Principle of RelativityA2290-04 1The Principle of RelativityRelativity and AstrophysicsLecture 04Terry HerterA2290-04 Principle of Relativity 2Outline Continuation of worked problems from textbook The Postulates of Relativity Simultaneity of events Lorentz Contraction Invariance of Spacetime Interval Reading Spacetime Physics: Chapter 3Principle of RelativityA2290-04 2A2290-04 Principle of Relativity 3Test Particles A test particle is a tool to probe spacetime with out affecting it Its mass should be small enough so that its presence does not affect the motion of other nearby particles Example: 10 kg object may not be a good test particle (depending upon desired accuracy)  Acceleration due to gravity only depends on mass! Particles of the same mass but different material, shapes, and sizes in the same location all fall towards Earth with the same acceleration! (Galileo) Allow us to define inertial reference frame – otherwise aluminum would behave differently than wood. Important property of nature.10 cm10 kgAssuming movement is small so that the force doesn’t change appreciably, the distance moved in 3 min (180 sec) ismm 08.1m 00108.0sec 180secm10673.621212282ats2rGMmmaF Force of gravity is:28222311m/sec 10673.6 kg 10m 1.0/kg/sm 10673.6aThe acceleration is then:Problem 2-10aA2290-04 Principle of Relativity 4Problem: SP 2-13 Deflection of light by the Sun A falling elevator is an inertial frame therefore a beam of light shot across it will travel in a straight line. However, with respect to the Earth the flash of light is falling because the elevator is falling. Therefore light is deflected by a gravitational field.  This effect is very small on the Earth but can be measure for the Sun because gravity is much stronger than on Earth and the travel time is larger.SunEarthLight from a starAngular deflection, , greatly exaggeratedPrinciple of RelativityA2290-04 3A2290-04 Principle of Relativity 5Problem: SP 2-13 (cont’d) A) The “effective time of fall” for a photon is The velocity of the fall is the maximum acceleration acting for this effective time. B) Deflection angle is the ratio of the transverse velocity to the forward speed. sec67.4sec/m103m104.189cDtsuneTime for photon to cross Sun’s diametersec/m1284sec67.4sec/m2752esuntrantavTransverse velocity of the photonarcseconds88.0rad103.46cvtransDeflection of photon by the Sun –Off from GR result by factor of 2A2290-04 Principle of Relativity 6Problem: SP2-13 Calculus ProofSunrrobvdbadtadvTTTTdvDeflection is very small so we can assume that light is very close to original path, so cos2rGMaTwhereThe photon is accelerated by gravitydbrvGMvdbavTT2costanorbsecorrdrdbo2sec& withthusoooTrvGMdrrvGMv2secseccos22/2/22now212crGMvvoTBut on the previous slide we had221212crGMccrrGMctavvoooesunTChecks!Principle of RelativityA2290-04 4A2290-04 Principle of Relativity 7Relativity  There is no absolute motion. Everything is relative. Suppose two people are alone in space and traveling towards one another: Which one is moving? They can’t tell! Example – A train is moving at 65 mph relative to the tracks. If the people inside the train cannot see out and the track is very smooth, they can not tell they are moving! Example 2 – The earth moves around the sun at 30 km/sec. Can you tell?A2290-04 Principle of Relativity 8Aside on Albert Einstein Perhaps the greatest physicist of all time.  See Wikipedia entry 1905: Published papers on  Special Relativity  Photoelectric effect (photons carry energy proportional to their frequency) Brownian motion (random movement of particles in a fluid) General Relativity – theory of gravity Including relativistic cosmology Critical opalescence Explains why the sky is blue Atomic transition probabilities Includes “stimulated” emission which led to lasers Statistical physics Bose-Einstein statistics - bosons1879 - 1955Principle of RelativityA2290-04 5A2290-04 Principle of Relativity 9Special Theory of Relativity Postulates:  Albert Einstein (1905)1. The speed of light is the same to all observers, irrespective of their motion.2. The laws of physics are the same everywhere no matter what the speed of the observer.1879 - 1955A2290-04 Principle of Relativity 10The speed of light is constant. Person in boat moving towards shore shines a beam of light at a person on the shore. The velocity of light as seen by the person in the boat and on the shore is the same, c.vboatcFlashlightPrinciple of RelativityA2290-04 6A2290-04 Principle of Relativity 11Same/Different in Different Frames Not necessarily the same – Space separations, time separations, velocities, accelerations, forces, and field (such as electric and magnetic fields) Same – Physical laws and physical constants in these laws Examples: Speed of light same Speed of a particle not necessarily the same Charge on an electron same Kinetic energy of proton not necessarily the same Time between two events not necessarily the same Newton’s first law sameLaw of Inertia: A remains at rest or at constant velocity unless acted on by an external, unbalanced force.A2290-04 Principle of Relativity 12Simultaneity The simultaneity of events is in the eye of the beholder.v A light bulb in the center of a high speed train flashes. An observer on the train sees the light reach the front and back simultaneouslyPrinciple of RelativityA2290-04 7A2290-04 Principle of Relativity 13From outside the train To the outside observer the light reaches the back first. The back moves towards the light and the front away. Not simultaneous! Simultaneity is in the eye of the beholder. Simultaneity is relative!vvFlash goes offFlash reaches back wall