A Lagrangian Solution for the Precession of Mercury's Perihelion
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Relativity with a Preferred Frame. Astrophysical and Cosmological Implications Monday, 21 August 2017 15:30 (30 Minutes)
6th International Conference on New Frontiers in Physics (ICNFP2017) Contribution ID: 1095 Type: Talk Relativity with a preferred frame. Astrophysical and cosmological implications Monday, 21 August 2017 15:30 (30 minutes) The present analysis is motivated by the fact that, although the local Lorentz invariance is one of thecorner- stones of modern physics, cosmologically a preferred system of reference does exist. Modern cosmological models are based on the assumption that there exists a typical (privileged) Lorentz frame, in which the universe appear isotropic to “typical” freely falling observers. The discovery of the cosmic microwave background provided a stronger support to that assumption (it is tacitly assumed that the privileged frame, in which the universe appears isotropic, coincides with the CMB frame). The view, that there exists a preferred frame of reference, seems to unambiguously lead to the abolishmentof the basic principles of the special relativity theory: the principle of relativity and the principle of universality of the speed of light. Correspondingly, the modern versions of experimental tests of special relativity and the “test theories” of special relativity reject those principles and presume that a preferred inertial reference frame, identified with the CMB frame, is the only frame in which the two-way speed of light (the average speed from source to observer and back) is isotropic while it is anisotropic in relatively moving frames. In the present study, the existence of a preferred frame is incorporated into the framework of the special relativity, based on the relativity principle and universality of the (two-way) speed of light, at the expense of the freedom in assigning the one-way speeds of light that exists in special relativity. -
WUN2K for LECTURE 19 These Are Notes Summarizing the Main Concepts You Need to Understand and Be Able to Apply
Duke University Department of Physics Physics 361 Spring Term 2020 WUN2K FOR LECTURE 19 These are notes summarizing the main concepts you need to understand and be able to apply. • Newton's Laws are valid only in inertial reference frames. However, it is often possible to treat motion in noninertial reference frames, i.e., accelerating ones. • For a frame with rectilinear acceleration A~ with respect to an inertial one, we can write the equation of motion as m~r¨ = F~ − mA~, where F~ is the force in the inertial frame, and −mA~ is the inertial force. The inertial force is a “fictitious” force: it's a quantity that one adds to the equation of motion to make it look as if Newton's second law is valid in a noninertial reference frame. • For a rotating frame: Euler's theorem says that the most general mo- tion of any body with respect to an origin is rotation about some axis through the origin. We define an axis directionu ^, a rate of rotation dθ about that axis ! = dt , and an instantaneous angular velocity ~! = !u^, with direction given by the right hand rule (fingers curl in the direction of rotation, thumb in the direction of ~!.) We'll generally use ~! to refer to the angular velocity of a body, and Ω~ to refer to the angular velocity of a noninertial, rotating reference frame. • We have for the velocity of a point at ~r on the rotating body, ~v = ~! ×~r. ~ dQ~ dQ~ ~ • Generally, for vectors Q, one can write dt = dt + ~! × Q, for S0 S0 S an inertial reference frame and S a rotating reference frame. -
Frames of Reference
Galilean Relativity 1 m/s 3 m/s Q. What is the women velocity? A. With respect to whom? Frames of Reference: A frame of reference is a set of coordinates (for example x, y & z axes) with respect to whom any physical quantity can be determined. Inertial Frames of Reference: - The inertia of a body is the resistance of changing its state of motion. - Uniformly moving reference frames (e.g. those considered at 'rest' or moving with constant velocity in a straight line) are called inertial reference frames. - Special relativity deals only with physics viewed from inertial reference frames. - If we can neglect the effect of the earth’s rotations, a frame of reference fixed in the earth is an inertial reference frame. Galilean Coordinate Transformations: For simplicity: - Let coordinates in both references equal at (t = 0 ). - Use Cartesian coordinate systems. t1 = t2 = 0 t1 = t2 At ( t1 = t2 ) Galilean Coordinate Transformations are: x2= x 1 − vt 1 x1= x 2+ vt 2 or y2= y 1 y1= y 2 z2= z 1 z1= z 2 Recall v is constant, differentiation of above equations gives Galilean velocity Transformations: dx dx dx dx 2 =1 − v 1 =2 − v dt 2 dt 1 dt 1 dt 2 dy dy dy dy 2 = 1 1 = 2 dt dt dt dt 2 1 1 2 dz dz dz dz 2 = 1 1 = 2 and dt2 dt 1 dt 1 dt 2 or v x1= v x 2 + v v x2 =v x1 − v and Similarly, Galilean acceleration Transformations: a2= a 1 Physics before Relativity Classical physics was developed between about 1650 and 1900 based on: * Idealized mechanical models that can be subjected to mathematical analysis and tested against observation. -
