron’s degree, as spoken to in “Quanta modules and material science” (1987) when considering wave atom, Earth particles, or particles, are prohibited. As far as the proton, living space and inside particles are equivalent. With the restricted appearance time, kaon, pion, and muon, the settlement are nearby, while the polyhedra above allude to particles’ mass. Inside the arrangement, these groups play oscillatory developments. 2.1 Fundamental of our Universe; “Particles.” In 1905, Einstein distributed a paper named ‘Concerning the Heuristic Point of View towards the Emission and Transformation of Light,’ where he figured light didn’t travel like waves, yet as a specific ‘amount quantum.’ Einstein proposed that this boost could be ‘presented or made more normal,’ as the particle ‘bounces’ between the vibrated vibration levels. This will work a similar way, as allowed a couple of years when the electron “bounces” between the tried circles. Underneath this model, Einstein’s lively power fuses the differentiation of ricochet imperativeness; when isolated by Planck’s soundness, the quality contrast decided the light shade sent by that number. With this ideal approach to look at the light, Einstein gave insights into the behavior of nine different phenomena, including the specific colors on the best way to eliminate electrons from metal surfaces, a wonder known as the “photoelectric impact.” However, Einstein was not given a lot of insurance against this heightening, said Stephen Klassen, a material science partner at the University of Winnipeg. In a 2008 paper, “The Photoelectric Effect: Reconstruction of the Physics Classroom Tale,” Klassen brings up that Einstein quanta’s imperativeness doesn’t clarify any of these nine miracles. For example, some light-producing medications are prepared to uncover certain hues that Planck appeared, such as light-radiating fiber and photoelectric impacts. To be sure, for Einstein’s notable 1921 Nobel laureate, the Nobel Committee as of late observed “his disclosure of the law of photoelectric effect,” which didn’t rely altogether upon the possibility of dynamic vitality. Almost twenty years after Einstein’s paper, the expression “photon” was authored to communicate quantum size based on Arthur Compton’s 1923 work. He brought up that light scattered through an electron changed the diminishing. This indicated splendid particles (photons) crashing into electron particles and affirmed Einstein’s reasoning. It was clear right now that light could travel like waves and atoms, setting a “wave-particle light” of light at the commencement of QP. Rising Waves and Stationary Waves Waves, for instance, discuss supposed ‘moving waves’ since they ‘travel’ in space. The model appeared, the improvement from left to right; nonetheless, it might be from left to right. Like the influxes of the ocean, we should think about the ‘standing waves.’ We see that the wave has a similar shape as recently examined, and the water is free once more; however, it doesn’t move, yet stays in a practically identical position - subsequently, the name. As a rule, a stop wave happens when it is obstructed by a ‘gap’ associated with two cutting focuses. A wave being built up shows up at one of the cutting focuses and is withdrawn toward another path. When the two-way waves are associated, the consequence of the net is a standing wave. If all else fails, the open territory’s dividers with the fundamental expectation that the lock can’t assault them, which makes the wave fulfillment equivalent to zero at the limits of the hole. This recommends halting flooding waves just in the drop - then again, actually, all together for the tide to be as low as could be expected under the circumstances, its repeat ought to be at tallness reasonable for the absolute number of pinnacles or posts to enter the space. This law bolsters the improvement of different apparatuses. For instance, a note communicated by a violin or guitar is guided by a frequency gave by a wire, for which it is attached to the length of the strings the player puts on the impact. To change the notes’ tallness, the player presses the line down to the sharp focuses that change the length of a specific vibration period of the series. 2 Standing waves anticipate a similar capacity in each instrument: wood and metal breezes set vertical waves with moderate air volumes. Simultaneously, the drums’ sound begins from the steep waves set on the skin of the drum. The sorts of sound communicated by different instruments have passed and shifted - even though the notes made share something practically speaking. Given this, we propose that vibration is in no way, shape, or form a reasonable ‘indistinct’ notice contrasted with one of the permitted frequencies, yet is comprised of a mix of fixed waves, the total of its waves bringing about a sharp drop or ‘head’ rehash. Stale waves happen when the tide is restricted to space. Now and again, it has become, however much as could be expected, not in the area. Regardless, if the waves were as yet the entire thing, the sound would not go to our ears. All together for the sound to be sent to the group, the instrument’s vibration must move waves evident around it, communicating sound to the group. All around, for instance, the metal body vibrates with the affectability of the rope and makes a movement wave that associates the gathering. A striking bit of science (or vitality) of altering instruments includes guaranteeing that the notes of the notes compacted by the waves consider static waves to emulate the relating travel waves. Full comprehension of the tools and how they send sound to the group is a unique point that we don’t have to push ahead. Influxes of Light Different encounters incorporate tremendous electric waves, reflected by radio waves sending signs to our radios and TVs and light. These waves have various frequencies and frequencies: for instance, standard FM radio signs have a recurrence of 3 meters, while the light power sparkles at their range, being around four × 10- - 8 m of blue light and seven × 10- - 8 m red light; different tones have frequencies between these components. Light waves are not equivalent to water waves and sound waves because there isn’t anything against the vibrating mode (e.g., water, link, or air) in the models referenced before. There is no uncertainty that light waves are ideal for void space, as is clear from how we see the light from the Sun and the stars. This little wave material knows a primary issue with experts in the eighteenth and nineteenth hundreds of years. Some find that space usually is not filled, yet is supplanted by a concealed item known as an ‘aether’ that was an idea to help impact the light waves. In any case, this speculation started to stress when it was accepted that structures need to give similarly high frequencies in light that can’t be implemented by how aether doesn’t protect articles’ improvement (e.g., earth in its drift). It was James Clerk Maxwell, and in the 1860’s he indicated that the hypothesis was silly. By then, the study of solidarity and interest was rehearsed. Maxwell had the choice to show that it was wholly contained in numerous unique situations (presently known as ‘Maxwell’s Conditions’). He likewise brought up that a solitary kind of reaction to these conditions breaks down the waves’ vicinity to the choppiness of electric and alluring spaces that can discover void area without a facilitator’s requirement. The speed at which these ‘electric’ waves travel is constrained by the principle seasons of power and energy, and once this speed is settled, it was viewed as immense from the rate of light force. This has dependably improved the likelihood that light is electric waves. It is currently justifiable that this model works similarly at different marvels, including radio waves, infrared radiation (warmth), and X-columns. Matter Waves The way light, regularly alluded to as waves, has sub-atomic properties makes French scholar Louis de Broglie estimate that the different components we, specifically, consider to be particles of wave components. With these lines, a brilliant light, frequently thought of as a surge of little particles like a slug, now and again, would travel like a wave. This misshaped see was first affirmed during the 1920s by Davidson and Germer: they passed the electron bar with a graphite gemstone and took a gander at an obstruction framework near the vital level sent when the light was cut. As we have seen, this material is significant in guaranteeing that light is a wave, so this test is a shred of speedy evidence that this model can be applied consistently to electrons. Afterward, close revelations were made in the properties of weighty molecule surfaces, for instance, neutrons. It has now been set up that wave-atom holding is a typical material in a broad particle scope. Without a doubt, even the most widely recognized articles, for instance, sand, soccer, or cars, have wave qualities, even though in these cases, the waves are not entirely accessible - predominantly because the amazing reiteration has neither rhyme nor reason. Yet, as the excellent style is made of particles, all with their frequencies and every one of these waves is dependably cut and created.  