What is the Quantum? (Week 1)

Definition of Quantum

• The Quantum it’s the smallest value, quantity or amount, which a Physics’/Mechanics’ entity/property can represent.

• This behaviours are represented in Physics’/Mechanics’ magnitudes/scales, acting and operating on the following microscopic levels:

  • Atomic:

    • In the Physics’/Mechanics’ magnitudes/scales of the atoms.

  
  

  • Subatomic:

    • In the Physics’/Mechanics’ magnitudes/scales where the behaviours of the particles occur (e.g., electrons, protons and protons) and the possible connections and interactions between atoms (e.g. atoms bounded and grouped together, in blocks, forming molecules).




• This notation started to be commonly used in Physics’/Mechanics’, since 1990, when Max Planck presented his research work on Black-body Radiation (i.e., Thermal Radiation).

• Thus, for that reason, the smallest knwon magnitude/scale is the Planck's Scale or Planck's Length, being equal to the length of:

  ○ 1.616199 x 10³⁵ meters

What is the Quantum Physics/Mechanics?

• The Quantum Physics/Mechanics is a fundamental theory in physics and mechanics, which describes the nature, at the previously shown and explained magnitudes/scales.

• Although, in the most of cases, the Quantum Physics/Mechanics are relevant for describing microscopic systems, but their specific effects are not only noticeable on such a scale.

• The Quantum Physics/Mechanics provides accurate descriptions for many previously unexplained phenomenons as Black-body Radiation and Stable Electron's Orbits.

• For example, the explanation of macroscopic phenomenons such as super-fluidity and super-conductivity are possible only if it's considered that the microscopic behavior of matter is Quantum.

• It's considered by many experts and specialists, the best existing theory allowing the study of the nature itself and all its behaviours.

What is the Quantization?

• The Quantization is the process of transition from a classical understanding of physical phenomena, to a new understanding, known as Quantum Physics/Mechanics.

• This new process was one of the several processes and aspects responsible for naming of Quantum Physics/Mechanics, being one of its broadest foundations.

• In this context, something is said to be quantized, if it only takes on definite values, and no other value, between those definite values.

• Quantum Physics/Mechanics assume that the smallest value, quantity or amount of energy, in any Quantum System is quantized (i.e., can only take on certain values).

• The fundamental notion of a Physics’/Mechanics’ entity/property which can be quantized, it’s referred as the Hypothesis of Quantization.

• This hypothesis means that, the magnitude/scale of a Physics’/Mechanics’ entity/property can only assume discrete values, which consist in integer numbers multiples of a quantum.

What is an Atom?

• An Atom it’s the smallest unit containing common matter, which contains a chemical element and cannot be broken down by any chemical mean.

• The Atom it’s composed by subatomic particles (as Protons, Electrons and Neutrons).

• All the objects in the solid, liquid, gaseous and of plasma are composed of neutral or ionized Atoms.

• The Atoms are extremely small, having typical sizes in the range of 100 picometers (10^-10 meters, i.e., 10^-7 millimeters, or even, ¹⁄_254,000,000 inches).

• In fact, it’s for that reason, why it’s not possible to predict precisely its behaviour, using the Classical Physics/Mechanics.

• This happen due to the Quantum Effects, making the current Atomic Models use Quantum Principles now, to explain and predict better that behaviours.

• The total number of Atoms in the entire Universe it’s estimated in a range between 4 x 10⁷⁸ and 6 x 10⁷⁹.





• You can see a simple 3D Representation of the Atom with 4 States and Orbits, in the following Live Code Preview, provided by Code SandBox:

The Components of an Atom

• The building blocks of Atoms are positively charged Protons (+), neutral Neutrons (N) and negatively charged Electrons (-).

• The Protons and Neutrons are very similar in mass, while Electrons are much smaller and lighter.

• Many Atoms consist of a positively charged Nucleus composed of Protons and Neutrons, surrounded by a negatively charged "cloud" of Electrons.

• At its most basic level, an Atom is any Particle of matter containing, at least, one Proton (which, it’s the case of the Hydrogen Atom). Some Electrons and Neutrons may be present, but aren’t required!!!

• The calculation of the number of Atomic Particles is used to indicate the number or amount of:

  • Protons, presented in the Nucleus

  • Electrons, presented in the Electrosphere

  • Neutrons, also presented in the Nucleus

• The Electrons, in the Electrosphere are orbiting around the Protons and Electrons, in the Nucleus (as demonstrated visually by the Bohr’s Model).

The Components of an Atom Demonstrated by the Bohr's Model

• You can see a simple demonstration of an Atom and its components demonstrated by the Bohr's Model (most specifically, the behaviour of the Ion's Ground and Excited States), in the following Live Code Preview, provided by Code SandBox:

Understanding the Components of an Atom

The Atoms and the Periodic Table

Atoms vs. Particles vs. Molecules

• The Atoms are the smallest pieces of matter.

• The Particles are the building blocks of matter (and not matter itself), forming an Atom.

• The Molecules are sets of Atoms grouped and bound together, which are smallest pieces of Compounds.

• The Atoms can be combined in several ways, in order to form new Molecules, which can be divided in two types:

  • Elements:

    • Molecules of only one type of Atom

  • Compounds:

    • Molecules of two or more different types of Atoms

Understanding the Molecules

Molecules: Elements vs. Compounds

• "When it comes to Atoms, language can be used only as in Poetry. The poet, too, is not nearly so concerned with describing facts, as with creating images."
  - Niels Bohr (1885 - 1962)

The Quantization of the Hydrogen Atom

Classical Physics/Mechanics vs. Quantum Physics/Mechanics

• So, basically, the main difference between the Classical Physics/Mechanics and the Quantum Physics/Mechanics, is precisely the magnitudes/scales, on each one of them operates.

