Episode 42: The Lorentz Transformation - The Mechanical Universe

[Music] [Music] last time I told you the conventional history of relativity there was the theory of the ether and then the Michelson Morley experiment showed that it was wrong and then Albert Einstein produced the theory of relativity as I told you then that story is logically correct but not historically correct well what is the real story I'll get back to that in a little while first of all I would like to tell you about a part of the theory which is still called the Lorentz transformation in the Lorentz transformation there is above all the speed of light the speed that sprang from Maxwell's equations the 300,000 kilometers per second that Michelson measured with landmark accuracy the speed which is essential in modern physics and vital to understanding the universe as it really is and at the end of the 19th century when Lorentz derived his transformation equations and it came to speed the most moving human experience was provided by trains the automobile which would eventually outpace the Train wasn't quite in gear and air travel was barely off the ground big or small sophisticated or child's play trains were the very image of speed and in fact the only thing on earth that moved people faster was the earth itself orbiting the Sun at 108 thousand kilometers per hour the inhabitants of the planet may not be aware of the speed but speed it is and to physicists at the turn of the century it was speed relative to the ether since the time of Aristotle the ether was believed to be the very stuff of which the heavens themselves were made that concept remain mere speculation until two Americans set out to prove once and for all that what was then called the luminiferous ether did in fact exist they were Albert a Michelson and Edward Morley and their goal was to detect motion through the ether by measuring its effects on the speed of light in one attempt after another with the most sensitive experimental device ever constructed they found exactly what they weren't looking for the interferometer showed that regardless of the motion of the observer the speed of light is the same for Michelson and Morley this was bad news and it traveled fast as fast as a boat could carry it to Ireland their physicist gia Fitzgerald an early champion of Maxwell's electromagnetic theory of light examined mikaelsons otherwise disappointing results fitzgerald's explanation was that in its motion through the ether one arm of the interferometer was contracted by a fraction of its length which was just the right amount to allow the two light beams to arrive simultaneously immediately most scientists scoffed at the idea however when Hendrik Lorentz arrived at the same idea no one was laughing not only was he the world's expert on Maxwell's electromagnetic theory but Lorentz gave a tangible explanation for the contraction phenomena he thought it had to be a property of the electron whose existence had just been confirmed by JJ Thompson and his colleagues in England it seemed that in electrons they found the inner parts of atoms the ultimate constituents of matter but they hadn't discovered all the things that electrons actually do one possibility the rents believed is that an electron will contract in the direction of motion if that were true and since everything is composed of electrons then an interferometer would contract in the direction of motion so would a ruler and so would a locomotive while length contraction took care of the Michelson Morley experiment the rents knew more was needed to explain all the experiments that had failed to detect motion through the ether since he still believed in the ether and the fact that the earth moved through it he felt that somehow the electron must be responsible for this amazing fact about life regardless of the speed with which they themselves are moving all observers measure the same speed of light certainly other speeds say the speed of a moving train aren't the same to all observers to an observer on a platform for example this trains passing had a good clip but to someone on the train the train speed seems to be zero and the ground outside seems to be moving instead therefore as Galileo was well aware in the Renaissance and as the Stalinist today the speed of an object depends on the observer speed but Lorentz said that perceptions of light waves would be radically different he suggested that even someone traveling at nearly the speed of light would still observe light moving at 300,000 kilometers per second how could that be consider two observers in relative motion in this case Albert and Henri just for the sake of argument at the exact place and time they pass each other they observe a flash of light a sphere of light expands outward from that point since each measure the speed of light relative to himself each believes correctly that he is always at the center of that expanding sphere even though they themselves move farther and farther apart how can two people in different places both be at the center of the same sphere to confirm his perception each sets up light detectors and equal distance apart however while Albert's detectors registered the light arriving simultaneously he believes the light strikes Henry's detectors at two different times meanwhile Henry sees the same thing in Reverse they agree on the speed of light but they disagree on whether events happen simultaneously or at different times this is not semantics nor