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Quantum MechanicsQuantum mechanics is the mathematical foundation of quantum physics, the branch of science that describes the behavior of systems at atomic and subatomic scales. While Newton's laws form the basis of classical mechanics—which explains how bridges, planes, and other everyday objects work—quantum mechanics abandons the precise results of those laws for a system based on probability.
This feature arose from attempts to resolve the prediction from classical mechanics that any object at a nonzero temperature should radiate an infinite amount of energy. The solution—quantization—set discrete minimum thresholds for energy and other properties that objects could have. Unable to reach those thresholds, quantization predicted a lower, finite amount of radiated energy that matched observations.
Applying quantization to experiments involving light led to the wave-particle duality, in which light could be modeled as either discrete particles or electromagnetic waves. After electrons in atoms were identified as existing in discrete (quantized) energy levels, all matter began to be mathematically modeled as both extended waves and localized particles.
Although this "fuzziness" introduced uncertainty into experimental outcomes—scientists can only predict the probability of outcomes rather than determine definitive results—quantum mechanics has been thoroughly experimentally verified, accurately modeling atoms and predicting the existence of antimatter four years before its discovery.Explore Quantum Mechanics
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Why quantum mechanics keeps gravity from collapsing neutron stars into black holesAccording to the Pauli exclusion principle, certain particles, such as neutrons, are forbidden from occupying identical states within a system. Like tennis balls tightly packed together, neutrons exert a resistive pressure against this compression—neutron degeneracy pressure—which can help prevent gravitational collapse. (Some readers may experience a paywall.) ForbesIn quantum mechanics, matter is not in one location until it's measuredThe probability that a particle is located at a given point is described by a wave function, in which peaks correspond to high probability and valleys to low probability. The wave nature of matter introduces uncertainty, allows it to exhibit complex behavior, such as interfering with itself, and also explains the observed structure of atoms. Domain of ScienceWhy quantum mechanics causes disagreement on where the edge of an atom is locatedThe quantum model of the atom describes it as having a dense nucleus at its center, surrounded by electrons in probability clouds where they are most likely to be found. The fundamental uncertainty of these clouds has led to various methods and resulting measurements of the atomic radius. (Some readers may experience a paywall.) Chemistry WorldQuantum mechanics-based technology may explain the Fermi paradoxIt describes the discrepancy between the high likelihood of life beyond Earth given the vastness of the universe and the lack of evidence for such life, since extraterrestrial civilizations have not communicated with us. However, quantum communication—a more information-dense and effective method than classical means—requires massive receivers and very narrow signals, which would easily miss Earth, making a lack of signals expected. minutephysicsUnlike quantum mechanics, classical physics suggests free will does not existModels based on Newton's laws of motion suggest all actions are predetermined and must follow specific trajectories and outcomes, such that everything that will ever occur in the future has already been set in motion by past causes. However, quantum mechanics challenges determinism because it is based on probability, where no outcome is certain. SpaceSome founders of quantum mechanics thought consciousness could influence phenomenaSince quantum systems exist as a superposition of states before producing a definitive outcome, some quantum pioneers wondered if the act of conscious observation was what collapsed the wave function of possibilities into one state. PBS Space TimeView 3D renderings of atomic orbitals created with quantum mechanicsScientists use the Schrödinger equation to determine how a system governed by a wavefunction—an equation that predicts the probability of certain outcomes—evolves with time. Computers can animate atomic structure and behavior by depicting the wavefunction as a fluid that guides a particle, like water moving a speck of dust. minutephysicsLasers, semiconductors, medical imaging, and atomic clocks rely on quantum mechanicsSemiconductors, crucial in electronics, operate based on quantum superposition. Lasers use stimulated emission, a quantum process, and MRI machines leverage the quantum spin of hydrogen atoms for imaging. Atomic clocks measure time with unprecedented precision using quantum transitions. Caltech Science ExchangeQuantum mechanics explains how particles behave like both matter and wavesIn the quantum world, particles such as electrons are “quantized,” meaning they can only hold specific values of energy or momentum. These particles also behave like waves, with their wave function predicting where they might be found at any moment as probability clouds called orbitals. US Department of EnergyA "no math" primer on quantum mechanicsQuantum mechanics may not immediately grasped, but it can be slowly understood through the experiments and discussions offered here by writer Dr. Miguel F. Morales. A professor of physics at the University of Washington in Seattle, Dr. Morales makes understanding the basics of quantum mechanics fun with a promised "no math" approach. Ars TechnicaA look at the giants of quantum mechanicsGerman physicist Max Planck publishes his groundbreaking study of the effect of radiation on a “blackbody” substance, and the quantum theory of modern physics HISTORYView the evolution of atomic models, with four successively overturned between 1900 and 1926Originally thought to be indivisible spheres unique to each element, the discovery of the electron by J.J. Thomson revealed them to be made of smaller