Chapter 3: Black Body Radiation (A Planckian Revolution) The classical theory of light and Planck’s calculations led not only to the conclusion that the distribution of wavelengths was concentrated in the blue-violet parts but even (due to the desperation of theoretical physicists, who were increasingly perplexed) that the intensity became infinite in the more remote regions of ultraviolet. There was someone, perhaps a journalist, who called the situation an “ultraviolet catastrophe.” It was a disaster because the theoretical prediction did not agree at all with the experimental data. The embers would not emit red light to listen to the calculations, as humanity has known for at least a thousand years, but blue light. It was one of the first cracks in the building of classical physics, which until then seemed unassailable. (Gibbs had found another one, probably the first-ever, about twenty-five years earlier; at the time, its importance had not been understood, except perhaps by Maxwell). The black body radiation curves shown in figure 4.1 have peaks that depend on temperature (more towards red at the low ones, more towards blue at the high ones). All of them, however, go down quickly to zero in the very short wave area. What happens when an elegant and well-tested theory, conceived by the greatest minds of the time and certified by all European academies, clashes with the brute and crude experimental data? If for religions, dogmas are untouchable, flawed theories are bound to be swept away sooner for science. The Discovery That Broke Classical Physics, Aka Planck’s Work On Black Body Radiations Classical physics predicts that the toaster will shine blue when everyone knows it is red. Remember this: every time you make toast, and you observe a phenomenon that blatantly violates classical laws. And even if you do not know it (for now), you have the experimental confirmation that light is made of discrete particles; it is quantized. It is quantum mechanics live! Young, it has been proved that light is a wave? Sure, and it is true. Let’s get ready because things are about to get very strange. We are still travelers exploring new and bizarre worlds far away - and yet we always get there even from a toaster. Max Planck Berlin, the epicenter of the ultraviolet catastrophe, was the realm of Max Planck, a theoretical physicist then in his forties, a great thermodynamic expert.7 Fully aware of the disaster, he was the first to want to understand something about it. In 1900, starting from his colleagues’ experimental data and using a mathematical trick, he managed to transform the formula derived from classical theory into another that matched the measurements very well. Planck’s manipulation allowed the long waves to show themselves quietly at all temperatures, more or less, as expected by classical physics. Still, he cut the short locks imposing a sort of “toll” on their emission. This obstacle limited the presence of blue light, which radiated less abundantly. The trick seemed to work. The “toll” made the higher frequencies (remember: short waves = high frequencies) were more “expensive,” that is, they required much more energy than the low ones. So, according to Planck’s right reasoning, at low temperatures, the power was not enough to “pay the toll,” and short waves were not emitted. To return to our theatrical metaphor, a way had been found to free the front rows and push the spectators towards the middle rows and the tunnels. A sudden intuition (which was not typical of his way of working) allowed Planck to connect wavelength (or frequency equivalent) to energy: the longer the length, the less power. It seems an elementary idea, and indeed it is because that’s how nature works. But classical physics did not contemplate it at all. According to Maxwell’s theory, an electromagnetic wave’s energy depended only on its intensity, not color or frequency. How did Planck put this characteristic in his treatment of the black body? How did he manage to pass the idea that energy depends on intensity but also frequency? There are still two missing pieces from the puzzle because you have to specify what has more power as the frequencies increase. To solve the problem, Planck found an efficient way to divide the emitted light, whatever the wavelength, into packets called a quantum, each of which has a quantity of energy-related to its frequency. Planck’s illuminating formula is as simple as possible: Put in words: “the energy of a quantum of light is directly proportional to its frequency.” So the electromagnetic radiation is composed of many small packages, each of which has a specific energy, equal to its frequency multiplied by a constant h. The emitted light’s power is similar to the number of those who register at a particular frequency multiplied by their energy. Planck’s effort to reconcile the data with the theory led to the idea that high frequencies (i.e., short waves) were expensive in power for the black body. His equation, at all temperatures, was in perfect harmony with the curves obtained from experimental measurements. It is interesting to note that Planck did not immediately realize that his modification to Maxwell’s theory had directly to do with light’s nature. Instead, he was convinced that the key to the phenomenon was in the atoms that made up the black body’s walls, that is the way the light was emitted. The preference for red over blue was not due to these wavelengths’ intrinsic properties, but to how the atoms moved and cast various colors. In this way, he hoped to avoid conflicts with classical theory, which had worked wonders until then: after all, electric motors were pushing trains and streetcars all over Europe, and Marconi had just patented the wireless telegraph. Maxwell’s theory was not wrong, and Planck had no intention of correcting it: better to try to amend the most mysterious thermodynamics. Yet his hypothesis about thermal radiation involved two sensational deviations from classical physics. First, the correlation between the intensity of the radiation and its frequency is utterly absent in the Maxwellian picture. Then, the introduction of discrete quantities, quanta. These are two aspects related to each other. For Maxwell, the intensity was a continuous quantity, assuming any real value, dependent only on the electric and magnetic fields associated with the light wave. For Planck, the power at a given frequency is equal to the quanta number corresponding to the frequency itself, each carrying energy. It was an idea that smelled suspiciously of “light particles,” yet all the diffraction and interference experiments confirmed the wave-like nature. Nobody then, including Planck, fully understood the meaning of this turning point. For their discoverer, the quanta were concentrated impulses of radiation, coming from the atoms of the black body in frantic movement due to thermal agitation, which emitted them according to unknown mechanisms. He could not have known that that h, now called Planck’s constant, would become the spark of a revolution that would lead to the first roars of quantum mechanics and modern physics. The great discovery of the “quantum energy” occurred when he was forty-two years old; Planck was granted the Nobel Prize for physics in 1918. Einstein enters the scene. The extraordinary consequences of quantum physics’s introduction were understood immediately afterward by a young physicist then unknown, none other than Albert Einstein. He read Planck’s article in 1900 and, as he declared, he felt “the earth beneath his feet is missing.” 8 The underlying problem was this: were the energy packets children of the emission mechanism, or were they an intrinsic characteristic of light? Einstein realized that the new theory was deploying a well-defined, disturbingly discreet, particle-like entity that intervened in the process of light emission by superheated substances. At first, however, the young physicist refrained from embracing the idea that quantization was a fundamental light characteristic. Here it is necessary to say a little word about Einstein. He was not a child prodigy and did not particularly like school. As a boy, no one would have predicted a prosperous future for him. But science had always fascinated him, ever since the day his father showed him a compass when he was four years old. He was bewitched by it: invisible forces forced the needle to always point north, in whatever direction it was turned. As he wrote in his old age: “I remember well, or instead, I think I remember well, the deep and lasting impression left by this experience. At sixteen, he wrote his first scientific article, dedicated to the ether in the magnetic field. At the point where our story has arrived, Einstein is still a stranger. Not having obtained a university assignment of any kind after the end of his studies, he began to give private lectures and make substitutes, and then came to the position of employee at the Swiss Patent Office in Bern. Although he only had weekends free for his research, in the seven years he spent in that office, he laid the foundations of 20th-century physics and discovered a way to count atoms (i.e., to measure Avogadro’s constant), invented narrow relativity (with all its profound consequences on our notions of space and time, without forgetting), made significant contributions to quantum theory and more. Among his many talents, Einstein could include synesthesia, i.e., the ability to combine data from different senses, for example, vision and hearing. When he meditated on a problem, his mental processes were always accompanied by images. He understood that he was on the right track because he felt a tingling sensation at his fingertips. His name would become synonymous with the great scientist in 1919 when thanks to a solar eclipse, there was experimental confirmation of his theory of general relativity. However, the Nobel Prize obtained him for 1905, different from relativity: explaining the photoelectric effect. When electromagnetic radiation of appropriate frequency is made to hit the metal’s surface like, say, sodium, electrons are emitted from the metal. This phenomenon of emission of electrons from certain materials (which include several metals and semiconductors) by electromagnetic radiation is referred to as the photoelectric effect. This effect can be demonstrated and studied with a set- up like the one shown in Figure 1.1. Figure 1.1: Set-up to study and analyze photoelectric effect; E is the emitting surface while C is the collecting electrode; A is a current- measuring device; S is a DC voltage source whose polarity can be reversed; R denotes a resistor; the actual circuit may not be as simple as shown here. A