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28.2 Simultaneity And Time Dilation

- Explain the difference between special relativity and general relativity.

- General relativity applies to accelerated motion.

- The elapsed time for a foot race is the same for everyone except for the relative motion of the observer and the event that is observed.

- The time for a process, such as the elapsed time for a foot race, should be the same for everyone.
- The accuracy of measuring time is what has led to disagreements over elapsed time.
- The relative motion of an observer with respect to the process being measured will determine the elapsed time.

How do we measure elapsed time?

- One way to use the light from the event is to start a drag race by observing a green light.
- If electronic detection is used, the timing will be more accurate.

- Suppose we use this method to measure the time between two flashes of light.

- 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 between the light flashes.
- The motion of the lamps relative to B does not affect the speed of light.
- Observer B measures the flashes at the same time.

- Observer B measures the elapsed time between the arrival of light flashes.
- Observer B is looking at the light flashes.
- Observer B looks at the light on the right before the light on the left.

- Think about what observer B sees and what observer A sees.
- Observer B can see the light from the right because she has moved toward the flash lamp, which will reduce the time it takes to get to her.
- Light travels at a slower pace relative to both observers, but observer B is equidistant between the points where the flashes were emitted, while A is closer to the emission point on the right.
- There is a time interval between the arrival of the flashes to observer A.
- Observer B measures the flashes to arrive at the same time relative to him.

- Consider what observer A sees.
- She sees the light from the right at the same time as she sees the light from the left.
- The flashes occurred at the same time because the lamps were the same distance from her reference frame.
- If two events are observed at the same time, a relative velocity between observers is important.

- This shows the power of clear thinking.
- Two observers halfway between the sources would see the flashes if light is emitted simultaneously.
- This isn't the case, according to careful analysis.

- Einstein was a genius at this type of thought experiment.
- He carefully considered how an observation is made.
- The validity of thought experiments is determined by observation.
- Experiments have repeatedly confirmed Einstein's theory of relativity.

- Two events are defined to be simultaneous if an observer measures them at the same time.
- There are two events that are not simultaneous.

- The measurement of elapsed time leads to a relativistic effect.

- An astronauts will measure the time it takes for light to cross her ship, bounce off a mirror and return.
- A profound result is produced by asking this question.
- The elapsed time for a process depends on who is measuring it.
- The time measured by the astronauts is smaller than the time measured by the Earth-bound observer.
- The distance between the Earth and the astronauts' frame is smaller than the distance between the Earth and the astronauts' frame for the observers.
- The Earth-bound frame takes longer to travel the greater distance because light travels at the same speed in each frame.

- Light travels a long way in the frame.

- Consider the paths followed by light as seen by each observer to verify that time depends on the observer.
- The light travels twice the width of the ship as it travels across and back.

- The observer sees the light travel a long way.
- Since the ship is moving to the right relative to the Earth, light moving to the right hits the mirror in this frame.

- The time measured by the Earth-bound observer has a separate name.

- In the case of the astronauts, they observe the reflecting light.

- We get if we square the first expression we had for.
- The preceding equation gives us a means to relate the two time intervals.

- This equation is amazing.
- Even though both are in inertial frames, elapsed time is not the same for different observers moving relative to one another.
- Time measured by other observers is larger than time measured by an observer.

- Time dilates for a system moving relative to the Earth.
- According to the Earth-bound observer, time slows in the moving frame since less time passes there.
- All clocks moving relative to an observer are slow compared with a clock stationary relative to the observer.

- Our everyday experiences have small effects on classical physics.

- The equation suggests that relative velocity can't exceed the speed of light.

- This would mean that the time in the frame stops at the speed of light.
- If exceeded, we would take the square root of a negative number and create an imaginary value.

- There is a lot of evidence that the equation is correct.
- Cosmic ray particles that rain down on the Earth from deep space are an example.
- There are particles in the upper atmosphere that have short-lived particles called muons.
- The amount of time for half of a muon to decay is called the half-life.
- This is the right time.
- Cosmic ray particles have a range of velocities, with some moving near the speed of light.
- The muon's halflife as measured by an Earth-bound observer is exactly as predicted by the equation.
- The muon can live longer if it moves fast.
- The muon decays more slowly when it is relative to us than it does when it is not.

- A muon is created when a Cosmic Ray collides with a nucleus in the Earth's upper atmosphere.

- The muon travels at constant speed and lives in its frame of reference.

- A muon in the Earth's atmosphere can be measured by an Earth-bound observer than by its internal clock.

- The time we are given is observed by a clock moving with the system being measured.
- As per the equation, the Earth-bound observer measures.
- The calculation is easy since we know the speed.

- The knowns should be identified.

- The appropriate equation can be chosen.

- The knowns should be plugged into the equation.

- The calculated value is used to determine.

- At the speed of light, the effects are significant.
- Classically, the two time intervals would be the same.

- An implication of the preceding example is that when viewed from the Earth, everything an astronauts does takes 3.20 times longer than when moving at the speed of light.
- If she looks outside her spaceship.
- The same factor of 3.20 will affect all methods of measuring time.
- She has a wristwatch, heart rate, cell metabolism rate, nerve impulse rate, and so on.
- She won't be able to tell since all of her clocks agree with one another.
- Motion is relative.

- It may seem that special relativity has no effect on your life, but it is more important than you realize.
- The global positioning system is one of the most common effects.
- Emergency vehicles, package delivery services, electronic maps, and communications devices are just a few of the common uses of the gps system.
- GPS satellites use precise time measurements to communicate.
- The signals travel fast.
- The satellites couldn't communicate and the gps system wouldn't work within minutes.

- A space traveler moving at a high speed relative to the Earth would age less than her twin.
- It would take 60.0 years for her twin's frame to be filled with the same amount of time.
- The astronauts traveled to another star system.
- She traveled 1.00 year back after briefly exploring the area.
- She would be 42 on her return if she was 40 years old when she left.
- The Earth would have been 60.0 years old.
- Her twin would be 100 years old.

- The situation wouldn't seem the same to the astronauts.
- The spaceship would seem to be stationary and the Earth would move.

- To her, the Earth-bound sister will be only 2/30 of a year older than she is.
- Both sisters can't be right.

- The traveling twin is younger than the Earth-bound twin.
- If we consider the twin's frame, we get that prediction.
- Time runs slower in the frame of the astronauts, as the Earth is moving.

- The premise is faulty and leads to conflicting conclusions.
- The motion of the Earth-bound twin is similar to that of the astronauts.
- The astronauts decelerates to view the star system.
- She decelerated and accelerated to return to the Earth.
- The Earth-bound twin doesn't experience these accelerations.
- It is not correct to say that the astronauts will observe the same effects as their twin.
- The theory of the twin paradoxes is based on the fact that the frames are not accelerated or rotating.
- Einstein developed general relativity to deal with gravity and accelerated frames.
- According to general relativity, the astronauts will age less than other people.
- In this course, some important aspects of general relativity are discussed.

- Physicists Joseph Hafele and Richard Keating flew atomic clocks around the Earth in 1971 to verify time dilation.
- They measured elapsed time and compared it to the time left behind.
- The results were within the predictions of relativity.
- Since gravity and accelerations were involved, special and general relativity had to be taken into account.

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