NOVA: Einstein’s Big Idea – Special and General Relativity In the middle of the 17th century, Sir Isaac Newton unified the Celestial and the Terrestrial with his description of gravity as an influence between two objects, which can best be considered as a force of attraction between objects as a result of the product of their masses and the square of the distance between them. The effect of this influence is to cause the velocity of objects to change, in accordance with Newton’s Laws of Motion. While his work in this area alone would have been sufficient secure his place as one of the greatest scientists in history, he is also credited with a number of achievements (see http://www.pbs.org/wgbh/nova/newton/legacy.html): Inventing the reflecting telescope Proposed a new theory of light and color Discovered calculus Developed three laws of motion Devised the law of universal gravitation Advanced early modern chemisty Became the father of modern science Independent of Newton’s work, Michael Faraday and James Clerk Maxwell collaborated to unify electricity and magnetism, into the electro-magnetic force. In my interpretation of the historical accounts, Michael Faraday was responsible for the majority of the science while James Clerk Maxwell was responsible for the mathematics. One of the most important results of their efforts was that electromagnetic energy can be thought of as a wave that travels at a single speed, regardless of its frequency … the speed of light. Below are excerpts from the NOVA Program entitled “Einstein’s Big Idea” that follow this body of work (all from the Phistory Channel on youtube): Part 1 (6:20 to end): https://www.youtube.com/watch?v=ROC8zSiw1x4 Part 2 (beginning to 7:45): https://www.youtube.com/watch?v=XUL9D0aHLmE Part 4 (6:10 to end): https://www.youtube.com/watch?v=BeOKwEUOTt0 Part 5 (Beginning to 0:42): https://www.youtube.com/watch?v=gT3BAWOpQ7Q Part 6 (Beginning to 7:58): https://www.youtube.com/watch?v=lPGWMUdaPYE In his efforts to unify gravity and electro-magnetism, Albert Einstein made some of the most incredible scientific advances in history. Through a variety of *thought experiments*, he developed the theories of special and general relativity, each of which have been supported by a variety of observations. Complete the following after reading the attached materials and conducting additional research: Special Relativity: o Write a paragraph that explains Special Relativity in your words o State the Two Postulates of Special Relativity o Submit and explain an illustration that you have found helpful in improving your understanding of time dilation, length contraction, and/or the twin paradox (include the source) General Relativity: o Write a paragraph that explains General Relativity in your own words o State the Equivalence Principle o Submit and explain an illustration that you have found helpful in improving your understanding of gravitational bending of light, and/or gravitational time dilation (include the source) Name: _____________________________________________ Total Grade: ____ /30 Topic Advanced (5 pts) Proficient (4pts) Working toward Submitted (2pts) proficiency (3pts) [some good stuff] [shows insight] [follows prompt] Special Relativity: Paragraph Special Relativity: Postulates Special Relativity: Time dilation Illustration and Length Explanation contraction Twin Paradox General Relativity: Paragraph General Relativity: Equivalence Principle General Bending of light Relativity: Illustration and Explanation Time dilation http://www.pbs.org/wgbh/nova/einstein The Theory Behind the Equation by Michio Kaku Imagine a police officer chasing after a speeding motorist. If he drives fast enough, the officer knows that he can catch the motorist. Anyone who has ever gotten a ticket for speeding knows that. But if we now replace the speeding motorist with a light beam, and an observer witnesses the whole thing, then the observer concludes that the officer is speeding just behind the light beam, traveling almost as fast as light. We are confident that the officer knows he is traveling neck and neck with the light beam. But later, when we interview him, we hear a strange tale. He claims that instead of riding alongside the light beam as we just witnessed, it sped away from him, leaving him in the dust. He says that no matter how much he gunned his engines, the light beam sped away at precisely the same velocity. In fact, he swears that he could not even make a dent in catching up to the light beam. No matter how fast he traveled, the light beam traveled away from him at the speed of light, as if he were stationary instead of speeding in a police car. But when you insist that you saw the police officer speeding neck and neck with the light beam, Einstein realized that the world within a hairsbreadth of catching up to it, he says you are crazy; he never even got close. To described by Isaac Newton Einstein, this was the central, nagging mystery: How was it possible for two people to see the (left), in which one could add same event in such totally different ways? If the speed of light was really a constant of nature, and subtract velocities, and that then how could a witness claim that the officer was neck and neck with the light beam, yet the described by James Clerk officer swears that he never even got close? Maxwell, in which the speed of light is constant, could not both be right. He decided to solve the Einstein had realized earlier that the Newtonian picture (where velocities can be added and problem—and special relativity subtracted) and the Maxwellian picture (where the speed of light was constant) were in total was the result. contradiction. Newtonian theory was a self-contained system, resting on a few assumptions. If only one of these assumptions were changed, it would unravel the entire theory in the same way that a loose thread can unravel a sweater. That thread would be Einstein's daydream of racing a light beam. SPECIAL RELATIVITY IS BORN One day around May of 1905, Einstein went to visit his good friend Michele Besso, who also worked at the patent office, and laid out the dimensions of the problem that had puzzled him for a decade. Using Besso as his favorite sounding board for ideas, Einstein presented the issue: Newtonian mechanics and Maxwell's equations, the two pillars of physics, were incompatible. One or the other was wrong. Whichever theory proved to be correct, the final resolution would require a vast reorganization of all of physics. He went over and over the paradox of racing a light beam. Einstein would later recall, "The germ of the special relativity theory was already present in that paradox." They talked for hours, discussing every aspect of the problem, including Newton's concept of absolute space and time, which seemed to violate Maxwell's constancy of the speed of light. Eventually, totally exhausted, Einstein announced that he was defeated and would give up the entire quest. It was no use; he had failed. Although Einstein was depressed, his thoughts were still churning in his mind when he returned home that night. In particular, he remembered riding in a streetcar in Bern and looking back at the famous clock tower that dominated the city. He then imagined what would happen if his streetcar raced away from the clock tower at the speed of light. He quickly realized that the clock would appear stopped, since light could not catch up to the streetcar, but his own clock in the streetcar would beat normally. Then it suddenly hit him, the key to the entire problem. Einstein recalled, "A storm broke loose in my mind." The answer was simple and elegant: time can beat at different rates throughout the universe, depending on how fast you moved. Imagine clocks scattered at different points in Einstein in the Bern patent office space, each one announcing a different time, each one ticking at a different rate. One second on in 1904, just months away from Earth was not the same length as one second on the moon or one second on Jupiter. In fact, the the brilliant insight that led to faster you moved, the more time slowed down. (Einstein once joked that in relativity theory, he his theory of special relativity— placed a clock at every point in the universe, each one running at a different rate, but in real life and, a few weeks later, to E = 2 he didn't have enough money to buy even one.) This meant that events that were simultaneous mc in one frame were not necessarily simultaneous in another frame, as Newton thought. He had finally tapped into "God's thoughts." He would recall excitedly, "The solution came to me suddenly with the thought that our concepts and laws of space and time can only claim validity insofar as they stand in a clear relation to our experiences.... By a revision of the concept of simultaneity into a more malleable form, I thus arrived at the theory of relativity." “Thank you, I’ve completely solved the problem.” For example, remember that in the paradox of the speeding motorist, the police officer was traveling neck and neck with the speeding light beam, while the officer himself claimed that the light beam was speeding away from him at precisely the speed of light, no matter how much he gunned his engines. The only way to reconcile these two pictures is to have the brain of the officer slow down. Time slows down for the policeman. If we could have seen the officer's wristwatch from the roadside, we would have seen that it nearly stopped and that his facial expressions were frozen in time.