metallic emitting electrode (E) and a collecting electrode (C) are enclosed in an evacuated chamber in which a window admits electromagnetic radiation of appropriate frequency to fall on E. A circuit made up of a source of EMF (S), a resistor (R), and a sensitive current-meter (A) is established between E and C. The polarity of S can be changed so that C can be either higher or a lower potential concerning E. Features Of Photoelectric Emission. This arrangement can be used to record several exciting features of photoelectric emission. Suppose that the potential (V) of C to E is positive for a given intensity of the incident radiation. In that case, all the electrons emitted from E are collected by C, and A records a current (I). This remains almost constant when V is increased because all the photoelectrons are collected by C whenever V is flattering. This is known as the saturation current for the given intensity of the incident radiation. However, this entire phenomenon of a current being recorded due to photoelectrons’ emission from E depends on the radiation frequency. If the frequency is sufficiently low, then photoelectric emission does not occur, and no photo-current is recorded. For the time being, we accept that the frequency is high enough for photoelectric emission to take place, and refer back to Figure 1.1. If holding the frequency and intensity of the radiation constant, one now reverses the polarity of S and records the photocurrent with increasing magnitude of V. One finds that the photo- current persists but decreases gradually till it becomes zero for a value Vs. of the potential of C concerning E. The magnitude (Vs) of V for which the photocurrent becomes zero is termed the stopping voltage for the incident radiation’s given frequency. This is shown graphically in fig. 1.1. The bottom of the two curves shown in Figure 1.1 describes this variation of I with V for a given intensity (J1) of the incident radiation. The frequency is also held constant at a sufficiently high value. Figure 1.1: Graphical representation of photoelectric emission; variation of photocurrent I with applied voltage V is shown for two values of intensity of radiation, J1, and J2 (> J1), while the frequency is held constant; the stopping potential Vs. is independent of power. If the experiment is repeated for some other value, say, J2, of the intensity of radiation, then one obtains a similar variation, as in the figure’s upper curve. 1.1, but with a different value of the saturation current, the latter being higher for J2 > J1. However, the stopping potential does not depend on the intensity since, as seen in the figure, both the curves give the same value of the stopping potential. On the other hand, if the testing is repeated with different frequency values, keeping the intensity fixed, one finds that the stopping potential increases with frequency (Figure 1.2). One finds that, if the frequency is made to decrease, the stopping potential reduces to zero at some finite value of the frequency. This value of the frequency is a characteristic of the emitting material and is referred to as the latter’s threshold frequency. Indeed, no photoelectric emission from the material under consideration can occur unless the incident radiation frequency is higher than the threshold frequency. Moreover, for photoelectric emission does take place for arbitrarily small values of the intensity. The effect of lowering the power is simply to decrease the photo-current, without stopping the emission altogether. Figure 1.2: Variation of stopping potential with frequency; no photoelectric emission occurs if the frequency is less than the threshold value, however large the intensity may be. The Role Of Photons In Photoelectric Emission,All these observed features of photoelectric emission could not be accounted for by the classical theory. For instance, classical theory tells us that whatever be the frequency, photoelectric emission should occur if the intensity of radiation is high enough since, for a high intensity of radiation, electrons within the emitting material should receive sufficient energy to come out, overcoming their binding force. Einstein first gave a complete account of the photoelectric effect’s observed features by invoking the photon’s idea as a quantum of energy, as introduced by Planck connected with his derivation of the black body spectrum formula. While the photons in the black body radiation were the energy quanta associated with standing wave modes, similar considerations apply to propagate radiation. Indeed, the components of electric and magnetic field intensities of propagating monochromatic electromagnetic radiation vary sinusoidally with time. Once again, a propagating mode of the field can be looked upon as a quantum mechanical harmonic oscillator of frequency, say, the minimum value by which the energy of the radiation can increase or decrease is once again, and this increase or decrease can once again be described as the appearance or disappearance of an energy quantum, or a photon, of frequency. Moreover, such a photon associated with a progressive wave mode carries a momentum just like any other particle such as an electron (by contrast, an energy quantum of black body radiation has no net rate). The terminologies for energy and momentum of a photon of frequency are the de Broglie relations by now familiar to us: The wavelength of the propagating monochromatic radiation and only the magnitude of the momentum has been considered. When monochromatic radiation of frequency is made to be incident on a metal or a semiconductor’s surface, photons of the same frequency interact with the material. These are some exchange energy with the electrons in it. This can be interpreted as collisions between the photons and the electrons, where the power of the photon engaged in a crash is transferred to the electron. This energy transfer may be sufficient to knock the electron out of the material, which is how photoelectric emissions occur. Bound Systems And Binding Energy A metal or a semiconductor is a crystalline material where many atoms are arranged in a regular periodic structure. Electrons in such material are bound with the entire crystalline structure. In this context, it is essential to grasp the concept of a bound system. For instance, a small piece of paper glued on to board makes up a set system, and it takes some energy to tear the piece of paper away from the board. If the power of the network made up of the paper separated from the board be taken as zero (in the process of energy accounting, anyone energy can be given a pre-assigned value, since power is undetermined to the extent of an additive constant), and if the energy required to tear the paper apart be E, then the principle of conservation of energy tells us that the power of the bound system with the paper glued on to the board must have been since the tearing energy E added to this initial energy gives the final power 0. As another instance of a bound system, consider a hydrogen atom made up of an electron ‘glued’ to a proton by the attractive Coulomb force between the two. Once again, it takes energy to knock the electron out of the atom, thereby yielding an unbound electron separated from the proton. The power of the divided system, with both the proton and the electron at rest, is taken to be zero by convention. The expression gives the energy of the bound hydrogen atom with the electron in the nth stationary state. Notice that this energy is a negative quantity, which means that positive energy of equal magnitude is necessary to tear the electron away from the proton. This method of knocking an electron out of an atom is known as ionization. It can be accomplished with the help of a photon, which supplies the necessary energy to the electron, and the process is termed photo-ionization. A hydrogen molecule is a bound system made up of two protons and two electrons in a precisely similar manner. Looking at any one of these electrons, one can say that it is not bound to any of the two protons but the pair of protons together. Indeed, the two electrons are shared by the protons team and form what is known as a covalent bond between the protons. Once again, it takes some energy to knock any of these electrons out of the hydrogen molecule. The minimum energy necessary to separate the components of a bound system is termed its binding energy. On receiving this energy, the details get separated from each other, without acquiring any kinetic energy in the detached configuration. If the bound system gets an amount of power more significant than the binding energy, the extra amount goes to generate kinetic energy. In this context, an impressive result relates to when one of the components happens to be much lighter than the other. In this case, the extra energy is used up almost entirely as the more lightweight component’s kinetic energy. When I speak of a bound system, I tacitly imply that it is looked at as a system made of two components. The same procedure may be looked at as one made up of more than two parts as well. For instance, in the paper glued on to the board, the components I have in mind are the paper and the board. But, given a sufficient supply of energy, the board can also be broken up into two or more pieces, and then one would have to think of a system made up of more than two components. Indeed, the board and the amount of paper are made up of many molecules, and the molecules can all be torn away from one another. Similarly, all of the two electrons and the two protons making up the hydrogen molecule can be pulled out from one another. A different energy amount would be required than the life required to yield just one electron separated from an ion. This latter we term the binding energy of the electron in the hydrogen molecule.  