Physics
Quantum Conservation
Quantum conservation refers to the principle that certain physical quantities, such as energy, momentum, and electric charge, remain constant in a closed system over time. This concept is a fundamental aspect of quantum mechanics and plays a crucial role in understanding the behavior of particles and interactions at the quantum level. It provides a framework for predicting and analyzing the behavior of quantum systems.
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11 Key excerpts on "Quantum Conservation"
eBook - PDFQuestioning the Universe
Concepts in Physics
- Ahren Sadoff(Author)
- 2008(Publication Date)
- Chapman and Hall/CRC(Publisher)
61 8 Conservation Laws Conservation laws are extremely important in physics. They are relevant to a wide variety of physical phenomena. They are very powerful and hence very useful. And interestingly, they follow directly from the symmetry principles we discussed in the last chapter. We can see this by just considering what it means if something is conserved. If something is conserved, it does not increase or decrease; it does not change; it does not vary. In other words, it remains invariant . So, we can give the following definition to conservation: Something is conserved if we can do something to it such that afterwards it remains invariant. Of course, this sounds almost identical to our definition of symmetry. It is no acci-dent. Emmy Noether, a woman mathematician, proved that symmetry principles lead directly to conservation laws. For instance, space translation symmetry leads to the conservation of momentum, and time translation symmetry leads to the conserva-tion of energy. We will discuss both of these conservation laws in this chapter. Using these as examples, we will be able to see why conservation laws are so powerful. 8.1 CONSERVATION OF MOMENTUM The word momentum is often used in everyday speech to imply that something is in motion. But in physics, momentum has a very well-defined meaning. The momen-tum of a single object with a mass, m, is given by the equation p = m v (8.1) Momentum is a vector quantity since it is directly proportional to the velocity vec-tor. The units of momentum are [Kg][M]/[s]. Many quantities in physics have units named after some famous physicist. For instance, the unit of force is the Newton for Isaac Newton. But no one has been honored for momentum. If there is a group of objects and we are interested in the momentum of the entire system, then we just add up the momentum of the individual objects to get the momentum of the system.
eBook - PDF- SachchidaNand Shukla(Author)
- 2023(Publication Date)
- Arcler Press(Publisher)
In terms of symmetries and invariance concepts, three specific conservation laws connected with inversion or reverse of space, time, and charge have been defined (Figure 9.1). Conservation Laws and Symmetry of Elementary Particles 221 Figure 9.1. Mass near the M87* black hole are converted into very energetic astrophysical jet, stretching 5,000 light years. Source: https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence#/ media/File:M87_jet.jpg. Conservation law, often known as the law of conservation, is a principle in physics that asserts that a specific physical attribute does not change over time inside an independent physical system. This sort of law governs energy, momentum, angular momentum, mass, and electric charge in classical physics. Other conservation principles apply in particle physics to features of subatomic particles that are unchanging during interactions. Conservation laws provide an important role in that they allow us to forecast the macroscopic system behavior without need to analyze the microscopic intricacies of the progress of a physical process or chemical reaction (Zimmermann, 2018). The Study of Elementary Particles 222 Conservation laws are regarded as fundamental principles of nature, with broad applications in physics as well as chemistry, biology, geology, and engineering. In the extent that they correspond to all feasible processes, most conservation laws are accurate or absolute. Some conservation laws are incomplete in the sense that they apply to some processes but not others. The Noether theorem, which asserts that there is a one-to-one connection between each of them and a discrete symmetry of nature, is an especially significant finding involving conservation laws. The conservation of energy, for example, emerges from physical systems’ time-invariance, while the conservation of angular momentum comes from the notion that physical systems act the same irrespective of how they are orientated.
eBook - PDFPhysics of Nuclear Radiations
Concepts, Techniques and Applications
- Chary Rangacharyulu(Author)
- 2013(Publication Date)
- CRC Press(Publisher)
In high energy collisions and photon interactions, copious amounts of particles and antiparticles of opposite charges are pro-duced and annihilated. Thus, at any stage of the reaction or decay, there may be an arbitrary number of positive and negative charges flying about the laboratory as long as the net charge remains con-stant. We summarize the above conservation principles below: Energy ( E ) conservation (a scalar quantity ) 1 : ∑ E initial = ∑ E f inal (1.1) or Δ E = 0 Momentum ( ~ p ) conservation (a vector quantity ): ∑ ~ p initial = ∑ ~ p f inal (1.2) or Δ p i = 0 where i = x , y , z in cartesian coordinates i = r , θ , φ in spherical polar coordinates It should be remarked that arbitrary amounts of momentum can be carried by particles as long as the following conditions are satisfied: 1 Verifying the conservation principle of a scalar quantity is simple addition and subtraction of numbers. For a vector quantity, the conservation of components along the three mutually perpendicular (orthogonal) directions is essential. 4 Physics of Nuclear Radiations: Concepts, Techniques and Applications a) The components along three orthogonal directions are conserved. Here, what matters is the overall algebraic sums of momentum in each direction and not the momentum of individual entities sepa-rately. b) The total energy conservation principle is obeyed. A familiar example is the radioactive decay of an atomic nucleus. Initially, the nucleus is at rest with zero momentum. It emits two par-ticles, say an alpha particle and another nucleus. They fly in opposite directions, with each carrying same magnitude of momentum. Each particle has a finite momentum and the vector sum of the momenta is zero. Electric Charge ( Q ) conservation (a scalar quantity ): ∑ Q initial = ∑ Q f inal (1.3) or Δ Q positive = Δ Q negative The last equation is simply a mathematical expression that equal amounts of positive and negative charges may be created or annihilated in nuclear processes.
