Report

Unveiling the Special Theory of Relativity Sunil Mukhi Tata Institute of Fundamental Research, Mumbai Pune, 1 October 2005 1 Introduction In 1905, Albert Einstein changed our perception of the world forever. He published the paper "On the Electrodynamics of Moving Bodies". In this, he presented what is now called the Special Theory of Relativity. Pune, 1 October 2005 Ann.Physik 17 (1905), 891-921. 2 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? Pune, 1 October 2005 3 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 it is a linear transformation: that preserves , . Pune, 1 October 2005 4 Special Relativity extends this invariance to certain transformations of space and time together. Collect the space coordinates time t into a four-component vector: Here c is the speed of light. According to Relativity, it is the same in every reference frame. Pune, 1 October 2005 as well as 5 Relativity states that all laws of physics are invariant under those linear transformations: which leave unchanged. This quantity is like a "length" in spacetime, rather than just space. Pune, 1 October 2005 6 We will now examine the physical meaning of this statement, as well as how it came to be proposed by Einstein. Pune, 1 October 2005 7 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. Pune, 1 October 2005 8 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. Pune, 1 October 2005 9 Michelson-Morley experiment: the design Experiments were performed to compare the speed of light when moving along or against the ether. Pune, 1 October 2005 10 The original experiment compared the backand-forth travel time of light, parallel and perpendicular to the supposed ether: v L c c+v ether, v c-v Pune, 1 October 2005 11 Using traditional mechanics, it follows that the transit times are: So there should be an observed discrepancy: Pune, 1 October 2005 12 However, the experiment did not find this result! In fact it found no discrepancy in the transit time. Michelson-Morley experiment: the actual apparatus Pune, 1 October 2005 13 The Fitzgerald-Lorentz Contraction Before 1905, various attempts (by Voigt, Fitzgerald, Larmor, Lorentz, Poincare) had been made to explain this strange result. It turns out that all these authors discovered some important aspects of the truth. In his short 1895 paper "Michelson's Interference Experiment", Lorentz presented a point of view directly related to the experiment. Pune, 1 October 2005 14 Lorentz noted that the excess transit time in the parallel direction could be compensated if the apparatus shrinks when oriented along the ether. For this we must assume that the contracted length L' is related to the original one by: Pune, 1 October 2005 Hendrik Antoon Lorentz 15 Lorentz and Fitzgerald never denied the existence of ether. They postulated an independent effect ("contraction") that masked its visible consequences. However Poincare, in 1900, asked the question: "Does the ether really exist?" Henri Poincare' Pune, 1 October 2005 16 Did Einstein know of these earlier works? His 1905 paper has no references! And he is once supposed to have said: “The secret to creativity is knowing how to hide your sources.” Pune, 1 October 2005 17 Einstein's Theory In 1905, at the age of 26, Einstein unveiled his own ideas on the issue. Like Poincare, he questioned the existence of ether, and like Lorentz, he ended up postulating a length contraction. But what was really striking was that he laid down a foundational principle, from which all the desired results flowed naturally and elegantly. Pune, 1 October 2005 18 Einstein started with a simple observation involving a magnet and a conductor in relative motion. Pune, 1 October 2005 19 He noted that in both cases, an identical electric current is induced on the conductor. It is not the case that the moving object always induces a current on the stationary one (that would be "reciprocity" rather than "relativity"). From this, he argued that only relative motion is physically meaningful: hence the laws of physics are the same in all (inertial) frames of reference. Pune, 1 October 2005 20 Next he added a startling corollary. The speed of light, being of fundamental importance in physics, must be the same in all reference frames. He realised that this was "apparently irreconcilable" with requiring that the laws of physics are the same in all frames, but then showed that it was perfectly consistent. And as a consequence, the concept of ether would turn out to be "superfluous". Pune, 1 October 2005 21 “The laws of physics are the same in all inertial frames.“ “The speed of light is constant in all frames." The Postulates of the Special Theory of Relativity Pune, 1 October 2005 22 Clocks, Rigid Bodies, Electromagnetism In a rather stern tone for a 26-year-old, Einstein stressed the need to understand: "the relationships between rigid bodies (systems of coordinates), clocks, and electromagnetic processes. Insufficient consideration of this circumstance lies at the root of the difficulties which the electrodynamics of moving bodies at present encounters." This opened the way for him to question a lot of common-sense notions. Pune, 1 October 2005 23 The rest of the paper is derived from the postulates with masterly confidence and no adhoc assumptions. He starts by questioning simultaneity and the absolute nature of time. He stresses the importance of physical interpretation: "a mathematical description of this kind has no physical meaning unless we are quite clear