Chapter 4: The Photoelectric Effect: Is Everything Quantized? We have seen how the theory of blackbody radiation fits the experimental evidence only if we assume that energy is always absorbed and emitted ‘packet wise,’ in the form of discrete quanta. However, blackbody radiation was only the first hint of this kind. Many other experiments showed how nature exchanges energy only in the form of quanta. These experiments told us the same story in different ways, but always with the same underlying plot, according to which energy and, therefore, also light can be conceived of as made of what we imagine to be particles. One of the most important constructs of evidence of this type came from the so-called ‘ photoelectric effect,’ which conventional physics considers proof of the particle of light, the ‘ photon’ (a word coined by the American physicist’s Gilbert N. Lewis). The photoelectric effect had already been discovered in 1887 by the German physicist H.R. Hertz. He observed that sending the light of sufficiently high frequency onto a metal plate leads to the emission of charged particles from the metal surface. These turned out to be electrons. Hertz, however, was not able to explain the true meaning and physical implications of the phenomenon. The theoretical understanding and explanation came in 1905, developed by Einstein. To identify what this is all about, we will outline only a brief sketch here, without going much into the technical details. The aim is simply to give you an intuitive idea. Imagine having a metal plate onto which you shine a beam of light. Suppose the light is in the far- infrared spectrum, much below the red-colored light, which means we are using only a relatively low-frequency (long wavelength) EM wave. This low-frequency light beam would have no effect on the metal plate (except, of course, that it would heat up or eventually melt); no emission of charged particles, the electrons, would be observed as long as the light was under a specific threshold frequency (or, equivalently, above a particular wavelength). This occurs regardless of the beam’s intensity; it will not happen even for strong light intensities. If the light goes beyond a threshold frequency, suddenly, a flux of electrons from the metal surface can be detected. Again, this occurs regardless of the beam’s intensity; it also happens for low-intensity light. This shows that light waves can extract the electrons, the so-called ‘ photoelectrons,’ from the atomic metal lattice. This occurs only for individual metal plates, making it clear that the photoelectric effect does not extract electrons directly from the atoms. Photoelectrons are trapped inside the atomic lattice and are nevertheless free to move inside when an electric field is applied. This property makes good conductors out of certain metals and allows us to transport electric energy through metal cables. Therefore, this extraction process from the metal lattice occurs only when the electrons acquire specific energy at a minimum extraction frequency (or extraction wavelength ). Fig. 20 illustrates this state of affairs; if we trace along the horizontal axis the frequency of the incident light and along the vertical axis the kinetic energy, of the outgoing photoelectron (not to confuse with the momentum, see Appendix A-III), we can see how only if the wavelength becomes small enough (or, equivalently, only if the frequency becomes high enough, that is, larger than ), the electrons will start being ‘kicked’ out from the surface and appear with some kinetic energy larger than zero. This implies that part of the light life incident on the metal surface must be employed to extract the electrons first from the metal lattice. This minimum energy is called the ‘work function.’ Every metal has a different work function, which means that every metal has a different threshold frequency. However, the effect remains qualitatively the same. Once the electrons are extracted from the plate, what remains of the energy of light will go into the electrons’ kinetic energy. So, in general, it turns out that the observed electrons’ kinetic energy must be the difference between the power contained in the incident light photons and the amount of work necessary to extract them from the metal. Note that this is not theoretical speculation, but an exclusively experimental fact: measuring for each light frequency with which one shines the metal plate the kinetic energy of the electrons for that frequency, one can plot it into a graph and obtain a strictly linear dependency between the light’s incident energy and the emerging electrons’ kinetic energy, like that depicted in Fig. 20. While the threshold wavelength (or threshold frequency) is determined by the type of metal one uses. Every metal and kind of substance one uses has a different —that is, the straight-line function is only shifted parallelly upward or downward but does not alter its form or steepness. The straight line of the slope is always identical. The slope of the kinetic energy linear function is a universal constant, namely, Planck’s constant. This is how Planck’s constant could be measured precisely. Moreover, increasing the intensity, which increases the number of incident photons, does not change the result. An increase in the light intensity, that is, the photon’s flux, does not alter the above graph. It merely changes the number of observed photoelectrons (if above the threshold), and not their kinetic energy. Higher light intensity does not lead to more energetic ejected electrons; it only determines its number. This is somewhat unusual for a classical understanding of where we imagine light as a wave. Why does light extract electrons from the metal only above a threshold frequency (say, in the spectral domain of ultraviolet light or x-rays) but not below it? Why can we not bombard the metal surface with a higher- intensity light of the same 40 wavelengths (imagine many waves with large amplitudes) to obtain the same result? How should we interpret this result? The generally accepted explanation, according to Einstein, is that, as we have seen with the blackbody radiation, we must conceive of light as made of single particles—that is, photons carrying a specific amount of energy and impulse, and which are absorbed by the electrons one by one. However, this happens only if the single photon has sufficient power to extract the electron from its crystal lattice in the metal. The electron will not absorb two or more photons to overcome the lattice’s energy barrier in which it is trapped. It must wait for the photon with all the necessary energy that will allow it to be removed from the metal lattice. And because it absorbs only one photon at a time, all the electrons emerging from the plate will never show up with energies higher than that of the single absorbed photon, even though a larger number of photons (higher intensity of light) can extract a larger number of electrons. Einstein issued his theory of the photoelectric effect alongside his historic paper on SR. For this explanation of the photoelectric effect and his ‘corpuscular’ (little particles) interpretation of light, Einstein received his Nobel Prize—not for relativity theory, as is sometimes wrongly believed. The Laws That Govern The Probabilistic Nature Of The Quantum World It is an easy experiment that you can do by yourself—just take a piece of paper, poke a little round hole with a pin or needle, and look towards a light source. You will observe the light source’s image surrounded by several concentric colored fringes (the colors appear only because, fortunately, the world we live in is not monochromatic). The diffraction that occurs whenever a wave encounters an object or a slit, especially when its size is the same as the wavelength, the plane wavefront is converted to a spherical or a distorted wavefront, which then travels towards the detector screen. In this case, you see that, even though we are dealing with only one slit, some weak but still clearly visible secondary minima and maxima fringes can be observed. True, it is easier to produce more pronounced interference patterns with more than one slit (or pinhole). For most applications, especially when the wavelength of the incident wave is much smaller than the aperture’s size, these effects can be neglected—transverse plane wave incident on a single slit with aperture. However, strictly speaking, a single slit also produces small diffraction and interference phenomena. An elegant explanation of how interference comes into being, also for a single slit, dates back to the French physicist A. J. Fresnel. He borrowed an idea from Huygens (hence the name ‘Huygens Fresnel principle’), according to which every single point on a wavefront should itself be considered a point-source of a spherical wave. Along the slit’s aperture emit at the same time their spherical wavefronts, which, however, when seen from a position on the screen, add up to produce an interference pattern. The reason for this is not so difficult to visualize. Since all fronts are initiated in different locations and the aperture, they will also travel an extra path length, which implies various phase shifts when they overlap on the screen. For instance, where we saw the two paths of the two sources from the edges. As in the double-slit case, these two rays have a relative phase shift by an amount, and, when superimposed together on the screen, they form a resultant intensity according to the interference laws. However, this holds not only for two waves but for an infinite number of point-sources along with the aperture. Fresnel, by making the appropriate calculations, was able to show that if one sums up all of the spherical wavefronts coming from the points of the aperture of the single slit and projects these onto all the facts along with the detector screen, then one obtains the known diffraction and interference patterns indeed.  