Spacetime algebra as a powerful tool for electromagnetism
... For the rest of my life I will reflect on what light is. ...
... For the rest of my life I will reflect on what light is. ...
Lecture Notes on General Relativity
... including all necessary steps or leaving gaps that can readily be filled in by the reader. Nevertheless, there are various ways in which these notes differ from a textbook; most importantly, they are not organized into short sections that can be approached in various orders, but are meant to be gone ...
... including all necessary steps or leaving gaps that can readily be filled in by the reader. Nevertheless, there are various ways in which these notes differ from a textbook; most importantly, they are not organized into short sections that can be approached in various orders, but are meant to be gone ...
Lecture Notes on General Relativity
... including all necessary steps or leaving gaps that can readily be filled in by the reader. Nevertheless, there are various ways in which these notes differ from a textbook; most importantly, they are not organized into short sections that can be approached in various orders, but are meant to be gone ...
... including all necessary steps or leaving gaps that can readily be filled in by the reader. Nevertheless, there are various ways in which these notes differ from a textbook; most importantly, they are not organized into short sections that can be approached in various orders, but are meant to be gone ...
Entanglement and the black hole information paradox
... bit older than 100 years. It is safe to say that quantum mechanics has had a radical effect on physics and how we see the world. By introducing the wave-particle duality, Heisenberg’s uncertainty principle and the fundamentally probabilistic nature of physics quantum mechanics has in some ways made ...
... bit older than 100 years. It is safe to say that quantum mechanics has had a radical effect on physics and how we see the world. By introducing the wave-particle duality, Heisenberg’s uncertainty principle and the fundamentally probabilistic nature of physics quantum mechanics has in some ways made ...
Relativity
... – Another thing which becomes relative is the mass of a body. – The greater the speed of a body (i.e., the greater the speed of its frame of reference is compared to another frame of reference), the larger will its mass be. – The mass of a body is a measure of its energy ...
... – Another thing which becomes relative is the mass of a body. – The greater the speed of a body (i.e., the greater the speed of its frame of reference is compared to another frame of reference), the larger will its mass be. – The mass of a body is a measure of its energy ...
7. Low Energy Effective Actions
... Here gαβ is again the worldsheet metric. This action describes a map from the worldsheet of the string into a spacetime with metric Gµν (X). (Despite its name, this metric is not to be confused with the Einstein tensor which we won’t have need for in this lecture notes). Actions of the form (7.1) ar ...
... Here gαβ is again the worldsheet metric. This action describes a map from the worldsheet of the string into a spacetime with metric Gµν (X). (Despite its name, this metric is not to be confused with the Einstein tensor which we won’t have need for in this lecture notes). Actions of the form (7.1) ar ...
A New Topological Perspective on Quantization in Physics
... second, we address the question of physical interpretation of this mathematical formalism, and how it relates to certain themes in mainstream quantum mechanics, in the next section. The fundamental idea driving the discussion is that, with (2.14), for instance, as a paradigm, there should be availab ...
... second, we address the question of physical interpretation of this mathematical formalism, and how it relates to certain themes in mainstream quantum mechanics, in the next section. The fundamental idea driving the discussion is that, with (2.14), for instance, as a paradigm, there should be availab ...
lectures 2014
... cancel before the last line. An exception to this rule arises where some terms are dimensionless factors which are simple fractions. 4. Check the dimensions Think about the dimensions of every quantity even as you write it down. You will find this a discipline which helps enormously to avoid errors ...
... cancel before the last line. An exception to this rule arises where some terms are dimensionless factors which are simple fractions. 4. Check the dimensions Think about the dimensions of every quantity even as you write it down. You will find this a discipline which helps enormously to avoid errors ...
CLASSICAL FIELDS - Instituto de Física Teórica
... always inspired by the notation, to write t = x0 for the first component, but there is a problem: all components in a column-vector should have the same dimension, which is not the case here. To get dimensional uniformity, it would be necessary to multiply t by some velocity. In Classical Physics, a ...
... always inspired by the notation, to write t = x0 for the first component, but there is a problem: all components in a column-vector should have the same dimension, which is not the case here. To get dimensional uniformity, it would be necessary to multiply t by some velocity. In Classical Physics, a ...