Classical Mechanics - Wikipedia, the Free Encyclopedia Page 1 of 13
Classical mechanics - Wikipedia, the free encyclopedia Page 1 of 13 Classical mechanics From Wikipedia, the free encyclopedia (Redirected from Newtonian mechanics) In physics, classical mechanics is one of the two major Classical mechanics sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the Newton's Second Law action of a system of forces. The study of the motion of bodies is an ancient one, making classical mechanics one of History of classical mechanics · the oldest and largest subjects in science, engineering and Timeline of classical mechanics technology. Branches Classical mechanics describes the motion of macroscopic Statics · Dynamics / Kinetics · Kinematics · objects, from projectiles to parts of machinery, as well as Applied mechanics · Celestial mechanics · astronomical objects, such as spacecraft, planets, stars, and Continuum mechanics · galaxies. Besides this, many specializations within the Statistical mechanics subject deal with gases, liquids, solids, and other specific sub-topics. Classical mechanics provides extremely Formulations accurate results as long as the domain of study is restricted Newtonian mechanics (Vectorial to large objects and the speeds involved do not approach mechanics) the speed of light. When the objects being dealt with become sufficiently small, it becomes necessary to Analytical mechanics: introduce the other major sub-field of mechanics, quantum Lagrangian mechanics mechanics, which reconciles the macroscopic laws of Hamiltonian mechanics physics with the atomic nature of matter and handles the Fundamental concepts wave-particle duality of atoms and molecules. In the case of high velocity objects approaching the speed of light, Space · Time · Velocity · Speed · Mass · classical mechanics is enhanced by special relativity. -
The Experimental Verdict on Spacetime from Gravity Probe B
The Experimental Verdict on Spacetime from Gravity Probe B James Overduin Abstract Concepts of space and time have been closely connected with matter since the time of the ancient Greeks. The history of these ideas is briefly reviewed, focusing on the debate between “absolute” and “relational” views of space and time and their influence on Einstein’s theory of general relativity, as formulated in the language of four-dimensional spacetime by Minkowski in 1908. After a brief detour through Minkowski’s modern-day legacy in higher dimensions, an overview is given of the current experimental status of general relativity. Gravity Probe B is the first test of this theory to focus on spin, and the first to produce direct and unambiguous detections of the geodetic effect (warped spacetime tugs on a spin- ning gyroscope) and the frame-dragging effect (the spinning earth pulls spacetime around with it). These effects have important implications for astrophysics, cosmol- ogy and the origin of inertia. Philosophically, they might also be viewed as tests of the propositions that spacetime acts on matter (geodetic effect) and that matter acts back on spacetime (frame-dragging effect). 1 Space and Time Before Minkowski The Stoic philosopher Zeno of Elea, author of Zeno’s paradoxes (c. 490-430 BCE), is said to have held that space and time were unreal since they could neither act nor be acted upon by matter [1]. This is perhaps the earliest version of the relational view of space and time, a view whose philosophical fortunes have waxed and waned with the centuries, but which has exercised enormous influence on physics. -
Rotating Reference Frame Control of Switched Reluctance
ROTATING REFERENCE FRAME CONTROL OF SWITCHED RELUCTANCE MACHINES A Thesis Presented to The Graduate Faculty of The University of Akron In Partial Fulfillment of the Requirements for the Degree Master of Science Tausif Husain August, 2013 ROTATING REFERENCE FRAME CONTROL OF SWITCHED RELUCTANCE MACHINES Tausif Husain Thesis Approved: Accepted: _____________________________ _____________________________ Advisor Department Chair Dr. Yilmaz Sozer Dr. J. Alexis De Abreu Garcia _____________________________ _____________________________ Committee Member Dean of the College Dr. Malik E. Elbuluk Dr. George K. Haritos _____________________________ _____________________________ Committee Member Dean of the Graduate School Dr. Tom T. Hartley Dr. George R. Newkome _____________________________ Date ii ABSTRACT A method to control switched reluctance motors (SRM) in the dq rotating frame is proposed in this thesis. The torque per phase is represented as the product of a sinusoidal inductance related term and a sinusoidal current term in the SRM controller. The SRM controller works with variables similar to those of a synchronous machine (SM) controller in dq reference frame, which allows the torque to be shared smoothly among different phases. The proposed controller provides efficient operation over the entire speed range and eliminates the need for computationally intensive sequencing algorithms. The controller achieves low torque ripple at low speeds and can apply phase advancing using a mechanism similar to the flux weakening of SM to operate at high speeds. A method of adaptive flux weakening for ensured operation over a wide speed range is also proposed. This method is developed for use with dq control of SRM but can also work in other controllers where phase advancing is required. -