Chapter 5: The Franck-Hertz Experiment In physics, Franck-Hertz’s experiment was the first experiment confirmed by James Franck and Gustav Hertz in 1914 to exist distinct forms of energy atoms. Franck and Hertz move low-energy electrons to an electron tube through the gas. With the increasing electron power, some critical electron forces were discovered. The electron stream has changed from an uninterrupted flow of gas to a full stop. Only after gaining some critical point, electric atoms can use electrons’ energy, indicating that electric particles themselves transmit unexpectedly to higher unknown forces in electric atoms. As long as there is fewer than that amount of energy in the electron bombardment, no change is possible, and the electron flux has no illuminated power. When they have a certain amount of energy, they lose everything when colliding with electric atoms, storing energy at a higher energy level. The experimental setup consists of Hg gas atoms (Hg is the symbol for the element mercury) inside a low-pressure bulb. An electric cathode—that is, something like the heated filament of a light bulb—emits electrons. Therefore, this part of the device emits not only light but also negatively charged particles. An electric field is applied between the electron-emitting cathode and a positively poled grating, with a battery or some other electric source, which builds up an electric potential. Gustav Ludwig Hertz James Franck (1887-1975). (1882-1964). Due to their negative charge, this difference in the potential electric field leads to the electrons’ acceleration and conveys some kinetic energy (as you might recall from school, appointments with the same polarity repel each other, whereas those with opposite polarity attract each other). When the electrons reach the grating, most of them will fly through because the grating mesh is kept sufficiently broad to allow for that. This first part functioned as a little electron accelerator. Then, between the grating and a collecting plate on the right side, another field is applied. However, in this second part of their journey, they will experience an inversely polarized electric field. After passing the grating, they will be repelled because they will begin to ‘feel’ the negatively charged collecting plate. Measures electric current (the number of electrons) can measure the flux of electrons that flow between the grating and the collecting plate. While the electrons’ initial energy is proportional to the applied electric field intensity (the voltage) between the emitting cathode and the grating, in this second part, they are decelerated due to the opposite polarity. Therefore, the current measurement allows one to determine the number of electrons that make it through to the collecting plate, which provides information about how their energy is affected by the atoms while flying through the gas in this second part of the bulb. This is done by varying that field, step by step, for several voltages. Franck and Hertz’s insight was that several electrons must sooner or later hit one or more atoms while flying through the gas of atoms and be scattered either elastically or inelastically. ‘Elastic scattering’ means that when objects hit a target, they change course but maintain the same kinetic energy. In contrast, ‘inelastic scattering’ implies that they lose part or all of their kinetic energy in the collision process (more on this in Appendix A-III). It follows that there must be a measurable difference between the energy of the injected electrons reaching the grating and the energy of those which flew through the gas, hitting the collecting plate. This difference is made clear to the observer by measuring the current between the grating and the collecting plate. This energy gap tells us something about the energy absorbed by the atoms in the gas. Therefore, if atoms absorb energy only in the form of quanta, this implies that, while we slowly increase the kinetic energy of the injected electrons, we should observe when and to what degree the gas of Hg atoms absorbs the electrons’ energy. While the injected electrons’ kinetic energy is increased steadily by application of electric potential from 0 to about 15 V between the cathode and the grating (horizontal axis), the current of the electrons measured at the collecting plate (vertical axis) increases accordingly, though not in a linear fashion. We observe that the electrons do not have final kinetic energy, which increases proportionally to the electrons’ input energy, according to what one would expect for an elastic scattering between classical objects (think, for example, of billiard balls). We see instead that at first (between 0 and 4 V), the relation between the input and output energy is approximately linear, which means that the electrons are scattered through the gas elastically; they do not lose considerable kinetic energy. At about 4.5 V, the first bump appears. Between 4 and 5 V, the electrons’ output energy decreases steadily, despite their increasing initial energy. This signals an inelastic scattering: Some of the electrons’ initial energy must have suddenly been absorbed in collisions with the Hg atoms. However, this does not happen before a certain kinetic energy threshold of the electrons hitting the Hg atoms. At about 5.8 V, almost all the kinetic energy is lost and goes into the atoms’ internal excitation. However, there is a remaining minimum energy gap shown in the figure with the vertical arrow. The difference between the first peak and the first minimum is the maximum amount of kinetic energy the atoms can absorb from the electrons. Therefore, it furnishes the first excited energy level of the Hg atom. Then, after about 6-9 V, the energy begins to increase again, meaning that the particles absorb only that aforementioned discrete amount of the electrons’ energy, but not more than that. The remaining energy also goes into elastic scattering. All this regularly repeats at about 9- 10 V and about 14 V. The existence of these ‘bumps’ at different input energies (until nowadays, experimental particle physics is all about the search for bumps appearing in graphs) means that atoms must have several different but discrete energy levels. Franck-Hertz’s was the first direct experimental proof confirming Planck’s idea that matter absorbs energy in discrete quanta. Moreover, this validated the discrete spectral lines of light spectra, as did Bohr’s idea of representing the atoms in the form of a model which resembles a tiny solar system—that is, with electrons moving only in specific orbits with their respective quantum numbers, which represent different but discrete energy levels.  Chapter 6: Atomic Model of Bohr The Quantum Hypothesis was introduced into the nuclear field by Neil Bohr in 1913 and contributed significantly to this. From the middle of the 19th century, a simple spectrum made of atoms of electricity has been studied extensively. Low-pressure atoms of atoms contain a set of different wavelengths. This is in stark contrast with the intensity of the radiation, which spreads over a long distance. The wavelength of different atoms is known as the line spectrum since the rays (light) consists of straight lines. The width of the lines is a feature of the objects and can create very intricate patterns. Atomic hydrogen and alkaline (e.g., lithium, sodium, and potassium) are the most straightforward spectra. In the case of helium, the analytical formula defines the wavelengths. When m and n, the numbers, commonly known as Rydberg, have a value of 1,097373157 × 107 per meter. With a given amount of m, the differential lines n are series. The Lyman series lines are in the spectrum; those of the Balmer series are in the visible area, and those of the Paschen series is infrared. Bohr began with a model proposed by British scientist Ernest Rutherford, who was born in New Zealand. The idea was based on the experiments of Ernest Marsden and Hans Geiger, who detonated gold atom bombs in 1909 to the point that the bombings were carried out in the same way as the original gold atom binding; and a test by Hans Geiger, who detonated a bomb in 1909. Rutherford concluded that the atom had a massively loaded spine. Rutherford’s view emerges as a small solar system with a heart that acts like the Sun as a rotating planet-like electron. Bohr has made three views. First, he argued that, unlike traditional physics, where there is an infinite number of possible paths, the electron could be one of the orbits of the so-called vertical regions. Second, he suggested that the only cycles allowed were those with a total number of times the electron angular power. Third, Bohr believed that Newton’s law of motion regulates planets’ movement around the Sun, even applied to the electrons orbiting the nucleus. Electron energy (the gravitational force similar to the Sun and the earth) is an electrostatic attraction between a well-loaded electron and a badly charged electron. With these basic structures, he has shown that the power of orbit has been created. Where E0 is a residual concentration of the known elements in, I, and, when in a stable state, the atom does not emit energy as light; however, when the electron shifts from the energy state of En to the form of Em energy at low power, the amount of energy is subtracted from the frequency, by a given number. We introduce the expression En, and use the relationship, where c is the most superficial velocity; Niels Bohr obtained a formula with the exact value of Rydberg always the length of the lines in the hydrogen spectrum.  