Course notes
... As we start this study of Particles and Symmetries it is appropriate to begin with a description of the overall goal of the course, which is to provide an introduction to an area of physics that has seen dramatic progress in the last 50 years — elementary particle physics. A central tool underlying ...
... As we start this study of Particles and Symmetries it is appropriate to begin with a description of the overall goal of the course, which is to provide an introduction to an area of physics that has seen dramatic progress in the last 50 years — elementary particle physics. A central tool underlying ...
Weak-Field General Relativity Compared with
... which for the three space coordinates is just the usual gravitational field. Allowing the potentials to vary with time yet still satisfying the Einstein equation, we arrive at the restriction that the zero component of the field f must be constant for all space and time. We use linearized versions o ...
... which for the three space coordinates is just the usual gravitational field. Allowing the potentials to vary with time yet still satisfying the Einstein equation, we arrive at the restriction that the zero component of the field f must be constant for all space and time. We use linearized versions o ...
Generalized Curvilinear Coordinates in Hybrid and Electromagnetic Codes Daniel W. Swift
... Earth. Yet processes driving field-aligned currents near the Earth take place many Earth Radii out in space, where it would be computationally expensive to maintain that resolution. Also, one might want a relatively high degree of spatial resolution across the plasma sheet and in the region of the b ...
... Earth. Yet processes driving field-aligned currents near the Earth take place many Earth Radii out in space, where it would be computationally expensive to maintain that resolution. Also, one might want a relatively high degree of spatial resolution across the plasma sheet and in the region of the b ...
Against Dogma: On Superluminal Propagation in Classical
... not clear how the constraints on the behavior of fields at infinity required for Fourier analysis are physically motivated, particularly in the source-free case. (If one assumes all fields are generated by localized sources, one might argue that fields should vanish at infinite distance from the sou ...
... not clear how the constraints on the behavior of fields at infinity required for Fourier analysis are physically motivated, particularly in the source-free case. (If one assumes all fields are generated by localized sources, one might argue that fields should vanish at infinite distance from the sou ...
lectures 2015
... have a strong notion that time and space are absolute quantities. We think that we can define a point in ‘absolute’ space and ‘absolute’ time, and that space and time are the same for everyone, no matter how they are moving with respect to each other. These ideas obviously work very well in everyday ...
... have a strong notion that time and space are absolute quantities. We think that we can define a point in ‘absolute’ space and ‘absolute’ time, and that space and time are the same for everyone, no matter how they are moving with respect to each other. These ideas obviously work very well in everyday ...
Tensorial spacetime geometries and background
... backgrounds, one would of course expect the new particle physics and gravitational physics to arise at the same time: On the one hand, the restriction to Lorentzian spacetimes also severely restricts the type of matter fields that can be considered [48], and this restriction is strongly used in part ...
... backgrounds, one would of course expect the new particle physics and gravitational physics to arise at the same time: On the one hand, the restriction to Lorentzian spacetimes also severely restricts the type of matter fields that can be considered [48], and this restriction is strongly used in part ...
PDF - at www.arxiv.org.
... regarding the Lorentz transformations. This lead us to a covariant theory of gravitation in a flat spacetime [4]. This theory also holds in a flat space but a curved time when the speed dependence of the gravitational force is taken into account. This covariance requirement implies that gravitomagne ...
... regarding the Lorentz transformations. This lead us to a covariant theory of gravitation in a flat spacetime [4]. This theory also holds in a flat space but a curved time when the speed dependence of the gravitational force is taken into account. This covariance requirement implies that gravitomagne ...
Chapter 8 Gravitational Attraction and Unification of Forces
... In chapter 5 we imagined a hypothetical perfect clock placed at a point on the “Compton circle” of a rotar as illustrated in figure 5‐1. This is the imaginary circle with radius equal to the rotar radius . This clock hereafter called the “dipole clock” with time τd was compared to the time o ...
... In chapter 5 we imagined a hypothetical perfect clock placed at a point on the “Compton circle” of a rotar as illustrated in figure 5‐1. This is the imaginary circle with radius equal to the rotar radius . This clock hereafter called the “dipole clock” with time τd was compared to the time o ...
