• Accelerated particles often reach speeds that are very close to the?speed of light
• At such high velocities and energies,?relativistic effects?begin to become important
• These are effects such as:
  • Time dilation
  • Length contraction

Time Dilation

• Clocks run slower for moving particles
  • This means that unstable particles, with a?short lifetime, actually survive for?much longer?in a laboratory if they are moving very quickly
  • This is useful because they will leave?longer tracks?in particle detectors (making detection easier)

• For example, muons created high up in the atmosphere, have a lifetime of about 2 μs
  • The time required to travel to sea-level is?too great?to survive the journey
  • However, they are detected at sea-level in large numbers
  • This is because they are travelling at?relativistic speeds?(e.g. 0.98c) so?time?dilation?means their lifetime is dilated to times much longer than 2 μs

Because muons travel so quickly, time dilation stretches muon lifetime to much longer than when they are at rest

Length Contraction

• Moving rulers are shorter than stationary rulers
  • This means that particles moving at very high velocities travel much further through detectors than expected
  • Unstable particles with very short lifetimes would not travel for appreciable distances without?relativistic?effects like length contraction

• For example, if exotic particles produced in particle accelerators decayed within the particle chamber before escaping it, none would be detectable
  • In fact,?many?types of exotic particles are detected
  • This is evidence of length contraction

Part (a)

Step 1: Write the known quantities

• • Muon lifetime,?t?= 2.2 × 10–6?s
  • Speed of light,?c?= 3 × 108?m s–1
  • Speed of muons,?v?= 0.99?c?= 0.99 × (3 × 108) = 2.97 × 108?m s–1

Step 2: Calculate distance travelled

• • Speed?v?= distance?d?÷ time?t
  • Therefore, the distance travelled by muons travelling at 0.99?c?is given by:

d?=?vt?= (2.97 × 108) × (2.2 × 10–6) = 653.4 m

Part (b)

Step 1: Compare the distance calculated to the distance required

• • The distance a muon travels with a lifetime of 2.2 × 10–6?s is only 653.4 m
    • This is much less than the 10 km required to sea level

Step 2: Conclude that relativistic effects must be at play

• • Therefore, time dilation must be allowing the muons to last much longer than 2.2 × 10–6?s
    • This is because they are detected in large numbers at sea level