What is an inertia frame of reference ?
- One in which newtons laws of motion hold
- One in which the frame of reference is either at constant velocity or rest
True or False:
Newtons’s laws of motion are invariant under Galilean transformations
True
What is gamma ?
gamma = 1/sqrt(1-v^2/c^2)
Describe what side of the light line you would find time like events and space like events
- You would find time like events in the upper part of the spacetime diagram (left)
- You would find the space like events in the lower part of the spacetime diagram (right)
What is the equation for time dilation and describe how you would go about deriving it
- delta t’ = gamma * delta t
- You would go about deriving the equation by setting up a Pythagoras triangle with (v delta t’ )/2 at the base, the height h and the hypotenuse (c delta t’)/2 and isolate the (c delta t’) term
What is the definition of the proper time and proper length of an event ?
- Proper time is the shortest time recorded for an event (the frame s , which is the moving clock rather than the stationary one)
- Proper length is the longest length of an object and that will also be in its own frame of reference (frame s)
What is the equation for length contraction ?
L’ = L/gamma
What are the Lorentz transformations for spacetime four vector?
- ct’ = gamma(ct-bx)
- x’ gamma(x-bct)
- y’ = y
- z’ = z
where b=v/c
The primes and signs can be swapped to interchange between frames
What is the space time interval and describe a property about it with regards to relativity
- (delta s)^2 = (c delta t)^2 - (delta x)^2 - (delta y)^2 -(delta z)^2
- The space time interval is invariant under Lorentz transformations
What is the equation for the proper time ?
Delta t = gamma . delta tao
What is the equation for the relativistic Doppler shift with respect to frequency?
f’ = f sqrt( (1+b)/(1-b) )
where b = v/c
The plus or minus values will change depending if the object is moving closer too or further away from the observer
Which side of the light line will simultaneous events take place and which side will events in the same location take place?
- Simultaneous events will take place on the right hand side of the light line
- Events in the same location will take place on the left hand side of the light line
What is the relativistic momentum equation ?
P= gamma m v
It is derived by taking the derivative of the normal momentum with respect to the proper time rather than time in general
How do you go about deriving the equation for velocity addition?
- Start with v’ = delta x’ / delta t ‘
- Sub in the equivalent Lorentz transformations for each of these
- Multiply both top and bottom by 1/ delta t and rearrange
How would you go about deriving the relativistic force?
Take the derivative of relativistic momentum with respect to time
Is this the correct equation for the rest energy ?
E=mc^2
No
It is E(0) = mc^2
What equation must we use to conserve energy between all reference frames?
E = gamma m c^2
Is this statement true?
The kinetic energy is simply the difference between the total energy and the rest energy
Yes
What are the Lorentz transformations for energy and momentum ?
E' = gamma (E - b P(x) c) P'(x) c = gamma (P(x) c - b E) where b=v/c Again these can be swapped between frames by swapping primes and signs
What are the Lorentz in-variance equations for space - time and momentum - energy ?
Space-Time
(c delta t)^2 - (delta x)^2=(c delta t’)^2 - (delta x’)^2
=> (delta s)^2 = (delta s’)^2
Momentum-Energy
(E)^2-(P(x) c)^2 = (E’)^2 - (P’(x) c)^2
=> (E)^2 - (P c)^2 = (m c^2)^2
What is key to setting up the Compton effect derivation ?
That to make sure energy conservation is conserved, that in the initial energy you take into account the rest energy of the particles