• Whereas Classical Physics/Mechanics operates at the macroscopic level of magnitudes/scales, the Quantum Physics/Mechanics operates at the microscopic level of magnitudes/scales.

• The macroscopic level of magnitudes/scales it's referred to large-scale things.

• The microscopic level of magnitudes/scales it's referred to small-scale things.

• The Classical Physics/Mechanics studies and describes the motion of macroscopic objects such as spacecraft, planets, stars, and galaxies.

• It provides extremely accurate results as long as the domain of study is restricted to large objects, and the speeds involved don't approach the speed of light.

• The Classical Physics/Mechanics are simple, but cannot be applied to extremely small particles moving at very high speed, as the results may turn inaccurate.

• Think, in a macroscopic level, how hard it's to determine the final states in the following situations... Now, imagine if that happened in a microscopic level...





• "In the world of the very small, where particle and wave aspects of reality are equally significant, things do not behave in any way that we can understand from our experience of the everyday world. All pictures are false, and there is no physical analogy we can make to understand what goes on inside atoms. Atoms behave like atoms, nothing else."
  - John Gribbin (1946 - Present)

From Classical Physics/Mechanics to Quantum Physics/Mechanics

• Thus, most of Classical Physics’/Mechanics’ theories can be derived from Quantum Physics/Mechanics as a valid approximation at large (or macroscopic) scale.

• The Quantum Physics/Mechanics differs from Classical Physics/Mechanics in that, the energy, the momentum, the angular momentum and, the other values, quantities or amounts, of a bound system are restricted to discrete values (described by the principle of quantization, explained previously).

• The objects have characteristics of particles and waves (Wave-Particle Duality), and there are limits to the precision of which of these characteristics can be measured (and, this is known as the old and very famous Principle of Uncertainty of Heisenberg.

• So, the Quantum Physics/Mechanics emerged gradually since the theories to explain observations which couldn’t be explained and described by Classical Physics/Mechanics.

Brief Timeline of Quantum Physics/Mechanics

• Some old Research Works like, the solution to the Problem of Black-body Radiation (or, Thermal Radiation), proposed by Max Planck, in 1900, or even, the Correspondence between Energy and Frequency to explain the Photoelectric Effect, proposed by Albert Einstein, in 1905, contributed to the birth of Quantum Physics/Mechanics.

• After that, the theory behind of Quantum Physics/Mechanics was deeply re-shaped in 1920s by many physics, mathematics, researchers and authors, such as:

  • Erwin Schrödinger, through the Schrödinger’s Cat Experiment;

  • Werner Heisenberg, through the Principle of Uncertainty of Heisenberg;

  • Max Born, through the Statistical Interpretation of Wave Function;

• This era is commonly referred as the The Gold Age of Quantum Physics/Mechanics or the The 1st Revolution of Quantum Physics/Mechanics.

• The modern theory based on Quantum Physics/Mechanics is formulated by mathematical and algebraic formulations, which are continuously being improved, until the current days!!!

• Currently, it's believed by many experts and specialists, that's being seen, at first hand, The 2nd Revolution of Quantum Physics/Mechanics!!!

Examples of Mathematical and Formulations of Quantum Physics/Mechanics

From Quantum Physics/Mechanics to Computing Models

• Nowadays, a Computer needs to perform millions of arithmetic operations (i.e., additions, subtractions, multiplications, divisions, among many other operations) in seconds to solve a Classical Differential Equation.

• While Isaac Newton (considered by many people as one of the fathers of the Differential Calculus) would take several hours to solve the same Differential Equation, by manual calculation, even if he were the discoverer of the solution for that particular Differential Equation.

• Because Isaac Newton, even knowing the solution for that Differential Calculus, would be only capable of performing an arithmetic operation at once, in order to solve it, doing all the process, in a sequential fashion (i.e., solving it step-by-step), and this is an inherent characteristic of human beings, we always act in a sequential way (or some kind of)!!!

• Thus, to perform this kind of tasks, Computers and Computing Models became very essential for many people, in the current days!!!

• And it's reasonable to say that, this kind of technology it's present everywhere in the people's lives and we cannot live it without it anymore!!!

• The Computer Modeling is essential for Quantum and Relativistic Physics. The Classic Physics/Mechanics is considered the limit of Quantum Physics/Mechanics for large number of Particles. But, on the the other hand, Classic Physics/Mechanics is derived from Relativistic Physics/Mechanics.

• Per example, in many formulations from Special Relativity, a Correction Factor ^v2⁄_c appears, where v is the velocity of the object and c is the speed of light.

• For velocities much smaller than speed of light, can be excluded the terms with c² and higher that appear. Then, these formulas are reduced to the standard definitions of Newtonian’s Kinetic Energy and Momentum, because Special Relativity must agree with Newtonian’s Physics/Mechanics at low velocities.

• The Computer Modeling has to be as realistic as possible and even, with some errors introduced by Classical Physics/Mechanics.

• In order to produce reliable models of our world, cannot be used the Classical Physics/Mechanics, but it’s reasonable to think that Quantum Theories would consume much time and computer resources, and the equations of Classical Physics/Mechanics could be used to provide a quick solution, which couldn’t be a completely precise and reliable one.

• The Computer Modeling would use only the Energy’s Criteria to determine if it would use the Relativistic Theory or the Quantum Theory, when attempting to describe (or, calculate) the behavior of an object. Then, would be used a model from Classical Physics/Mechanics to provide an approximation before more accurate models are applied and, those descriptions and calculations proceed.

• In a Computer Model, there’s no need to use the speed of the object if the Classical Physics/Mechanics is excluded. The low energy objects would be handled by Quantum Theory and, the high energy objects would be handled by Relativistic Theory.