Principle of Relativity and Inertial Dragging
ThePrincipleofRelativityandInertialDragging By ØyvindG.Grøn OsloUniversityCollege,Departmentofengineering,St.OlavsPl.4,0130Oslo, Norway Email: [email protected] Mach’s principle and the principle of relativity have been discussed by H. I. HartmanandC.Nissim-Sabatinthisjournal.Severalphenomenaweresaidtoviolate the principle of relativity as applied to rotating motion. These claims have recently been contested. However, in neither of these articles have the general relativistic phenomenonofinertialdraggingbeeninvoked,andnocalculationhavebeenoffered byeithersidetosubstantiatetheirclaims.HereIdiscussthepossiblevalidityofthe principleofrelativityforrotatingmotionwithinthecontextofthegeneraltheoryof relativity, and point out the significance of inertial dragging in this connection. Although my main points are of a qualitative nature, I also provide the necessary calculationstodemonstratehowthesepointscomeoutasconsequencesofthegeneral theoryofrelativity. 1 1.Introduction H. I. Hartman and C. Nissim-Sabat 1 have argued that “one cannot ascribe all pertinentobservationssolelytorelativemotionbetweenasystemandtheuniverse”. They consider an UR-scenario in which a bucket with water is atrest in a rotating universe,andaBR-scenariowherethebucketrotatesinanon-rotatinguniverseand givefiveexamplestoshowthatthesesituationsarenotphysicallyequivalent,i.e.that theprincipleofrelativityisnotvalidforrotationalmotion. When Einstein 2 presented the general theory of relativity he emphasized the importanceofthegeneralprincipleofrelativity.Inasectiontitled“TheNeedforan -
Newton's First Law of Motion the Principle of Relativity
MATHEMATICS 7302 (Analytical Dynamics) YEAR 2017–2018, TERM 2 HANDOUT #1: NEWTON’S FIRST LAW AND THE PRINCIPLE OF RELATIVITY Newton’s First Law of Motion Our experience seems to teach us that the “natural” state of all objects is at rest (i.e. zero velocity), and that objects move (i.e. have a nonzero velocity) only when forces are being exerted on them. Aristotle (384 BCE – 322 BCE) thought so, and many (but not all) philosophers and scientists agreed with him for nearly two thousand years. It was Galileo Galilei (1564–1642) who first realized, through a combination of experi- mentation and theoretical reflection, that our everyday belief is utterly wrong: it is an illusion caused by the fact that we live in a world dominated by friction. By using lubricants to re- duce friction to smaller and smaller values, Galileo showed experimentally that objects tend to maintain nearly their initial velocity — whatever that velocity may be — for longer and longer times. He then guessed that, in the idealized situation in which friction is completely eliminated, an object would move forever at whatever velocity it initially had. Thus, an object initially at rest would stay at rest, but an object initially moving at 100 m/s east (for example) would continue moving forever at 100 m/s east. In other words, Galileo guessed: An isolated object (i.e. one subject to no forces from other objects) moves at constant velocity, i.e. in a straight line at constant speed. Any constant velocity is as good as any other. This principle was later incorporated in the physical theory of Isaac Newton (1642–1727); it is nowadays known as Newton’s first law of motion. -
+ Gravity Probe B
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION Gravity Probe B Experiment “Testing Einstein’s Universe” Press Kit April 2004 2- Media Contacts Donald Savage Policy/Program Management 202/358-1547 Headquarters [email protected] Washington, D.C. Steve Roy Program Management/Science 256/544-6535 Marshall Space Flight Center steve.roy @msfc.nasa.gov Huntsville, AL Bob Kahn Science/Technology & Mission 650/723-2540 Stanford University Operations [email protected] Stanford, CA Tom Langenstein Science/Technology & Mission 650/725-4108 Stanford University Operations [email protected] Stanford, CA Buddy Nelson Space Vehicle & Payload 510/797-0349 Lockheed Martin [email protected] Palo Alto, CA George Diller Launch Operations 321/867-2468 Kennedy Space Center [email protected] Cape Canaveral, FL Contents GENERAL RELEASE & MEDIA SERVICES INFORMATION .............................5 GRAVITY PROBE B IN A NUTSHELL ................................................................9 GENERAL RELATIVITY — A BRIEF INTRODUCTION ....................................17 THE GP-B EXPERIMENT ..................................................................................27 THE SPACE VEHICLE.......................................................................................31 THE MISSION.....................................................................................................39 THE AMAZING TECHNOLOGY OF GP-B.........................................................49 SEVEN NEAR ZEROES.....................................................................................58 -
Static Limit and Penrose Effect in Rotating Reference Frames
