Question

Relativistic Phone 10 The resolution of the timer on your phone is 0.01 s How fast would your phone need to be moving (relative to you) in m/s so that the effects of special relativity on its accuracy become significant when measuring a 1 minute process?

Answer 1

To find the speed at which special relativity would cause a timer on a phone to become significantly inaccurate over a 1 minute period, we use the principles of time dilation. By considering a 1% time dilation to be significant, we can use the time dilation formula to solve for the relative velocity that would cause this effect.

Step-by-step explanation:

To determine the speed at which the effects of special relativity become significant for a timer on a phone measuring a 1 minute process, we first need to understand what constitutes a 'significant' effect. We can consider a time dilation of 1% (0.01×60 seconds = 0.6 seconds) to be significant for the purposes of this question. The formula for time dilation in special relativity is Δt' = Δt / √(1 - v^2/c^2), where Δt is the proper time interval (time measured by a stationary observer), Δt' is the dilated time interval (time measured by an observer in relative motion), v is the relative velocity, and c is the speed of light.

To find the value of v that results in a 0.6 second increase over a 60-second interval, we can rearrange the formula to solve for v and obtain the expression v = c √(1 - (Δt/Δt')^2). Substituting the known values (Δt = 60s, Δt' = 60.6s, c = 299,792,458 m/s), we can calculate the required velocity v.