week 2 Flashcards
list all lorentz transformations
x’ = γ(x-vt)
t’ = γ(t-vx)
y’ = y
z’ = z
what is γ?
γ= 1/√(1-v^2 )
What is important about γ?
Its always bigger than 1
What is an invariant quantity?
A quantity whose value is the same in all frames of reference
What is the time dialation eqn?
t= γτ
where t is the time observed in the frame where the clock is moving and τ is the time interval observed where the clock is at rest
What does time dilation say?
The time observed in the frame where the clock is moving will always be DILATED as when observed in the frame where it is at rest.
What is the total energy of a particle?
E = K+m
(c=1 for NU)
how would you find the velocity of a particle?
v=P/E
(momentum divided by velocity)
How do you find the invariant mass?
E^2 - p^2 = m^2
What is the invariant mass?
The rest mass of the particle squared. This value is the same in all frames.
What is the rule for Energy and momentum transformations?
Energy transforms like time while momentum transforms like space
how do we write the 4 momentum?
(E,Px,Py,Pz)
What happens when you multiply the 4 momentum by itself?
(sum of all E)^2-(sum of all p)^2 = s
What are the properties of 2 body decays?
- Back to back with some general angle between them
- Mx>=Ma+Mb
- you can find energies of A or B after the decay happens
How would you find the energies of A or B during decays?
Write Energy and momentum conservation equations and solve simoultaneously and eliminate the one you dont need.
What are the 2 types of collision problems?
- synchrotoron (2 beams colliding)
- Fixed targets (beam dumps)
Which frame of reference is best for synchrotrons?
use the COM frame because sum of incoming momenta is 0
Which frame of reference is best for fixed targets?
use LAB frame as momenta of the target is 0
What is the centre of mass energy?
E =√(s)
where s is the invariant
what is important about s?
s is conserved in all colisions so can be used in different frames
How can we find the masses of particles in collisions?
compare S_initial and S_final
What is the threshold energy?
minimum energy requiered to start a reaction for particles
whats the condition for Thresh E in the COM or LAB frame?
daughter particles must be produced at rest
What is the threshld E in COM?
E>=Mx+My
