Electromagnetism: The simplest gauge theory.
... This guarantees that dF = 0, which is equivalent to the homogeneous Maxwell equations Fαβ,γ + Fβγ,α + Fγα,β = 0. Thus the only remaining Maxwell equations to be considered are F αβ ,β = 4πj α . The 6 independent components of F in an inertial Cartesian coordinate chart (t, x, y, z) define the electr ...
... This guarantees that dF = 0, which is equivalent to the homogeneous Maxwell equations Fαβ,γ + Fβγ,α + Fγα,β = 0. Thus the only remaining Maxwell equations to be considered are F αβ ,β = 4πj α . The 6 independent components of F in an inertial Cartesian coordinate chart (t, x, y, z) define the electr ...
IOSR Journal of Applied Physics (IOSR-JAP) e-ISSN: 2278-4861. www.iosrjournals.org
... action. Just like the Lagrangian density is used to describe many physical principles so does the action principle in a quite different way. It is present in general relativity as the Einstein – Hilbert action, in string theory and many other theoretical principles of physics. The difficulty with th ...
... action. Just like the Lagrangian density is used to describe many physical principles so does the action principle in a quite different way. It is present in general relativity as the Einstein – Hilbert action, in string theory and many other theoretical principles of physics. The difficulty with th ...
General relativity and Its applications - UoN Repository
... reference frames of classical mechanics, objects in free motion move along straight lines at constant speed. In modern parlance, their paths are geodesics, straight world lines in curved spacetime. ...
... reference frames of classical mechanics, objects in free motion move along straight lines at constant speed. In modern parlance, their paths are geodesics, straight world lines in curved spacetime. ...
Changing Coordinate Systems
... getting around them. One idea might be to generalize Newton’s laws. Maybe there is a more general law, which takes into account all possible types of frames, and the form of this equation always stays true, no matter what. The other idea is that perhaps if empty space seems to care about acceleratio ...
... getting around them. One idea might be to generalize Newton’s laws. Maybe there is a more general law, which takes into account all possible types of frames, and the form of this equation always stays true, no matter what. The other idea is that perhaps if empty space seems to care about acceleratio ...
Canonical Quantum Gravity as a Gauge Theory with Constraints
... Thusly, our theory will be formulated most naturally in terms of a gauge theory, a class of field theories that are in some ways generalizations of Maxwell’s electrodynamics. Taking the place of the matter fields in this gauge theory will be the “field of frames” eI , or, a choice of four arrows at ...
... Thusly, our theory will be formulated most naturally in terms of a gauge theory, a class of field theories that are in some ways generalizations of Maxwell’s electrodynamics. Taking the place of the matter fields in this gauge theory will be the “field of frames” eI , or, a choice of four arrows at ...
Applications of Clifford Algebras in Physics
... specified angles, one can avoid degeneracies in the Euler-angle decomposition. The simple rotor expression allows smooth rotations in a single plane and thus interpolations between arbitrary orientations. Exercise 14 Show that the magnitude of Θ in the rotor R = exp (Θ) is the area swept out by any ...
... specified angles, one can avoid degeneracies in the Euler-angle decomposition. The simple rotor expression allows smooth rotations in a single plane and thus interpolations between arbitrary orientations. Exercise 14 Show that the magnitude of Θ in the rotor R = exp (Θ) is the area swept out by any ...
Radiation from a Uniformly Accelerated Charge and the
... the flow (3). This curve is also the worldline of a uniformly accelerated particle with proper acceleration 1/X. The set of all such curves for all X, y, z may be regarded as the worldlines of a collection of uniformly accelerated observers all of whom are at rest in the Minkowski frame at time t = ...
... the flow (3). This curve is also the worldline of a uniformly accelerated particle with proper acceleration 1/X. The set of all such curves for all X, y, z may be regarded as the worldlines of a collection of uniformly accelerated observers all of whom are at rest in the Minkowski frame at time t = ...
INTRODUCTION TO THE THEORY OF BLACK HOLES∗
... Now, we know that such simple considerations are misleading. To understand what happens with such extremely heavy objects, one has to consider Einstein’s theory of relativity, both Special Relativity and General Relativity, the theory that describes the gravitational field when velocities are genera ...
