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Name: _________________ Introduction T he first person to understand the Quantum Physics pertains to the incredibly relationship between space and time was small-scale structure of atoms and nuclei. Albert Einstein. Three important papers Relativity applies to the incredibly large-scale were published in the early part of the 20th structure of the entire universe. There are two Century that established Einstein as one of the parts to relativity: Special relativity describes greatest scientists of all time. There were also how space and time are related at constant many other very talented scientists who laid the velocity, and General Relativity describes how groundwork for Einstein‟s research, and many space and time are related in accelerating other scientists working after to prove his reference frames, a more „general‟ case. Today, theories in the laboratory. The physics of Isaac scientists are attempting to develop a theory that Newton do not apply in the relativistic world of encompasses everything, both the very big and Einstein, nor do they apply in the sub-atomic very small. world -–the other great 20th Century scientific revolution. Newton‟s world of Classical Physics is the everyday ordinary medium sized universe. Reference Frames et‟s say you are on a train with absolutely L have a lap full of tea. Uncover the windows and smooth tracks. On board you can play only now can you detect your motion. catch with a football, pour tea into a cup, and jump up and down like you could at rest. Imagine you and your friend are playing catch on The ball, while in the air, does not suddenly hit the moving train, and a third friend is outside not the rear of the train, nor does the tea or you. You moving on the station platform. How would this all continue to move with the train. In fact, if the stationary person detect and measure the motion windows were all covered you couldn‟t even of the ball? determine if you were moving or not. Until, of course, you turn the corner or hit that bump and Question 1. Suppose you can throw a ball at 80 km/h. 80 km/h a) You throw the ball from the back of a stationary truck. How fast is the ball moving relative to your catcher friend when he catches the ball? 80 km/h b) Now suppose you throw the ball toward 140 km/h your friend from the back of a moving truck. The truck is moving toward your friend at 60 km/h. How fast is the ball moving as your friend catches the ball? 140 km/h c) You throw the ball from the 20 km/h back of a truck moving away at 60 km /h from your friend. How fast is the ball moving as your friend catches the ball? Postulates of Special Relativity A ccording to Einstein, these examples of motion of the truck. If a rocket travelling at 0.9c adding and subtracting velocities (90% speed of light) were to fire missiles at 0.9c developed by Galileo are wrong for relative to the motion of the rocket, a stationary objects that travel near the speed of light. A observer would see those missiles travelling at beam of light shines at the speed of light 0.99c. regardless of the motion of the source of light. If you and your friend were to perform the same Einstein was an inquisitive thinker. He asked the experiment as before but this time shining light question: “What would it be like to travel rather than throwing balls the results would not alongside a beam of light?” From thinking about be the same. If you were able to measure the and answering that question he formulated the speed of light coming from a flashlight, it would Two Postulates of Special Relativity have the same measured value regardless of the First Postulate All the laws of nature are the same in all uniformly moving reference frames. The consequence is that you cannot detect your own motion. Coins flip as if they would when travelling near the speed of light or at rest. This is where the term „relativity‟ originates: All motion is relative. If you are travelling in one spaceship past another spaceship, it would be the same as, and indistinguishable from, another spaceship travelling backwards relative to your stationary spaceship. Second Postulate The speed of light in empty space will always have the same value regardless of the motion of the source or the motion of the observer. The consequence is that there is an upper speed limit in the universe, the speed of light, and nothing can travel faster. Time Dilation T ime runs more slowly on moving objects Proof: High-speed radioactive cosmic particles as measured by stationary observers. decay more slowly, as measured by us in the However, on the spaceship, everything stationary laboratory. appears normal. And according to the spaceship, everything is moving around the stationary spaceship, and all of their clocks run slowly. Twin Trip One twin rides a high-speed spaceship, the other on the whether the spaceship is receding or stays at home. If the travelling twin maintains a approaching, according to the Doppler Effect. speed of 0.87c for one year, 2 years elapses on Receding 10 pulses @12 min = 120 min the Earth. At 0.995c for one year, 10 years will Approaching 10 pulses @ 3 min = 30 min elapse on then Earth. The travelling twin will come back younger than the twin who stayed on Total 2 ½ hours the Earth. This is a result of the constancy of the More time has elapsed on the Earth. This makes speed of light. time travel possible! (Sort of) If you travel near Proof: Let the spaceship send a pulse of light the speed of light for a long time, say 5 years, every 6 minutes. 20 pulses of light at 6 minutes you could travel 1000 light years distance, as are 120 minutes or 2 hours. On the Earth the measured relative to Earth distance. How is this pulses are received at different rates depending possible? This is a result of length contraction. Length Contraction M oving objects undergo changes in length contraction. The muon would measure length as well as time. Moving objects the distance travelled as shorter. appear to contract along the length of motion. To explain how this works take the Earth measures 9000 m @ 30 s 300 m/s example of the radioactive cosmic particle the the muon travel muon. The muon half-life at rest is 2 s and the half-life while moving as measured by stationary Muon measures 600 m @ 2 s 300 m/s itself travel observers on the Earth is 30 s. Therefore, as the muon decays 30 s passes on the Earth, and Both measure the same relative motion, 2 s passes for the muon. But how does the therefore, this example still obeys Einstein‟s muon see this change in time. How is this First Postulate. explained? Einstein‟s First Postulate must be obeyed, which states that everyone in all reference frames moving or not must get the same results. This problem is explained using Relativistic Momentum F or a stationary observer they will measure electron is deflected less than what would be objects moving with an increased predicted using classical Newtonian Physics. momentum. Indeed, the momentum, as Magnet measured by a stationary observer, approaches infinity as the object travels closer and closer to the speed of light. That object, of course, would not measure any change in its own