Physics

"The Kochen–Specker theorem has been discussed intensely ever since its original proof in 1967. It is one of the central no-go theorems of quantum theory, showing the non-existence of a certain kind of hidden states models."

"In my own field of many-body physics, we are, perhaps, closer to our fundamental, intensive underpinnings than in any other science in which non-trivial complexities occur, and as a result we have begun to formulate a general theory of just how this shift from quantitative to qualitative differentation takes place. This formulation called the theory of "broken symmetry," may be of help in making more generally clear the breakdown of the constructive converse of reductionism."

"One possibility that comes to mind is that the spin-two graviton might arise as a composite of two spin-one gauge bosons. This interesting idea would seem to be rigorously excluded by a no-go theorem of Weinberg & Witten ... The Weinberg–Witten theorem appears to assume nothing more than the existence of a Lorentz-covariant energy momentum tensor, which indeed holds in gauge theory. The theorem does forbid a wide range of possibilities, but (as with several other beautiful and powerful no-go theorems) it has at least one hidden assumption that seems so trivial as to escape notice, but which later developments show to be unnecessary. The crucial assumption here is that the graviton moves in the same spacetime as the gauge bosons of which it is made!"

"... a solid differs from a liquid because its crystal structure breaks the translational and rotational symmetries of space. Moreover, solids with different crystal structures should be viewed as different phases of matter because they break these symmetries in different ways. Perhaps more surprisingly, liquids and gases break no such symmetries and so should be viewed as the same phase. When you include further symmetries, such as rotations of spins in a magnet or more subtle quantum counterparts, this classification opens up a wide range of possibilities that allows us to understand almost all the known forms of matter... First, we can be sure that any attempt to change a material from one symmetry class to another will necessarily involve a violent phase transition. Second, it turns out that understanding the symmetries of a system will immediately determine many of its properties, especially at low temperature."

"Explicit symmetry breaking occurs when a dynamical system having a certain symmetry group is perturbed to a system which has strictly less symmetry. We give a geometric approach to study this phenomenon in the setting of Hamiltonian systems. We provide a method for determining the equilibria and relative equilibria that persist after a symmetry breaking perturbation. In particular a lower bound for the number of each is found, in terms of the equivariant Lyusternik–Schnirelmann category of the group orbit."

"The question of the possibility for a completion of quantum mechanics received its most famous (partial) answer in 1964 by, again, Bell ... He proved what today is known simply as Bell's theorem, to wit, that is such a more complete description exists, it cannot be local, i.e. dependent only on the events in a system's past lightcone, and agree with quantum mechanics in all instances. To this day, this result forms the paradigm example of a 'no-go' theorem."

"... If you start off with switches and gears, or whatever, you can never construct a universe in which you see quantum mechanical phenomena, according to Bell. We call such a thing a 'no-go theorem'. You may already suspect that I still believe in the hidden variables hypothesis. Surely our world must be constructed in such an ingenious way that some of the assumptions that Einstein, Bell and others found quite natural will turn out to be wrong. But how this will come about, I do not know. Anyway, for me, the hidden variables hypothesis is still the best way to ease my conscience about quantum mechanics. And as for 'no-go theorems', we will encounter several of these and discuss their fate."

"Wavelets were developed independently by mathematicians, quantum physicists, electrical engineers and geologists, but collaborations among these fields during the last decade have led to new and varied applications. What are wavelets, and why might they be useful to you? The fundamental idea behind wavelets is to analyze according to scale. Indeed, some researchers feel that using wavelets means adopting a whole new mind-set or perspective in processing data. Wavelets are functions that satisfy certain mathematical requirements and are used in representing data or other functions."

"Wavelet theory is nowadays a very active field of approximation theory with a wide impact on signal analysis, high-performance imaging applications, and adaptive transversal filter theory. It is concerned with the modeling of univariate and multivariate signals with a set of specific signals. The specific signals are just the wavelets. Families of wavelets are used to approximate a given signal (with respect to the L2 norm, say), and each element in the wavelet set is constructed from the same original window, the mother wavelet."

"Wavelets are everywhere nowadays. Whether in signal or image processing, in astronomy, in fluid dynamics (turbulence), or in condensed matter physics, wavelets have found applications in almost every corner of physics. Furthermore, wavelet methods have become standard fare in applied mathematics, numerical analysis, and approximation theory."

