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# INTRO MOD MECHANICS PHYS 225

UW

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This 35 page Class Notes was uploaded by Dr. Simeon Wiza on Wednesday September 9, 2015. The Class Notes belongs to PHYS 225 at University of Washington taught by Staff in Fall. Since its upload, it has received 10 views. For similar materials see /class/192460/phys-225-university-of-washington in Physics 2 at University of Washington.

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Date Created: 09/09/15

Logistics Prof Schlarnrninger will return for class on Wednesday I m Dr Scott Pollack I work with Stephan 39 taught 225 last year I have the exam solutions if you re interested in seeing them after class Homework Sheet 4 is due this Friday Today we cover Einstein s Theory of General Relativity you ll need very little from this lecture only one question on the HW covers GR Most of today s lecture is for your edification Phys 225 Spring 2007 April 16 7 l Phys 225 Spring 2007 I mmT READ LT B SE PH PmEHTE WT TD PM THE GRANT EM E39H39 HH nutu spuncs April 16 7 3 Albert Einstein 1879 1955 Determination of Molecular Dimensions 1905 Doctoral Dissertation Brownian Motion 1905 The Photoelectric Effect 1905 Special Theory of Relativity 1905 E0n1c2 paper 1905 Gravity s in uence on light 191 1 General Theory of Relativity 1916 Phys 225 Spring 2007 Universal Gravitation Limitations What is the fundamental aw of Newton s Universal Law of Gravitation GMm R 2 Newton s law says gravity is instantaneous F Special Relativity says information cannot travel faster than the speed of light in vacuum This should apply to gravity so there needs to be a t added to Newton s law somewhere Phys 225 Spring 2007 April 16 7 5 Known Problem of Newtonian Gravity in the early 20th Century Anomalous Perihelion Precessjon ofMercuzy Mer ury s orbit was measured to precess about 5600 seconds of arc per century ie about l56 1000yr Using Newton s equations taking into account effects from all planets rotational deformation of the Sun inertial effects of the Earth leads to only 5557 arcsecondscentury predicted This was 43 arcsecondscentury short of the measured shift Not an easy problem to solve using GR but one of the first Einstein did Einstein s theory predicts the measured discrepancy from Newton within experimental errors Phys 225 Spring 2007 April 15 r 5 You walk forward a bit Then turn left and walk forward a bit more You then turn left once again You are back where you started A bear walks by what color is it Phys 225 Spring 2007 April 16 7 7 A long time ago you learned that the sum of the three angles of a triangle add up to 180 Is this always true 60 Sum of Angles 90 90 90 270 30 elem of Angles 60 30 90 180 Phys 225 Spring 2007 April 16 7 8 Straight Lines The shortest distance between two points is called a geodest In at Euclidean space geodesics are straight lines in the ordinary sense On the Earth they are great circles Light travels along geodesics through spacetime Phys 225 Spring 2007 April 16 7 9 Potential Airline Routes to Calgary ms 225 gym m7 Ayn is an Phys 225 Spring 2007 April 16 7 11 Einstein s T11 e013 of Genera Relativity HE LHDM DLD WWW THhT GENMW I W SPEC arms as w SPK E way A EFT FLF I QRWCE 1139s TIME Phys 225 Spring 2007 MW MMT ER LIKE MUS 5mm mm mt gamma m6 LNEJ 5mm SF mum I m A NICEER or hMTHIHE PMSSLNG E t Lmi EWDE mu m mam new quotmu quot12mquot TWP95D m WEN m ME THE D1 M 5 MM 31 THE MEET mam 1395 Amhm Ema EH mam AHAIMEMLM SEATES SL39L39P PED HUN CNN K1133 KNEW SE MUCH MEI STILL BE 30 NH April 16713 z x E in BE mnzmm mNN if manna I all II i 151 hw l m BEBIIB EL More massive objects curve space more Softball VS Bowling Ball Phys 225 Spring 2007 April 16 7 15 E x E 2amp4 Sow macaw mam a Bad Names General relativity is not a superset of special relativity It is NOT generalized relativity True it does allow one to deal with accelerated or non inertial reference frames in a convenient manner But not in a more generalized sense than in special relativity Special relativity ie Lorentz transformations live within the Lorentz group which is a proper subset of the Poincar group in 4 dimensions General relativity is a theo which is a subset of differential geometry In a dition it can be described as the theory of a spin 2 boson