Simultaneity And Time Dilation Quiz

PDF page 1340: the lamps on a rail car. Observer B views the light flashes occurring simultaneously. Observer B views the light on the right reaching observer A before the light on the left does. Now consider what observer A sees happening. Since both lamps are the same distance from her in her reference frame and the train is moving to the right, she perceives the flash from the right-hand bulb occurring before the lefthand bulb. Here a relative velocity between observers affects whether two events are observed to be simultaneous. Simultaneity is not absolute.. This illustrates the power of clear thinking. We might have guessed incorrectly that if light is emitted simultaneously, then two observers halfway between the sources would see the flashes simultaneously. But careful analysis shows this not to be the case. Einstein was brilliant at this type of thought experiment (in German, “Gedankenexperiment”). He very carefully considered how an observation is made and disregarded what might seem obvious. The validity of thought experiments, of course, is determined by actual observation. The genius of Einstein is evidenced by the fact that experiments have repeatedly confirmed his theory of relativity. In summary: Two events are defined to be simultaneous if an observer measures them as occurring at the same time (such as by receiving light from the events). Two events are not necessarily simultaneous to all observers.

PDF page 1340: the lamps on a rail car. Observer B views the light flashes occurring simultaneously. Observer B views the light on the right reaching observer A before the light on the left does. Now consider what observer A sees happening. Since both lamps are the same distance from her in her reference frame and the train is moving to the right, she perceives the flash from the right-hand bulb occurring before the lefthand bulb. Here a relative velocity between observers affects whether two events are observed to be simultaneous. Simultaneity is not absolute.. This illustrates the power of clear thinking. We might have guessed incorrectly that if light is emitted simultaneously, then two observers halfway between the sources would see the flashes simultaneously. But careful analysis shows this not to be the case. Einstein was brilliant at this type of thought experiment (in German, “Gedankenexperiment”). He very carefully considered how an observation is made and disregarded what might seem obvious. The validity of thought experiments, of course, is determined by actual observation. The genius of Einstein is evidenced by the fact that experiments have repeatedly confirmed his theory of relativity. In summary: Two events are defined to be simultaneous if an observer measures them as occurring at the same time (such as by receiving light from the events). Two events are not necessarily simultaneous to all observers.

PDF page 1340: Suppose, for example, an astronaut measures the time it takes for light to cross her ship, bounce off a mirror, and return. (See Figure 28.6.) How does the elapsed time the astronaut measures compare with the elapsed time measured for the same event by a person on the Earth? Asking this question (another thought experiment) produces a profound result. We find that the elapsed time for a process depends on who is measuring it. In this case, the time measured by the astronaut is smaller than the time measured by the Earth-bound observer. The passage of time is different for the observers because the distance the light travels in the astronaut’s frame is smaller than in the

PDF page 1339: Consider how we measure elapsed time. If we use a stopwatch, for example, how do we know when to start and stop the watch? One method is to use the arrival of light from the event, such as observing a light turning green to start a drag race. The timing will be more accurate if some sort of electronic detection is used, avoiding human reaction times and other complications. Now suppose we use this method to measure the time interval between two flashes of light produced by flash lamps. (See Figure 28.5.) Two flash lamps with observer A midway between them are on a rail car that moves to the right relative to observer B. Observer B arranges for the light flashes to be emitted just as A passes B, so that both A and B are equidistant from the lamps when the light is emitted. Observer B measures the time interval between the arrival of the light flashes. According to postulate 2, the speed of light is not affected by the motion of the lamps relative to B. Therefore, light travels equal distances to him at equal speeds. Thus observer B measures the flashes to be simultaneous.

PDF page 1340: the lamps on a rail car. Observer B views the light flashes occurring simultaneously. Observer B views the light on the right reaching observer A before the light on the left does. Now consider what observer A sees happening. Since both lamps are the same distance from her in her reference frame and the train is moving to the right, she perceives the flash from the right-hand bulb occurring before the lefthand bulb. Here a relative velocity between observers affects whether two events are observed to be simultaneous. Simultaneity is not absolute.. This illustrates the power of clear thinking. We might have guessed incorrectly that if light is emitted simultaneously, then two observers halfway between the sources would see the flashes simultaneously. But careful analysis shows this not to be the case. Einstein was brilliant at this type of thought experiment (in German, “Gedankenexperiment”). He very carefully considered how an observation is made and disregarded what might seem obvious. The validity of thought experiments, of course, is determined by actual observation. The genius of Einstein is evidenced by the fact that experiments have repeatedly confirmed his theory of relativity. In summary: Two events are defined to be simultaneous if an observer measures them as occurring at the same time (such as by receiving light from the events). Two events are not necessarily simultaneous to all observers.