as to what we understand by `time'." Pune, 1 October 2005 24 Einstein then proposes a definition of simultaneity based on synchronizing clocks using a light ray. It follows that two events which are simultaneous in one frame need not be simultaneous in another. Within this simple framework, he then derives the Lorentz contraction of a moving rod. Pune, 1 October 2005 25 z z' y v y' x x' Given two frames, one moving at constant velocity with respect to the other, how do we transform the coordinates? The traditional answer would have been: Pune, 1 October 2005 26 Lorentz transformation Using his own postulates, and nothing else, Einstein imagines an experiment with light rays, and demonstrates that Special Relativity gives a different answer: Pune, 1 October 2005 27 It is easily checked that this equation, unlike the traditional one, preserves . In fact, this had to be the case. A light ray from the origin reaches at time: Requiring this equation to hold in both systems immediately tells us that is equal in both frames. Pune, 1 October 2005 28 It is reassuring to notice that all the formulae of Relativity reduce to those of traditional mechanics if we take . This is the limit of velocities v that are small compared to the speed of light c. Pune, 1 October 2005 29 In the rest of the paper, Einstein worked out most of the consequences of the Relativity axioms that we are familiar with today: – – – – – – Time dilation and "twin paradox" Addition law for velocities Lorentz transformation of Maxwell equations Doppler shift Radiation pressure on perfect mirrors Relativistic dynamics of accelerated electrons Pune, 1 October 2005 30 Inertia and Energy One final consequence of his ideas remained to be worked out. In a subsequent paper in the same year: "Does the Inertia of a Body Depend on Its Energy Content", Einstein presented his most famous equation. Combining energy conservation with Relativity, he showed that if a body emits an energy E in the form of radiation, its mass decreases by E/c2. Pune, 1 October 2005 31 This turned out to be one of the most far-reaching conclusions from Relativity. "The mass of a body is a measure of its energy content" Pune, 1 October 2005 32 Experimental Tests An excellent source of information on experimental tests of Special Relativity is the webpage: http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html Early experiments (pre-1905): Roentgen, Eichenwald, Wilson, Rayleigh, Arago, Fizeau, Hoek, Bradley, Airy. Round-trip tests of light speed isotropy: Michelson and Morley, Kennedy and Thorndike, Modern Laser/Maser Tests, One-way tests of light speed isotropy: Cialdea, Krisher, Champeny, Turner & Hill. Tests of light speed from moving sources: Cosmological Sources: DeSitter, Brecher; Terrestrial Sources: Alvaeger, Sadeh, Measurements of the speed of light and other limits on it: NBS Measurements, 1983 Redefinition of the Meter, Limits on Variations with Frequency, Limits on Photon Mass. Tests of the principle of relativity and Lorentz invariance: Trouton Noble, Other. Tests of the isotropy of space: Hughes-Drever, Prestage, Lamoreaux, Chupp, Phillips, Brillet and Hall. Pune, 1 October 2005 33 Tests of time dilation and transverse Doppler effect: Ives and Stilwell; Particle Lifetimes, Doppler Shift Measurements. Tests of the twin paradox: Haefle and Keating, Vessot et al, Alley, Bailey et al., The Clock Hypothesis. Tests of relativistic kinematics: Elastic Scattering, Limiting Velocity c, Relativistic Mass Variations, Calorimetric Test of SR. Other experiments: Fizeau, Sagnac, Michelson and Gale, g-2 Tests of SR, The Global Positioning System (GPS), Lunar Laser Ranging, Cosmic Background Radiation (CMBR), Constancy of Physical Constants, Other. Experiments which apparently are NOT consistent with SR/GR Pune, 1 October 2005 34 Influence on Modern Physics Today, fundamental physics is formulated in the language of Relativistic Quantum Field Theory. This (difficult!) subject combines the postulates of Special Relativity with those of Quantum Mechanics. The result is the "Standard Model" of particle physics, that in principle explains every interaction in nature not involving gravity. Pune, 1 October 2005 35 The Standard Model has been subjected to extremely sophisticated precision tests. Each of these, among other things, is a test of Special Relativity! In the realm of elementary particle physics, we have learned to think relativistically. Pune, 1 October 2005 36 What can we learn from Einstein’s style of research? He was motivated by logic, clarity and physical meaning. And he had no great love for mathematics. But it would be wrong to deduce that he was strongly experiment-driven. Indeed, he said: "A theory can be proved by experiment; but no path leads from experiment to the birth of a theory.” Pune, 1 October 2005 37 The true lessons to be derived from Einstein’s life and work are perhaps the following: – – – – – – Think clearly Follow your intuition Do not be discouraged by others Work hard Learn all you can – but use only what you need And above all, have a goal that you care about. There are also lessons to be learned from Einstein’s critics: – Criticism if right will be forgotten, if wrong then remembered – Each new idea looks jarring. That neither makes it right nor wrong. – Progress usually comes from the least expected direction. But for this reason, we cannot guess where to expect it! Pune, 1 October 2005 38 "On the Electrodynamics of Moving Bodies" Pune, 1 October 2005 39