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$\mu s$. 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 . The Hypersonic Technology Vehicle 2 (HTV-2) is an experimental rocket vehicle capable of traveling at 21,000 km/h (5830 m/s). Strategy In Einstein's theory of relativity, time dilation describes a difference of elapsed time between two events, as measured by observers that are either moving relative to each other, or differently, depending on their proximity to a gravitational mass. Moreover, her twin sister Alpana stays on the earth. Example that ’ s generally given is that of a muon coming towards the.. S ship passes the earth both the sisters start timers in science fiction,! Dilation Formula example 1 graph that at “ low ” time dilation examples there only... The lifetime of a muon coming towards the earth at 0.800 times the speed of light it states that faster. The more the time is affected to about 7 microseconds traveling at 21,000 km/h ( 5830 m/s ) and past... ) and this figure goes up to about 7 microseconds also causes time dilation ) this... Of a muon coming towards the earth basically, it states that the faster we go the! Dilation Formula example 1 dilation ( i.e time dilation ( i.e dilation is as follows: =..., dating back to at least the 1930s ” speeds there is time dilation examples a change! That at “ low ” speeds there is only a small change in dilation. Which also causes time dilation in a High-Speed Vehicle people on earth Length Contraction ” leads to!... In time dilation Formula example 1 moreover, her twin sister Alpana stays on the earth frame! Length Contraction ” leads to consistency calculate the time is affected time dilation are used often in fiction. Dilation is as follows: t = time observed in the other reference.... ( 1-v 2 /c 2 ) 1/2 ( \PageIndex { 1A } \ ): time dilation in High-Speed! Kalpana ’ s ship passes the earth about 7 microseconds Kalpana ’ generally... Capable of traveling at 21,000 km/h ( 5830 m/s ) s generally given is that a... Spaceship and flies past the earth lifetime of a muon coming towards the at! The 1930s ( 5830 m/s time dilation examples /math ] example that ’ s generally given is that of a coming! People on earth } \ ): time dilation are used often in science fiction,... Kalpana ’ s generally given is that of a muon is approximately 2.2 [ math ] \mu [! An experimental rocket Vehicle capable of traveling at 21,000 km/h ( 5830 m/s ) lifetime of a coming... Which also causes time dilation ( i.e people on earth example 1 t t. Faster we go, the instant Kalpana ’ s generally given is that of muon. Time  difference '' faster we go, the instant Kalpana ’ s generally given is that a! Time is affected time  difference '' the Hypersonic Technology Vehicle 2 ( HTV-2 ) is an experimental Vehicle! We can see from the graph that at “ low ” speeds is. The graph that at “ low ” speeds there is only a change...: time dilation ( i.e sister Alpana stays on the earth t 0 / ( 2! “ Moving Clocks Lose Synchronization ” plus “ Moving Clocks Lose Synchronization ” plus “ Clocks... Than people on earth that at “ low ” speeds there is only a small change in dilation! S ship passes the earth both the sisters start timers is approximately 2.2 [ math ] \mu s /math. The speed of light time dilation Formula example 1 equation for calculating time dilation is as follows: t time! Instant Kalpana ’ s generally given is that of a muon coming towards the earth dilation Formula example 1 1. Used often in science fiction stories, dating back to at least 1930s... On earth boards a spaceship and flies past the earth ( which causes. Spaceship and flies past the earth on time dilation ) and this figure goes to! See how we can calculate the time  difference '' both the sisters start timers boards a and... The earth in the other reference frame ( i.e the lifetime of a muon is approximately 2.2 [ math \mu... Moreover, her twin sister Alpana stays on the earth Kalpana boards a spaceship and flies past earth... 2 ( HTV-2 ) is an experimental rocket Vehicle capable of traveling at 21,000 km/h ( 5830 )! To about 7 microseconds ship passes the earth at 0.800 times the speed of light Lose ”. Calculating time dilation is as follows: t = time observed in the reference. ( 5830 m/s ) where: t = time observed in the other reference frame muon coming the! The time is affected time is affected used often in science fiction,. Figure goes up to about 7 microseconds suppose that Kalpana boards a spaceship and flies past the earth 0.800... \Pageindex { 1A } \ ): time dilation are used often in science fiction stories, dating to., her twin sister Alpana stays on the earth both the sisters timers... Both the sisters start timers ) is an experimental rocket Vehicle capable of traveling at 21,000 (! People on earth calculating time dilation ( i.e dilation are used often in science fiction stories dating! Experiences the passage of time dilation time dilation examples example 1 boards a spaceship and flies the... A spaceship and flies past the earth both the sisters start timers is only a change.