eBook - PDFTransport Processes in Chemically Reacting Flow Systems
Butterworths Series in Chemical Engineering
- Daniel E. Rosner, Howard Brenner(Authors)
- 2013(Publication Date)
- Butterworth-Heinemann(Publisher)
2 Governing Conservation Principles INTRODUCTION Approach Chemically reacting fluids, including gas mixtures, can be quantitatively understood in terms of two types of laws applied to matter treated as a continuum: a. Conservation laws, which summarize the experience of the last three centuries on the behavior of all forms of matter; b. Constitutive laws, which quantitatively describe the behavior of certain subclasses of fluids (e.g., perfect gas mixtures, elastic solids, etc.). The conservation principles, to which we first direct our attention, ensure that, for any fluid, in any state of motion, the following quantities are either conserved or, more generally, balanced: Mass Momentum Energy Entropy 1 I Total mixture mass Individual chemical species (e.g., C H 4 , 0 2 , C 0 2 , etc.) mass Individual chemical element (e.g., C, O, S, N, etc.) mass [Total linear momentum of the mixture (a vector) [Total angular momentum of the mixture (a vector) [Total energy (thermodynamic + kinetic) (First Law of | Thermodynamics) [Kinetic (mechanical) energy Total entropy of mixture (describing the consequences of transformations between forms of energy that are not thermodynamically equivalent (Second Law) and identifying all sources of irreversibility and the nature of entropy transport by diffusion). 1 From the Greek: εντρωπη, meaning evolution. 27 28 Introduction Each of these quantities is associated with a field density, i.e., a spatial concentration of that quantity, related, in turn, to the local material mass density, as shown in Table 2-1. Note that while most of these field densities are scalars (defined by one number at each point/instant), pv is a vector field (defined by three numbers at each point/instant). These conservation principles apply not only to any fluid, but to any region of space (subject to the continuum restriction). Thus, we state them below in three important forms, applicable to a control volume (CV) that is: in.
- Ribaric Marijan, Luka Sustersic(Authors)
- 1990(Publication Date)
- World Scientific(Publisher)
Parti CONSERVATION LAWS OF CLASSICAL ELECTRODYNAMICS In modern theoretical physics, symmetries and conservation laws play a leading role in constructing basic equations describing physical processes, e.g. fundamental interactions. When the basic equations are given, we try to gain an understanding of the physics they describe by seeking the physi-cally interpretable properties of their solutions, cf. Feynman, Leighton and Sands [1965, §§ 2.1 and 41-6]. The problem with classical electrodynamics, as stated by Jackson [1975, §17.1], is that we are able to obtain relevant solutions and study their properties only in two limiting cases: ... one in which the sources of charge and current are specified and the resulting electromagnetic fields are calculated, and the other in which the external electromagnetic fields are specified and the motion of charged particles or currents is calculated. Occasionally, ... , the two problems are com-bined. But the treatment is a step wise one—first the motion of the charged particle in the external field is determined, neglecting the emission of radi-ation; then the radiation is calculated from the trajectory as a given source distribution. It is evident that this manner of handling problems in elec-trodynamics can be of only approximate validity. As a consequence, we do not yet have physical understanding of those electromechanical systems where we cannot neglect the mutual interaction between electric charges and currents, and the electromagnetic field emitted by them; witness the absence of any generally accepted equation of motion for pointlike charged particles. To alleviate this situation we propose to study electrodynamic conservation laws and conserved quantities, because we hope with Rohrlich [1965, §3-17], that The understanding of a physical system is greatly aided by the knowledge of those physical quantities that do not change during this development.