Chapter 7: Confirming The Quantum Theory Of Light: Compton Effect As with everything in quantum mechanics, equations are the math created to explain various molecular levels. Scientists are always looking for an enhanced way to explain how electrons, as expressed by light or other matter, are moving and the energy released and gained through that movement. One such equation was created by the Compton Effect, otherwise known as the Compton scattering. It was found to come from a high energy photon, engaging an individual target within a collision. Thus the process allows the release of loosely bound electrons out of that outer shell found as part of the molecule or a specific atom. As a result of the collision, scattered radiation practices a shift in the wavelength that didn’t fit into the classical wave theory; remember, the classic wave theory has been taking a beating, so to speak, from these experiments and hypotheses so focused on how electrons and matter can be moving in terms of particles and waves. This is yet another blow to the classic wave theory. As we have seen with all these experiments, most of them start with Einstein’s photon theory’s premise and appear to support that theory. Arthur Holly Compton received a Nobel Prize in 1927, but the effect named after him was initially demonstrated in 1923. So how does this process known as the Compton Effect work? Simply put, the gamma or x-ray high energy photon hits a defined target that has loosely bound electrons on the outer shell. This photon, known as the incident photon, is defined with the following energy E and linear momentum p. Within the Compton Effect, the photon gives a portion of its energy away to another almost free electron in the form of kinetic energy, which is expected when you have a particle collision. Scientists have come to understand that energy and linear momentum must be preserved. When analyzing these relationships, three equations are the result. These equations include energy, an x- and y-component momentum. There are also four variables involved as listed below: Phi – an electron’s angle of scattering Theta – which is the photon’s scattering angle Ee – which is the electron’s final energy E’ – which is the photon’s final energy Suppose we only focus on the photon’s direction and energy; then, we can treat the electrons always. As a result, we can potentially solve the system of equations for effect. Compton combined several equations and using a few tricks he picked up from algebra to eliminate some variables. He was able to create the two equations that are related because the energy and wavelength are both described in photons. The Compton Wavelength of the Electron has a value of 2.426 x 10 -12 m. This value can be used as a proportionality constant designated for a wavelength shift. So why does this particular effect support protons? In part, this analysis and derivation are based upon a particle perspective. The results have been easy to test for overtime. When observing the equation, the shift can easily be quantified in the angle’s terms from which the photon is scattered. Simply put, everything on the right side of the equation is used as a constant. Since experiments have consistently shown this to be the case, thus supporting the photon interpretation of light. Understanding some of these theories and the experiments behind them is vital to understanding quantum physics. However, nature always throws curve balls. So it is no wonder that there are effects that cannot be explained through these theories. How do scientists define the uncertainty inherent in this study of the smallest things on earth known as quantum mechanics? One such way is by the cornerstone of quantum physics, otherwise known as the Heisenberg Uncertainty Principle.  Chapter 8: The Wave-Particle Duality Dilemma Despite the typical wave behavior observed in the experiment, light still has particles’ properties as well. Firstly, as we already know, it is divided into quanta called photons. Secondly, it can leave shadows and patterns resulting from holes on the wall. Additionally, if only one slot is left open during the experiment, one neat band is formed opposite this slit, resulted from the particles’ flux. How do we understand this dual nature of light, and how can we describe it? Why does light act like waves in one case and like particles in another? At first, scientists tried to explain where the waves come from using the water analogy: light is a collection of particles, just like a water body is a collection of water molecules, and a set of particles, like a large number of water molecules in water bodies, can form waves. Therefore, each quantum, each photon (single unit of light), must be a particle. It was easy to test in a new version of the two-slit experiment, but this experiment did not confirm expectations! When the photons were fired one by one (for example, one per minute) towards the slit, each one appeared on the second wall, not in front of either slit, but randomly in one of those scattered places where interference bands had appeared in the standard version of the experiment! The wall retained a visual trace of the light particle (this was not just a wall, but a unique screen that contained all the light traces), and over time, with each subsequent photon, an interference pattern was increasingly evident. Why do the individual photons not appear on the screen directly in front of the slits? Why don’t two stripes form on the screen? This behavior of every single photon was utterly unexpected and incomprehensible. The individual photons could not interact with any other particle because the photons were fired one at a time with a gap in between, much more spaced apart than light quanta usually travel. However, the final position of each photon at the screen was the result of interference. At the same time, upon getting to the screen, every single photon still left a point trace, just as would be expected of a particle. These results cannot be explained in terms of the reality known to us. It seems evident that those photons could somehow move between the state of either particles or waves. No one had ever encountered anything like this before. The facts of quantum reality that we will discuss are no less weird, but these are real facts of the microcosmic world since all of these are the results of observations and controlled experiments. Is it so unusual that this field is difficult to understand, since it consists of a range of entirely new phenomena from the microcosmic level of reality that cannot be explained by the notions customary to us, and even contradict them? Our perceptions of what is generally possible turned out not to be final since, until then, we had been dealing only with our macro world with its simpler laws and interconnections between the facts. The new facts related to the micro world, which have no analogs in the macro world, seem strange and often even unbelievable. In the language of science, this refers to the difference between quantum physics and regular classical (Newtonian) physics, known to a certain extent to each of us from school and everyday experience. The fact that individual photons exhibit properties of both particles and waves proves that our strict division of reality into particles and waves is not entirely correct. Things aren’t as simple as we thought. It turns out that particles and waves are concepts that may relate to the same phenomenon (for example, waves of radiation and photons of radiation. The term “photon” is used concerning not only visible light). But what about the solid matter, which consists of particles? Solid matter consists of atoms. An atom consists of particles: electrons, protons, and neutrons (the latter two consist of even smaller particles, namely, quarks). Further experiments showed wave properties displayed by electrons, neutrons, and even entire atoms and molecules! Everything that makes up what seems to be solid matter acts like waves as well! Each particle of matter can “blur” its position. This dual nature of the whole of reality is called wave-particle duality. Everything is made of particle-waves. But why does everything sometimes acts like particles, and sometimes like waves? This is hard for people to imagine, even today.  Chapter 9: The Double-Slit Experiment Imagine an “electron gun” that fires electrons towards a wall with two holes (or slits) that are at equal distance (D) away from it and equal distance away from the center of the wall (Figure 1.0). The electron gun is mounted on a turret, which moves back and forth from side to side, much like an oscillating fan. Given this motion, it’s clear that we are not aiming the electrons at the holes; instead, they are simply being fired very much in a random fashion. The caves themselves are the same size and just big enough to let an electron through. Figure 1.0. An “electron gun” fires at random upon a wall containing two holes. The electrons are stopped at the back border, where the detector records their positions and sends information to the computer. Image A is the distribution we get when we place sensors beside each hole to observe a passing electron. Here, we see no interference pattern, and in fact, we get the results we anticipated for an electron acting strictly as a particle, in which case it merely passes through one hole or the other. However, Image B is the distribution we get when there are no detectors present. Here, we do see an interference pattern as electrons pass through the holes. As the electrons head towards the holes, some of them will pass through, and some of them won’t. The passing electrons continue on their way until they end up hitting yet another wall located much farther down that acts as a backstop. Each electron's final position is recorded by a detector at this back wall, sending this information to a different processing computer. As we keep terminating an ever-increasing number of electrons (we need to get excellent measurements), an ever-increasing number of electrons go through and hit the back divider. From the development of all the many- electron positions, the PC can make an example or dissemination. On the off chance that our measurements are adequate, at that point from this dissemination, we gain proficiency with the likelihood of finding an electron at a given situation on the back divider when terminated arbitrarily at the two openings. All in all, what does the dissemination resemble? Before we acquire this, let’s take a moment to try and anticipate the results. If an electron acts