Cloud insurance is any type of financial or data protection obtained by a cloud service provider. Kilo, mega, giga, tera, peta, exa, zetta are among the list of prefixes used to denote the quantity of something, such as a byte Home Topics Computer Science Nanotechnology quantum theory. This was last updated in January Login Forgot your password? Forgot your password? No problem! Submit your e-mail address below. We'll send you an email containing your password. Your password has been sent to:.

Please create a username to comment. I'm doing a report on this and it was really helpful But Einstein was never actually alive, was he? I am sorry but I think he was a fake guy: :! You have a good point both of you but in quantum theory there is a universe for both. Correction Ender Albert Einstein. Check yourself before talking about others. And AnonymousUser: yes, Einstein is real.. Google him. He's real, alright.

The guy who thinks Einstein wasn't real is hilarious. Was he the Robin Hood of the science world? Quantum mechanics QM -- also known as quantum physics, or quantum theory is a branch of physics which deals with physical phenomena at nanoscopic scales where the action is on the order of the Planck constant. It departs from classical mechanics primarily at the quantum realm of atomic and subatomic length scales. Quantum mechanics provides a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter.

Quantum mechanics provides a substantially useful framework for many features of the modern periodic table of elements including the behavior of atoms during chemical bonding and has played a significant role in the development of many modern technologies.

In advanced topics of quantum mechanics, some of these behaviors are macroscopic see macroscopic quantum phenomena and emerge at only extreme i. For example, the angular momentum of an electron bound to an atom or molecule is quantized. In contrast, the angular momentum of an unbound electron is not quantized. In the context of quantum mechanics, the wave--particle duality of energy and matter and the uncertainty principle provide a unified view of the behavior of photons, electrons, and other atomic-scale objects. The mathematical formulations of quantum mechanics are abstract.

Five fundamental particles predicted by the theory, namely the charm and top quarks, the tau neutrino, and the W and Z bosons, have been discovered. The theory predicted many properties of each of these particles; they were found as predicted. For the W and the Z boson, the masses around times that of the proton were a key part of the structure of the theory. The theory of the strong interaction began to take its modern shape once it was realized that all the observed strongly interacting particles baryons and mesons could be explained as built from more elementary building blocks: the quarks.

Compelling evidence for quarks came from experiments that directly measured the fractional electrical charge and other properties of these pointlike constituents of protons, neutrons, and mesons these and particles like them are collectively called hadrons. However, the interactions among the quarks had to have very peculiar properties. The strength or intensity of these interactions must be tiny when the quarks are close together, but must grow enormously in strength as the quarks are pulled apart.

This property, requiring infinite energy to move two quarks completely away from each other, explains why individual quarks are never observed: they are always found bound in triads as in the proton and neutron and other baryons or paired with antiquarks as in the mesons. Although required by the observations, this force between quarks was a new pattern.

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Physicists had great difficulty finding a consistent theory to describe it. All previous experience, and all simple calculations in quantum field theory, suggested that forces between particles always grow weaker at large separation. A solution to the problem was found in the quantum correction effects mentioned above, which must be included in a correct calculation. For most theories examined up until that time, this effect also leads to forces that grow weaker at larger distances. However, physicists found a class of theories in which quantum corrections have just the opposite effect: forces grow weaker at small distances.

This property is called asymptotic freedom. With the need for asymptotic freedom in explaining the strong interaction, a unique theory emerged, one that could explain many observations. It introduces particles called gluons as the carriers of the strong force just as photons carry electromagnetic forces. This theory, which describes the strong interactions, is an essential part of the Standard Model and was dubbed quantum chromodynamics, or QCD. Since achieving its mature form in the s, QCD has explained many observations and correctly predicted many others see Figure 2.

Shown are theoretical predictions black solid curve , which agree well with experimental data red points over 11 orders of magnitude. The plot shows the relative rate of quark and gluon jet production carrying energy of the amount shown on the horizontal axis, in a direction transverse to the incoming proton and antiproton directions. Adapted from an image courtesy of the D0 Collaboration. Highlights include the discovery of direct effects of gluons, verification of the asymptotic freedom property and its consequences in many and varied experiments, and continued success in modeling the outcomes of high-energy collision processes.

Together with the weak interaction theory, QCD is now a firmly established part of the Standard Model. The story of how experimental evidence for the top quark also called the t quark was discovered provides an impressive illustration of the power of the Standard Model. The patterns of the electroweak interaction required such a particle to exist and specified how it would decay. Further, as mentioned above, calculation of its indirect effect on well-measured quantities, via quantum corrections, predicted an approximate value for its mass.