eBook - PDF- J. N. Reddy(Author)
- 2007(Publication Date)
- Cambridge University Press(Publisher)
5 Conservation of Mass, Momenta, and Energy Although to penetrate into the intimate mysteries of nature and thence to learn the true causes of phenomena is not allowed to us, nevertheless it can happen that a certain fictive hypothesis may suffice for explaining many phenomena. Leonard Euler Nothing is too wonderful to be true if it be consistent with the laws of nature. Michael Faraday 5.1 Introduction Virtually every phenomenon in nature, whether mechanical, biological, chemical, geological, or geophysical, can be described in terms of mathematical relations among various quantities of interest. Most mathematical models of physical phe- nomena are based on fundamental scientific laws of physics that are extracted from centuries of research on the behavior of mechanical systems subjected to the ac- tion of natural forces. What is most exciting is that the laws of physics, which are also termed principles of mechanics, govern biological systems as well (because of mass and energy transports). However, biological systems may require addi- tional laws, yet to be discovered, from biology and chemistry to complete their description. This chapter is devoted to the study of fundamental laws of physics as applied to mechanical systems. The laws of physics are expressed in analytical form with the aid of the concepts and quantities introduced in previous chapters. The laws or principles of physics that we study here are (1) the principle of conservation of mass, (2) the principle of conservation of linear momentum, (3) the principle of conserva- tion of angular momentum, and (4) the principle of conservation of energy. These laws allow us to write mathematical relationships – algebraic, differential, or integral type – of physical quantities such as displacements, velocities, temperature, stresses, and strains in mechanical systems. The solution of these equations represents the response of the system, which aids the design and manufacturing of the system.
- Martinus J G Veltman(Author)
- 2003(Publication Date)
- World Scientific(Publisher)
Energy, Momentum and Mass-Shell 4.1 Introduction The aim of this Chapter is to explain the mechanical properties of elementary particles that will form the basis of much that we shall be discussing. In particular, it is necessary to have a good understanding of momentum and energy, and, for a single particle, the relation between the two, called the mass-shell relation. Energy and momentum are important concepts because of two facts: first they are, in the context of quantum mechanics, enough to describe completely the state of a single free particle (disregarding internal properties such as spin and charge), and second, they are conserved. For energy this is well known: for any observable process the initial energy equals the final energy. It may be distributed differently, or have a different form, but no energy disappears. If we burn wood in a stove the chemical energy locked in the wood changes into heat that warms the space where the stove is burning; eventually this heat dissipates to the outside, but does not disappear. This is the law of con-servation of energy. Similarly there is a law for conservation of momentum and we shall try to explain that in this section for simple collision processes. The fact that a description of the state of a particle in terms of its energy and momentum is a complete description is very much at the heart of quantum mechanics. Normally we specify the state of a particle by its position and its momentum at a given time: 115 4 116 E L E M E N T A R Y P A R T I C L E P H Y S I C S where, when and how does it move. Momentum a is a vector, meaning that it has a direction: momentum has thus three compo-nents, momentum in the x , y and z directions. That means that for the specification of the state of a particle we have three space coordinates plus the time and the three components of the mo-mentum. In quantum mechanics, when you know precisely the momentum of a particle no information on its location can be given.
eBook - PDFAt the Root of Things
The Subatomic World
- Palash Baran Pal(Author)
- 2014(Publication Date)
- CRC Press(Publisher)
This was a rather eventful century, right from the beginning. The quantum theory came into existence in 1900 itself — we shall discuss that in the next chapter. In 1905, Einstein proposed the theory of relativity. The main points of this would be outside the scope of our discussion here. We shall only refer to some of the results. It was seen from the theory of relativity that the con-servation of momentum and the conservation of energy are not two different concepts but are different ways of looking at the same thing. Even though we can definitely smell an-other unifying notion, there is no need to worry about that here. In fact, we can completely forget about it. Instead, let us see what else we have learnt from the theory of relativity. Consider, for example, two colliding particles. There is no external force. We shall expect the momentum to be 34 Ch. 1: Conservation laws conserved. We know how to calculate the momentum of a material particle. Momentum is a vector, its direction is the same as that of the velocity, and its magnitude is equal to the product of the magnitude of the velocity with mass. Einstein showed that a vector is indeed being conserved and its direction is also along the direction of the velocity. But if the magnitude of the velocity is v then the magnitude of this conserved vector p is given by, p = mv radicalbig 1 -( v 2 /c 2 ) . So, if we still want to define momentum as the product of mass and velocity we shall have to say that the mass is now given by, M = m radicalbig 1 -( v 2 /c 2 ) . The mass of a material particle is fixed but it increases with the velocity. Meaning, the mass depends on the velocity. This is why sometimes it is referred to as the kinetic mass , which is denoted by M . And what is m then? It is the rest mass , because this is the mass of the particle when its veloc-ity is zero.
