If a traveler is moving at a velocity of 0.05% the speed of light, we can calculate the time dilation they would experience using the time dilation formula derived from special relativity. The formula for time dilation is as follows:
Δt' = Δt / √(1 - (v^2 / c^2))
Where: Δt' is the time experienced by the traveler (time dilation) Δt is the time observed by an observer at rest (proper time) v is the velocity of the traveler c is the speed of light in a vacuum
Given that the velocity (v) is 0.05% of the speed of light (c), which can be expressed as:
v = 0.0005c
We can substitute the values into the time dilation formula:
Δt' = Δt / √(1 - (0.0005c)^2 / c^2)
Simplifying the equation:
Δt' = Δt / √(1 - 0.00000025)
Calculating the square root and simplifying further:
Δt' = Δt / √(0.99999975)
Δt' = Δt / 0.999999875
This equation implies that the traveler would experience time that is approximately 0.999999875 times the time observed by an observer at rest. In other words, the time dilation factor is very close to 1, indicating that the time dilation effect would be extremely small at this velocity.
To put it in perspective, if the traveler spends a certain amount of time on their journey, the difference in experienced time would be minimal compared to the time observed by a stationary observer. The effect of time dilation becomes more significant as the velocity approaches the speed of light, but at 0.05% of the speed of light, the time dilation would be virtually negligible.