Special Relativity
SI units & Physics constants
Special relativity investigates motion of objects at high speeds approaching the speed of light in inertial reference frames
Here (all units see here):
x, y, z is fixed inertial reference frame
x', y', z' is inertial reference frame moving at constant velocity along xaxis
v is velocity of frame x', y', z' with respect to frame x, y, z
m_{o} is rest mass of the object measured in frame x', y', z'
t is instant of time of position of the object measured in frame x, y, z
t' is proper instant of time of position of the object measured in frame x', y', z'
is proper force with components F_{ox}, and F_{oy} acting on the object measured in frame x', y', z'
c is speed of light
General formulas
Lorentz transformation between coordinates and time for frames x', y', z' and x, y, z
Inverse transformation
Einstein's Postulates of Special Relativity
Relativity Postulate. All laws of physic are the same (have the same form) in every inertial reference frame
Speed of Light Postulate. The speed of light in vacuum, measured in any inertial reference frame, always has the same value, no matter how the source of light and the object are moving relative to each other
Relativistic effects
Time Dilation. The time interval between two events, measured by observer standing in fixed frame x, y, z
where is proper time interval between the same two events taking place at the same point, measured by observer standing in moving frame x', y', z'
Length Contraction. The length or distance between two points in direction of motion, measured at the same time by observer standing in frame x, y, z
where L_{o} is proper length or distance between the same points, measured by observer standing in frame x', y', z'
Simultaneity Violation. The time interval between two events which are simultaneous in frame x', y', z', measured by observer standing in frame x, y, z
where L_{o} is proper distance between the points where the simultaneous events take place, measured by observer standing in frame x', y', z'
Relativistic law of adding velocities. The velocity of object, measured by observer standing in frame x, y, z
where u_{o} is relative velocity of the object moving in xdirection, measured by observer standing in frame x', y', z'
Relativistic mass. The mass of object, measured by observer standing in frame x, y, z
where m_{o} is rest mass, measured by observer standing in frame x', y', z'
Relativistic momentum. The linear momentum of object moving with velocity
Relativistic force vector. The x and y components of force acting on object, measured by observer standing in frame x, y, z
where F_{ox} and F_{oy} are components of proper force, measured by observer standing in frame x', y', z'
The relativistic Newton's Second Law for motion
Total energy of mass moving with speed v
where m_{o} is rest mass
Rest energy of mass
Relativistic kinetic energy of object moving with speed v
Relation between relativistic energy and momentum
