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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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