Lecture physics a2 einstein’s special relativity phd pham tan thi

Einstein’s Special Relativity Pham Tan Thi, Ph.D Department of Biomedical Engineering Faculty of Applied Sciences Ho Chi Minh University of Technology Contents • Statement for Special Relativity • Reference Frame and Inertial Frame • Newton Relativity or Galilean Invariance/Transformation • A need of “Ether” (a Medium for propagating Light) • Michelson-Morley Experiment • Lorentz - FriztGerald Proposal • The Problem of Simultaneity • Lorentz Transformation • Consequence of Lorentz Transformation • Twin Paradox Classic Picture for Relative Motion Consider a Situation Reference #1 Reference #2 Consider a Situation Reference #1 Speed of light 0.5c 0.5c From the girl’s point of view on the platform, that light would not look like it is going faster than the speed of light It would just look like it is moving at exactly the speed of light Classical and Modern Physics Classical Physics Modern Physics Large, Slow moving Object • Newtonian Mechanics • Electromagnetism and Waves • Thermodynamics Small, Fast moving Object • Relativistic Mechanics • Quantum Mechanics 10% of c • Below 10% of the speed of light, c, classical mechanics holds (relativistic effects are minimal) • Above 10%, relativistic mechanics holds (more general theory) SPECIAL THEORY OF RELATIVITY Aims to answer some burning questions: • Could Maxwell’s equations for electricity and magnetism be reconciled with the laws of mechanics? • Where was the ether? History Albert Einstein surprised the world in 1905 when • He theorized that time and distance cannot be measured absolutely • They only have meaning when they are measured relative to something Einstein published his theory in two steps: • Special theory of relativity (1905) ➔ How space and time are interwoven • General theory of relativity (1915) ➔ Effects of gravity on space & time What is “relative” in relativity? • Motion … all motions is relative • Measurements of motion (and space & time) make no sense unless we are told what they are being measured relative to What is “absolute” in relativity? • The laws of nature are the same for everyone • The sped of light, c, is the same for everyone What is Relative? • A plane flies from Nairobi to Quito at 1,650 km/hr • The Earth rotates at the equator at 1,650 km/hr • An observer… ✦on the Earth’s surface sees the plane flies westward overhead ✦at a far distance sees the plane stands still and the Earth rotate underneath it Origin of Special Theory of Relativity Albert Einstein (1879 - 1955) • In 1905, Albert Einstein changed our perception of the world forever • He published the paper on the electrodynamics of a moving body • In this, he presented what is now called the Special Theory of Relativity Albert Einstein, Ann Phys 17, 891 (1905) Einstein’s Discussion ✴What was the background to this work? ✴What was the new idea that he proposed? ✴How was this experimentally confirmed? ✴How does this influence our thinking today? The Special Theory of Relativity • The laws of Physics are known to be unchanged (“invariant”) under rotations • A rotation mixes the space coordinates but does not change the length of any object • So there should be a linear transformation The Special Theory of Relativity • Special Relativity extends this invariance to certain transformations of space and time together • Collect the space coordinates (x,y,z) as well as time t into a four component vector • c is the speed of light According to Relativity, it is the same in every reference frame • Relativity states that all laws of physics are invariant under those linear transformations: xi → X Mij xj j=1 which leave x2 + y2 + z2 - c2t2 unchanged • This quantity is like a “length” in space-time, rather than just space The Special Theory of Relativity We will now examine the physical meaning of this statement, as well as how it came to be proposed by Einstein Electrodynamics • The crisis that motivated Einstein’s work was related to the laws of electricity and magnetism, or Electrodynamics • These laws were known, thanks to Maxwell, and embodied in his famous equations Gauss’ Law ⇢ ~ r·E = "0 Gauss’ Law for Magnetism ~ =0 r·B Faraday’s Law ~ @ B ~ =– r⇥E @t Ampere’s Law ~ @ E ~ = µ0 J~ + µ0 "0 r⇥B @t Electrodynamics These equations depend on the speed of light, c • In what frame is this speed to be measured? • It was thought that light propagates via a medium called “ether”, much as sound waves propagate via air or water • In that case, the speed of light should change when we move with respect to the ether - just as for sound in air • So c would be the speed of light as measured while one is at rest relative to the ether Reference Frames Two or more objects which not move relative to each other share the same reference frame • they experience time and measure distance & mass in the same way Objects moving relative to the other are in difference reference frames • like the plane and ground • they experience time and measure distance and mass in different ways Reference Frames A reference frame in physics, may refer to a coordinate system or set of axes within which to measure the position, orientation, and other properties of object in it Inertial frames • in which no accelerations are observed in the absence of external forces • that is not accelerating • Newton’s laws hold in all inertial reference frames Non-Inertial frames • that is accelerating with respect to an inertial reference frame • bodies have acceleration in the absence of applied forces Inertial Reference Frame • A reference frame is called an inertial frame if Newton laws are valid in that frame • Such a frame is established when a body, not subjected to net external forces, is observed to move in rectilinear motion at constant velocity NEWTONIAN PRINCIPLE OF RELATIVITY • If Newton’s law are valid in one reference frame, then they are also valid in another reference frame moving at a uniform velocity • This is referred to as the Newtonian Principle of Relativity or Galilean Invariance ... new idea that he proposed? ✴How was this experimentally confirmed? ✴How does this influence our thinking today? The Special Theory of Relativity • The laws of Physics are known to be unchanged... moving body • In this, he presented what is now called the Special Theory of Relativity Albert Einstein, Ann Phys 17, 891 (1905) Einstein’s Discussion ✴What was the background to this work? ✴What... length of any object • So there should be a linear transformation The Special Theory of Relativity • Special Relativity extends this invariance to certain transformations of space and time together