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Special relativity Einstein originally proposed his theory of special relativity in 1905 and it is often taken as the beginning of modern physics. It opened the door to whole new ways of thinking about the universe. VIDEO

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2 + 2 = 3 Imagine you are on a train going at 60 mph. You are travelling at 60 mph when viewed by an observer at the side of the track, but you are at rest when viewed by the passenger sitting opposite you. These two points of view are known as frames of reference in physics and relativity is all about how the physics measured in these frames of reference compares. If the observer was on a train travelling at 60 mph in the opposite direction, then in their frame of reference you would be travelling at 120 mph. This works well for objects travelling at low speed but we find that it doesn't work so well when moving close to the speed of light. Use this calculator to see what speed objects appear to approach when the speeds are close to the speed of light.this calculator

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Experiment to find the speed of light Can we produce a simulation version?

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The principles 1.When two observers are moving at constant speeds relative to one another, they will observe the same laws of physics. 2.The speed of light (in a vacuum) is the same for all observers. Einstein started with just these two principles. These were two almost philosophical statements that he could not prove to be true, but using them he was able to derive his theory of special relativity. The consequences of this theory could then be tested against what we observe to be true in the universe. It was also impressive that Einstein was able to derive all the results of his predecessors using just a few pages rather than the volumes of scientific writing they had needed.

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Time dilation A very simple thought experiment shows that one consequence of the speed of light being the same for all observers is that time experienced by all observers is not necessarily the same. There is no universal clock that we can all refer to - we can simply make measurements of time as we experience it. This calculatorThis calculator can be used to see how much time dilation takes place at various speeds. This song (Queen, 39) is about the effects of special relativity. See if you can work out what is going on.song Animations: http://www.phys.unsw.edu.au/einsteinlight/jw/module4_time_dil ation.htm, http://www.upscale.utoronto.ca/PVB/Harrison/Flash/#relativity http://www.phys.unsw.edu.au/einsteinlight/jw/module4_time_dil ation.htm http://www.upscale.utoronto.ca/PVB/Harrison/Flash/#relativity

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Why do we not notice these time differences in everyday life? We can see that for small speeds (ie less than 0.1 times the speed of light) the Lorentz factor is approximately 1 and relativistic effects are negligibly small. Even 0.1 times the speed of light is a tremendously fast speed compared to everyday life.

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Implications for everyday life The speed of satellites is fast enough that even these small changes will add up over time and affect the synchronisation of global positioning systems (GPS) and television broadcasters with users on the Earth. Satellites have to be specially programmed to adapt for the effects of special relativity (and also general relativity, which is not covered here). Very precise measurements of these small changes in time have been performed on fast aircraft and agree with predicted results within experimental error.

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Muon detection Further evidence in support of special relativity comes from the field of particle physics, in the form of the detection of a particle called a muon at the surface of the Earth. Muons are produced about 25 km up in the atmosphere by cosmic rays. Their measured lifetime is about 2.2 μs and their speed is 99.9653% of the speed of light. Flash Simulation Calculate how far muons can travel in their lifetime. How can we detect them? Calculate the lifetime of the muon as seen from our stationary reference frame. How far can muons travel in this time?

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Length contraction Another implication of Einstein's theory is the shortening of length when an object is moving. Consider the muons discussed above. Because of their large speed they experience a longer lifetime as a result of time dilation. An equivalent way of thinking about this is that muons experience the height of the atmosphere as smaller (or contracted) by the same amount as the time has increased (or dilated). There is a symmetrical formula to that for time dilation, which can be derived. Note that the contraction only takes place in the direction that the object is travelling. Formula http://www.physicsclassroom.com/mmedia/specrel/lc.cfm

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Ladder paradox Consider a ladder that is just longer than a garage. If we fly the ladder at high speed through the garage does length contraction mean that from our stationary perspective it fits inside the garage? How can this be reconciled with the fact that from the ladder's reference frame the garage appears even shorter as it moves towards the ladder? http://en.wikipedia.org/wiki/Ladder_paradox Or produce one like http://www.yteach.com/index.php/search/results/Twin_Paradox, 0,0,0,twin_paradox,25,1,tn,1.html http://www.yteach.com/index.php/search/results/Twin_Paradox, 0,0,0,twin_paradox,25,1,tn,1.html

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Exam II Median Score: 78. Today: Continue Einstein’s Special Relativity Short intro to General Relativity Monday: What is Quantum Mechanics? (15 minutes)

Exam II Median Score: 78. Today: Continue Einstein’s Special Relativity Short intro to General Relativity Monday: What is Quantum Mechanics? (15 minutes)

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