1 Static limit and Penrose effect in rotating reference frames A. A. Grib∗ and Yu. V. Pavlov† We show that effects similar to those for a rotating black hole arise for an observer using a uniformly rotating reference frame in a flat space-time: a surface appears such that no body can be stationary beyond this surface, while the particle energy can be either zero or negative. Beyond this surface, which is similar to the static limit for a rotating black hole, an effect similar to the Penrose effect is possible. We consider the example where one of the fragments of a particle that has decayed into two particles beyond the static limit flies into the rotating reference frame inside the static limit and has an energy greater than the original particle energy. We obtain constraints on the relative velocity of the decay products during the Penrose process in the rotating reference frame. We consider the problem of defining energy in a noninertial reference frame. For a uniformly rotating reference frame, we consider the states of particles with minimum energy and show the relation of this quantity to the radiation frequency shift of the rotating body due to the transverse Doppler effect. Keywords: rotating reference frame, negative-energy particle, Penrose effect 1. Introduction The study of relativistic effects related to rotation began immediately after the theory of relativity appeared [1], and such effects are still actively discussed in the literature [2]. The importance of studying such effects is obvious in relation to the Earth’s rotation. In [3], we compared the properties of particles in rotating reference frames in a flat space with the properties of particles in the metric of a rotating black hole. -
11. General Relativistic Models for Time, Coordinates And
CHAPTER 11 GENERAL RELATIVISTIC MODELS FOR TIME, COORDINATES AND EQUATIONS OF MOTION The relativistic treatment of the near-Earth satellite orbit determination problem includes cor rections to the equations of motion, the time transformations, and the measurement model. The two coordinate Systems generally used when including relativity in near-Earth orbit determination Solu tions are the solar system barycentric frame of reference and the geocentric or Earth-centered frame of reference. Ashby and Bertotti (1986) constructed a locally inertial E-frame in the neighborhood of the gravitating Earth and demonstrated that the gravitational effects of the Sun, Moon, and other planets are basically reduced to their tidal forces, with very small relativistic corrections. Thus the main relativistic effects on a near-Earth satellite are those described by the Schwarzschild field of the Earth itself. This result makes the geocentric frame more suitable for describing the motion of a near-Earth satellite (Ries et ai, 1988). The time coordinate in the inertial E-frame is Terrestrial Time (designated TT) (Guinot, 1991) which can be considered to be equivalent to the previously defined Terrestrial Dynamical Time (TDT). This time coordinate (TT) is realized in practice by International Atomic Time (TAI), whose rate is defined by the atomic second in the International System of Units (SI). Terrestrial Time adopted by the International Astronomical Union in 1991 differs from Geocentric Coordinate Time (TCG) by a scaling factor: TCG - TT = LG x (MJD - 43144.0) x 86400 seconds, where MJD refers to the modified Julian date. Figure 11.1 shows graphically the relationships between the time scales. -
Relativistic Kinematics & Dynamics Momentum and Energy
Physics 106a, Caltech | 3 December, 2019 Lecture 18 { Relativistic kinematics & dynamics Momentum and energy Our discussion of 4-vectors in general led us to the energy-momentum 4-vector p with components in some inertial frame (E; ~p) = (mγu; mγu~u) with ~u the velocity of the particle in that inertial 2 −1=2 1 2 frame and γu = (1 − u ) . The length-squared of the 4-vector is (since u = 1) p2 = m2 = E2 − p2 (1) where the last expression is the evaluation in some inertial frame and p = j~pj. In conventional units this is E2 = p2c2 + m2c4 : (2) For a light particle (photon) m = 0 and so E = p (going back to c = 1). Thus the energy-momentum 4-vector for a photon is E(1; n^) withn ^ the direction of propagation. This is consistent with the quantum expressions E = hν; ~p = (h/λ)^n with ν the frequency and λ the wave length, and νλ = 1 (the speed of light) We are led to the expression for the relativistic 3-momentum and energy m~u m ~p = p ;E = p : (3) 1 − u2 1 − u2 Note that ~u = ~p=E. The frame independent statement that the energy-momentum 4-vector is conserved leads to the conservation of this 3-momentum and energy in each inertial frame, with the new implication that mass can be converted to and from energy. Since (E; ~p) form the components of a 4-vector they transform between inertial frames in the same way as (t; ~x), i.e. in our standard configuration 0 px = γ(px − vE) (4) 0 py = py (5) 0 pz = pz (6) 0 E = γ(E − vpx) (7) and the inverse 0 0 px = γ(px + vE ) (8) 0 py = py (9) 0 pz = pz (10) 0 0 E = γ(E + vpx) (11) These reduce to the Galilean expressions for small particle speeds and small transformation speeds.