Time Dilation in Special Relativity

Study Notes

Time dilation is a concept in special relativity where the faster you move relative to the speed of light, the slower time passes for you.
The concept of time dilation is demonstrated through a thought experiment involving an observer on earth and another in a spaceship moving at a constant velocity relative to the earth.
The spaceship has a device that emits a light pulse that hits a mirror and bounces back to a detector, allowing the astronaut to measure the time it takes for the light to make the trip.
For the person on earth, the light pulse has a horizontal component of motion in addition to the vertical one, making the distance traveled by the light pulse longer, which means the observer on earth registers a greater time interval.
This is why this phenomenon is called time dilation, because the time interval delta t has expanded relative to delta t 0, meaning the clock on the spaceship is running more slowly than the one on earth.
The equation relating delta t zero (the proper time interval) and delta t (the dilated time interval) is derived through algebra and allows us to calculate the precise time dilation that will result.
An example calculation is shown where an astronaut is in a ship moving at 80% light speed, and if they move at this constant speed for one year, it will be equivalent to 1.67 years on earth.
Time dilation has practical applications, such as in GPS satellites in orbit around the Earth, which must be programmed with correction factors to report time the same way as clocks on earth.
Even for an object moving slowly, like a plane, time dilation still occurs and has been measured with ultra-precise clocks.
The time dilation equation shows that as v gets very small relative to the speed of light, the dilated time interval approaches the proper time interval, which is why we don't notice time dilation on earth.
The twin paradox is an example of time dilation, where one twin travels at high speed and returns younger than the other twin who stayed on earth, due to the difference in their relative motion.