mediator Differential geometry 7395 Poincar group Phys 225 Spring 2007 April 16 7 l7 You get In an elevator on the rst floor and hegm gomg up to the sixth floor You happen to he standmg on a scale lWiat does the scale read at the moment the elevator hegms to mo ve Scales measure the force of gravity via a compression of a spring Acceleration appears to be like the force of gravity 9 The Principle of Equivalence Phys 225 Spring 2007 April 16 7 18 Equivalence Principle GR An accelerated en vir0nn1ent is equivalent to a gra vitating environment Example A rocket firing in empty space could be equivalent to you standing on the surface of the Earth This implies free fall is an inertial reference frame The Equivalence Principle is often stated that the inertial mass is identical to the gravitational mass G M This is actually the Weak EP m F g F ma the Strong EP IS that phySIcs R2 l is the same everywhere GMm GM 2 Cl mg mi R2 R Phys 225 Spring 2007 April 16 7 l9 Gravitational Redshift A classical derivation E E0 different from the one in the book C raltgtltgtc2 myhfc2 i1GMR1 UGM7f 62 CZ r rc Result from GR i12 p12 fo 2 2 PC 7396 E hf GMff hf1 G Mj C Phys 225 Spring 2007 April 16 7 2l Facts Gravitational Redshift was first experimentally veri ed by the Pound Rebka experiment in 1959 The Sun is actually bluer than it appears to be As light climbs out of the Sun s gravitational potential well it is shifted to the red but only by a small amount 2 parts in 106 A clock at the surface of the Sun ticks slower than a clock at the surface of the Earth Gravitational redshift is equivalent to a time dilation The GPS clocks in orbit about the Earth eXperience GR a time advance of about 459 ps per day for being in a higher gravitational potential homework problem SR a time delay of about 72 ps per day for moving with a high velocity relative to us The net is a time advance of 38 ps per day 9 or about 45 parts in 1010 To compensate for this the frequency of the clocks on the GPS are actually set differently than the clocks on the ground to 10229 999 995 43 MHZ instead of 1023 MHz Phys 225 Spring 2007 April 16 7 22 Vita I13 an inertial fbsari r Fiaw me i l lS E 71h Elt tm Phys 225 Spring 2007 April 16 7 23 Bending of Light by the Sun Apparent position If star Eddington s Expedition 1919 Einstein published in 1911 the effects gravity has on light Arthur Eddington lead one of several expeditions to measure the de ection of starlight by the Sun during a total eclipse in 1919 Newton s theory could predict de ection but the amount would be half that of Einstein s The measurements had considerable error and there were many skeptics It wasn t until the 19605 when deflection of light in the radio was accurately measured to agree completer with Einstein if x Gravitational Lensing x Sometimes thereis more than one ch01ce Con31der the followusg ource and mass distribution Lensing is therefore a proxy for mass distribution Phys 225 Spring 2 April 16 7 26 Eravita anal G223 Do you believe it Experimental Data The perihelion precession of Mercury is exactly explained by Einstein s theory Gravitational lensing of starlight by massive bodies Recently measured with the Cassini spacecraft Gravitational redshift has been measured Gravitational time dilation is seen between clocks at NIST Boulder and clocks at NIST Gaithersburg Washington DC and GPS satellites Orbital decay of binary pulsar systems is consistent with the emission of gravitational radiation Phys 225 Spring 2007 April 16 7 30 Gravitational Waves Gravitational waves are ripples in the fabric of spacetime Akin to water waves they propagate gravitational signals just like light propagates electromagnetic signals Gravitational waves produce a strain in spacetime h 10 21 Pad 109W 1quot Wave is traveling into the page Phys 225 Spring 2007 April 16 7 31 But There might be other possibilities Most current theories of gravity expand upon Einstein s theory ie making it more general Each has predictions about black holes and strong gravity regions of spacetime Gravitational Astronomy the observation of gravitational radiation will be a key element in determining What the true theory of gravity really is Phys 225 Spring 2007 April 16 7 32 Laser Interferometer Space Antenna current launch dat 20761312

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