"On the one hand, the concept of wavelets can be viewed as a synthesis of ideas which originated during the last twenty or thirty years in engineering (subbing coding), physics (coherent states, renormalization group), and pure mathematics (study of Calderón-Zygmund operators). As a conseuqence of these interdiscplinary origins, wavelets appeal to scientists and engineers of many different backgrounds. On the other hand, wavelets are a fairly simple mathematical tool with a great variety of possible applications."

"Wavelets were introduced at the beginning of the 'eighties by J. Morlet, a French geophysicist at Elf-Aquitaine, as a tool for signal analysis in view of applications for the analysis of seismic data. The numerical success of Morlet prompted A. Grossmann to make a more detailed study of the wavelet transform, which resulted in a paper giving the mathematical foundations (see Grossmann & Morlet ..., where the title of the paper still shows the name wavelets of constant shape. In 1985, the harmonic analyst Y. Meyer became aware of this theory and he recognised many classical results inside it. Meyer pointed out to Grossmann and Morlet that there was a connection between their signal analysis methods and existing, powerful techniques in the mathematical study of singular integral operators. Then Ingrid Daubechies became involved, and all this resulted in the first construction of a special type of frames (see Daubechies, Grossmann & Meyer ..), (the concept frame generalizes the concept basis in a Hilbert space). It was also the start of a cross-fertilization between the signal analysis applications and the purely mathematical aspects of techniques based on dilations and translations."

"A Haar wavelet is the simplest type of wavelet. In discrete form, Haar wavelets are related to a mathematical operation called the Haar transform. The Haar transform serves as a prototype for all other wavelet transforms."

"Soweit es sich hier um „Paria"-Intellektualismus handelt, ... beruht dessen Intensität darauf, daß die außerhalb oder am unteren Ende der sozialen Hierarchie stehenden Schichten gewissermaßen auf dem archimedischen Punkt gegenüber den gesellschaftlichen Konventionen, sowohl was die äußere Ordnung wie was die üblichen Meinungen angeht, stehen. Sie sind daher einer durch jene Konvention nicht gebundenen originären Stellungnahme zum „Sinn" des Kosmos und eines starken, durch materielle Rücksicht nicht gehemmten, ethischen und religiösen Pathos fähig."

"δῶς μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω."

"One needs occasionally to stand aside from the hum and rush of human interests and passions to hear the voices of God. And it not unfrequently happens that the All-loving gives a great push to certain souls to thrust them out, as it were, from the distracting current for awhile to promote their discipline and growth, or to enrich them by communion and reflection. And similarly it may be woman's privilege from her peculiar coigne of vantage as a quiet observer, to whisper just the needed suggestion or the almost forgotten truth. The colored woman, then, should not be ignored because her bark is resting in the silent waters of the sheltered cove. She is watching the movements of the contestants none the less and is all the better qualified, perhaps, to weigh and judge and advise because not herself in the excitement of the race."

"Make Christianity your own, and it will show you a point outside the world, and by means of this you will move heaven and earth."

"The ions of solutions exposed to the propagation of ultrasound in the presence of a magnetic field experience Lorentz force. Their movement gives rise to a local electric current density, which is proportional to the electric conductivity of the medium. In vitro assessment of this current is performed using simple models of biological media."

"Needle-free drug delivery by jet injection is achieved by ejecting a liquid drug through a narrow orifice at high pressure, thereby creating a fine high-speed fluid jet that can readily penetrate skin and tissue. Until very recently, all jet injectors utilized force- and pressure-generating principles that progress injection in an uncontrolled manner with limited ability to regulate delivery volume and injection depth. In order to address these shortcomings, we have developed a controllable jet injection device, based on a custom high-stroke linear Lorentz-force motor that is feed-back controlled during the time-course of an injection."

"The interior of a neutron star is likely to be predominantly a mixture of superfluid neutrons and superconducting protons. This results in the quantization of the star’s magnetic field into an array of thin flux tubes, producing a macroscopic force very different from the Lorentz force of normal matter."

"... the Lorentz force law does double service (1) as definer of fields and (2) as predicter of motions. Here and elsewhere in science, as stressed not least by Henri Poincaré, that view is out of date which used to say, "Define your terms before you proceed." All the laws and theories of physics, including the Lorentz force law, have this deep and subtle character, that they both define the concepts they use (here B and E ) and make statements about these concepts. Contrariwise, the absence of some body of theory, law, and principle deprives one of the means properly to define or even to use concepts. Any forward step in human knowledge is truly creative in this sense: that theory, concept, law, and method of measurement—forever inseparable—are born into the world in union."

