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What Is Relativity ? Inertial Frames of Reference

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What Is Relativity ? Inertial Frames of Reference What is Relativity ? Inertial frames of reference A body at rest remains at rest and a body in motion continues to move at constant velocity unless acted upon by an external force Newton's first law Newton's laws are valid only in 'special' reference frames called Inertial reference frames - An inertial reference frame is a coordinate system at rest or travelling with a constant velocity with respect to another coordinate system. v V = 0 V 0 Those reference frames in which the law is valid are inertial reference frames. In the reference frame of ground, the ball is at rest. In the reference frame of an accelerating train, the same ball has a spontaneous acceleration in the opposite direction, in contracdiction to Newton©s first law. The reference frame of the ground is an inertial reference frame. The reference frame of the accelerating train is NOT an inertial reference frame. Newton©s laws can be reformulated as If a free body is at rest or uniform motion in a given reference frame, then so will other free bodies in that reference frame. There is no preferred frame of reference for describing physics Laws of mechanics are the same in all inertial reference frames No mechanical experiment can detect any intrinsic difference between two inertial frames . Are the laws of electromagnetism and optics same in all reference frames ? Laws of electromagnetism are invariant NO in a reference frame called ETHER- an absolute standard of rest. YES Galilean law of addition of velocities should be discarded !! Special theory of relativity Ether hypothesis Effect of ether on the propa -gation of light C v C = velocity of light v = Velocity of the moving frame S© S = Rest frame - Failed to detect any ether wind! velocity of light through ether is zero ! Michelson-Morley experiment to measure the ether wind gave a null result disproving the theory of ether – failure of non-mechanical experiments. Modification of Galilean transformations rely upon the notions of absolute length and absolute time Modification of velocity addition rule Counter-intuitive ideas about space-time Special Theory of relativity In 1905, the Principle of relativity was proposed by Einstein. All the laws of physics are the same in all inertial frames The velocity of light, C = 3 108 ms-1 is the same in all inertial frames. Strange behaviour of length and time – length contraction and time-dilation. Concept of simultaneity Lorentz transformation equations Transformation rules, for space time coordinates, of an event measured in two inertial reference frames (x, y, z, t) and (x', y', z', t'), taking into account the relativity of length and time. In one dimension, Galilean equations Lorentz equations 2 t' = ( t – V x/c ) t' = t ( 1 – V2/c2 ) x' = x - Vt x' = ( x – V t ) ( 1 – V2/c2 ) y' = y y' = y z' = z z' = z Time-dilation The measurements of elapsed time between events occuring at the same position as measured in one frame are less than those made by an observer in another frame moving at a speed V with respect to the first Moving clocks run slow. ¢ 1 ¢ t© = t ¡ ( 1 ± V2 / c2) Very drastic time-dilation effects were observed in the decay of short lived elementary particles. The usual lifetime of a muon (lepton, charge = -1) is about 2.2 £ 10-6 s. At relativistic speeds, the internal process leading to the decay suffer a time dilation, which increases the life time to 29 times the lifetime of muons at rest. Length contraction The measurements of length of an object made within a frame in which the object is stationary are larger than those made by an observer in another frame moving at a velocity ©V© with respect to the first. ¡ X = ( 1 ± V2/ c2 ) X© Twin paradox Time dilation formula is only valid if the time of a moving clock is measured from the point of view of an inertial reference frame. Hence, our calculation of time-dilation of the space-ship clock is valid. The reference frame of the space-ship is not inertial ± It decelerates, stops and accelerates during it©s journey to the earth. The twin paradox ! Mass-energy relation Mass is a form of energy and energy has mass. The amount of energy contained in an amount of mass m is E2 = c2 p2 + m2 c4 C = speed of light If p = 0, E = m c2 -- rest mass energy The most spectacular demonstration of this relationship is found in the annihilation of matter and antimatter. - Lead to the unification of law of conservation of energy and law of of conservation of mass. Absolute brain! http://www.javad.8m.com/index.html Mirror paradox ! Try not to look at your image in the mirror for a long time. Possibly you and your image are being changed with each other ! Because every two -sided relation could be optional and relative! May be, we in front of the mirror are false and our images are true! http://www.javad.8m.com/index.html http://www.javad.8m.com/index.html Monaliza analiza! http://www.javad.8m.com/index.html http://casa.colorado.edu/~ajsh/sr/timebig_gif.html http://casa.colorado.edu/~ajsh/sr/timevbig_gif.html .
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