Brady Haran for the University of Nottingham. "γ – Lorentz Factor (and time dilation)". et al., iPTF14yb: The First Discovery of a Gamma-Ray Burst Afterglow Independent of a High-Energy Trigger, Astrophysical Journal Letters 803, 2015, L24 (6 pp). ^ Cameron R D Bunney and Jorma Louko 2023 Class. Jackson, See page 7 for definition of rapidity. ^ Kinematics Archived at the Wayback Machine, by J.D.Sears' and Zemansky's University Physics (12th ed.). ^ Yaakov Friedman, Physical Applications of Homogeneous Balls, Progress in Mathematical Physics 40 Birkhäuser, Boston, 2004, pages 1-21.^ a b Forshaw, Jeffrey Smith, Gavin (2014).^ One universe, by Neil deGrasse Tyson, Charles Tsun-Chu Liu, and Robert Irion.However, it has been found that ~10% of muons are still detected on the surface, thereby proving that to be detectable they have had their decay rates slow down relative to our inertial frame of reference. As an example, muons generally have a mean lifetime of about 2.2 μs which means muons generated from cosmic ray collisions at about 10 km up in the atmosphere should be non-detectable on the ground due to their decay rate. Subatomic particles called muons travel at a speed such that they have a relatively high Lorentz factor and therefore experience extreme time dilation. The standard model of long-duration gamma-ray bursts (GRBs) holds that these explosions are ultra-relativistic (initial γ greater than approximately 100), which is invoked to explain the so-called "compactness" problem: absent this ultra-relativistic expansion, the ejecta would be optically thick to pair production at typical peak spectral energies of a few 100 keV, whereas the prompt emission is observed to be non-thermal. We reserve the right to discontinue or alter the terms of this offer at any time.E k = E − E 0 = ( γ − 1 ) m 0 c 2 holds to within 1% tolerance for γ > 2, and to within 0.1% tolerance for γ > 3.5. Existing cardholders: See your credit card agreement terms. For New Accounts: Purchase APR is 29.99%. Regular account terms apply to non-promo purchases. A down payment may be required on in-store purchases. These payments may be higher than the payments that would be required if this purchase was a non-promo purchase. The payments equal the initial total promo purchase amount divided by the number of months in the promo period, rounded up to the next whole dollar. No interest will be charged, and equal monthly payments are required on promo purchase until it is paid in full. ^°Qualifying purchase amount must be on one receipt. Down payment, tax and delivery may be required on in-store purchases. On in-store purchases made with your Ashley Advantage™ Synchrony credit card. Regular account terms apply to non-promo purchases and, after promo period ends, to the promo balance. The required minimum monthly payments may or may not pay off the promo balance before the end of the promo period, depending on the purchase amount, promo length and payment allocation. If you do not, interest will be charged on the promo balance from the purchase date. No interest will be charged on the promo balance if you pay it off, in full, within the promo period. ††For Ashley Advantage™ Synchrony Accounts: Qualifying purchase amount must be on one receipt. Can be combined with online discount offers on qualifying purchases. Interest will be charged to your account from the purchase date if the promotional balance is not paid in full within 12 months. No minimum purchase required for Ashley Advantage™ Synchrony purchases. No interest if paid in full within 12 Months††
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