"The electrical conductivity of biological tissues can be measured through their sonication in a magnetic field: the vibration of the tissues inside the field induces an electrical current by Lorentz force. This current, detected by electrodes placed around the sample, is proportional to the ultrasonic pressure, to the strength of the magnetic field and to the electrical conductivity gradient along the acoustic axis. By focusing at different places inside the sample, a map of the electrical conductivity gradient can be established."

"[I]n order to investigate this... [I]f you have a Maxwell demon or something like a Szilard engine in , could you use it, as Maxwell envisaged, to use information to extract energy from De Sitter space and lift a weight or do some sort of useful work? ...[T]he answer would seem to be, only if you can create a region of the De Sitter space that is screened out from that horizon, screened out from that thermal nature. If you put a reflective barrier around the demon, you then have De Sitter space, but with the horizon screened out. ...[T]hat's a problem I'm working on now ..."

"Theory of Heat"

"Paul Davies"

"[T]he demon... is transferring heat from a colder region to a warmer region in apparent defiance of the second law of thermodynamics. "And hold on," you're thinking, "doesn't my refrigerator do that?" Sure... a refrigerator... costs energy to run... but the demon is operating using information instead... The demon... runs without any energy expenditure."

"So in effect, information serves as a fuel, and this leads to the whole concept of information engines. Engines that will run on information power, and... there is an FQXi initiative on this..."

"Information"

"Life was onto this... billions of years ago. Life uses many many nano-molecules which are, in effect, Maxwell demons. Our bodies are full of little Maxwell demons... doing the business of life. These little molecular machines are not quite perfect... but they're coming pretty close to the theoretical limit, in terms of energy expenditure."

"Thermodynamics"

"But if we conceive of a being whose faculties are so sharpened that he can follow every molecule in its course, such a being, whose attributes are as essentially finite as our own, would be able to do what is impossible to us. For we have seen that molecules in a vessel full of air at uniform temperature are moving with velocities by no means uniform, though the mean velocity of any great number of them, arbitrarily selected, is almost exactly uniform."

"Now let us suppose that such a vessel is divided into two portions, A and B, by a division in which there is a small hole, and that a being, who can see the individual molecules, opens and closes this hole, so as to allow only the swifter molecules to pass from A to B, and only the slower molecules to pass from B to A. He will thus, without expenditure of work, raise the temperature of B and lower that of A, in contradiction to the second law of thermodynamics."

"[T]he Diffusion of Heat ...invariably transfers heat from a hotter body to a colder one, so as to cool the hotter body and warm the colder... This process would go on till all bodies were brought to the same temperature if it were not for certain other processes..."

"One of the best established facts in thermodynamics is that it is impossible in a system enclosed in an envelope which permits neither change of volume nor passage of heat, and in which both the temperature and the pressure are every where the same, to produce any inequality of temperature or of pressure without the expenditure of work. This is the second law of thermodynamics, and it is undoubtedly true as long as we can deal with bodies only in mass, and have no power of perceiving or handling the separate molecules of which they are made up."

"[[Information theory|[I]nformation.]].. does enter into physics and has been in physics for a long time, in the most obvious way with ... [which] is able to use information about the motions of molecules to operate a shutter mechanism and put all the fast-moving ones on the left and the slow-moving ones on the right, thus establishing a temperature difference from which work can be extracted. You can run a heat engine, lift a weight [etc.]"

"s are the way in which, even now, you are thinking and paying attention, because the signals that travel between neurons, down the s, are controlled by the flow of s across the membranes of the axons... [T]hey are, in effect, little demons that sense the incoming signal and open and close the gates; and the ions flow. ...[T]his is so incredibly energy efficient that ...your brain, which is like a megawatt supercomputer, operates with the energy equivalent of a small light bulb."

"Information theory"

"It was... just a Gedanken-Experiment... in 1867, but just in recent years, engineers (nanotechnologists) have built real Maxwell demons, and this is now something of a cottage industry."

