PHYS 242 Lecture 1: PHYS242_Lecture_10-12

• School: Queen's University
• Department: Physics
• Course: PHYS 242
• Professor: Wolfgang Rau

Document Summary

The velocity is defined as change of position with time: for the velocity of an object observed within a given frame. We will separate the three spatial components starting with the. After we have derived the relativistically correct transformation law for the space and time coordinates we go to the next step and discuss the velocity transformation. In the third step we pull the (cid:2011) out and use (cid:1856)(cid:4666)(cid:1876)(cid:3397)(cid:1877)(cid:4667)(cid:3404)(cid:1856)(cid:1876)(cid:3397)(cid:1856)(cid:1877). Then we cancel (cid:2011) and divide numerator and denominator by (cid:1856)(cid:1872)(cid:4593). In the last step we use similar in structure to the square of the relativistic (cid:2011) factor, except that instead of (cid:1874)(cid:2870) it contains the term (cid:1873)(cid:3051)(cid:4593)(cid:1874). If we apply the same procedure to the (cid:1877)-direction we find: (cid:3031)(cid:3436)(cid:3082)(cid:4672)(cid:3047)(cid:4594)(cid:2878)(cid:3051)(cid:4594)(cid:3297)(cid:3278)(cid:3118)(cid:4673)(cid:3440)(cid:3404) (cid:3031)(cid:3052)(cid:4594)/(cid:3031)(cid:3047)(cid:4594) (cid:3082)(cid:3436)(cid:2869)(cid:2878)(cid:3297)(cid:3278)(cid:3118)(cid:3279)(cid:3299)(cid:4594)(cid:3279)(cid:3295)(cid:4594)(cid:3440)(cid:3404) (cid:3048)(cid:3300)(cid:4594) (cid:3031)(cid:3052)(cid:4594) (cid:3082)(cid:3436)(cid:2869)(cid:2878)(cid:3296)(cid:3299)(cid:4594)(cid:3297)(cid:3278)(cid:3118)(cid:3440) In classical physics we would just add the velocities (galilean velocity transformation). Here we also add the velocities (note the numerator in the above equation), but we have to apply a correction factor which is.