## Quantum Theory

The strong interaction part of the Standard Model predicted the easiest methods by which it could be produced and how often. Equally important, since QCD describes other particle production processes as well, physicists could calculate the rates for various other processes that can mimic the process of t production and decay. This knowledge enabled them to devise a way to search for it in which these competing processes were minimized.

This capability is vital, because the relevant events are extremely rare—less than one in a trillion collisions! By putting all this information together, physicists were able to develop appropriate procedures for the search. In , the top quark was discovered in experiments done at Fermilab, as illustrated in Figure 2. While its mass was unexpectedly large about that of an atom of gold , its other properties were as predicted. The Standard Model has now been tested in so many ways, and so precisely, that its basic validity is hardly in question.

In this sense, it is very likely the definitive theory of known matter, and this marks an epoch in physics. To solve the equations in useful detail in complicated situations is another question. Particle physicists make no claim that achieving this theory of matter answers the important practical questions posed by materials scientists, chemists, or astrophysicists. Significant challenges remain to complete the Standard Model and understand all that it implies.

The Higgs particle is yet to be found. The equations of QCD must be solved with greater accuracy in more complicated and real situations. Occasionally, a pair of top quarks is produced, each of which has about the mass of a gold atom. The top quarks quickly decay further into lighter particles. The Collider Detector Facility above and the D0 detector right are two experiments located at different points where the particles are brought into collision.

Images courtesy of Fermilab. Such calculations have many potential applications. For example, to understand the properties of neutron star interiors and supernova explosions, QCD must be used to calculate the behavior of matter at higher densities than can be achieved in the laboratory.

Advances in computer hardware and software, as well as in theoretical understanding, are crucial to maintaining the progress now under way.

## quantum theory

A remarkable consequence of the Standard Model, and particularly the asymptotic freedom property, is that the laws can be extended or extrapolated without contradiction well beyond conditions where the model has been tested directly. In fact, the equations become simpler and easier to solve at extremely high energy or temperature. This newfound ability to describe matter in extreme conditions has revolutionized understanding of the very early universe.

The big bang picture, the basis of modern cosmology, postulates that extraordinarily high temperatures were attained in the very early universe. The Standard Model permits the calculation with reasonable confidence of how matter behaves in circumstances present at very early times after the big bang.

However, researchers cannot test all of these extrapolations directly. In addition, at the very earliest times, quantum gravitational effects become important and must be treated in concert with all the other interactions. Fortunately, some extrapolations can be tested. In collisions of very-high-energy heavy ions gold, lead, or uranium conditions similar to those present 10 microseconds after the big bang can be created. The Standard Model has brought understanding of the fundamental principles governing matter to an extraordinary new level of beauty and precision. It has been tested in many ways.

All details of its predictions must continue to be scrutinized with great care and high critical standards. History teaches us that further clues to the ultimate nature of physical reality can lie at the unexplored limits of such a well-tested and accepted theory. Ideas for extending the theory are readily found, although there is, as yet, no evidence to indicate which, if any, of these ideas are correct. The core of each part of the Standard Model is a description of how different types of force-carrying bosons respond to charges. For QED it is the photon and electrical charge, for QCD it is the color gluons and color charges, and for the weak interactions it is the W and Z bosons and yet other.

In this sense, the whole Standard Model is a vast generalization of electrodynamics. It is astounding, but true, that the vast diversity of physical behaviors observed for matter in nature is captured within this circle of ideas. The deep mathematical and conceptual similarities among theories of the strong, electromagnetic, and weak interactions suggest a larger theory unifying them.

Indeed, the structure of the theory seems to invite it. In QED, photons respond to electrical charge but never change it. QCD has gluons that respond to the different quark color charges. But gluons also change the color charge of a quark into a different color charge, because gluons themselves carry both color charge and anticolor charge.

Similarly, a W boson changes the weak charge of matter, for example in the transformation of an electron into a neutrino. Each known boson responds to, and carries or changes, only one particular kind of charge. What could be more natural than to make the theory of matter complete and symmetrical by postulating additional bosons that transform one kind of charge such as color into another such as electric charge , because these additional bosons complete the pattern by carrying both charge types?

