Include the effects of gravity (which also causes time dilation) and this figure goes up to about 7 microseconds. Let's see how we can calculate the time "difference". previous index next. The main example that’s generally given is that of a muon coming towards the earth. In addition, the instant Kalpana’s ship passes the earth both the sisters start timers. the flow of time doesn't change very much), but at speeds over about 75% of the speed of light the effect of time dilation is quite dramatic. The equation for calculating time dilation is as follows: t = t 0 /(1-v 2 /c 2) 1/2 . The effects of time dilation are used often in science fiction stories, dating back to at least the 1930s. t 0 = time in observers own frame of reference (rest time) v = the speed … For v = c, T = T 0 For small velocities at which the relativity factor is very close to 1, then the time dilation can be expanded in a binomial expansion to get the approximate expression: One of the earliest and most well-known thought experiments to feature time dilation is the famous Twin Paradox, which demonstrates the curious effects of time dilation at its most extreme. Suppose that Kalpana boards a spaceship and flies past the earth at 0.800 times the speed of light. Time Dilation Examples . Example \(\PageIndex{1A}\): Time Dilation in a High-Speed Vehicle. Basically, it states that the faster we go, the more the time is affected. The satellite experiences the passage of time faster than people on Earth. The lifetime of a muon is approximately 2.2[math] \mu s[/math]. We can see from the graph that at “low” speeds there is only a small change in time dilation (i.e. The time measured in the frame in which the clock is at rest is called the "proper time". “Moving Clocks Run Slow” plus “Moving Clocks Lose Synchronization” plus “Length Contraction” leads to consistency! Solved Example on Time Dilation Formula Example 1. If an electronic clock in the HTV-2 measures a time interval of exactly 1-s duration, what would observers on Earth measure the time interval to be? Michael Fowler, UVa Physics. The observer's time is known, and so the amount of time that passes in the muon's reference frame can be found by rearranging the time dilation formula: In the muon's reference frame, approximately 2.82 x 10 -6 seconds pass between when the muon is created and when it reaches the Earth's surface. where: t = time observed in the other reference frame. Time Dilation: A Worked Example . 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