particles. Ernest Rutherford's gold foil experiment uncovered the existence of nuclei, which Niels Bohr suggested were surrounded by electrons in fixed orbits. By applying quantum mechanics, Erwin Schrödinger replaced orbits with probability clouds. Compound InterestLearn why modern scientific patterns have been described as theories rather than lawsAfter confirming that the accuracy of some laws of physics is limited to certain domains, science became more hesitant to categorize identified mathematical relationships, such as quantum mechanics, as unchanging laws. Instead, these recent, complex frameworks are designated as theories to acknowledge that they are conditional and may be part of a larger, more complete future framework. StarTalkWithin mathematics, some infinities are bigger than othersWhile the concept of infinity refers to a countless set of items, these infinite sets can be compared to one another by matching an item from one set to an item in another, one by one. This analysis shows that certain sets must be larger than others because some infinite sets have leftover, unmatched items. Quanta MagazineView a step-by-step breakdown of how helium is forged in stars alongside antimatterDuring the proton-proton chain, four hydrogen nuclei—protons—are fused together to create an alpha particle—a helium nucleus—and produce the energy that supports a star's own weight. Through radioactive decay, two of these protons become neutrons, with each releasing an antielectron, or positron, and an electron neutrino. HyperPhysicsWhy trying to freeze helium creates a fluid that can travel through solids and climb wallsOnce cooled to temperatures just above 2 Kelvin, helium-4 atoms begin to exhibit superfluidity, a quantum property in which all atoms collectively inhabit the same low-energy state and behave in perfect unison. This coordination removes the internal friction that causes liquids to cling to surfaces, allowing them to slide through microscopic pores and scale container walls. SciShowThe discovery of antimatter came from addressing a prediction of negative energyCombining the mathematics of quantum mechanics and special relativity, Paul Dirac came up with an equation that suggested a matter particle, such as an electron, could exist in four quantum states—two of which possessed negative energy. The solution came from realizing that the states referred to positive-energy antiparticles, whose charge is the opposite of that of their normal-matter equivalent. VeritasiumListen to the audiobook version of 'A Brief History of Time'First published in 1988, Stephen Hawking's most famous novel has sold more than 25 million copies in 40 languages. Through non-technical terminology, Hawking discusses the nature of space and time, general relativity, quantum mechanics, gravity, black holes, and cosmology. AudioVox - BooksDespite claims of limitless free energy, zero-point energy cannot be harnessedBecause quantum mechanics prevents systems from ever reaching an energy value of zero, a seemingly empty vacuum of space still contains some amount of energy associated with its lowest allowed state. Since descending to even lower states is forbidden, extracting meaningful amounts of energy from an empty vacuum is impossible. Big ThinkFermilab's ICARUS experiment is searching for hypothetical sterile neutrinosNeutrinos are a group of three chargeless, lightweight particles that can transform into one another via a quantum mechanical phenomenon called neutrino oscillations. The rate of these oscillations can be determined by measuring the amount of each type at different distances, where data inconsistencies would suggest the existence of new physics. FermilabLight has been modeled as a wave and a stream of particles throughout historyIsaac Newton first identified white light as composed of a spectrum of colors, which he believed consisted of particles of different hues. Various light phenomena, including refraction, led Christiaan Huygens to develop an alternative wave model. Quantum mechanics validated both models through the concept of wave-particle duality. Be SmartUnderstanding how and when time began requires a theory of quantum gravityRewinding the universe to the big bang compresses all matter, energy, space, and time into a single point, necessitating a model that combines general relativity with quantum mechanics. Although physicists understand time to have begun when the universe did, a clear understanding of the mechanisms involved remains unclear. PBS Space TimeThe wave nature of matter can produce phenomena like negative time and retrocausalityWithin quantum mechanics, matter simultaneously exists as both fixed particles and extended waves, allowing it to emerge across barriers—just as sound travels through walls—before it fully enters the obstacle. The resulting measurements can show that particles spent negative time within a barrier, with the future occurring before the past. BBCThe graviton may be the last missing piece of the Standard ModelWhile the electromagnetic, strong nuclear, and weak nuclear forces can be explained through interactions with particles, gravity is instead best modeled through spacetime curvature. Discovering a quantum particle of gravity would unite the two pillars of modern physics—quantum mechanics and general relativity—toward developing a theory of everything. PBS Space TimeEmergent quantum phenomena can produce nonfundamental quasiparticlesWhile physicists have discovered new particles by colliding known ones at high speeds, placing known particles in extreme environments or configurations can allow quantum mechanics to produce bizarre behaviors, making them seem like new types of matter. minutephysicsUnderstanding how gravity works at the quantum scale is physics's greatest challengeWhile the theory of general relativity explains how gravity works and quantum mechanics explains interactions at the subatomic scale, the two frameworks contradict one another. Developing a model of gravity mediated by particles can help complete the Standard Model. PBS Space TimeThe Higgs boson provides a mechanism that explains why some particles have massThe mathematics of quantum field theory suggested that force particles