"James Clerk Maxwell"

"An electronic semiconductor is typically a valence crystal whose conductivity depends markedly on temperature and on the presence of minute amounts of foreign impurities. The ideal crystal at the absolute zero is an insulator. When the valence bonds are completely occupied and there are no extra electrons in the crystal, there is no possibility for current to flow. Charges can be transferred only when imperfections are present in the electronic structure, and these can be of two types: excess electrons which do not fit into the valence bonds and can move through the crystal, and holes, places from which electrons are missing in the bonds, which also behave as mobile carriers. While the excess electrons have the normal negative electronic charge -e, holes have a positive charge, +e. It is a case of two negatives making a positive ; a missing negative charge is a positive defect in the electron structure. The bulk of a semiconductor is electrically neutral; there are as many positive charges as negative. In an intrinsic semiconductor, in which current carriers are created by thermal excitation, there are approximately equal numbers of excess electrons and holes. Conductivity in an extrinsic semiconductor results from impurity ions in the lattice. In n-type material, the negative charge of the excess electrons is balanced by a net positive space charge of impurity ions. In p-type, the positive charge of the holes is balanced by negatively charged impurities. Foreign atoms which can become positively charged on introduction to the lattice are called donors; atoms which become negatively ionized are called acceptors. Thus donors make a semiconductor n-type, acceptors p-type. When both donors and acceptors are present, the conductivity type depends on which is in excess. Mobile carriers then balance the net space charge of the impurity ions."

"One of the remarkable and dramatic developments in recent years has been the application of solid state science to technical developments in electrical devices such as transistors. The study of semiconductors led to the discovery of their useful properties and to a large number of practical applications. ... The semiconductor substances in most common use today are silicon and germanium. These elements crystallize in the diamond lattice, a kind of cubic structure in which the atoms have tetrahedral bonding with their four nearest neighbors. They are insulators at very low temperatures—near absolute zero—although they do conduct electricity somewhat at room temperature. ... somehow put an extra electron into a crystal of silicon or germanium which is at a low temperature ... The electron will be able to wander around in the crystal jumping from one atomic site to the next. Actually, we have looked only at the behavior of electrons in a rectangular lattice, and the equations would be somewhat different for the real lattice of silicon or germanium. All of the essential points are, however, illustrated by the results for the rectangular lattice."

"A consequence of the discovery of electricity was the observation that metals are good conductors while nonmetals are poor conductors. The latter were called insulators. Metallic onductivity is typically between 106 and 104 (Ω cm)–1, while typical insulators have conductivities of less than 10–10 (Ω cm)–1. Some solids with conductivities between 104 and 10–10 (Ω cm)–1 are classified as semiconductors. ... semiconductors have an energy gap while semimetals and metals have no such gap. However, very impure semiconductors show a more or less metallic behavior and with many substances, the art of purification is not so far advanced that a distinction can easily be made. The transition between semiconductors and insulators is even more gradual and depends on the ratio of the energy gap to the temperature of investigation. Very pure semiconductors may become insulators when the temperature approaches the absolute zero."

"When I began life as a particle physicist fifty years ago, most of the major discoveries were made in Europe by people studying the cosmic rays that bombard the earth from outer space. Particle physics was done by observing the debris produced by cosmic rays as they pass through the atmosphere and the experimental apparatus. The debris consists of particles with short lifetimes and unfamiliar names. ... Three young Italians, Conversi, Pancini, and Piccioni, working with home-made particle counters in the chaos of postwar Italy, discovered that the common cosmic ray particle, later called the muon, had only weak interactions with matter. Cecil Powell, working with microscopes and photographic plates at Bristol in England, discovered the strongly interacting cosmic ray particle, which he called the pion. Other strange new particles were discovered by Rochester and Butler using old-fashioned cosmic ray cloud-chambers in Manchester."

"Why does the atmosphere have conductivity? Here and there among the air molecules there is an ion—a molecule of oxygen, say, which has acquired an extra electron, or perhaps lost one. These ions do not stay as single molecules; because of their electric field they usually accumulate a few other molecules around them. Each ion then becomes a little lump which, along with other lumps, drifts in the field—moving slowly upward or downward—making the observed current. Where do the ions come from? It was first guessed that the ions were produced by the radioactivity of the earth. (It was known that the radiation from radioactive materials would make air conducting by ionizing the air molecules.) Particles like β-rays coming out of the atomic nuclei are moving so fast that they tear electrons from the atoms, leaving ions behind. This would imply, of course, that if we were to go to higher altitudes, we should find less ionization, because the radioactivity is all in the dirt on the ground—in the traces of radium, uranium, potassium, etc. ... To test this theory, some physicists carried an experiment up in balloons to measure the ionization of the air (Hess, in 1912) and discovered that the opposite was true—the ionization per unit volume increased with altitude! ... This was a most mysterious result—the most dramatic finding in the entire history of atmospheric electricity. It was so dramatic, in fact, that it required a branching off of an entirely new subject—cosmic rays."

