Special Relativity Flashcards
What is an event?
Something that occurs with definite space and time coordinates
What are the principles of relativity?
- All inertial frames are equivalent
- The speed of light in vacuum has the same value of c in any inertial frame
What are the effects of the principle of relatvity?
- Loss of simultaneity
- Time dilation
- Length contraction
What is time dilation?
When the time interval between the same events measured in second frame of reference is larger than the proper time between two events (measured in rest frame)
TIME RUNS SLOW
What is the time dilation equation?
dt = dt0/(1-v^2/c^2)^1/2
or dt =γ dt0
What is the Lorentz factor?
γ = 1/ (1-v^2/c^2)^1/2
What are the steps for solving a time dilation problem?
- Check if we are comparing the time interval between events as measure by observers in different interial frames of reference
- What two event define the beginning and the end of the time interval?
- What is the target variable(s)?
- Decide which frame the time interval dt0 and in which frame dt.
What is the loss of simultaneity?
Whether or not two events at different x-axis location are simultaneous depends on the state of motion of the observer
What is β?
β = v^2/c^2
What is the length contraction equation( length parallel to the relative motion?
l= l0/γ
What is proper length?
A length measured in the frame in which the body is at rest
What is length contraction?
When the length measured in any other rest frame moving relative to another frame is less than the proper length.
MOVING OBJECTS BECOME SHORT
Derive the equation for length contraction (lengths perpendicular to the relative motion)
Lengths that are measured
perpendicular to the direction of motion are not contracted.
What are the steps for solving a length contraction question?
- Check if we are comparing the length of an object as measured by the observes in different inertial frames of reference
- What defines the length in the question(from the distance between two points of what?)
- What is the target variable(s)?
- What is the reference frame when the object is at rest (proper length)
- Remember l is never larger than l0
What is a Lorentz Transformation?
General transformation that considers the principles of relativity
What are Lorentz coordinate Transformation equations ?
t’=γ (t-vx/c^2)
x’ =γ (x-vt)
y’=y
z’=z
*NEGATIVE - velocity of s’ relative to s in the positive direction
*POSTIVE - velocity s relative to s’ in the negative direction
What are Lorentz velocity transformation equation ?
ux’ = (ux - v)/(1-uxv/c^2)
- NEGATIVE - x velocity in frame s’
- POSITIVE - x velocity in frame s
Derive the Lorentz velocity transformation
*
What are the steps for solving a Lorentz transformation question?
- Identify target variable
- Define the two inertial frame ( prime moves relative to unprime in the positive direction)
- For coordinates: make list of space time coordinates
- For velocity: Identify the relative velocity of the two frames of reference, the velocity of the object in unprime and prime frame
What is the Lorentz coordinate transformation?
Relate the spacetime coordinates of an event in
one inertial reference frame to the coordinates of the same event in
a second inertial frame.
What is the Lorentz velocity transformation?
Relate the velocity of an object in one inertial reference frame
to its velocity in a second inertial frame.
What is the Lorentz Invariant?
s^2 - Does not depend on the frame
Two events separated by dx ant dt in one frame is the same.
What is the Doppler effect,
electromagnetic waves,
source approaching
observer equation?
f = (c+v/c-v)^1/2f0
What is the Doppler effect, electromagnetic waves,
source moving away from observer equation?
f = (c-v/c+v)^1/2f0
What is the doppler shift?
The difference in the source and the observe frequency
df = f-f0
What is the relativistic momentum equation?
p = γmv
What is the relativistic kinetic energy equation?
(γ-1)mc^2
What is the total energy of a moving particle?
Etotal = K + mc^2 = γmc^2
What is the rest energy of a particle?
E = γmc^2
What is the equation used to relate total energy and momentum?
E^2 = (mc^2)^2 + (pc)^2
What are the steps for solving a collison problem?
- Sketch
- Identify target variable
- Use Lorentz velocity transformation of coordinates equations
- Relate equations to each other to energy and momentum
Why are space-time diagrams useful?
Helps use to visualise events
Helps use to resolve relativistic paradoxes
How do you make a space-time diagram?
Frame unprime ct - y-axis x = x axis Frame prime The axes are angled
