Slide 1Slide 2Slide 3Slide 4Slide 5Chapter 26 Special RelativitySlide 7Slide 8RelativitySlide 10Key IdeasSlide 12Theory of relativityTwo Principles of the Special Theory of RelativitySlide 15Newton's UniverseEinstein's ChallengeSpacetimeSlide 19Slide 20Slide 21Time DilationRelative TimeSlide 24Slide 25Slide 26Slide 27Length ContractionSlide 29Slide 30Mass Increase and Kinetic EnergySlide 32Consequences of RelativityEssential RelativityThe World We Live inLight the UnifierImportant FormulasDiffraction: Waves are able to bend around the edge of an obstacle in their path. The diffracted waves spread out as though they originated at narrow slits or gaps.dsin=mm      Constructive inferencem =1/2,3/2,5/2, . . . Destructive inferenceQuestion: A two slit experiment is performed in the air. Later, the same apparatus is immersed in water, and the experiment is repeated. When the apparatus is in the water, are the interference fringes (a) more closely spaced(b) more widely spaced (c) spaced the same as when the apparatus is in air. Answer: adsin=m, v=c/n, n=/nQuestion: If the width of slit through which light passes is reduced, does the central bright fringe(a) become wider(b) become narrower,(c) remain the same sizeAnswer: a Approximate width of central fringe=2/WQuestion: If a radio station broadcasts its signal through two different antennas simultaneously, does this guarantee that the signal you receive will be stronger?Answer: No. The net signal could be near zero if the waves from the two antennas interfere destructively.Chapter 6Chapter 6Special RelativitySpecial RelativityIntroductionIntroductionTime Dilation Time Dilation Length ContractionLength ContractionMass IncreaseThe 1905 paper on Special Relativity: On the electrodynamics of moving bodiesThis paper starts with a very simple example: if a magnet is moved inside a coil a current is generated, if the magnet is kept fixed and the coil is moved again the same current is produced. This led Einstein to postulate that the same laws of electrodynamics and optics same laws of electrodynamics and optics will be valid for all frames of reference for will be valid for all frames of reference for which the laws of mechanics hold goodwhich the laws of mechanics hold good, which is known as the Principle of RelativityRelativityRelativityRelativity links time and space, matter and energy, electricity and magnetism. The theory of relativity was proposed in 1905 by Albert Einstein, and little of physical science since then has remained unaffected by his ideas."Common sense is the collection of prejudices acquired by age eighteen."Albert Einstein (1952) Please give up commonsense notions of space and time for 30 minutes!Key IdeasKey Ideas Two Principles of Relativity:Two Principles of Relativity: •The laws of physics are the samesame for all uniformly moving observers. •The speed of light is the samesame for all observers. Consequences: Consequences: •Different observers measure differentdifferent times, lengths, and masses. •Only spacetimespacetime is observer-independent.All motion is relative to the observer; absolute motion does not exist.Theory of relativityTheory of relativityThe theory of relativity is concerned with physical consequences of the absence of a universal frame of reference. The Special Theory of Relativity (1905):Problems involving the motion of frames of reference at constant velocity with respect to one another.The General Theory (1915):Problems involving frames of references accelerated with respect to one anotherTwo Principles of the Special Two Principles of the Special Theory of RelativityTheory of Relativity1. The laws of physics are the same in all frames of references moving at constant velocity with respect to one another.2. The speed of the light in free space has the same value for all observers, regardless of their state of motion or the state of motion of the source.1st Principle of Relativity The laws of physics are the same for all uniformly moving observers. "Uniformly" = "with a constant velocity" Implications: •No such thing as "absolute rest". •Any uniformly moving observer can consider themselves to be "at rest". 2nd Pricinple of Relativity The speed of light in a vacuum is the same for all observers, regardless of their motion relative to the source. Implications: •The speed of light is a Universal Constant. •We cannot send or receive information faster than the speed of light. This has been experimentally verified in all cases.Newton's UniverseNewton's Universe •The universe keeps absolute time. •Objects move through absolute space. •Universe looks the same to all observers, regardless of how they move through it.Einstein's ChallengeEinstein's Challenge 1905: Albert Einstein challenged Newton: •We can only compare our view with that of other observers. •All information we have is carried by light. •But, light moves at a finite speed. The result is an irreducible relativity of our physical perspective.SpacetimeSpacetime Newton's View: •Space & Time are separate and absolute. •Universe looks the same to all observers. Einstein's View: •Space & Time are relative. •United by light into Spacetime. •Only spacetime has an absolute reality independent of the observer.Question: The theory of relativity is in conflict with (a) experiment (b) Newtonian mechanics(c) electromagnetic theroy(d) ordinary mathematcsAnswer: bQuestion: According to the principle of relativity, the laws of physics are the same in all frames of reference(a) at rest with respect to one another(b) moving toward or away from one another at constant velocity(c) moving parallel to one another at constant velocity(d) all of the aboveAnswer: d(cT)2 = (vT)2 + d2 = (vT)2 + (ct)2 t = T[1 - (v/c)2]1/2 i.e. T>tMoving Clock is running slow The Relativity of Time: A Thought Experiment On a spaceshipOn the Earth Observer moving with respect to the clock Observer at rest with respect to aclockTime DilationTime DilationMoving clocks runs slowlyt = T[1 - (v/c)2]1/2 or T = t/[1 - (v/c)2]1/2 (v has to be reasonably close to c)Relative TimeRelative Time The result is true for all clocks. Conclusion: There is no absolute time•Time passes at different rates for observers moving relative to each other. •At speeds small compared to c, the difference is very small. This has been verified experimentally using atomic clocks on airplanes