Time Dilation Calculator

• According to theory of relativity, traveling at any speed (compared to a startionary observer) casues time to dilate from the perspective of the observer
• This time dilation effect exists at all speeds, but is undetectable at small speed
• As the traveling speed increases the time dilation effect becomes more noticeable
• The following equation calculates the time dilation, relative to traveling speed:

Source: https://www.pinterest.com/pin/69876231694436244

• The classic example: consider twin bothers -
  
  • One twin (the stationary observer) remains on Earth, while the other twin (the traveler) boards a spacecraft that travels at a certain percentage of the speed of light.
  • After traveling for a certain period of time at a certain speed, the traveler returns to Earth and reunites with the stationary observer twin
• Assuming the traveler travels at 80% of the speed of light, for a duration of 10 years, the resulting time dilation calculation and effect is as follows:

speedOfLight <- 299792458 / 1000 # speed of light in vacuum (In Kilometers Per Second) 
percent <- 0.8; years <- 10
travelingSpeed <- percent * speedOfLight
timeDilationFactor <- (1 / sqrt(1 - (travelingSpeed^2 / speedOfLight^2) ))
durationFromStationaryObserverPerspective <- timeDilationFactor * years
sprintf("Elasped years from stationary observer perspective: %1$1.2f", durationFromStationaryObserverPerspective)

## [1] "Elasped years from stationary observer perspective: 16.67"

• The calculator requires two input parameters (visualized as sliders):
  1. Traveling speed (as a % of the speed of light in a vacuum)
  2. Duration of travel (in years, from the perspective of the traveler)
• The X axis of the graph illustrates the input of the speed as a percent of the speed of light
  • (0 to 99.9, since 100% of the speed of light is not calculable)
• The Y axis of the graph displays the server-side calculated time dilation factor
  • (i.e. how much time dilates from the perspective of the stationary observer compared to the traveler)

Link: ShinyApps.io Time Dilation Calculator