... Now, we know that such simple considerations are misleading. To understand what happens with such extremely heavy objects, one has to consider Einstein’s theory of relativity, both Special Relativity and General Relativity, the theory that describes the gravitational field when velocities are genera ...
The Age of Einstein
... 4. EINSTEIN’S THEORY OF SPECIAL RELATIVITY In 1905, Einstein published three great papers in unrelated areas of Physics. In this chapter, we shall discuss his new ideas concerning the relative motion of beams of light, and of objects that move at speeds close to that of light. His independent invest ...
... 4. EINSTEIN’S THEORY OF SPECIAL RELATIVITY In 1905, Einstein published three great papers in unrelated areas of Physics. In this chapter, we shall discuss his new ideas concerning the relative motion of beams of light, and of objects that move at speeds close to that of light. His independent invest ...
Wormholes and nontrivial topology.
... • GR by itself does not seem to place particularly strong constraints on topology. • Nevertheless we have not directly observed any nontrivial topology. • Maybe, to get an accurate representation of empirical reality, we should be using Einstein equations plus some extra conditions? – Prior geometry ...
... • GR by itself does not seem to place particularly strong constraints on topology. • Nevertheless we have not directly observed any nontrivial topology. • Maybe, to get an accurate representation of empirical reality, we should be using Einstein equations plus some extra conditions? – Prior geometry ...
pages 401-450 - Light and Matter
... a little later. Although this scenario is fanciful, it shows a real feature of Newton’s laws: that information can be transmitted from one place in the universe to another with zero time delay, so that transmission and reception occur at exactly the same instant. Newton was sharp enough to realize t ...
... a little later. Although this scenario is fanciful, it shows a real feature of Newton’s laws: that information can be transmitted from one place in the universe to another with zero time delay, so that transmission and reception occur at exactly the same instant. Newton was sharp enough to realize t ...
Appendix B: On inertial forces, inertial energy
... lengths. It is obvious that these cross-sections of the worldtube of the same three-dimensional body would be impossible if its worldtube were not real, i.e. if it were a mere geometrical abstraction [1] (see also [4, Chap. 5], [5]). In fact, the reality of the worldtubes of physical objects and the ...
... lengths. It is obvious that these cross-sections of the worldtube of the same three-dimensional body would be impossible if its worldtube were not real, i.e. if it were a mere geometrical abstraction [1] (see also [4, Chap. 5], [5]). In fact, the reality of the worldtubes of physical objects and the ...
Entropic origin of the fundamental forces
... Verlinde obtained the Newton’s law of motion and the gravitational field equations in the framework of entropic origination and it could motivate Freund to ask whether the electromagnetic force and the other fundamental forces can be described as a force having an entropic origin [8]. He could quali ...
... Verlinde obtained the Newton’s law of motion and the gravitational field equations in the framework of entropic origination and it could motivate Freund to ask whether the electromagnetic force and the other fundamental forces can be described as a force having an entropic origin [8]. He could quali ...
Chapter 3: Relativistic dynamics
... the tangent vector u has a constant square, u2 = −c2 . So you can think of u/c as a tangent vector which has unit “length” everywhere along the worldline. The fact that u2 is negative shows that the 4-velocity is always a timelike vector. Having picked a specific reference frame in which to evaluate ...
... the tangent vector u has a constant square, u2 = −c2 . So you can think of u/c as a tangent vector which has unit “length” everywhere along the worldline. The fact that u2 is negative shows that the 4-velocity is always a timelike vector. Having picked a specific reference frame in which to evaluate ...
5. Electromagnetism and Relativity
... All the four-vectors that we’ve met so far have upper indices. But all can be lowered in the same way. For example, we have Uµ = γ ...
... All the four-vectors that we’ve met so far have upper indices. But all can be lowered in the same way. For example, we have Uµ = γ ...
