Reference FramesA2290-02 1Spacetime and Inertial Reference FramesRelativity and AstrophysicsLecture 02Terry HerterA2290-02 Reference Frames 2Outline Events and Intervals Definitions Proper time, Timelike, and Spacelike Sample Problems Inertial (Free Float) Reference Frames Definition Note – only applies of limited regions of time and space Test Particles Synchronizing clocks The “Observer” Some worked problems from end of chapters 1 and 2 of Spacetime Physics Readings Spacetime Physics: Chapters 1 and 2Reference FramesA2290-02 2A2290-02 Reference Frames 3Events and Intervals – alone Event Fundamental concept which represents something happening at a point in spacetime Examples: two particles colliding, emission of a photon from an atom, lighting striking the engine of an airplane, etc. Spacetime interval Observers, regardless of their velocity, will agree on the spacetime interval between two events! If we travel at constant velocity from event to event then the spacetime interval it just the time separation (since the events all occur at the same location in our frame, the space separation is zero). Intervals between events are all that is needed to specify the location of every event in spacetime. Using a reference frame is okay But the coordinates we specify are frame dependentA2290-02 Reference Frames 4Proper Time, Timelike, & Spacelike Proper Time  Measured with a special clock (called the proper clock) that is carried so that it is present at each event as it occurs Implies space separation is zero Note – called wristwatch time (proper time) and wristwatch (proper clock) by textbook. Timelike intervals A frame can be chosen so that the two events occur at the same location (time separation predominates over space separation). Measured by using a wristwatch carried from one event to anotherin a special frame so that the event occur at the same place. Spacelike intervals Spatial distance is always larger than temporal distance  Cannot choose a frame to make events occur at the same location Measured by using a ruler to directly measure the distance between two events at the same time in your frame. It is convention to change the sign of the interval when the spatial distance is larger than the temporal distance  => squared interval is never negative.More later …Reference FramesA2290-02 3A2290-02 Reference Frames 5Lightspeed! The speed of light is defined (since 1983) to be:c = 299,792,458 m/sec This is very, very fast indeed! Some sample light travel times are given below.2.16x10222,280,000 yrSun – Andromeda Galaxy4.05x10164.280 yrSun – Proxima Centauri149,600,000,0008.317 minSun – Earth384,000,0001.281 secEarth – Moon40,080,0000.1337 secAround the Earth4,166,0000.0139 secJFK – SFOTime (m)TimeRouteNote: A lightyear (lyr) is the distance light travels in 1 year = 9.46x1015meter. Astronomers typically use parsecs (pc) where 1 pc = 3.26 lyr. Space is big!A2290-02 Reference Frames 6Sample Problem: 1-2a A proton is moving at 0.75c with respect to your laboratory and passes through two detectors 2 meters apart. Events 1 and 2 are the transits through two detectors.1. What are the laboratory space and time separations between the two events, in meters?2. What are the space and time separations in the proton frame? Part 1: The space separation in the lab is just 2 m, as given. The travel time (in meters) is  Part 2: Both events occur at the position of the proton=> space separation is 0 m in proton frame.  We use invariance of spacetime interval to get time separation in the proton frame: 2222lablabprotprotdtdt 222222m 1111.3m 41111.7m 0.2m 66667.2m 0prottm 764.1prott75.0metersin labprotlabprotlablabdccvcdcvdt m6667.275.0m2labtReference FramesA2290-02 4A2290-02 Reference Frames 7Sample Problem: 1-2b A speeding rock from space streaks through Earth’s out atmosphere, creating a fiery trail (Event 1) and crashes into the Sun (Event 2) 10 minutes later as observed in the Earth frame. Take the Sun-Earth distance to be 1.4960x1011meters.1. In the Earth frame what are the space and time separation between the two events in minutes?2. What are the space and time separations in the frame of the rock? Part 1: The time separation is 10 minutes, as stated in the problem. The space separation (in minutes is):  Part 2: Both events occur at the position of the rock=> space separation is 0 m in rock frame.  Again, we use invariance of spacetime interval to get time separation in the proton frame: 2222earthearthrockrockdtdt 22222min 8292.30min 1708.69100min .31698min 01rocktm 5524.5rocktminutes-light 3169.860299792458104960.1sec 60min 1m/secm11cddearthsunearthA2290-02 Reference Frames 8Sample Problem: 1-2c A starship leaves Earth (Event 1) and travel at 95% light speed, later arriving at Proxima Centauri (Event 2), which lies 4.3 light-years from Earth.1. What are the space and time separation between the two events asmeasured in the Earth frame, in years?2. What are the space and time separations in the frame of the starship? Part 1: The distance separation is 4.3 light-years, as stated in the problem. The time separation is:  Part 2: Both events occur at the position of the starship=> space separation is 0 m in starship frame.  Once more, we use invariance of spacetime interval to get time separation in the proton frame: 2222earthearthshipshipdtdt 22222yr 03.2yr 49.1852.20yr .34yr 53.4shiptyears 42.1shiptyears 53.4(lyr/yr) 95.0lyr 3.4earthtThis is the famous “twin paradox” – time goes by more slowly on the starship than Earth.Reference FramesA2290-02 5A2290-02 Reference Frames 9Unity of Spacetime Space and time go together to form spacetime Space is different for different observers Time is different for different observers Spacetime is the same for everyone Some physical quantities are the same for every observer Spacetime, electric charge and particle mass Other physical quantities are relative and depend on the relative motion of the observers Velocity, momentum, energy, separation in time, and separation in space  Note – time and space are NOT identical in