ENTER RELATIVITY THE HELIOCENTRISM VS GEOCENTRISM DEBATE ARISES FROM MATTER OF CHOOSING THE BEST REFERENCE POINT. GALILEAN TRANSFORMATION 8/19/2016

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1 ENTER RELATIVITY RVBAUTISTA THE HELIOCENTRISM VS GEOCENTRISM DEBATE ARISES FROM MATTER OF CHOOSING THE BEST REFERENCE POINT. GALILEAN TRANSFORMATION The laws of mechanics must be the same in all inertial frames of reference. 1

2 GALILEAN TRANSFORMATION GALILEAN TRANSFORMATION MICHELSON-MORLEY EXPERIMENT Bouncing light through series of mirrors and then combine them back to form an interference pattern 2

3 MICHELSON-MORLEY EXPERIMENT The experiment yielded negative results No ether Apparently value of c does not change TWO POSTULATES (SPECIAL RELATIVITY) 1. The principle of relativity: The laws of physics must be the same in all inertial reference frames. 2. The constancy of the speed of light: The speed of light in vacuum has the same value, c = m/s, in all inertial frames, regardless of the velocity of the observer or the velocity of the source emitting the light. SIMULTANEITY SIMULTANEITY 3

4 TIME DILATION TIME DILATION is time measured from reference frame of a clock is time measured from reference frame moving relative to a clock is called proper time GAMMA FACTOR LENGTH CONTRACTION LENGTH CONTRACTION is length measured from reference frame of a ruler is length measured from reference frame moving relative to a ruler is called proper length Only occurs parallel to velocity 1 4

5 LORENTZ TRANSFORMATION LORENTZ TRANSFORMATION 1 ; / / 1 1 / 5

6 DOPPLER EFFECT FOR LIGHT DOPPLER EFFECT FOR LIGHT Source approaching observer Source moving away from observer A number of galaxies have supermassive black holes at their centers (see Section 12.8). As material swirls around such a black hole, it is heated, become ionized, and generates strong magnetic fields. The resulting magnetic forces steer some of the material into high-speed jets that blast out of the galaxy and into intergalactic space (Fig ). The blue light we observe from the jet in Fig has a frequency of 6.66 x Hz, but in the frame of reference of the jet material the light has a frequency of 5.55 x Hz (in the infrared region of the electromagnetic spectrum). At what speed is the jet material moving towards us? MOMENTUM 1 / 6

7 FORCE FORCE F and v parallel to each other 1 1 F and v perpendicular to each other 1 / IMPORTANT POINTS 1. Momentum is not directly proportional to velocity 2. Constant force does not cause constant acceleration 3. The net force and acceleration vectors are not parallel KINETIC ENERGY TOTAL ENERGY 1 / 1 7

8 IMPORTANT POINTS Mass and energy are equivalent CORRESPONDENCE PRINCIPLE Newtonian mechanics is a special case of relativistic mechanics EQUIVALENCE PRINCIPLE An observer in a closed laboratory cannot distinguish between the effects produced by a gravitational field and those produced by acceleration of the laboratory IMPLICATION We can define any gravitational field in terms of special characteristics of a coordinate system (geometry) 8

9 GRAVITY AND LIGHT TWO POSTULATES (GENERAL RELATIVITY) 1. The laws of physics must be the same in observers in any frame of reference, whether accelerated or not. 2. Equivalence principle: in the vicinity of any point, a gravitational field is indistinguishable from accelerated frame of reference in gravity-free space. EFFECTS 1. Gravitational lensing 2. Gravitational time dilation 3. Gravitational redshift 9

10 LIGHT CONES AND WORLDLINES Light cone cone formed by light as it travels in 4-dimensional spacetime Worldline path taken by object in 4- dimensional space time GEODESIC Straightest possible worldline in a given space EINSTEIN FIELD EQUATIONS Combination of equations describing gravitation as curvature of spacetime by matter and energy 1 2 Λ 8 EINSTEIN FIELD EQUATIONS 1. Local energy and momentum conservation 2. Newtonian gravity COSMOLOGICAL CONSTANT (LAMBDA) Energy density of vacuum of space Added to achieve a static universe 10

11 SOLUTIONS TO EINSTEIN FIELD EQUATIONS Angular momentum Angular momentum = 0 0 Electric charge = 0 Schwarzschild Kerr Electric charge 0 Reissner Kerr-Newman Nordström 11