Special Relativity

Question 1

What is an event?

Answer 1

Something that occurs with definite space and time coordinates

Question 2

What are the principles of relativity?

Answer 2

• All inertial frames are equivalent

- The speed of light in vacuum has the same value of c in any inertial frame

Question 3

What are the effects of the principle of relatvity?

Answer 3

• Loss of simultaneity
• Time dilation
• Length contraction

Question 4

What is time dilation?

Answer 4

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

Question 5

What is the time dilation equation?

Answer 5

dt = dt0/(1-v^2/c^2)^1/2

or dt =γ dt0

Question 6

What is the Lorentz factor?

Answer 6

γ = 1/ (1-v^2/c^2)^1/2

Question 7

What are the steps for solving a time dilation problem?

Answer 7

• 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.

Question 8

What is the loss of simultaneity?

Answer 8

Whether or not two events at different x-axis location are simultaneous depends on the state of motion of the observer

Question 9

What is β?

Answer 9

β = v^2/c^2

Question 10

What is the length contraction equation( length parallel to the relative motion?

Answer 10

l= l0/γ

Question 11

What is proper length?

Answer 11

A length measured in the frame in which the body is at rest

Question 12

What is length contraction?

Answer 12

When the length measured in any other rest frame moving relative to another frame is less than the proper length.

MOVING OBJECTS BECOME SHORT

Question 13

Derive the equation for length contraction (lengths perpendicular to the relative motion)

Answer 13

Lengths that are measured

perpendicular to the direction of motion are not contracted.

Question 14

What are the steps for solving a length contraction question?

Answer 14

• 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

Question 15

What is a Lorentz Transformation?

Answer 15

General transformation that considers the principles of relativity

Question 16

What are Lorentz coordinate Transformation equations ?

Answer 16

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

Question 17

What are Lorentz velocity transformation equation ?

Answer 17

ux’ = (ux - v)/(1-uxv/c^2)

• NEGATIVE - x velocity in frame s’
• POSITIVE - x velocity in frame s

Question 18

Derive the Lorentz velocity transformation

Answer 18

*

Question 19

What are the steps for solving a Lorentz transformation question?

Answer 19

• 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

Question 20

What is the Lorentz coordinate transformation?

Answer 20

Relate the spacetime coordinates of an event in
one inertial reference frame to the coordinates of the same event in
a second inertial frame.

Question 21

What is the Lorentz velocity transformation?

Answer 21

Relate the velocity of an object in one inertial reference frame
to its velocity in a second inertial frame.

Question 22

What is the Lorentz Invariant?

Answer 22

s^2 - Does not depend on the frame

Two events separated by dx ant dt in one frame is the same.

Question 23

What is the Doppler effect,
electromagnetic waves,
source approaching
observer equation?

Answer 23

f = (c+v/c-v)^1/2f0

Question 24

What is the Doppler effect, electromagnetic waves,

source moving away from observer equation?

Answer 24

f = (c-v/c+v)^1/2f0

Question 25

What is the doppler shift?

Answer 25

The difference in the source and the observe frequency

df = f-f0

Question 26

What is the relativistic momentum equation?

Answer 26

p = γmv

Question 27

What is the relativistic kinetic energy equation?

Answer 27

(γ-1)mc^2

Question 28

What is the total energy of a moving particle?

Answer 28

Etotal = K + mc^2 = γmc^2

Question 29

What is the rest energy of a particle?

Answer 29

E = γmc^2

Question 30

What is the equation used to relate total energy and momentum?

Answer 30

E^2 = (mc^2)^2 + (pc)^2

Question 31

What are the steps for solving a collison problem?

Answer 31

• Sketch
• Identify target variable
• Use Lorentz velocity transformation of coordinates equations
• Relate equations to each other to energy and momentum

Question 32

Why are space-time diagrams useful?

Answer 32

Helps use to visualise events

Helps use to resolve relativistic paradoxes

Question 33

How do you make a space-time diagram?

Answer 33

Frame unprime
ct - y-axis
x = x axis 
Frame prime
The axes are angled