Question

Modern Physics: Special Relativity

In its own reference frame, a proton crosses the Milky Way (diameter ? 10⁵ light-years) in 5 minutes.

a) What is the energy of the proton in eV?

b) How long would it take the proton to cross the galaxy to an observer in the galaxy’s rest frame?

Answer 1

a] A light-year is a distance light travels in a year. So, if a proton crosses Milky way of diameter 105 light-years in merely 5 minutes, it must be strongly relativistic (meaning that the length contraction effect in its own frame will be strong thereby shortening its path).  

Energy of the proton is:

for strongly relativistic particles,

therefore,

also,

so,

L_o = 105 light years

L = length the proton travels in its own frame. Since the relativistic effects are very large,

this is the energy of the proton.

b] Because of the above assumptions, here v can be approximated to c

therefore, the time it would take for the proton to cross the galaxy in the rest frame will be:

.