momentum. Relativistic (observed) Consequently, no object of any mass can travel at the speed of light. Magnet Classical prediction Proof: In a particle accelerator, very small (not observed) nuclear particles routinely travel near the speed To the particles, they see no change in their own of light. The physicists who study these momentum. So how is it explained to be particles must use the concepts of relativity to consistent with the First Postulate? To the explain their results. In a particle accelerator particles, the distance travelled would decrease; charged particles are deflected when they pass therefore there is less deflection. through a magnetic field. A faster moving Equivalence of Mass and Energy M ass is simply a form of energy. Even Rest energy, like other forms of energy, can be if an object is not moving it has rest converted into other forms. When striking a energy. The relationship between match the mass of the products is slightly less, mass and energy is in the form of the 20th about 1 part in a billion, because of the kinetic Century‟s most famous equation: energy of the products (the fiery hotness). For nuclear reactions the mass difference (mass of E0 = mc2. products < mass of reactants) is more substantial which results in a huge release of energy E0 is the rest energy of the object, m is the mass (enough to obliterate entire cities). Hot tea has and c is the speed of light. Because c is such a more mass than cold tea, because there has been large number already, its square is even larger, an increase in the energy of the tea. the rest energy of even the smallest amount of matter is enormous. Review Questions 1. The speed of a ball you catch that is thrown from a moving truck depends on the speed and direction of the truck. Does the speed of light measured from a moving source depend on the speed and direction of the source? Explain. Yes, the speed of the truck and ball matters at these low velocities; the velocity is either added or subtracted depending on the direction. But the speed of light does not matter as the speed of light is the same in all reference frames, moving or not. 2. What are Einstein‟s Two Postulates of Special Relativity? First Postulate All the laws of nature are the same in all uniformly moving reference frames. Second Postulate The speed of light in empty space will always have the same value regardless of the motion of the source or the motion of the observer. 3. If a spaceship moves away from you at half the speed of light and fires a missile at half the speed of light relative to the spaceship, common sense may tell you that the missile moves at the speed of light relative to you. But it doesn‟t. The relativistic addition of velocities is given by: v1 v 2 V vv 1 1 22 c 0.5c 0.5c 1.0c V 0.8c (0.5c)(0.5c) 1 0.25 1 c2 Substitute 0.5c for both velocities to determine the velocity of the missile relative to the stationary observer. 4. Use the equation in question #3 to show that for small everyday velocities this equation is practically the same as v1+v2. m V 0.01c 3 106 3000km / s s 0.01c 0.01c 0.02c V 0.02c (0.01c)(0.01c) 1 0.0001 1 c2 5. Use the equation of question #3 to show that even if the spaceship could move at the speed of light and fired a missile at the speed of light, the velocity relative to the stationary observer is still the speed of light. There is indeed an upper speed limit in the universe. cc 2c V c c c 11 1 2 c 6. If we view a passing spaceship and see their clocks running slow, how do they see our time running? They also see our clocks as running slow. They have to, because every reference frame must have the same results. 7. Is it possible for a person with a 70 year life span to travel farther than light travels in 70 years? but Explain. Yes, because the clocks on the spacecraft will not have elapsed 70 years, something less. To accommodate this, the spacecraft does not travel 70 light years, but due to length contraction, it has traveled some distance less. 8. Suppose you were travelling in a smooth riding train with no windows could you sense between uniform motion and rest? Between accelerated motion and rest? Explain how you could do this with a bowl filled with water. You cannot tell the difference between uniform motion (constant velocity) and rest. All the laws will be the same. You can juggle, pour tea or walk with the same results at rest as you would on a train. But you can tell when you are accelerating, this is not uniform motion. A bowl filled with water will slosh back when accelerating and slosh forward when stopping. Einstein’s Theory of General Relativity says that an accelerating frame of reference is indistinguishable from gravity. 9. If you were travelling in a high-speed spaceship, how would the meter sticks on board appear? How would these meter sticks on board appear to a stationary observer outside? The meter sticks on board traveling with you would be the same length as at rest – one meter. But if a stationary observer were to see those meter sticks moving past, they would be shorter than one meter. 10. How does the distance to Pluto as measured by a fast moving spaceship compare to our measurement on a stationary Earth? The distance to Pluto as measured by a fast moving spaceship would be less than when measured by a stationary observer on the Earth. nuclear fusion within the Sun. When hydrogen 11. Where does solar energy originate? From nuclei combine to form helium nuclei, the mass of the products is less than the mass of the reactants. The missing mass is energy. 12. What would be the momentum of an object as it is pushed toward the speed of light? How much energy would it take to get objects of any mass to travel at the speed of light? The momentum of an object as measured by a stationary observer would approach infinity. So it would take a corresponding infinite amount of energy to get a massive object to travel at the speed of light. Only mass less particles – photons – travel at the speed of light. 13. The two-mile long particle accelerator at Stanford University in California appears to be less than a meter long to the electrons that travel it. Explain. This is due to length contraction. The electrons measure the length they travel as less than the stationary observers. 14. Does the concept of relativity mean that all of Newton‟s equations are wrong? Explain. No, Newton’s equations work perfectly well for objects traveling at slow speeds (non- relativistic speeds, that is, no where near the speed of light.) Our everyday world of science on the earth and planets fits this model very well. Any research 15. Describe the types of physics research in which knowledge of relativity is required. that explores very fast particles must use the concept of relativity. As well as any cosmology, the large scale structure of the universe.

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Special relativity, General relativity, speed of light, Albert Einstein, The theory of relativity, Theory of relativity, space and time, reference frame, gravitational field, time dilation

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posted: | 2/3/2010 |

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