Modern Physics Physics oldest science intuitive Intuition is limited by our daily experiences We are not born with intuition we acquired it Based on speed and dimension we are used to We have to accept that we don t have any idea about things outside these limits Modern physics started when scientific instruments exceeded these limitations To understand and make use of physics under extreme conditions Einstein gave it a simple and clear physical interpretation and applied to everything else General relativity All from Einstein with no experimental proof at the time Then I would feel sorry for the good Lord because the theory was correct anyway said Einstein when asked what if some of the predictions were not confirmed Chapter 26 Special Relativity The speed of a bullet very fast can be as high as 1000 m s In modern physics it is very very slow A little bit of history Special relativity was mostly in the theory of electromagnetism but no one noticed it H A Lorentz noticed it and extracted some equations called Lorentz transformation He considered it mostly number manipulating without any physical meaning A car travels at 30mph How fast do you think it goes when you are traveling 15 mph head on 1 30 mph 2 45 mph 3 15 mph 1 26 5 Principle of Relativity 3x108 If a photon travels at m s towards you and you are going at 1 5 x 108 m s head on How fast do you think the photon moves 1 3 x 108 m s 2 4 5x108 m s 3 1 5x108 m s away Inertial frame of reference Moving is OK but No acceleration No Rotation Technically Earth is not inertial but it s close enough 1 Not reasonable but who are we to decide Laws of physics are the same in every inertial frame Perform experiment on train going east gives same results as on train going west 2 Speed of light in vacuum is c for everyone moving or not Measure c 3x108 m s regardless if the source is moving or you are moving 26 6 Consequences of Special Relativity Your GPS won t work well without it Use the two principles and some math Simultaneous A flash of light is emitted from the exact center of a moving box Does the light reach all the sides at the same time Sitting in the YES moving box Standing on the ground Classically Standing on the ground In reality Yes but not what happens NO Simultaneity depends on frame Time Dilation D L v Dt D vDt cDt0 2 D 2D Dt0 c vDt cDt 2 D 2 2 Dt0 1 t0 is proper time Dt 2 D Dt 2 c v2 v Because it is rest 1 2 1 2 c frame of event c 2 2 Example Time Dilation You and a friend are having a drinking contest Your friend is on a train traveling at speed v 0 9 c By her watch she finishes her drink in 5 seconds Determine the time you measure if you are standing still at the train station 5 Dt0 5 Dt 11 5 seconds 1 81 v2 0 9c 2 1 2 1 2 c c Since drinking happens on the train her time is the proper time Planes can show small but measurable dilation At LHC 1 second for the proton going at 0 999999991c is a little over 2 hours for us on the ground Example Length Contraction People on ship and on earth agree on relative velocity v 0 95 c But they disagree on the time 4 5 vs 1 4 years What about the distance between the planets Earth Alpha How long did the clock go when people in the ship looked at it People on ship have proper time Dt0 Dt0 Dt v2 4 5 1 952 Dt0 Dt 1 2 v2 c 1 2 c Dt 1 4 years 0 Length Contraction v 0 1 c L0 v tearth 95 3x108 m s x 4 5 years 4x1016m 4 3 light years Ship Length in moving frame Length in object s rest frame Example Space Travel Alpha Centauri is 4 3 light years from earth It takes light 4 3 years to get to Alpha Centauri How long would people on earth think it takes for a spaceship traveling v 0 95c to reach A C d 4 3 light years 4 5 years Dt 0 95 c v If there is a clock on the ship we would see that the clock moved by 4 5 years L v tship 95 3x108 m s x 1 4 years 1 25x1016m 1 3 light years L L0 1 v2 c2 v 0 8 c v 0 95 c 3 v Example A right triangle has a 60o angle as seen by an observer standing next to it What is the angle if it moves to the right at v 0 99c No equation for angles only length Don t know length headache The physics thing call the bottom side L0 vertical side L0 x tan 60o 1 732 L0 60o Only the length in the direction of motion contracts You are in a spaceship cruising along A speeder zooms by in an identical ship From your perspective their ship looks 1 longer than your ship 2 shorter than your ship 3 exactly the same as your ship This is not an illusion This is what you see when you take a photograph of the spaceship 1 There is no such a thing as a time or a distance They are all related to an observer 2 Ways to determine proper time and proper length Key Put yourself in the position of the observer Any clock or ruler you can put your hand on has the proper time or proper length Proper times Your heart beat The time it takes for an event that happens without moving relative to the observer Proper length Something you stand next to that is not moving like the dimension of the classroom you are sitting in The distance from NYC to Buffalo when you sit here The length of your car when you sit inside regardless if it is moving or not because there is no relative motion between you and the car 4 26 7 Relativistic Momentum Relativistic Momentum Note for v c p mv Note for v c 26 9 Relativistic Energy m0c 2 E v2 1 2 c mv p v2 1 2 c p infinity Note for v 0 E m0c2 Note for v c E m0c2 m0v2 Note for v c E infinity if m 0 Objects with mass can t have a speed of c Example how much energy is created from converting 1 kg of mass E mc2 1 x 3 x 108 2 9 x 1016 J Not enough energy to accelerate it to speed c Example How much mass is equivalent to a gallon of gasoline Gasoline 1 3 x 108 J gallon How long can it keep 1 million 100W light bulbs going Total power P 100W x 106 …