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Quantum Physics is easily one of the oddest theories you will come across. It turns your knowledge of the physical world upside down, rendering Newton Mechanics almost useless. Though many people are familiar with its name, few are aware of what the theory really entails. Nevertheless, Quantum Physics is at the very core of our current understanding of everything as it provides the basic mathematical framework upon which the most advanced models of the Universe are built. On top of that, much of our modern technology such as photocopiers, lasers, solar arrays, transistors, solid state devices or computers were only possible due to the breakthroughs in science provided by Quantum Physics. Before reading any further be warned that you must forget everything you learned in high school and possibly in engineering courses. Namely, forget about Newton Mechanics.
The theory explains matter at its most fundamental level. Thus, we will be dealing with the subatomic world from now onwards. If you still think elementary particles comprise only the atom made up of protons and neutrons with electrons orbiting around like planets then you are still in the early stages of the 20th century since this simple model was ruled out in 1926 by Erwin Schrödinger. Dozens of smaller particles have already been discovered like quarks, muons, photons, gluons and so on... Electrons are indeed close to the nucleus but their motion is far from resembling a predictable orbit for reasons that should become clear soon. Particles behave in a strange unpredictable way, unlike the ordered world governed by the Newton laws. It is absolutely paramount that you temporarily forget everything you take for granted. Throw your common sense to the garbage bin for a few moments and open your mind.
Learning Quantum Physics in detail is obviously a life time experience for theoretical particle physicists, therefore I should only introduce you to the subject. As always I expect you to delve deeper into what it involves after reading this introductory article. There are roughly four main topics at the heart of the theory which will seem utter nonsense for someone used to classical mechanics:
Particles are not really particles in the sense of microscopic billiard balls. They are also not waves. Rather they are both particles and waves at the same time. That is right, there is a duality in each and every particle which means the classical physics separation between particle-like and wave-like phenomena was plainly wrong. Thus an electron for instance is not always a point-like particle, it can exhibit both a particle and wave behavior depending on the situation. Conversely, electromagnetic radiation like a photon of light for instance is not merely a wave, it acts like a wave sometimes but it can be a particle too.
The movement of wave-particles is not predictable by using motion equations. It is impossible to pinpoint its exact location at a given instance of time in the future. At best, only a probabilistic guess can be made. Hence, movement is inherently random and subject to the laws of probability. If you were to use Newton's laws of gravity to predict the orbit of an electron you would find out that it would crash into the nucleus, that is not what happens though! The same rules which work perfectly at the macroscopic level of the solar system yield ridiculous results on the atomic scale which is totally different from the world our eyes can see! They cannot be used here and are thus ruled out as general laws, working only in particular cases. Instead Quantum Physics uses the concept of wave functions as the mathematical tool to describe the movement of particles. The wave function of a an electron gives its probability of being located at a certain position. The function says there is for instance a probability of 10% that it is located at point A, a probability of 20% that it is located at point B and so on... In reality we never actually know where a particle really is, we can only say where the particle is most likely to be.
The afore mentioned wave function has a catch though. It turns out that observation plays a dramatic role in Quantum Physics. As weird as it may sound, simply observing the wave-particle has an effect. If you are not watching it, the wave function beholds true and maps a certain probability for each position in space. In other words, the wave-particle is not at any given position at any time, it just has different chances to be at different places. The wave-particle is the wave function itself and can be interpreted as a wave. However, as soon as you look at it, the wave function is collapsed into a single value, indicating a precise position for the wave-particle which then becomes a point-like particle at the exact moment you see it! If you do not look at an electron it is a wave, if you do, it becomes a particle! Hence the wave-particle duality. The uncertainty principle itself builds upon this fact and states that the more you know about the position of a wave-particle the less you know about its momentum (mass times velocity). This is true because knowing the position of the wave-particle means the wave function length has been infinitely collapsed and the momentum is derived precisely from the wave length.
Strangely enough the energy of a particle does not have a continuous range of possible values. That is to say that not all energy values are possible, only some are valid. Therefore we say that energy is a discrete quantity where only some particular values are legal. There is also a minimum, undividable unit of energy, called quantum (this is actually where the theory gets its name from). Energy is quantized only in integer multiples of this quantum. Finally bear in mind that Quantum Physics is the state of the art of modern physics and all this has been tested by numerous experiments. One of the earliest and possibly the most famous of them all is the double slit experiment.