Mathematically, such extensions appear to be an obvious next step. See Box 2. This is a beautiful idea. But does nature use it? There are good reasons to suspect the answer is yes. In the Standard Model, bosons fall into 3 independent groupings or sets, while the fermions fall into no fewer than 15 independent sets. The postulate of complete symmetry among charges simplifies this situation.

The bosons are then organized into a single unified set, while the fermions fall into just three sets each copies of the other, but with different masses. Theories built to have such a unified approach are called grand unified theories. They predict new effects due to the added bosons. In such theories the proton is unstable. Its observed stability, with a half-life of not less than 10 32 years, is a severe constraint on this idea. It means that the new force-carrying bosons predicted to simplify the theory must be very massive indeed, so that their effects will occur slowly enough to be consistent with this limit.

Even such very heavy particles, however, could be copiously produced in the very earliest times after the big bang. So the postulate of such interactions changes the view of what might occur at. In nature, symmetries abound and correspond to the appearance of something e. In physics, symmetries are transformations that leave the laws of physics for a system invariant. For example, rotational symmetry is manifested as invariance under redefinition of the spatial coordinates by rotating the axes.

### Introduction

In field theories there are many possible types of transformation that lead to invariance. In addition to coordinate redefinitions, there are often symmetries of field redefinitions. For example, consider a field that takes complex number values: If the equations depend only on the absolute value, then the physics will be invariant under changes of the phase of the field. Symmetries are a powerful tool in physics. They greatly simplify the work of defining a theory and its predictions. Any symmetry imposed on the equations limits the variety of solutions that must be investigated.

In addition, as shown by Emmy Noether in , any invariance in the equations under a continuous change of variables engenders a related conservation law in the predictions for physical processes. Thus rotational invariance in the equations leads to conservation of angular momentum, while invariance under complex phase definitions leads to predictions such as the conservation of electric charge. Any such conservation law has powerful consequences in predictions for physical processes. Often the conservation law is first found by observation; this then tells physicists what symmetry property the system possesses.

It is useful to categorize the symmetries of different interactions. The strong interactions have symmetries, and thus conservation laws, that are not preserved by the weak interactions. For example, conservation of the number of particles minus antiparticles of each flavor is observed separately in all strong and electromagnetic processes but not in weak processes.

Because symmetries are such a successful tool, physicists today try to build theories that have, at some very-high-energy scale, more symmetries than are observed in current experiments. This approach has been used for building the Standard Model itself. Speculative extensions of the Standard Model, known as grand unified theories or as supersymmetric extensions, add even more symmetries. Another feature of these grand unified theories is that they typically incorporate tiny neutrino masses and predict other effects for neutrinos quite different from Standard Model patterns.

Both these features, proton decay and neutrino masses, are discussed further in Chapter 3 , which explores the implications of physics beyond the Standard Model in cosmological and astrophysical situations. Another consequence of the hypothetical symmetry of the grand unified theories is at first glance as much at odds with observation as is proton. For mathematical consistency, the strengths of the forces and the radiation rates associated with various kinds of charges must be equal. But the strong force is obviously more powerful than the electromagnetic force.

Yet, it is just here at the precipice of paradox that the deepest lessons of the Standard Model come to the rescue. The first lesson, from unification of the electromagnetic and weak interactions, teaches that the true symmetry of the basic equations can be obscured by pervasive condensates. The Higgs condensate was necessary to accommodate particle masses. In the unified theory, an additional condensate is required to make the additional bosons very massive.

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The existence of the condensate hides the symmetry and makes it appear to be broken. The second lesson is that the observed force strengths reflect both intrinsic strength and the modification of this strength by quantum corrections. Thus the strength of an interaction changes depending on the energy scale at which the interaction is observed. The perfect symmetry among various charges is spoiled by the condensate, which gives different masses to different particle types.

## Atom - The laws of quantum mechanics | pilifysopysy.tk

The strengths of the three types of interaction, while the same at extremely high energies, are thus modified differently by quantum corrections and hence can be very different for the energies at which they are observed. These ideas can be made mathematically precise. Calculations determine how the forces change with energy and whether they can adequately account for the various strengths observed at everyday energies, with a single common strength at very high energy.

The parameters of the theory that determine the strength of the forces are called couplings. The result of the calculation of how couplings vary with energy is shown in Figure 2. It works remarkably well. Note the extremely large energy scale at which the couplings merge. This sets the scale of the masses for the bosons that mediate proton decay. This is a second remarkable success. Not only do the three couplings merge, but they also do so at an energy scale that is large enough to suppress proton decay.

