Surfing the Quantum World

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Musical Instrument ◽  
Popular Science ◽  
Quantum Spin ◽  
Exclusion Principle ◽  
Maximum Height ◽  
Core Concepts ◽  
The Many ◽  
The One

Surfing the Quantum World bridges the gap between in-depth textbooks and typical popular science books on quantum ideas and phenomena. Among its significant features is the description of a host of mind-bending phenomena, such as a quantum object being in two places at once or a certain minus sign being the most consequential in the universe. Much of its first part is historical, starting with the ancient Greeks and their concepts of light, and ending with the creation of quantum mechanics. The second part begins by applying quantum mechanics and its probability nature to a pedagogical system, the one-dimensional box, an analog of which is a musical-instrument string. This is followed by a gentle introduction to the fundamental principles of quantum theory, whose core concepts and symbolic representations are the foundation for most of the subsequent chapters. For instance, it is shown how quantum theory explains the properties of the hydrogen atom and, via quantum spin and Pauli’s Exclusion Principle, how it accounts for the structure of the periodic table. White dwarf and neutron stars are seen to be gigantic quantum objects, while the maximum height of mountains is shown to have a quantum basis. Among the many other topics considered are a variety of interference phenomena, those that display the wave properties of particles like electrons and photons, and even of large molecules. The book concludes with a wide-ranging discussion of interpretational and philosophic issues, introduced in Chapters 14 by entanglement and 15 by Schrödinger’s cat.

scholarly journals Lectures on dynamical models for quantum measurements

2014 ◽  
Vol 28 (21) ◽  
pp. 1430014
Author(s):  
Theo M. Nieuwenhuizen ◽  
Marti Perarnau-Llobet ◽  
Roger Balian
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Density Matrix ◽  
Quantum Measurements ◽  
Quantum Spin ◽  
Spin Component ◽  
Time Interval ◽  
Large Set ◽  
Standard Quantum ◽  
The One

In textbooks, ideal quantum measurements are described in terms of the tested system only by the collapse postulate and Born's rule. This level of description offers a rather flexible position for the interpretation of quantum mechanics. Here we analyse an ideal measurement as a process of interaction between the tested system S and an apparatus A, so as to derive the properties postulated in textbooks. We thus consider within standard quantum mechanics the measurement of a quantum spin component ŝz by an apparatus A, being a magnet coupled to a bath. We first consider the evolution of the density operator of S + A describing a large set of runs of the measurement process. The approach describes the disappearance of the off-diagonal terms ("truncation") of the density matrix as a physical effect due to A, while the registration of the outcome has classical features due to the large size of the pointer variable, the magnetization. A quantum ambiguity implies that the density matrix at the final time can be decomposed on many bases, not only the one of the measurement. This quantum oddity prevents to connect individual outcomes to measurements, a difficulty known as the "measurement problem". It is shown that it is circumvented by the apparatus as well, since the evolution in a small time interval erases all decompositions, except the one on the measurement basis. Once one can derive the outcome of individual events from quantum theory, the so-called collapse of the wavefunction or the reduction of the state appears as the result of a selection of runs among the original large set. Hence nothing more than standard quantum mechanics is needed to explain features of measurements. The employed statistical formulation is advocated for the teaching of quantum theory.

Quantum Theory

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Uncertainty Principle ◽  
Quantum Spin ◽  
Quantum States ◽  
Wave Functions ◽  
Symbolic Representations ◽  
Quantum Numbers ◽  
The Subject ◽  
Heisenberg's Uncertainty Principle

The subject of Chapter 8 is the fundamental principles of quantum theory, the abstract extension of quantum mechanics. Two of the entities explored are kets and operators, with kets being representations of quantum states as well as a source of wave functions. The quantum box and quantum spin kets are specified, as are the quantum numbers that identify them. Operators are introduced and defined in part as the symbolic representations of observable quantities such as position, momentum and quantum spin. Eigenvalues and eigenkets are defined and discussed, with the former identified as the possible outcomes of a measurement. Bras, the counterpart to kets, are introduced as the means of forming probability amplitudes from kets. Products of operators are examined, as is their role underpinning Heisenberg’s Uncertainty Principle. A variety of symbol manipulations are presented. How measurements are believed to collapse linear superpositions to one term of the sum is explored.