strictly as a particle, we would reasonably expect it to pass through one hole or the other. Moreover, an electron passing through a hole will either “bump” off the side or edge or pass straight through unscathed. If it gives straight through, we’ll find it directly behind the hole – at the “center,” so to speak – when it hits the back wall, whereas if it gets bumped, we’ll find it hits some distance farther away on either side of center. With all this in mind, we anticipate the distribution for a given hole to be such that the maximum number of hits occurs directly at the center. Further away from there, the number of hits steadily decreases. Lastly, the distribution will look the same on both sides of the center. In other words, it will be symmetric. Ok, we have a pretty clear picture of what we’ll see. But we experiment and find that the resulting distribution on the computer screen is nothing like what we imagined. Instead, we find a distribution with the maximum located between the two holes – it’s not even located at the center of either hole! The distribution is still symmetric on each side of this maximum (so at least there’s that), but we don’t see the steady decrease in the number of hits that we had envisioned as we move away. Instead, on either side, we find peaks where the number of hits is high, and then from these peaks, there’s a steady drop-off to zero, where not a single electron shows up. What happened? Well, in our foresight, we assumed that an electron behaves as a particle, but we really should have known better since all quantum particles exhibit wave-particle duality. In short, the distribution formed by the collection of the many-electron positions is showing an interference pattern. Earlier, we briefly talked about how interference can occur between waves. There must be waves associated with our electrons that are causing this interference pattern. What are they? Recall that the quantum probability will determine each electron's position at the back wall, as we mentioned earlier. In turn, the quantum probability is given by (the absolute square of the) wave function; it looks like we’ve found the “wave” causing the interference. Let’s try to recognize this in more detail. Instead of shooting many electrons at once towards the holes, let’s just shoot one electron at a time. Initially, we notice that shortly after firing off an electron, it arrives at the back wall, and its position is detected. So far, so good. However, as we continue to shoot individual electrons at the holes, we noticed something quite peculiar. Eventually, we end up with the same interference pattern that we saw before firing many electrons. In other words, it doesn’t matter if we fire several electrons at once or one at a time; the same interference pattern appears! This means that a single electron encounters the two holes and ends up interfering with itself. This seems so odd that we decide to perform one last experiment to get to the bottom of things. Beside each hole, we place a detector that will record an electron passing by it. Indeed, this will shed some light on the strange results we are getting. Once again, we shoot one electron at a time towards the holes, over and over, until we can see the distribution on the computer screen. This time we find that the interference pattern has totally disappeared. Instead, we are left with the distribution of electron positions that we had anticipated in the first place! In other words, when we’re not looking at the holes (with our detectors), a single electron incurs interference. Still, when we look, we find that the electron passes through either one hole or the other. The interference pattern completely disappears. These experiments illustrate the very essence of quantum mechanics. We see an electron acts as a particle when it hits the back wall and is detected by the detector as a localized entity. Still, somewhere in between, there’s interference due to its wave nature and its “interaction” with both holes at the same time. This wave nature is intimately tied to the quantum probability of finding the electron at a particular position on the back wall, ultimately leading to the distribution of hits we see. Suppose we attempt to determine exactly where an electron will end up on the back wall by trying to see which of the holes it passes through. In that case, the whole thing falls apart, and the interference disappears altogether. Although we chose to experiment with electrons, all quantum particles show this type of weird behavior. If all this seems like more science fiction than actual science to you, you’re not alone. The physical consequences of quantum mechanics are, simply put, plain strange, compared to our everyday experience.  Chapter 10: De Broglie Hypothesis This was one of the most acclaimed logical meetings ever. Of the 29 up- and-comers, 17 got or got Nobel prizes. The gathering is significant for two titans of material science: Niels Bohr and Albert Einstein. 1927 was per year, and researchers were stunned. The very presence of such an astounding thing is in peril. Are electrons, lights, and similar articles, waves, or particles? In specific tests, the little bodies act like waves, and in others, they act like particles. This isn't going on in our massive world. The sound waves don't act like rocks - and fortunately, your ears would nibble at present. The 1927 Quantum Mechanics meeting talked about a blend of terms that appeared to be conflicting. Schrödinger and de Broglie introduced their perspectives. Be that as it may, 800 gorillas were Bohr. It was called the Copenhagen interpretation. Bohr recommended that wave estimations were characterized as materials, for example, electrons; however, as particles, associations didn't exist until somebody needed them. The demonstration of appropriation turned into the beginning of life. Utilizing Bohr's own words, the individuals included had no "obvious life in the typical setting." None of that would have been Einstein. Einstein would not have had that. The electron was an electron, and because somebody was not taking a gander at it, it was still there - any place it "was." Towards the finish of the meeting, Einstein tested Bohr's view. Yet, that was just the start. When thirty, Einstein was dead, Bohr and Einstein were entangled in warmed dealings - eye to eye and printing. The discussions were of a courteous fellow. Bohr and Einstein were old buddies and regarded each other. Notwithstanding, they persevered. He stated, "It's not reasonable to believe that material science needs to discover what nature resembles," Bohr said. Einstein opposes this idea. "The main reason we disclose to science is to discover what it is." For all its unpredictability, Bohr's meaning of Copenhagen stays one of the world's most broadly acknowledged quantum material science ideas. Numerous standard definitions seem like most outsiders. In any case, they all highlight one straightforward truth. Our Universe is a secret, as all researchers will let you know. It derides us with unfathomable realities and gives us meaning. Possibly one day, we'll go to it. However, we should confront the great secrets around us before that. Moreover, Planck's time is the fundamental unit of time in the arranging of Planck Units. Significant: tp = 5.39 × 10-44 s In SI units, time estimations are made quickly (generally given s pictures). Aside from the way that the utilization of seconds has the benefit of everyday presence, for instance, estimating the time it takes for a contender to run 100 meters or the length of a telephone, notably, it is little on the planet when we talk about ordered occasions in the early Universe, for instance. Which occurred in the 10-35s after the Big Bang). The consequence of utilizing seconds to quantify time is that massive changes take esteems that are not frequently accommodating in recalling circumstances: Light speed c = 299792458 m (s) (s) Gravity G = 6.673 (10) x 10-11 m3 kg (- 1) s (- 2) Board Strength (diminished) Boltzmann strong k = 1.3806502 (24) x 10-23kg m2 s-2K-1 Planck's time is resolved to utilize the size of a mix of these critical components: By revising the base units long, size, and time comparative with Planck units, the main points of interest are: Presently, Planck-Time is the time it takes for a photon to have any kind of effect equivalent to the length of Planck: = 1.62 × 10-35 m This is the briefest time limit conceivable. With its overall length of Planck, Planck's time characterizes the scale at which the current assemblage of thought is clamoring. At this level, the absolute time figures are as wide as the relative associates. Along these lines, on such scales, to date, vague speculation that consolidates typical cooperation with quantum machines is relied upon to mirror the laws of material science. Accordingly, our present introduction of the main Universe improvement starts at tp = 5.39 × 10-44 seconds after the Big Bang.  