Suppose that a particular kind of subatomic particle lives on average for exactly 1.0 microsecond (1.0 × 10^-6 s) before it decays, when this particle is created at rest in the laboratory. If a beam of such particles is created that travels at 97% of the speed of light as measured by a scientist standing beside the beam, what lifetime does the scientist measure for these particles?

Question

Quizplus · Accepted Answer

The phenomenon described is time dilation, a concept from Einstein's theory of relativity. When particles move at speeds close to the speed of light, time appears to slow down for them from the perspective of a stationary observer. The formula for time dilation is $ t' = \frac{t}{\sqrt{1 - v^2/c^2}} $, where $ t' $ is the dilated time, $ t $ is the proper time (1.0 microsecond in this case), $ v $ is the velocity of the object (97% of the speed of light, or 0.97c), and $ c $ is the speed of light. Plugging the values into the formula gives a dilated time greater than the proper time, which matches the choice indicating a longer observed lifetime (4.1 microseconds) due to the effects of high velocity on time perception.

Suppose That a Particular Kind of Subatomic Particle Lives on Average