A particle at the Large Hadron collider in CERN is moving at 0.99 c as it emerges from a collision event.
A) If these particles live 2.0 microseconds on average when they are at rest, how long would you expect this particle to last in the reference frame of the physicist measuring the particle?
To answer this question, we need to consider time dilation, which is a consequence of special relativity. According to special relativity, time appears to pass more slowly for objects that are moving relative to an observer. The formula to calculate time dilation is given by:
t' = t / √(1 - v^2/c^2)
Where:
t' is the time observed by the physicist measuring the particle (in their reference frame)
t is the time experienced by the particle (in its rest frame)
v is the velocity of the particle
c is the speed of light in a vacuum
In this case, the velocity of the particle, v, is given as 0.99c. We also know that the average time the particle lives at rest, t, is 2.0 microseconds.
Plugging these values into the equation, we can calculate the time observed by the physicist, t':
t' = 2.0 microseconds / √(1 - (0.99c)^2/c^2)
To simplify the calculation, we can convert the velocity of the particle to a decimal fraction of the speed of light:
0.99c = 0.99 * 299,792,458 m/s ≈ 296,793,533 m/s
Now, let's substitute the values into the equation:
t' = 2.0 microseconds / √(1 - (296,793,533 m/s)^2 / (299,792,458 m/s)^2)
Using a calculator or a computer program, we can simplify and solve this equation:
t' ≈ 28.2 microseconds
Therefore, the physicist measuring the particle would expect it to last approximately 28.2 microseconds in their reference frame.