Chapter 11: Heisenberg’s Uncertainty Principle “Anyone who is not surprised by quantum theory has not understood it,” said Neils Bohr, a pivotal contributor to quantum mechanics theory. Such is the beauty of entanglement theory; as more and more years go by, and as more and more scientists get their hands on it, they have to find new ways of explaining their shortcomings—the uncertainty principle is the most prominent. Also called the Heisenberg uncertainty principle and the indeterminacy principle, the uncertainty principle states that there is no exact measurement of position or velocity of an object in the quantum world. The concept of exactness has no place in this realm, not even in theory. The uncertainty principle regards only tiny objects as immeasurable because it applies to the quantum world. For this reason, ordinary objects do not apply to the uncertainty principle. There is proof of this: any person can find an exact measurement of a car because they can weigh it. It is ordinary and, therefore, large enough to be accurately pinpointed. Even a category of tiny objects qualifies for more accurate measurement than the uncertainty principle makes a room. These objects are ones whose velocity and position are equal to or greater than Planck’s constant, 6.6 x 10^-34 joule-second. Small items below Planck’s constant apply to the uncertainty principle. The uncertainty principle arose from classic wave-particle duality. Every particle has an accompanying wave. The more undulating that lock is, the more uncertain its measurement is. The more specific its accompanying particle’s position, but indefinite its momentum. Heisenberg also made another significant contribution to quantum mechanics in 1927. He argued that because matter behaves like waves, some properties, such as the position and speed of the electron, are "complementary," implying that there is a limit (related on the Planck constant) to how well the accuracy of and property can be understood. Under what would come to be called the "Heisenberg Theory of Uncertainty," it was argued that the more precisely the electron's position is determined, the less precisely its speed can be known and vice versa. This uncertainty theory often applies to everyday objects but is not apparent since the lack of precision is too high. Werner Heisenberg (1901-1976) was the theorists' prince, so disinterested in laboratory practice that he risked flunking his thesis at the University of Munich because he did not know how batteries worked. Fortunately for him and physics as a whole, he was also promoted. There were other not easy moments in his life. During the First World War, while his father was at the front as a soldier, the scarcity of food and fuel in the city was such that schools and universities were often forced to suspend classes. And in the summer of 1918, young Werner, weakened and malnourished, was forced together with other students to help the farmers on a Bavarian farm harvest. With the end of the war, in the first years of the twenties, we find him in the shoes of the young prodigy: pianist of high level poured in the classical languages, skillful skier and alpinist, as well as mathematician of rank lent to the physics. During the lessons of the old teacher Arnold Sommerfeld, he met another promising young man, Wolfgang Pauli, who would later become his closest collaborator and his fiercest critic. In 1922 Sommerfeld took the 21-year-old Heisenberg to Göttingen. The beacon of European science attended a series of lectures dedicated to the nascent quantum atomic physics, given by Niels Bohr himself. On that occasion, the young researcher, not intimidated, dared to counter some guru statements and challenge at the root of his theoretical model. However, after this first confrontation between the two was born a long and fruitful collaboration, marked by mutual admiration. From that moment, Heisenberg devoted himself body and soul to the enigmas of quantum mechanics. In 1924 he spent some time in Copenhagen to work directly with Bohr on radiation emission and absorption problems. There he learned to appreciate the "philosophical attitude" (in Pauli's words) of the great Danish physicist. Frustrated by the difficulties to make concrete the atomic model of Bohr, with its orbits put in that way, who knows how the young man was convinced that there must be something wrong at the root. The more he thought about it, the more it seemed to him that those simple, almost circular orbits were a surplus, a purely intellectual construct. To get rid of them, he began to think that the very idea of rotation was a Newtonian residue that had to be done. The young Werner imposed himself a fierce doctrine: no model had to be based on classical physics (so no miniature solar systems, even if they are so cute to draw). The way to salvation was not intuition or aesthetics, but mathematical rigor. Another of his conceptual digits was the renunciation of all entities (such as orbits, in fact) that could not be measured directly. Measurable in the atoms were the spectral lines, the witness of photons' emission or absorption by the particles resulting from jumping between the electron levels. So it was to those net, visible, and verifiable lines corresponding to the inaccessible subatomic world, that Heisenberg turned his attention. To solve this diabolically complicated problem and find relief from hay fever, in 1925, he retired to Helgoland, a remote island in the North Sea. His starting point was the so-called "correspondence principle," enunciated by Bohr, according to which quantum laws had to be transformed without problems into the corresponding classical rules when applied to sufficiently large systems. But how big? Enough to allow to neglect the Planck constant h in the relative equations. A typical object of the atomic world has a mass equal to 10-27 kg; let's consider that a grain of dust barely visible to the naked eye can weigh 10-7 kg: very little, but it is still more significant by a factor of 100000000000000, that is 1020, one followed by twenty zeros. So the atmospheric dust is clearly in the domain of classical physics: it is a macroscopic object. Its motion is not affected by the presence of factors dependent on Planck's constant. The fundamental quantum laws apply naturally to the phenomena of the atomic and subatomic world. Simultaneously, it loses sense to use them to describe phenomena related to aggregates larger than atoms, as the dimensions grow, and quantum physics gives way to the classical laws of Newton and Maxwell. The foundation of this principle (as we will repeat several times) is that the strange and unpublished quantum effects "correspond" directly to physics's classical concepts as you leave the atomic field to enter the macroscopic one. Driven by Bohr's ideas, Heisenberg redefined the banalest notions of classical physics in a quantum field, as the position and velocity of an electron. They were in correspondence with the Newtonian equivalents. But he soon realized that his reconciliation efforts between two worlds led to the birth of a new and bizarre, "algebra of physics." In school, we all learned the so-called commutative property of multiplication. The fact that, given any two numbers a and b, their product does not change if we exchange them between them; in symbols: a×b=b×a. It is evident, for example, that 3×4 =4×3=12. However, in Heisenberg's time, abstract numerical systems in which the commutative property does not always apply. It is not said that a × b is equal to b × a. To well think about it, examples of non-commutative operations are also found in nature. A classic case is rotations and tilts (try to perform two different wheels on an object like a book, and you will find examples where the order they happen is essential).  Chapter 12: Introduction To Quantum Superposition: Schrödinger’s Cat During the 1930s, many questions arose about quantum mechanics' meaning, and even whether it had any relevance to the everyday, macroscopic world we all experience. Unlike a ball in sports, the quantum realm is one of the tiny particles that none of us can directly see, so maybe it does not affect our lives. Albert Einstein, perhaps his era's leading proponent of the concrete and physical, took issue with quantum probabilities. Of an ideal coin flip expressed by a single equation, he would point out that no one ever sees a coin that is 50% heads and 50% tails all at once. If we keep our eyes closed as flipped coin lands, even though we can't see the result, we know it has to be one of heads or tails, not some bizarre amalgam of both. A coin never being in all states simultaneously was one reason he concluded quantum mechanics lacks in some fashion, or as he said, incomplete. For taking that position, Einstein was, to some extent, vilified by many in quantum physics, and considered past his prime, unable to adjust to the new theories. Subsequently, we have learned Einstein was at least partially correct, but so were those who doubted him, as will be explained ahead. Einstein's primary point is an important one: How can the equations be trusted when they do not represent our actual world? Even in the year 2020, that remains a central puzzle of quantum mechanics, with various interpretations advanced to explain it, including the one by this author. As part of the debate, in 1935, Erwin Schrödinger put forth a now-famous thought experiment known as Schrödinger's Cat. A thought experiment, or Gedankenexperiment in German, is not actually performed, but instead pondered via the mental application of a set of ideal scientific rules and situations. Many thought experiments explore the boundaries of new science with no intent for them ever to be performed or cannot be achieved unless suitable technology is invented subsequently. The Schrödinger's Cat thought experiment amplifies a quantum event to a macroscopic level, one we could conceivably encounter in real life. By doing so, it makes it more accessible to study the unintuitive condition known as quantum superposition. In general, macroscopic refers to an object's properties that can be observed without specialized equipment assistance. The large-scale properties of soccer balls are apparent to humans, and thus macroscopic to us. At the same time, atoms' properties are too small to observe directly, so they are not macroscopic. However, for quantum mechanics, macroscopic is not so much about size, but rather an observability. A cat is as macroscopic as a soccer ball. Still, it is just as unobservable as the tiniest subatomic particle if hidden within a box. This was one of the quantum areas Erwin Schrödinger sought to explore via his well-known experiment. When employed in quantum mechanics, the terms "observation" and "measurement" refer not just to people seeing an object, but to any item interacting with any other and influencing it in any way. The Schrödinger's Cat experiment is one in which a reader can easily participate mentally. As Erwin