18.3 Special Relativity 1

Chapter 18 Objectives Calculate the frequency or wavelength of light when given one of the two. Describe the relationship between frequency, energy, color, and wavelength. Identify at least three different waves of the electromagnetic spectrum and an application of each. Interpret the interference pattern from a diffraction grating. Use the concept of polarization to explain what happens as light passes through two polarizers. Describe at least two implications of special relativity with regards to energy, time, mass, or distance. 2

Chapter 18 Vocabulary Terms diffraction grating electromagnetic spectrum electromagnetic wave gamma ray inference pattern microwave polarization polarizer radio wave rest energy special relativity spectrometer spectrum time dilation transmission axis visible light x-ray

Inv 18.3 Special Relativity Investigation Key Question: What are some of the implications of special relativity? 4

18.3 Special Relativity The theory of special relativity describes what happens to matter, energy, time, and space at speeds close to the speed of light.

18.3 Special Relativity These effects are observed in physics labs: Time moves more slowly for an object in motion than it does for objects that are not in motion. This is called time dilation. As objects move faster, their mass increases. The definition of the word “simultaneous” changes. Space itself gets smaller for an observer moving near the speed of light.

18.3 Speed of light paradox The theory of special relativity comes from thinking about light. A ball thrown from a moving train approaches you at the speed of the ball relative to the train plus the speed of the train relative to you. The speed of light appears the same to all observers independent of their relative motion.

18.3 Speed of light paradox If the person on the train were to shine a flashlight toward you, you would expect the light to approach you faster. The light should come toward you at 3 × 108 m/sec plus the speed of the train. Michelson and Morley found experimentally that the light comes toward you at a speed of 3 × 108 m/sec no matter how fast the train approaches you!

18.3 Consequences of time dilation In the early 1970s an experiment was performed by synchronizing two precise atomic clocks. One was put on a plane and flown around the world, the other was left on the ground. When the flying clock returned home, the clocks were compared. The clock on the plane measured less time than the clock on the ground. The difference agreed precisely with special relativity.

18.3 Einstein's formula E = mc2 This equation tells us that matter and energy are really two forms of the same thing. E = mc2 Speed of light 3.0 x108 m/sec Energy (J) Mass (kg)

18.3 The equivalence of energy and mass If a particle of matter is as rest, it has a total amount of energy equal to its rest energy. If work is done to a particle by applying force, the energy of the particle increases. At speeds that are far from the speed of light, all the work done increases the kinetic energy of the particle. It would take an infinite amount of work to accelerate a particle to the speed of light, because at the speed of light the mass of a particle also becomes infinite.

18.3 The equivalence of energy and mass Einstein’s was able to deduce the equivalent of mass and energy by thinking about the momentum of two particles moving near the speed of light. Since the speed of light must be the same for all observers regardless of their relative motion and energy and momentum must be conserved, as the speed of an object gets near the speed of light, the increase in mass must come from energy.

Calculating equivalence A nuclear reactor converts 0.7% of the mass of uranium to energy. If the reactor used 100 kg of uranium in a year, how much energy is released? One gallon of gasoline releases 1.3 × 108 joules. How many gallons of gasoline does it take to release the same energy as the uranium? You are asked for energy and no. of gallons. You are given mass of uranium, % converted to energy, rate Use Einstein’s formula: E = mc2 Solve for mass converted to energy: m = (.007) ( 100 kg)= 0.7 kg Solve for energy released: E = (0.7 kg)( 3 x 108 m/s)2 E = 6.3 x 1016 J Calculate equivalent using rate: 6.3 x 1016 J ÷ 1.3 x 108 J/gal = 4.8 108 J 1 kg of U releases same energy as 480 million gallons of gas.

18.3 Simultaneity When we say that two events are simultaneous, we mean they happen at the same time. Since time is not constant for all observers, whether two events are simultaneous depends on the relative motion of the observers.

18.3 Simultaneity The two lightning strikes are simultaneous to the observer at rest, but the observer moving with the train sees the lightning strike the front of the train first.

Holography A well-made hologram appears to have depth and perspective as if the actual three-dimensional scene was embedded in the picture. A true 3D scene looks different when seen from different angles. A hologram duplicates the three-dimensional shape of the wave front that is coming from the real object.