In special relativity, time dilation occurs when an object is moving relative to an observer. The formula for time dilation, derived from the principles of special relativity, relates the observed time interval (Δt') to the proper time interval (Δt) experienced by the moving object. The formula is given by:
Δt' = Δt / √(1 - v^2/c^2)
where v is the relative velocity between the observer and the moving object, and c is the speed of light.
If you find that the calculated time interval Δt' is larger than the proper time interval Δt, it suggests that the moving object's clock appears to be running slower from the perspective of the observer. This is indeed one of the fundamental consequences of special relativity.
When an object is moving relative to an observer, time dilation occurs because the speed of light is constant for all observers. As the relative velocity between the observer and the moving object increases, the denominator of the formula (√(1 - v^2/c^2)) becomes larger, resulting in a larger time dilation factor. This means that the observed time interval appears to be longer (larger) than the proper time interval experienced by the moving object.
It's important to note that the observer's perception of time dilation is consistent with the fundamental principles of special relativity. The moving object itself experiences time passing at its proper rate, while the observer perceives time running slower for the moving object. This effect has been experimentally confirmed in various ways, including particle accelerators and measurements of high-speed particles.
If you have specific values for the velocity and other variables in the formula, I can help you with the calculation and clarify any further questions you may have.