a petty debate it means that time as well as distance has to be affected by motion however as profound as this works the French mathematician only Pontellier objected to the limited nature of Lawrence's explanation what was needed he said was a new fundamental law of physics the principle of relativity according to which the laws of physical phenomena should be the same whether for an observer fixed or for an observer carried along in a uniform movement of translation in other words as Galileo had suggested one state of uniform motion is as good as any other after all this idea was the basis of Galileo's reasoning and the law of inertia almost 300 years earlier but Poincare a was suggesting that the idea of Galilean relativity should be generalized to include all physical phenomena including life for example an observer could not determine whether he was in motion by measuring the speed of light since that speed is the same for all observers and that meant age-old notions about time and space had to change and the park la himself shied away from examining the consequences Lorentz developed the equations needed to show precisely how much rulers would have to contract and clocks would have to slow down when they were in motion the essence of his reasoning can be seen with the aid of the simplest possible clock two mirrors a fixed distance apart with a light beam bouncing back and forth between them each bounce of the beam is a tick or a talk of the timepiece to Henry his clock is stationary and altogether ordinary but for Albert that clock is moving and between tick and tock he sees the light beam trace a diagonal path which means it's traveling a longer distance but the speed of light is the same for all observers so the light must take a longer time to travel the longer distance therefore Albert believes the moving clock runs slow but how slug the relativity of time is derived from the right triangle formed by the distances traveled the Pythagorean theorem shows that the path of the moving light is longer than the distance between mirrors by the factor 1 over the square root of 1 minus V squared over C squared this factor occurs so often in relativity that it is given its own symbol the Greek letter gamma [Music] so to an observer at rest a moving light clock seems to be running too slowly by the factor gamma a ruler or anything else in motion also seems contracted by that same factor and it's called the Fitzgerald contraction for speeds much less than the speed of light gamma isn't very large for example the earth in its headlong dash around the Sun is shortened by no more than the length of one blade of grass as for speed on the earth while the rents was busy developing his theory the steam locomotive barrier of 100 miles per hour was broken at that speed the entire Train is shortened by less than the width of one atom of the paint on its engine and Lorentz himself didn't move slowly he was the International physicist young physicists from around the world attended his lectures at the University of Leiden in the Netherlands where he'd been a professor for a quarter of a century among those who came to lighten was Albert Einstein over the years the rents would have an enormous professional and personal influence on Einstein just before his death Einstein said I have admired and loved Lorentz perhaps more than anyone else I have ever known but it was Lawrence's work as a theoretical physicist that went beyond his privileged circle of friends and travelled freely through time and space knowing he was on the right track the rents pursued the consequences as far as he could if movie things appear shorter and moving clocks run slower then how can two people moving in relation to each other agree on a consistent description of where and when some event happened to answer that what's needed is a set of equations to replace the old Galilean transfer these equations were hard to find but some of their implications were hard to believe in Galilean relativity the position of a point X Prime in a moving frame is related to its coordinate in a fixed frame by X minus VT Lorentz found that for the new relativity this must be multiplied by the factor gamma that's the equation along the direction of motion in directions perpendicular to the motion distances are the same in both frames and as for time although clocks can be synchronized in any one frame their readings in another frame they depend on where they are the time in the moving frame is gamma times the quantity t minus VX over C squared [Music] together these equations are the Lorentz transformation they express the mathematical essence of the special theory of relativity the Lorentz transformation slows time and contracts distances in a moving frame no matter which frame is taken to be moving the observer in the moving frame thinks he's at rest and that the other frame is really moving but these equations do more than that they actually join time and space together when an event occurred has no meaning without saying where it occurred [Music] 19:04 the netherlands the rents publishes the definitive version of his electron theory it contains the essential equations of the theory of relativity but Albert Einstein has not yet been heard from which is caused some to say that history has given him more credit than he deserved 1905 Baron Switzerland Einstein a young physics student supporting himself as a patent clerk finds himself disturbed by seeming inconsistencies at