scholarly journals ON THE QUANTUM THEORY OF MASSLESS SPIN-3/2 FIELD IN MINKOWSKI SPACETIME

2006 ◽  
Vol 03 (07) ◽  
pp. 1303-1312 ◽  
Author(s):  
WEIGANG QIU ◽  
FEI SUN ◽  
HONGBAO ZHANG
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Theory ◽  
Casimir Effect ◽  
Minkowski Spacetime ◽  
Quantum Field ◽  
Explicit Result ◽  
Massless Spin ◽  
The Many ◽  
The One

From the modern viewpoint and by the geometric method, this paper provides a concise foundation for the quantum theory of massless spin-3/2 field in Minkowski spacetime, which includes both the one-particle's quantum mechanics and the many-particle's quantum field theory. The explicit result presented here is useful for the investigation of spin-3/2 field in various circumstances such as supergravity, twistor programme, Casimir effect, and quantum inequality.

Philosophy of Quantum Mechanics: Dynamical Collapse Theories

2021 ◽  
Author(s):  
Angelo Bassi
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
New Technologies ◽  
Stochastic Dynamics ◽  
Laws Of Nature ◽  
Nonlinear Effects ◽  
Foundation Of Quantum Mechanics ◽  
Quantum Phenomena ◽  
The One ◽  
Collapse Theories

Quantum Mechanics is one of the most successful theories of nature. It accounts for all known properties of matter and light, and it does so with an unprecedented level of accuracy. On top of this, it generated many new technologies that now are part of daily life. In many ways, it can be said that we live in a quantum world. Yet, quantum theory is subject to an intense debate about its meaning as a theory of nature, which started from the very beginning and has never ended. The essence was captured by Schrödinger with the cat paradox: why do cats behave classically instead of being quantum like the one imagined by Schrödinger? Answering this question digs deep into the foundation of quantum mechanics. A possible answer is Dynamical Collapse Theories. The fundamental assumption is that the Schrödinger equation, which is supposed to govern all quantum phenomena (at the non-relativistic level) is only approximately correct. It is an approximation of a nonlinear and stochastic dynamics, according to which the wave functions of microscopic objects can be in a superposition of different states because the nonlinear effects are negligible, while those of macroscopic objects are always very well localized in space because the nonlinear effects dominate for increasingly massive systems. Then, microscopic systems behave quantum mechanically, while macroscopic ones such as Schrödinger’s cat behave classically simply because the (newly postulated) laws of nature say so. By changing the dynamics, collapse theories make predictions that are different from quantum-mechanical predictions. Then it becomes interesting to test the various collapse models that have been proposed. Experimental effort is increasing worldwide, so far limiting values of the theory’s parameters quantifying the collapse, since no collapse signal was detected, but possibly in the future finding such a signal and opening up a window beyond quantum theory.

Quantum Schmuntum: Lights, Camera, Action!

2018 ◽  
Author(s):  
Vlatko Vedral
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Hair Loss ◽  
Popular Science ◽  
Phone Call ◽  
The Public ◽  
Physics Department ◽  
Physical Laws ◽  
The Voice ◽  
Science Magazine

Spring 2005, whilst sitting at my desk in the physics department at Leeds University, marking yet more exam papers, I was interrupted by a phone call. Interruptions were not such a surprise at the time, a few weeks previously I had published an article on quantum theory in the popular science magazine, New Scientist, and had since been inundated with all sorts of calls from the public. Most callers were very enthusiastic, clearly demonstrating a healthy appetite for more information on this fascinating topic, albeit occasionally one or two either hadn’t read the article, or perhaps had read into it a little too much. Comments ranging from ‘Can quantum mechanics help prevent my hair loss?’ to someone telling me that they had met their twin brother in a parallel Universe, were par for the course, and I was getting a couple of such questions each day. At Oxford we used to have a board for the most creative questions, especially the ones that clearly demonstrated the person had grasped some of the principles very well, but had then taken them to an extreme, and often, unbeknown to them, had violated several other physical laws on the way. Such questions served to remind us of the responsibility we had in communicating science – to make it clear and approachable but yet to be pragmatic. As a colleague of mine often said – sometimes working with a little physics can be more dangerous than working with none at all. ‘Hello Professor Vedral, my name is Jon Spooner, I’m a theatre director and I am putting together a play on quantum theory’, said the voice as I picked up the phone. ‘I am weaving elements of quantum theory into the play and we want you as a consultant to verify whether we are interpreting it accurately’. Totally stunned for at least a good couple of seconds, I asked myself, ‘This guy is doing what?’ Had I misheard? A play on quantum theory? Anyway it occurred to me that there might be an appetite for something like this, given how successful the production of Copenhagen, a play by Michael Freyn, had been a few years back.