"If one begins by considering a kind of state or condition for Bose particles which do not interact with each other (we have assumed that the photons do not interact with each other), and then considers that into this state there can be put either zero, or one, or two, ... up to any number n of particles, one finds that this system behaves for all quantum mechanical purposes exactly like a harmonic oscillator. By such an oscillator we mean a dynamic system like a weight on a spring or a standing wave in a resonant cavity. And that is why it is possible to represent the electromagnetic field by photon particles. From one point of view, we can analyze the electromagnetic field in a box or cavity in terms of a lot of harmonic oscillators, treating each mode of oscillation according to quantum mechanics as a harmonic oscillator. From a different point of view, we can analyze the same physics in terms of identical Bose particles. And the results of both ways of working are always in exact agreement. There is no way to make up your mind whether the electromagnetic field is really to be described as a quantized harmonic oscillator or by giving how many photons there are in each condition. The two views turn out to be mathematically identical. So in the future we can speak either about the number of photons in a particular state in a box or the number of the energy level associated with a particular mode of oscillation of the electromagnetic field. They are two ways of saying the same thing. The same is true of photons in free space. They are equivalent to oscillations of a cavity whose walls have receded to infinity."

"The Universe is in fact observed not only through the different windows of the electromagnetic spectrum, but also through other cosmic messengers, i.e. through cosmic rays (CRs), neutrinos and gravitational waves (GWs). In general, gamma rays are the perfect companions for multi-messenger astronomy ... gamma-ray production is intimately related to the production of CRs. The latter are charged particles, mainly protons, whose energy spectrum covers a very wide range in energy and flux. Many questions regarding CRs are still open, especially looking at the most energetic ones above 1015 eV (1 PeV). The CR spectrum is approximately described by a power law: dN/dE ∼ E−Γ , where Γ is the spectral index. Γ is not constant, indicating a change in the properties of CRs, like their acceleration sites and chemical composition. For energies around ∼ 4 × 1015 eV, the flux starts to decrease more steeply: Γ changes from about 2.7 to about 3. This feature, marked with the term knee, is thought to indicate the maximum acceleration energy of Galactic sources ..."

"Many of the mechanical elements constituting a musical instrument behave approximately as linear systems. By this we mean that the acoustic output is a linear function of the mechanical input, so that the output obtained from two inputs applied simultaneousl is just the sum of the outputs that would be obtained if they were applied separately. For this statement to be true for the instrument as a whole, it must also be true for all of its parts, so that deflections must be proportional to applied forces, flows to applied pressures, and so on. Mathematically, this property is reflected in the requirement that the differential equations describing the behavior of the system are also linear, in the sense that the dependent variable occurs only to the first power. An example is the equation for the displacement y of a simple harmonic oscillator under the action of an applied force F(t): m \frac{\mathrm{d}^2y}{\mathrm{d}t^2} + R\frac{\mathrm{d}y}{\mathrm{d}t} + Ky = F(t), ... where m, R, and K are, respectively, the mass, damping coefficeint, and spring coefficent, all of which are taken to be constants. ... A little consideration shows, of course, that this description must be an over-simplification ..."

"The simple mechanical system of the classical harmonic oscillator underlies important areas of modern physiccal theory. ... The concept of degeneracy arises in the two-dimensional oscillation of a square plate or diaphragm. Three-dimensional harmonic oscillation relates to oscillatory modes in the Rayleigh-Jeans equation ... Vibration of a macroscopic three-dimensional crystal is treated by Debye's theory ... Harmonic oscillator theory is important when it succeeds and also when if fails, as we shall see in the motivation to find a theory of radiation that we now call the quantum theory ..."

"As the concept of a phonon originates from relative motion of the atoms, rather than the motion of their centre of mass, a phonon in a crystal does not carry a momentum. However, for practical purposes we assign a momentum \hbarq to a phonon in the qth mode. For this reason a phonon is called a quasi-particle."

"That electron-phonon interactions lead to an effective attractive interaction between electrons by exchange of virtual photons was shown by Fröhlich by use of field-theoretic methods. His analysis was extended by Pines and myself to include Coulomb interactions. In second order, there is an effective interaction between the quasi-particle excitations of the normal state which is the sum of the attractive phonon-induced interaction and a screened Coulomb interaction. In the Handbuch article, I suggested that one should take the complete interaction, not just the self-energy tens, and use it for a theory of superconductivity."