An introduction to the mechanics of black holes
... the behavior of solutions of hyperbolic PDE’s outside D + (Σ) is not determined by initial data on Σ. If no causal curves have past end-points, then the behavior of solutions inside D + (Σ) is entirely determined in terms of data on Σ. The past domain of dependence D − (Σ) is defined similarly. A Ca ...
... the behavior of solutions of hyperbolic PDE’s outside D + (Σ) is not determined by initial data on Σ. If no causal curves have past end-points, then the behavior of solutions inside D + (Σ) is entirely determined in terms of data on Σ. The past domain of dependence D − (Σ) is defined similarly. A Ca ...
Maxwell`s Equations in Terms of Differential Forms
... Maxwell’s equations have been generalized to other areas of physical interest. Our picture of the standard model consists of three forces: electromagnetism and the weak and strong nuclear forces are all gauge fields (invariant under gauge transformations), which means that they are described by equa ...
... Maxwell’s equations have been generalized to other areas of physical interest. Our picture of the standard model consists of three forces: electromagnetism and the weak and strong nuclear forces are all gauge fields (invariant under gauge transformations), which means that they are described by equa ...
Abraham-Solution to Schwarzschild Metric Implies
... even more extensive than the one soon to be launched – because as a first step a far-out spaceplatform would need to be built. This would at least double the cost compared to the earthbased endeavor. No matter how defective, however, the above theory is currently about to be tested on earth: near th ...
... even more extensive than the one soon to be launched – because as a first step a far-out spaceplatform would need to be built. This would at least double the cost compared to the earthbased endeavor. No matter how defective, however, the above theory is currently about to be tested on earth: near th ...
Relativity without tears - Philsci
... Group theory provides another argument to prefer the Lorentzian world over the Galilean one [46] because mathematically the Lorentz group G c has much simpler and elegant structure than its singular limit G ∞ which is the symmetry group of the Galilean world. This argument goes back to Minkowski. In ...
... Group theory provides another argument to prefer the Lorentzian world over the Galilean one [46] because mathematically the Lorentz group G c has much simpler and elegant structure than its singular limit G ∞ which is the symmetry group of the Galilean world. This argument goes back to Minkowski. In ...
7 The Schwarzschild Solution and Black Holes
... Newtonian mass that we would measure by studying orbits at large distances from the gravitating source. Note that as M → 0 we recover Minkowski space, which is to be expected. Note also that the metric becomes progressively Minkowskian as we go to r → ∞; this property is known as asymptotic flatness ...
... Newtonian mass that we would measure by studying orbits at large distances from the gravitating source. Note that as M → 0 we recover Minkowski space, which is to be expected. Note also that the metric becomes progressively Minkowskian as we go to r → ∞; this property is known as asymptotic flatness ...
Supplemental Lecture II: Special Relativity in Tensor Notation
... we call a quantity a vector; this material should be familiar, but the concepts involved will come in handy when trying to understand what we mean by a four-vector. Given three-dimensional Euclidean space, we can define a coordinate system, known as Cartesian coordinates, involving three mutually-pe ...
... we call a quantity a vector; this material should be familiar, but the concepts involved will come in handy when trying to understand what we mean by a four-vector. Given three-dimensional Euclidean space, we can define a coordinate system, known as Cartesian coordinates, involving three mutually-pe ...
Time, what is it? Dynamical Properties of Time
... coordinate of some event in one inertial reference frame is expressed in terms of the temporal and spatial coordinates of this event in the other. Such an entanglement of coordinates indicates that time, as well as space, becomes a direct participant of physical processes. The idea about the existen ...
... coordinate of some event in one inertial reference frame is expressed in terms of the temporal and spatial coordinates of this event in the other. Such an entanglement of coordinates indicates that time, as well as space, becomes a direct participant of physical processes. The idea about the existen ...
Relativity Presentation
... mass and gravity, relative motion, waves and light, nature of space and time, electromagnetism. ...
... mass and gravity, relative motion, waves and light, nature of space and time, electromagnetism. ...