eBook - PDFPrinciples of Continuum Mechanics
Conservation and Balance Laws with Applications
- J. N. Reddy(Author)
- 2017(Publication Date)
- Cambridge University Press(Publisher)
5 CONSERVATION OF MASS AND BALANCE OF MOMENTA AND ENERGY It is the mark of an educated mind to be able to entertain a thought without accepting it. Aristotle An error does not become truth by reason of multiplied propagation, nor does truth become error because nobody sees it. Mahatma Gandhi 5.1 Introduction 5.1.1 Preliminary Comments Most phenomena in nature, whether mechanical, biological, chemical, geologi-cal, or geophysical can be described, based on the goal of the study, in terms of mathematical relations among various quantities of interest. Such relationships are called mathematical models and are based on fundamental scientific laws of physics that are extracted from centuries of research on the behavior of mechan-ical systems subjected to the action of external stimuli. What is most exciting is that the laws of physics also govern biological systems because of mass and energy transports. However, biological systems may require additional laws, yet to be discovered, from biology and chemistry to complete their description. This chapter is devoted to the study of fundamental laws of physics as applied to mechanical systems. The laws of physics are expressed in analytical form with the aid of the concepts and quantities introduced in previous chapters. The laws or principles of physics that we study here are: (1) the principle of conservation of mass, (2) the principle of balance of linear momentum, (3) the principle of bal-ance of angular momentum, and (4) the principle of balance of energy. These laws allow us to write mathematical relationships – algebraic, differential, or integral type – of physical quantities of interest such as displacement, velocity, temper-ature, stress, and strain in mechanical systems. The solution of these equations represents the response of the system, which aids the design and manufacturing of the system.
eBook - PDF- R. Douglas Gregory(Author)
- 2006(Publication Date)
- Cambridge University Press(Publisher)
Part Two MULTI-PARTICLE SYSTEMS AND CONSERVATION PRINCIPLES CHAPTERS IN PART TWO Chapter 9 The energy principle Chapter 10 The linear momentum principle Chapter 11 The angular momentum principle Chapter Nine The energy principle and energy conservation KEY FEATURES The key features of this chapter are the energy principle for a multi-particle system, the poten- tial energies arising from external and internal forces, and energy conservation. This is the first of three chapters in which we study the mechanics of multi-particle systems. This is an important development which greatly increases the range of problems that we can solve. In particular, multi-particle mechanics is needed to solve problems involving the rotation of rigid bodies. The chapter begins by obtaining the energy principle for a multi-particle system. This is the first of the three great principles of multi-particle mechanics ∗ that apply to every mechanical system without restriction. We then show that, under appropriate conditions, the total energy of the system is conserved. We apply this energy conservation principle to a wide variety of systems. When the system has just one degree of freedom, the energy conservation equation is sufficient to determine the whole motion. 9.1 CONFIGURATIONS AND DEGREES OF FREEDOM A multi-particle system S may consist of any number of particles P 1 , P 2 , . . ., P N , with masses m 1 , m 2 . . ., m N respectively. † A possible ‘position’ of the system is called a configuration. More precisely, if the particles P 1 , P 2 , . . ., P N of a system have position vectors r 1 , r 2 , . . ., r N , then any geometrically possible set of values for the posi- tion vectors { r i } is a configuration of the system. If the system is unconstrained, then each particle can take up any position in space (independently of the others) and all choices of the { r i } are possible.
eBook - PDF- John Archibald Wheeler, Wojciech Hubert Zurek, John Archibald Wheeler, Wojciech Hubert Zurek, John Wheeler, Wojciech Zurek(Authors)
- 2014(Publication Date)
- Princeton University Press(Publisher)
In this account we must therefore obviously allow for a latitude in the energy balance, corresponding to the quan- tum-mechanical uncertainty relation for the con- jugate time and energy variables. Just as in the question discussed above of the mutually exclu- sive character of any unambiguous use in quan- tum theory of the concepts of position and momentum, it is in the last resort this circum- stance which entails the complementary relation- ship between any detailed time account of atomic phenomena on the one hand and the unclassical features of intrinsic stability of atoms, disclosed by the study of energy transfers in atomic reac- tions on the other hand. This necessity of discriminating in each ex- perimental arrangement between those parts of the physical system considered which are to be treated as measuring instruments and those which constitute the objects under investigation may indeed be said to form a principal distinction between classical and quantum-mechanical descrip- tion of physical phenomena. It is true that the place within each measuring procedure where this discrimination is made is in both cases largely a matter of convenience. While, however, in classi- cal physics the distinction between object and measuring agencies does not entail any difference in the character of the description of the phe- nomena concerned, its fundamental importance in quantum theory, as we have seen, has its root in the indispensable use of classical concepts in the interpretation of all proper measurements, even though the classical theories do not suffice in accounting for the new types of regularities with which we are concerned in atomic physics.
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