Suppose the time taken for light to bounce to and fro between the parallel mirrors of a light clock is 1 second, in the frame of reference of the light clock. As seen by another observer moving at high speed at right angles to the to-and-fro motion of the bouncing light, the time taken would be
less 1
also 1 second
To calculate the time taken as seen by another observer moving at high speed at right angles to the to-and-fro motion of the bouncing light, we need to apply the principles of special relativity. Here's how you can do it:
1. Determine the relative velocity: Let's denote the speed of the observer with respect to the light clock as v. Since the observer is moving at right angles to the to-and-fro motion of the light, the relative velocity in this case will still be v.
2. Apply time dilation formula: According to the theory of special relativity, time dilation occurs when an observer moves at a relative velocity with respect to a clock. The formula to calculate time dilation is:
Δt' = γ * Δt
Where:
Δt' is the time observed by the moving observer,
Δt is the time measured by the stationary observer (in this case, 1 second),
and γ (gamma) is the Lorentz factor given by: γ = 1 / √(1 - v^2/c^2).
In this formula, c represents the speed of light in a vacuum, which is approximately 3 x 10^8 meters per second.
3. Substitute values and calculate: Plugging in the given values, the formula becomes:
Δt' = γ * Δt
Δt' = (1 / √(1 - v^2/c^2)) * 1
Note: When calculating the Lorentz factor, make sure to express the velocity v and speed of light c in the same units (e.g., meters per second).
You can now calculate Δt' using the Lorentz factor calculated from v and c.
This will give you the time taken as seen by the observer moving at high speed at right angles to the to-and-fro motion of the bouncing light.