the very core of physics can inertia and the laws of mechanics be made consistent with Maxwell's theory of optics and electromagnetism Einstein decides that they must even if that means giving up not only the ether but the traditional meanings of time and space he sets forth two fundamental postulates the first is Frank evades relativity principle the laws of physics are the same for all inertial frames his second postulate states that the speed of light is the same for all observers he simply assumes the phenomenon that Lorentz has been struggling to explain from these two postulates alone Einstein deduce is exactly the same equations Lorentz discovered earlier but now they have a very different meaning the fundamental concepts of space and time have become intertwined the essence of the idea can be understood by visualizing time as if it were another dimension Albert standing still in space flows through time so that a vertical line represents a fixed point x equals zero in his reference frame at different times [Music] while a horizontal cross-section represents simultaneous times in different places [Music] on the other hand someone in motion Galileo for example traces an oblique path [Music] so while what Albert thinks of as a fixed point makes a vertical line Galileo's idea of nothing happening appears as a tilted line at X prime equals zero or anywhere else in his frame but of course if Galileo had drawn the picture his line for standing still would be vertical and Albert's would be tilted backward the same idea can be used to show the relativity of time when Henry and Albert observed the same expanding light sphere it reaches their detectors at definite points in time and space [Music] ah these are called events meanwhile the light itself traces out a cone [Music] to Albert events on the horizontal cross-section are simultaneous for him one of Henry's detectors flashes first then both of his own flash simultaneously and finally Henry's other detector flashes so he thinks these two events are simultaneous but Henry thinks these two events are simultaneous so not only are Henry's lines of constant position tilted but so are his lines of simultaneous time for Henry simultaneous events take place everywhere on a tilted cross-section so he thinks one of Albert's signals goes first then both of his and Albert's other signal of course if Henry were drawing the picture he would draw his lines of constant place and constant time perpendicular to each other amazingly that wouldn't change the light-cone at all this way of looking at things is called a spacetime diagram and many of the strange effects of relativity can be visualized this way for example Albert thinks that Henry's ruler isn't quite a meter long while Henry seeing Albert's speed by thinks Albert's ruler is shorter [Music] on the spacetime diagram [Music] Albert measures lengths on his space axis where Henry's ruler is shorter [Music] but on Henry's axes the situation is reversed and Albert's ruler is shorter and what about the mystery of the clocks how can each think the others clock is slow on the space-time diagram just follow the bouncing light beams [Music] on Albert's time axis Henry's tics are farther apart than his own but on henry's time axis Albert's tics are farther apart no matter how he looks at it actually there's more than one way to look at the Lorentz transformation itself while it was first derived by Lorentz Einstein arrived at the same equations but from a completely different direction Lorentz used the equations to explain the Michelson Morley experiment while Einsteins goal was to establish relativity as a fundamental and universal principle for all of physics for Lorentz the constant speed of life for all observers was a mirror appearance for Einstein this constant speed was a principle from which all else should be derived Lorentz was perhaps the last great classical physicist but the equations that bear his name are at the heart of relativity and the future it created in any case there are two completely independent histories of the theory of relativity one of them goes this way there was the Etha theory and in the Michelson Morley experiment and other experiments failed to detect its existence and then one car a and Lorentz with great difficulty produce the formulas that were necessary to explain the results of those experiments and then completely separately and independently young Albert Einstein was worried about a deep problem having to do with the nature of light and electricity and he decided that this was the way the world had to work and he came up with exactly the same theory but with a far far deeper understanding of what it meant so it's possible to say that Einstein made only minor you shion's to the theory of relativity just as it's possible to say that Copernicus did nothing but a trivial mathematical transformation of coordinates but to say that ignores in the most profound possible way the real history of both of those subjects will go on without discussion of the theory of relativity next time [Applause] [Applause] Annenberg media [Music] for information about this and other Annenberg media programs call 1-800 lerner and visit us at WWE

Channel: caltech

Views: 51,900

Rating: 4.9343495 out of 5

Keywords: Caltech, science, technology, research, physics, lecture, David Goodstein, The Mechanical Universe, The Lorentz Transformation

Id: feBT0Anpg4A

Length: 28min 46sec (1726 seconds)

Published: Mon Dec 19 2016