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- Sample Problems and Solutions
- Time dilation
- 5.4: Time Dilation
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Sample Problems and Solutions
We have used the postulates of relativity to examine, in particular examples, how observers in different frames of reference measure different values for lengths and the time intervals. We can gain further insight into how the postulates of relativity change the Newtonian view of time and space by examining the transformation equations that give the space and time coordinates of events in one inertial reference frame in terms of those in another. We first examine how position and time coordinates transform between inertial frames according to the view in Newtonian physics. Then we examine how this has to be changed to agree with the postulates of relativity. Finally, we examine the resulting Lorentz transformation equations and some of their consequences in terms of four-dimensional space-time diagrams, to support the view that the consequences of special relativity result from the properties of time and space itself, rather than electromagnetism. An event is specified by its location and time x , y , z , t relative to one particular inertial frame of reference S.
It turns out that as an object moves with relativistic speeds a "strange" thing seems to happen to its time as observed by "us" the stationary observer observer in an inertial reference frame. What we see happen is that the "clock" in motion slows down according to our clock, therefore we read two different times. Which time is correct??? Let's look at the following classic example. There is a set of twins, one an astronaut, the other works for mission control of NASA. Upon returning the astronauts clock has measured ten years, so yhe astronaut has aged 10 years.
5.4: Time Dilation
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It only takes a minute to sign up. Let there be two bodies a and b. Then let the time interval which has passed on the earth be twice that of the time interval of which passed in space for b, i. Does b also feel that the time interval which it passed with a spaceship in space is twice that of the time interval of a which passed on the earth?
In physics and relativity , time dilation is the difference in the elapsed time as measured by two clocks. It is either due to a relative velocity between them "kinetic" time dilation, from special relativity or to a difference in gravitational potential between their locations gravitational time dilation , from general relativity. When unspecified, "time dilation" usually refers to the effect due to velocity. After compensating for varying signal delays due to the changing distance between an observer and a moving clock i. Doppler effect , the observer will measure the moving clock as ticking slower than a clock that is at rest in the observer's own reference frame.
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In special relativity, an observer in inertial i. A second inertial observer, who is in relative motion with respect to the first, however, will disagree with the first observer regarding which events are simultaneous with that given event. Neither observer is wrong in this determination; rather, their disagreement merely reflects the fact that simultaneity is an observer-dependent notion in special relativity. A notion of simultaneity is required in order to make a comparison of the rates of clocks carried by the two observers. A closely related phenomenon predicted by special relativity is the so-called twin paradox.
Time and the Metaphysics of Relativity pp Cite as. The relativity of simultaneity and the relativity of length lead naturally to the strangest consequences of relativity theory: time dilation and length contraction. Time dilation means that relative to a clock taken to be at rest, a moving clock runs slow, so that relative to the moving clock the amount of time recorded by the clock at rest expands or dilates. Let us suppose that we have two clocks A and B in motion relative to each other Figure 3. Unable to display preview. Download preview PDF. Skip to main content.
How does the elapsed time that the astronaut measures in the spacecraft compare with the elapsed time that an earthbound observer measures by observing what is happening in the spacecraft? Examining this question leads to a profound result. The elapsed time for a process depends on which observer is measuring it. In this case, the time measured by the astronaut within the spaceship where the astronaut is at rest is smaller than the time measured by the earthbound observer to whom the astronaut is moving. Light travels at the same speed in each frame, so it takes more time to travel the greater distance in the earthbound frame.
Note that time dilation and length contraction are just special cases: it is time-dilation if ∆x = 0 and length contraction if ∆t = 0. 3. The spacetime interval (∆s)2.