Title: Special relativity Content: Special relativity (or the special theory of relativity) is a theory in physics that was developed and explained by Albert Einstein in 1905. It applies to all physical phenomena, so long as gravitation is not significant. Special relativity applies to Minkowski space, or "flat spacetime" (phenomena which are not influenced by gravitation). Einstein knew that some weaknesses had been discovered in older physics. For example, older physics thought light moved in luminiferous aether. Various tiny effects were expected if this theory were true. Gradually it seemed these predictions were not going to work out. Eventually, Einstein (1905) drew the conclusion that the concepts of space and time needed a fundamental revision. The result was special relativity theory, which brought together a new principle "the constancy of the speed of light" and the previously established "principle of relativity". Galileo had already established the principle of relativity, which said that physical events must look the same to all observers, and no observer has the "right" way to look at the things studied by physics. For example, the Earth is moving very fast around the Sun, but we do not notice it because we are moving with the Earth at the same speed; therefore, from our point of view, the Earth is at rest. However, Galileo's math could not explain some things, such as the speed of light. According to him, the measured speed of light should be different for different speeds of the observer in comparison with its source. However, the Michelson-Morley experiment showed that this is not true, at least not for all cases. Einstein's theory of special relativity explained this among other things. == Basics of special relativity == Suppose that you are moving toward something that is moving toward you. If you measure its speed, it will seem to be moving faster than if you were not moving. Now suppose you are moving away from something that is moving toward you. If you measure its speed again, it will seem to be moving more slowly. This is the idea of "relative speed"—the speed of the object relative to you. Before Albert Einstein, scientists were trying to measure the "relative speed" of light. They were doing this by measuring the speed of star light reaching the Earth. They expected that if the Earth was moving toward a star, the light from that star should seem faster than if the Earth was moving away from that star. However, they noticed that no matter who performed the experiments, where the experiments were performed, or what star light was used, the measured speed of light in a vacuum was always the same.Light in different media (water,air..) may travel at different speeds. Einstein said this happens because there is something unexpected about length and duration, or how long something lasts. He thought that as Earth moves through space, all measurable durations change very slightly. Any clock used to measure a duration will be wrong by exactly the right amount so that the speed of light remains the same. Imagining a "light clock" allows us to better understand this remarkable fact for the case of a single light wave. Also, Einstein said that as Earth moves through space, all measurable lengths change (ever so slightly). Any device measuring length will give a length off by exactly the right amount so that the speed of light remains the same. The most difficult thing to understand is that events that appear to be simultaneous in one frame may not be simultaneous in another. This has many effects that are not easy to perceive or understand. Since the length of an object is the distance from head to tail at one simultaneous moment, it follows that if two observers disagree about what events are simultaneous then this will affect (sometimes dramatically) their measurements of the length of objects. Furthermore, if a line of clocks appear synchronized to a stationary observer and appear to be out of sync to that same observer after accelerating to a certain velocity then it follows that during the acceleration the clocks ran at different speeds. Some may even run backwards. This line of reasoning leads to general relativity. Other scientists before Einstein had written about light seeming to go the same speed no matter how it was observed. What made Einstein's theory so revolutionary is that it considers the measurement of the speed of light to be constant by definition, in other words it is a law of nature. This has the remarkable implications that speed-related measurements, length and duration, change in order to accommodate this. == The Lorentz transformations == The mathematical bases of special relativity are the Lorentz transformations, which mathematically describe the views of space and time for two observers who are moving relative to each other but are not experiencing acceleration. :To define the transformations we use a Cartesian coordinate system to mathematically describe the time and space of "events". :Each observer can describe an event as the position of something in space at a certain time, using coordinates (x,y,z,t). :The location of the event is defined in the first three coordinates (x,y,z) in relation to an arbitrary center (0,0,0) so that (3,3,3) is a diagonal going 3 units of distance (like meters or miles) out in each direction. :The time of the event is described with the fourth coordinate t in relation to an arbitrary (0) point in time in some unit of time (like seconds or hours or years). Let there be an observer K who describes when events occur with a time coordinate t, and who describes where events occur with spatial coordinates x, y, and z. This is mathematically defining the first observer whose "point of view" will be our first reference. Let us specify that the time of an event is given: by the time that it is observed t(observed) (say today, at 12 o'clock) minus the time that it took for the observation to reach the observer. :This can be calculated as the distance from the observer to the event d(observed) (say the event is on a star which is 1 light year away, so it takes the light 1 year to reach the observer) divided by c, the speed of light (several million miles per hour), which we define as being the same for all observers. :This is correct because distance, divided by speed gives the time it takes to go that distance at that speed (e.g. 30 miles divided by 10 mph: give us 3 hours, because if you go at 10 mph for 3 hours, you reach 30 miles). So we have: ::t = d/c :This is mathematically defining what any "time" means for any observer. Now with these definitions in place, let there be another observer K' who is * moving along the x axis of K at a rate of v, * has a spatial coordinate system of x' , y' , and z' , where x axis is coincident with the x axis, and with the y' and z' axes - "always being parallel" to the y and z axes. This means that when K' gives a location like (3,1,2), the x (which is 3 in this example) is the same place that K, the first observer would be talking about, but the 1 on the y axis or the 2 on the z axis are only parallel to some location on the K' observer's coordinate system, and * where K and K' are coincident at t = t' = 0 :This means that the coordinate (0,0,0,0) is the same event for both observers. :In other words, both observers have (at least) one time and location that they both agree on, which is location and time zero. The Lorentz Transformations then are : t' = (t - vx/c^2)/ \sqrt pc.) * The transverse doppler effect, which is where the light emitted by a quickly moving object is red-shifted due to time dilation. * The presence of muons created in the upper atmosphere at the surface of Earth. The issue is that it takes much longer than the half- life of the muons to get down to Earth surface even at nearly the speed of light. Their presence can be seen as either being due to time dilation (in our view) or length contraction of the distance to the earth surface (in the muon's view). * Particle accelerators cannot be constructed without accounting for relativistic physics.