A lower scale could have given a prediction inconsistent with observation, thereby ruling out such theories. In truth, the simplest versions of this idea predicted proton lifetimes that were subsequently excluded by sensitive experiments, but many variants survive this test. The precise effects of quantum corrections depend on the kinds and the masses of all particles that exist.

So the predictions of unification and the observed pattern of couplings may perhaps provide a way to learn something about additional massive particles without actually producing them. This leads to an extremely tantalizing discovery. A rough merging of the three. The figure is drawn for a minimal supersymmetric extension of the Standard Model.

Without supersymmetry, the three couplings do not precisely meet. Image courtesy of J. Bagger, K. Matchev, and D. Pierce, Johns Hopkins University. Figure 2. Not only do the couplings all merge cleanly, but also, unlike the version without supersymmetry, the simplest supersymmetric version of the theory predicts a proton half-life that is somewhat above the current lower bound from measurements.

Physicists are intrigued by these two results and are actively searching in accelerator experiments for evidence of any of the many additional particles introduced by the postulate of supersymmetry. Of great interest for the physics of the universe is the prediction by supersymmetry of a new, stable weakly interacting particle, known as a neutralino.

Supersymmetry is a bold and profoundly original proposal to extend the space-time symmetry of special relativity. Supersymmetry thus predicts that every particle has a supersymmetric partner particle—normal particles of integer spin have spin one-half partners, while spin one-half particles have integer spin partners, as shown in Figure 2.

Since the matter particles quarks and leptons have spin one half and the force carriers photons, gluons, and W and Z bosons have spin one, supersymmetry relates the constituents of matter to the particles that mediate the forces that hold matter together. Not only may supersymmetry unify the matter constituents with the force carriers, but it may also unify gravity with the other forces of nature. Although supersymmetry was invented for other purposes and has a rich history, it is a key element of string theory, the most promising idea that physicists have for incorporating quantum mechanics into gravity and putting gravity on an equal basis with the other forces.

Supersymmetry may help to explain the enormous range of energy scales found in particle physics often referred to as the hierarchy-of-energy-scale problem. Supersymmetry is mathematically elegant. Nature, however, always has the last word. Is supersymmetry a property of the physical world, or just interesting mathematics?

As yet there is no direct evidence for supersymmetry. It is attractive to theorists both for its elegance and because it makes certain features of the Standard Model occur more naturally. At best it is imperfectly realized. Perfect symmetry requires equal mass pairings of particles and their superpartners. No such pairings are found among the known particles, and thus a whole family of superpartners must be postulated. However, valid symmetries of the fundamental laws can be obscured by the existence of pervasive fields called condensates in the vacuum. Supersymmetry is such a hidden symmetry.

All the superpartners of the known particles can only be as-yet-undiscovered massive particles, and many versions of supersymmetry, in particular those that account best for the merging of the three couplings, predict that these particles should be found at masses accessible with existing or planned accelerators.

Searches for these particles may soon reveal or exclude these versions of supersymmetry theory. Because the superpartners are expected to be very massive, they have not yet been directly observed. The neutralino is discussed further in later chapters. It incorporated several concepts quite new to physics, including the curvature of space-time and the bending of light, and led to the prediction of other completely new phenomena, including gravitational radiation, the expanding universe, and black holes.

General relativity was widely accepted and admired by physicists almost from the start. For many years, however, general relativity was not very relevant to the rest of physics; it made few testable new predictions. This book is devoted to the construction of a deductive theory of the electron, starting from first principles and using a simple mathematical tool, geometric analysis.

Its purpose is to present a comprehensive theory of the electron to the point where a connection can be made with the main approaches to the study of the electron in physics. The introduction describes the methodology. Chapter 2 presents the concept of space-time-action relativity theory and in chapter 3 the mathematical structures describing action are analyzed. Chapters 4, 5, and 6 deal with the theory of the electron in a series of aspects where the geometrical analysis is more relevant.

Finally in chapter 7 the form of geometrical analysis used in the book is presented to elucidate the broad range of topics which are covered and the range of mathematical structures which are implicitly or explicitly included. The book is directed to two different audiences of graduate students and research scientists: primarily to theoretical physicists in the field of electron physics as well as those in the more general field of quantum mechanics, elementary particle physics, and general relativity; secondly, to mathematicians in the field of geometric analysis.

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