▁− 2 ▁holds ▁to ▁within ▁ 1 % ▁toler ance ▁for ▁ ▁> ▁ 2 , ▁and ▁to ▁within ▁ 0 . 1 % ▁toler ance ▁for ▁ ▁> ▁ 3 . 5 . ▁ ▁App lications ▁in ▁astronom y ▁The ▁standard ▁model ▁of ▁long - duration ▁g amma - ray ▁burst s ▁( GR B s ) ▁holds ▁that ▁these ▁explos ions ▁are ▁ult ra - rel ativ istic ▁( initial ▁ ▁greater ▁than ▁approximately ▁ 1 0 0 ), ▁which ▁is ▁invoked ▁to ▁explain ▁the ▁so - called ▁" comp act ness " ▁problem : ▁absent ▁this ▁ult ra - rel ativ istic ▁expansion , ▁the ▁e ject a ▁would ▁be ▁opt ically ▁thick ▁to ▁pair ▁production ▁at ▁typical ▁peak ▁spectral ▁energ ies ▁of ▁a ▁few ▁ 1 0 0   ke V , ▁whereas ▁the ▁prompt ▁emission ▁is ▁observed ▁to ▁be ▁non - ther mal . ▁ ▁Sub atomic ▁particles ▁called ▁mu ons , ▁have ▁a ▁relatively ▁high ▁Lor ent z ▁factor ▁and ▁therefore ▁experience ▁extreme ▁time ▁d ilation . ▁As ▁an ▁example , ▁mu ons ▁generally ▁have ▁a ▁mean ▁lifetime ▁of ▁about ▁ ▁which ▁means ▁mu ons ▁generated ▁from ▁cos mic ▁ray ▁coll isions ▁at ▁about ▁ 1 0   km ▁up ▁in ▁the ▁atmosphere ▁should ▁be ▁non - det ect able ▁on ▁the ▁ground ▁due ▁to ▁their ▁decay ▁rate . ▁However , ▁it ▁has ▁been ▁found ▁that ▁~ 1 0 % ▁of ▁mu ons ▁are ▁still ▁detected ▁on ▁the ▁surface , ▁thereby ▁prov ing ▁that ▁to ▁be ▁detect