Maxwell and Special Relativity - Physics Department, Princeton
... where the constants 0 and μ0 can be determined in any (inertial) frame via electrostatic and magnetostatic experiments (nominally in vacuum).3 Even in æther theories, the velocity of the laboratory with respect to the hypothetical æther should not affect the results of these static experiments,4 so ...
... where the constants 0 and μ0 can be determined in any (inertial) frame via electrostatic and magnetostatic experiments (nominally in vacuum).3 Even in æther theories, the velocity of the laboratory with respect to the hypothetical æther should not affect the results of these static experiments,4 so ...
Relations Between Physical Constants
... A coincidence group of points, drawing elements of the set of images of the object A, is a finite symmetric system, which can be considered as a topological spread mapped into the spherical space Rn . The surface of an (n + 1)dimensional sphere, being equivalent to the volume of an n-dimensional tor ...
... A coincidence group of points, drawing elements of the set of images of the object A, is a finite symmetric system, which can be considered as a topological spread mapped into the spherical space Rn . The surface of an (n + 1)dimensional sphere, being equivalent to the volume of an n-dimensional tor ...
The Geometry of Forces Along Equidistant Particle Paths
... a two dimensional space with constant sectional curvature. It is well known that geodesics in positively curved space will tend to converge. On the other hand, particles traveling along geodesic paths in negatively curved space will tend to diverge. Even though we will restrict our attention to part ...
... a two dimensional space with constant sectional curvature. It is well known that geodesics in positively curved space will tend to converge. On the other hand, particles traveling along geodesic paths in negatively curved space will tend to diverge. Even though we will restrict our attention to part ...
Need for the General Theory
... etc. It can be shown that, in the absence of matter, Maxwell's equations combine to give a wave equation, describing electromagnetic waves, the velocity of such waves being given by the formula c ( o o )1/ 2 .When numerical values are inserted, the result is c = 2.998 x108 m s-1, the same as t ...
... etc. It can be shown that, in the absence of matter, Maxwell's equations combine to give a wave equation, describing electromagnetic waves, the velocity of such waves being given by the formula c ( o o )1/ 2 .When numerical values are inserted, the result is c = 2.998 x108 m s-1, the same as t ...
Fall 2003 Digression: on the constancy of c.
... flowing. It is not valid to talk about a separate “magnetic” force. You must talk about the “electromagnetic” force. ...
... flowing. It is not valid to talk about a separate “magnetic” force. You must talk about the “electromagnetic” force. ...
On inertial forces, inertial energy and the origin
... at different angles and the two resulting three-dimensional cross-sections have different lengths. It is obvious that these cross-sections of the worldtube of the same three-dimensional body would be impossible if its worldtube were not real, i.e. if it were a mere geometrical abstraction [1] (see als ...
... at different angles and the two resulting three-dimensional cross-sections have different lengths. It is obvious that these cross-sections of the worldtube of the same three-dimensional body would be impossible if its worldtube were not real, i.e. if it were a mere geometrical abstraction [1] (see als ...
General Relativity: An Informal Primer 1 Introduction
... one free index, ν, in the lower position; and so does the righthand side. Tensors of higher rank transform following the pattern of Eqs. (2.29) - (2.31), namely, mutliply by one factor of (∂x0µ /∂xα ) for every contravariant index, µ, and one factor of (∂xβ /∂x0ν ) for every covariant index, ν, and ...
... one free index, ν, in the lower position; and so does the righthand side. Tensors of higher rank transform following the pattern of Eqs. (2.29) - (2.31), namely, mutliply by one factor of (∂x0µ /∂xα ) for every contravariant index, µ, and one factor of (∂xβ /∂x0ν ) for every covariant index, ν, and ...
Exam 2013 with Answers File - QMplus
... Identify a frame S’ in which events O and A occur at the same place. What is the time between events O and A in this frame? Give the value of for the relative speed between S and S’ and state how the time interval of 13 in S is related to the time interval in S’. [On a Minkowski diagram, if they d ...
... Identify a frame S’ in which events O and A occur at the same place. What is the time between events O and A in this frame? Give the value of for the relative speed between S and S’ and state how the time interval of 13 in S is related to the time interval in S’. [On a Minkowski diagram, if they d ...