Quantum Mechanics and the Periodic Table

2019 ◽  
Author(s):  
Eric Scerri
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Periodic Table ◽  
Chemical Properties ◽  
Pauli Exclusion Principle ◽  
Niels Bohr ◽  
Exclusion Principle ◽  
Old Quantum Theory ◽  
Set Up ◽  
Three Body

In chapter 7, the influence of the old quantum theory on the periodic system was considered. Although the development of this theory provided a way of reexpressing the periodic table in terms of the number of outer-shell electrons, it did not yield anything essentially new to the understanding of chemistry. Indeed, in several cases, chemists such as Irving Langmuir, J.D. Main Smith, and Charles Bury were able to go further than physicists in assigning electronic configurations, as described in chapter 8, because they were more familiar with the chemical properties of individual elements. Moreover, despite the rhetoric in favor of quantum mechanics that was propagated by Niels Bohr and others, the discovery that hafnium was a transition metal and not a rare earth was not made deductively from the quantum theory. It was essentially a chemical fact that was accommodated in terms of the quantum mechanical understanding of the periodic table. The old quantum theory was quantitatively impotent in the context of the periodic table since it was not possible to even set up the necessary equations to begin to obtain solutions for the atoms with more than one electron. An explanation could be given for the periodic table in terms of numbers of electrons in the outer shells of atoms, but generally only after the fact. But when it came to trying to predict quantitative aspects of atoms, such as the ground-state energy of the helium atom, the old quantum theory was quite hopeless. As one physicist stated, “We should not be surprised . . . even the astronomers have not yet satisfactorily solved the three-body problem in spite of efforts over the centuries.” A succession of the best minds in physics, including Hendrik Kramers, Werner Heisenberg, and Arnold Sommerfeld, made strenuous attempts to calculate the spectrum of helium but to no avail. It was only following the introduction of the Pauli exclusion principle and the development of the new quantum mechanics that Heisenberg succeeded where everyone else had failed.

scholarly journals Observability, Unobservability and the Copenhagen Interpretation in Dirac's Methodology of Physics

Quanta ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 68-87 ◽  
Author(s):  
Andrea Oldofredi ◽  
Michael Esfeld
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Close Contact ◽  
Copenhagen Interpretation ◽  
The Other ◽  
Interpretation Of Quantum Mechanics ◽  
Present Essay ◽  
Other Hand ◽  
Methodological Principles ◽  
The One

Paul Dirac has been undoubtedly one of the central figures of the last century physics, contributing in several and remarkable ways to the development of quantum mechanics; he was also at the centre of an active community of physicists, with whom he had extensive interactions and correspondence. In particular, Dirac was in close contact with Bohr, Heisenberg and Pauli. For this reason, among others, Dirac is generally considered a supporter of the Copenhagen interpretation of quantum mechanics. Similarly, he was considered a physicist sympathetic with the positivistic attitude which shaped the development of quantum theory in the 1920s. Against this background, the aim of the present essay is twofold: on the one hand, we will argue that, analyzing specific examples taken from Dirac's published works, he can neither be considered a positivist nor a physicist methodologically guided by the observability doctrine. On the other hand, we will try to disentangle Dirac's figure from the mentioned Copenhagen interpretation, since in his long career he employed remarkably different—and often contradicting—methodological principles and philosophical perspectives with respect to those followed by the supporters of that interpretation.Quanta 2019; 8: 68–87.

scholarly journals Schrodinger Wave Equation

2020 ◽  
Vol 4 (1) ◽  
Author(s):  
Aaron C.H. Davey
Keyword(s):  
Quantum Mechanics ◽  
Wave Equation ◽  
Quantum Theory ◽  
System Change ◽  
Wave Functions ◽  
Quantum Mechanical ◽  
One Dimensional ◽  
Erwin Schrödinger ◽  
The One ◽  
Over Time

