SR Flashcards
(35 cards)
Inertial frame
A frame in which newtons 1st law is valid, all accelerating frames are non-inertial
Galilean-Newtonian
Principle of relativity and ideas
Basic laws of physics are the same in all inertial reference frames
Length time mass and force all the same position and velocity not
G-N
Transformation of position and time and acceleration mass and force
x’=x-vt and t’=t
Differentiating gives a’=a so m’=m and F’=F
When is G-N valid
When v«c
Michaelson- Morley experiment
Constant speed of light not hold up in G-N
Experiment= special inertial frame constant c proposed luminiferous aether, medium light travels through. Sun= rest. Use interferometer and predicts c splits and comes back together created fringe pattern. Time derivation in notes. Rotation= different lag predict.
No lag no aether
G-N and maxwells theory incomplete
Special relativity basis
Relativity principle (1st postulate) and constant c (2nd postulate)
Einstein
Also no absolute clock unless special frame
Event
An instantaneous physical situation or occurrence associated with a point in space time
Simultaneity
Dependant on observers reference frame, if two events are equidistance they are observed as simultaneous light reaches observer at same time
Time dilation def and equation
Clocks moving relative to an observer will be measured to run slow
Delta t= delta t_0 gamma
Proper time
Tau or delta t_0 when two events occur at the same position
Gamma factor
1/ root( 1- v squared/ c squared)
Beta
Beta= v/c
Lorentz transformations
For position and time boost in x direction
t’= gamma (t-vx/c squared)
x’= gamma(x-vt)
y’=y
z’=z
Length contraction equation
L= L_0 / gamma
Space time invariance
c squared delta t squared - delta x squared - delta y squared - delta z squared = delta s squared
Delta s = c delta t_0
Galilean velocity addition
u=u’+v where u’ is on v , u is observed
Special relativity velocity addition
Derived from u’ = delta x’/delta t’ and delta x/ delta t = u and Lorentz forms
u=u’+v/(1+(u’v)/csquared)
Relativistic Doppler effect derivation and equation source moving towards
c delta t= v delta t + lambda, where v delta t is distance source moved , substitute in proper time and rearrange for f= using c=f lambda
f= f_0 root((c+v)/(c-v)) change signs for source moving away
Newtonian limit
Wavelength Doppler effect of source moving away rearrange for all lambdas on one side
Taylor expand root
Delta lambda/ lambda_0 = v/c when v/c «1
Red and blue shift cases
Doppler effect v>0 moving away = red shift
v<0 moving towards = blue shift
Relativistic momentum
p=m dx/dt
v=dx/d tau = dx/dt times dt/ dtau= gamma dx/dt
p= gamma mv
Relativistic Kinetic energy derivation and equat8on
Work done= integral F dx between 0 and x(t’)= integral F v dt between t’ and 0
F= dp/dt where p= gamma mv remember gamma is dt too so product rule simplify to W= integral m gamma cubed v dV/dt dt between t’ and 0 then rearrange in terms of gamma use d gamma / dt from above so W= mc squared ( gamma -1)
KE= mc squared ( gamma -1)
Rest energy
E_0 = mc squared
Total energy
E= gamma m c squared = E_0 + KE