PDF page 1340: the lamps on a rail car. Observer B views the light flashes occurring simultaneously. Observer B views the light on the right reaching observer A before the light on the left does. Now consider what observer A sees happening. Since both lamps are the same distance from her in her reference frame and the train is moving to the right, she perceives the flash from the right-hand bulb occurring before the lefthand bulb. Here a relative velocity between observers affects whether two events are observed to be simultaneous. Simultaneity is not absolute.. This illustrates the power of clear thinking. We might have guessed incorrectly that if light is emitted simultaneously, then two observers halfway between the sources would see the flashes simultaneously. But careful analysis shows this not to be the case. Einstein was brilliant at this type of thought experiment (in German, “Gedankenexperiment”). He very carefully considered how an observation is made and disregarded what might seem obvious. The validity of thought experiments, of course, is determined by actual observation. The genius of Einstein is evidenced by the fact that experiments have repeatedly confirmed his theory of relativity. In summary: Two events are defined to be simultaneous if an observer measures them as occurring at the same time (such as by receiving light from the events). Two events are not necessarily simultaneous to all observers.

PDF page 1343: There is considerable experimental evidence that the equation is correct. One example is found in cosmic ray particles that continuously rain down on the Earth from deep space. Some collisions of these particles with nuclei in the upper atmosphere result in short-lived particles called muons. The half-life (amount of time for half of a material to decay) of a muon is when it is at rest relative to the observer who measures the half-life. This is the proper time . Muons produced by cosmic ray particles have a range of velocities, with some moving near the speed of light. It has been found that the muon’s half-life as measured by an Earth-bound observer ( ) varies with velocity exactly as predicted by the equation . The faster the muon moves, the longer it lives. We on the Earth see the muon’s half-life time dilated—as viewed from our frame, the muon decays more slowly than it does when at rest relative to us.

PDF page 1343: There is considerable experimental evidence that the equation is correct. One example is found in cosmic ray particles that continuously rain down on the Earth from deep space. Some collisions of these particles with nuclei in the upper atmosphere result in short-lived particles called muons. The half-life (amount of time for half of a material to decay) of a muon is when it is at rest relative to the observer who measures the half-life. This is the proper time . Muons produced by cosmic ray particles have a range of velocities, with some moving near the speed of light. It has been found that the muon’s half-life as measured by an Earth-bound observer ( ) varies with velocity exactly as predicted by the equation . The faster the muon moves, the longer it lives. We on the Earth see the muon’s half-life time dilated—as viewed from our frame, the muon decays more slowly than it does when at rest relative to us.

PDF page 1342: Note that if the relative velocity is much less than the speed of light ( ), then is extremely small, and the elapsed times and are nearly equal. At low velocities, modern relativity approaches classical physics—our everyday experiences have very small relativistic effects. The equation also implies that relative velocity cannot exceed the speed of light. As approaches , approaches infinity. This would imply that time in the astronaut’s frame stops at the speed of light. If exceeded , then we would be taking the square root of a negative number, producing an imaginary value for .

PDF page 1342: Note that if the relative velocity is much less than the speed of light ( ), then is extremely small, and the elapsed times and are nearly equal. At low velocities, modern relativity approaches classical physics—our everyday experiences have very small relativistic effects. The equation also implies that relative velocity cannot exceed the speed of light. As approaches , approaches infinity. This would imply that time in the astronaut’s frame stops at the speed of light. If exceeded , then we would be taking the square root of a negative number, producing an imaginary value for .

PDF page 1342: Note that if the relative velocity is much less than the speed of light ( ), then is extremely small, and the elapsed times and are nearly equal. At low velocities, modern relativity approaches classical physics—our everyday experiences have very small relativistic effects. The equation also implies that relative velocity cannot exceed the speed of light. As approaches , approaches infinity. This would imply that time in the astronaut’s frame stops at the speed of light. If exceeded , then we would be taking the square root of a negative number, producing an imaginary value for .

PDF page 1344: An intriguing consequence of time dilation is that a space traveler moving at a high velocity relative to the Earth would age less than her Earth-bound twin. Imagine the astronaut moving at such a velocity that , as in

PDF page 1345: consider the Earth-bound twin’s frame. In the astronaut’s frame, however, the Earth is moving and time runs slower there. Who is correct? As with all paradoxes, the premise is faulty and leads to contradictory conclusions. In fact, the astronaut’s motion is significantly different from that of the Earth-bound twin. The astronaut accelerates to a high velocity and then decelerates to view the star system. To return to the Earth, she again accelerates and decelerates. The Earth-bound twin does not experience these accelerations. So the situation is not symmetric, and it is not correct to claim that the astronaut will observe the same effects as her Earth-bound twin. If you use special relativity to examine the twin paradox, you must keep in mind that the theory is expressly based on inertial frames, which by definition are not accelerated or rotating. Einstein developed general relativity to deal with accelerated frames and with gravity, a prime source of acceleration. You can also use general relativity to address the twin paradox and, according to general relativity, the astronaut will age less. Some important conceptual aspects of general relativity are discussed in General Relativity and Quantum Gravity of this course. In 1971, American physicists Joseph Hafele and Richard Keating verified time dilation at low relative velocities by flying extremely accurate atomic clocks around the Earth on commercial aircraft. They measured elapsed time to an accuracy of a few nanoseconds and compared it with the time measured by clocks left behind. Hafele and Keating’s results were within experimental uncertainties of the predictions of relativity. Both special and general relativity had to be taken into account, since gravity and accelerations were involved as well as relative motion.