The father of quantum mechanics, Erwin Schrodinger, was one of the most important figures in the development of quantum theory. He is perhaps best known for his contribution of the wave equation, which would later result in his winning of the Nobel Prize for Physics in 1933. The Schrodinger wave equation describes the quantum mechanical behaviour of particles and explores how the Schrodinger wave functions of a system change over time. This project is concerned about exploring the one-dimensional case of the Schrodinger wave equation in a harmonic oscillator system. We will give the solutions, called eigenfunctions, of the equation that satisfy certain conditions. Furthermore, we will show that this happens only for particular values called eigenvalues.

Identity in Physics

Philosophy ◽  
2014 ◽  
Author(s):  
Décio Krause ◽  
Jonas R. B. Arenhart
Keyword(s):  
Quantum Mechanics ◽  
Classical Mechanics ◽  
Structural Realism ◽  
Exclusion Principle ◽  
Qualitative Properties ◽  
Identity Of Indiscernibles ◽  
Quantum Particles ◽  
Controversial Topic ◽  
The Difference ◽  
The One

Traditionally, the problem of identity is closely associated with the problem of individuality: What is it that makes something being what it is? Approaches to the problem may be classified into two classes: reductionism and transcendental identity. The first group tries to reduce identity to some qualitative feature of the entities dealt with, while the second either grounds identity on some feature other than qualitative properties or else take it to be primitive. The debate is generally centred on the validity of the Principle of the Identity of Indiscernibles (PII), which states that qualitative indiscernibility amounts to numerical identity. If PII is valid, then reductionism concerning identity is at least viable; if PII is invalid, then reductionism seems less plausible and some form of transcendental identity seems required. It is common to say that objects in classical mechanics are individuals. This fact is exhibited by postulating that physical objects obey Maxwell-Boltzmann statistics; if we have containers A and B to accommodate two objects a and b, there are four equiprobable situations: (1) both objects in A, (2) both in B, (3) a in A and b in B, and finally (4) a in B and b in A. Since situations (3) and (4) differ, there may be something that makes the difference—a transcendental individuality or some quality. In quantum mechanics, assuming that we have two containers A and B to accommodate objects a and b, there are just three equiprobable situations for bosons: (1) both objects in A, (2) both in B, (3) one object in A and one in B. It makes no sense to say that it is a or b that is in A: Switching them makes no difference. For fermions we have only one possibility due to the exclusion principle: (1) one object in A and one in B. Again, switching them makes no difference whatsoever. The dispute in quantum mechanics concerns non-individuality on the one side and individuality (be it reductionism or transcendental individuality) on the other. That distinction was grounded on the fact that quantum particles may be qualitatively indiscernible, and, as the statistics show, permutations are unobservable. The actual debate concerns whether some form of reductionism may survive in quantum mechanics or whether some form of transcendental identity should be adopted on the one hand and whether non-individuality is a viable option. Furthermore, a third option, Ontic Structural Realism (OSR), proposes that we transcend the debate and choose a metaphysics of structures and relations, leaving the controversial topic individuals × non-individuals behind.

Macroscopic Manifestations of Quantum Mechanics

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Quantum Mechanics ◽  
Neutron Stars ◽  
Stellar Evolution ◽  
White Dwarf ◽  
Pauli Exclusion Principle ◽  
Exclusion Principle ◽  
Energy Sources ◽  
Maximum Height ◽  
Quantum Behavior ◽  
The Way

Some possibly unexpected macroscopic manifestations of quantum mechanics are described in Chapter 12. The first is a laser, a device both man-made and one that relies on phase effects to achieve its potent beam. How this is done is illustrated by a diagram. The next is an estimate of the maximum height of a mountain, whose result was originally shown to rely on quantum mechanics. That result, approximately 30 km, is followed by showing that white dwarf and neutron stars are each gigantic manifestations of the Pauli Exclusion Principle, the first mainly consisting of carbon nuclei and electrons, the second mainly of neutrons. In each case, the primary constituent is a fermion, whose quantum behavior is governed by the Exclusion Principle. Along the way to showing this is a review of stellar evolution and energy sources. The final example is the first quantum machine, which is barely macroscopic.

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