Resolved the conflict between Newtonian Mechanics and Maxwell's Electromagnetic Theory
Newtonian Mechanics
Laws of Motion
Law of Universal Gravitation
James Clerk Maxwell
Proposed the Electromagnetic Theory
Maxwell's Equations
Like charges repel; unlike charges attract
Magnetic monopoles do not exist
A changing electric field produces magnetic field
A changing magnetic field produces an electric field
Maxwell's Equations
Explain why electromagnetic waves can propagate in a vacuum
Calculated the exact value of the speed of light (symbol: c)
Speed of light from the headlight of a moving vehicle
Newtonian Mechanics: The speed of light is the sum of its speed plus the speed of the vehicle
Maxwell's EMT: The speed of light is constant and is not affected by the speed of its source
Special Relativity
Proposed by Albert Einstein and solved the conflict
Postulates of Special Relativity
The laws of Physics are the same in all inertial frame of reference moving with constant velocity relative to one another
The speed of light is the same in all inertial frame of reference
Inertial Frame of Reference
A frame where the observed object that is either at rest or moving with a constant velocity relative to the observer
Newtonian mechanics is only valid when the velocity of the objects involved are much less than the speed of light plus the inertial frame of reference is considered
Consequences of Special Relativity
Time Dilation
Length Contraction
Relativistic Mass
Time Dilation
Difference of the time interval between two events measured by an observer in a stationary frame and by another observer in a moving frame
Proper Time Interval is the time interval measured by the astronaut and always the shortest
Dilated Time Interval is the time interval measured by the observed on Earth and always the longest
Time Dilation Equation
Δt = Δto / √(1 - (v/c)^2)
Length Contraction
A phenomenon that is experienced by a moving object near the speed of light where its length is observed to be contracting
An observer at rest relative to the moving object will observe that the moving object is shorter than its original length
The faster the speed of the moving objects, the more it gets contracted to the observer
Length Contraction Equation
L = Lo / √(1 - (v/c)^2)
Relativistic Mass
The mass of a moving object as it approaches the speed of light in vacuum is greater than its mass at rest relative to the observer
The faster the speed of the moving object, the greater its mass as compared with its original mass
Relativistic Mass Equations
m = mo / √(1 - (v/c)^2)
p = m*v
Sample Problem #1
Given: Initial Age = 30 y/o, v = 0.95c, Δto = 20 years
Step 1: Compute the dilated time
Step 2: Add the dilated time to Christian's initial age. While for Leo, simply add the time recorded in the shipboard clock
Sample Problem #2
Given: v = 0.75c, Δt = 25 years
The astronaut aged by 16.54 years during the trip
Sample Problem #3
Given: v = 0.50c, Lo = 45 m
The spaceship as measured by the mission control in Texas is 38.97 m
Sample Problem #4
Given: v = 0.70c, Lo = 76 m
The dimension measured by an observer on Earth is 54.27 m