should be massless, like the photon for electromagnetism, but the weak nuclear force’s equivalent W and Z particles are not. The Higgs field provides mass when interacting with such particles. CERNExplore a series of interdisciplinary explainers on climate scienceFrom animations on the quantum mechanics of greenhouse gases to a photo essay on how scientists acquire climate data, this collection provides detailed explorations of how different branches of science have contributed to our understanding of climatology. Quanta MagazineString theory replaces black hole singularities with fuzzballs of tangled stringsBlack holes contain singularities where information about the material that fell in is lost, violating quantum mechanics. Instead, modeled as a bundle of strings, information is stored and slowly released as the black hole evaporates. PBS Space TimeEven in a perfect vacuum, empty space is full of quantum activityScientists have tried to create “nothing” by removing all matter, energy, and heat from a container, but the uncertainty principle and relativity prevent such conditions within any period of time. This means the universe is full of quantum foam, which can produce forces from nothingness. Big ThinkQuantum mechanical principles are responsible for chemical propertiesBesides quantization, the wave-particle duality, and probabilistic features, quantum theory's mathematics introduces the exclusion principle, quantum tunneling, quantum entanglement, and other phenomena foreign to our everyday experiences. Some suggest that all possibilities for a quantum system may also occur across the multiverse. The Science of Everything PodcastSpecial relativity shows how motion at high speeds reshapes time, space, and energyEinstein’s 1905 special theory of relativity revealed that the speed of light is absolute in the universe, forcing time and space to vary with one's speed. This idea led to the famous equation E=mc2, which shows that mass and energy are interchangeable. Space.comView the quantum mechanical depiction of electrons as waves around the atomic nucleusUnlike Bohr's fixed paths, the quantum model describes electrons as exhibiting behavior resembling standing waves—waves that have fixed points at the end while vibrating, like a plucked guitar string. Rather than determining their exact positions, only the probabilities of electrons being in a specific region can be determined. Texas GatewayThe ultraviolet catastrophe is the infinite energy prediction of classical physicsWhen scientists first tried calculating the radiation emitted by a heated object, their assumption was that energy was equally distributed across wavelengths and produced infinite energy at low wavelengths. This contradicted observations, which showed near-zero energy intensity at those values. FloatHeadPhysicsClassical mechanics describes the motion of and forces on everyday objects Newton's laws form the core of classical mechanics, suitable for everyday objects and speeds. The term is relatively new, distinguishing the branch of physics from quantum and relativistic mechanics. Live ScienceQuantum physics explained in 22 minutesBrian Cox, Royal Society Professor for Public Engagement in Science, discusses the fundamental principles of quantum mechanics, emphasizing their importance in understanding the nature of reality and their practical applications in emerging technologies like quantum computers. Big ThinkWhat is gravity made of?Our world at very small scales is governed by quantum mechanics, in which forces and energy come in discrete packets. At large scales, our world is governed by gravity, which moves the planets and stars and can create waves in spacetime. To merge... YouTubeExplaining the many-worlds interpretationA mind-bending, jargon-free account of the popular interpretation of quantum mechanics, helping to explain how something can be in two states at once. Massachusetts Institute of TechnologyMisunderstandings about how quantum computing works may have overhyped their abilityQuantum computers are often viewed as machines that can solve all problems instantly by trying every solution simultaneously. Instead, they amplify correct answers and cancel out wrong ones, which only works for specific kinds of problems with special structures. Quanta MagazineThe black hole information paradox comes to an endQuanta Magazine provides a deep dive into black holes and the black hole information paradox. For a very long time it was believed nothing could escape a black hole. Therein lies the paradox. Per quantum mechanics, whatever falls into a black hole should not necessarily be lost forever, and may eventually return. In a landmark series of calculations, physicists have proved that black holes can shed information. Quanta MagazineBlack holes are formed from massive stars collapsing under their own gravityThis creates a region where spacetime curves infinitely, known as a singularity. Black holes' intense mass and energy allow them to trap light, distort time and space, and present challenges with reconciling Einstein's theory with quantum mechanics. Scientific AmericanHow entanglement lies at the heart of quantum computingTheoretical physicist and mathematician Frank Wilczek boils down the complex notion of quantum entanglement into this reasonably understandable summary. Wilczek discusses the concepts of quantum entanglement and how it relates to other ideas like the Many-Worlds Interpretation (MWI) of quantum mechanics. What sounds a bit "science-fictiony" can have actual real-world and concrete applications. Quanta MagazineOne of Einstein's papers challenged quantum theory but helped confirm entanglementIn 1935, Einstein suggested that quantum mechanics was incomplete due to its strange implications about entangled particles. Their challenge led to decades of experiments that eventually proved distant particles could affect each other instantly. TED TalksFour video explainers on quantum fundamentals Ready to level up your working knowledge of quantum mechanics? Check out these four TED-Ed Lessons written by Chad Orzel, associate professor in the Department of Physics and Astronomy at Union College TED
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