Wolfram Computation Meets Knowledge

Wolfram Formula Repository (Under Development)

Relativistic Addition of Velocities

In relativistic physics, a velocity-addition formula is an equation that relates the velocities of objects in different reference frames.

The velocity in a stationary observer reference frame equals the sum of the velocity of a moving observer with respect to the stationary observer and the velocity in the moving observer reference frame divided by the sum of 1 and the velocity of the moving observer with respect to the stationary observer times the velocity in the moving observer reference frame divided by the speed of light squared.

Formula

QuantityVariable["V", "Speed"] == (QuantityVariable["u", "Speed"] + QuantityVariable[Superscript["v", "′"], "Speed"])/(1 + Quantity[1, "SpeedOfLight"^(-2)]*QuantityVariable["u", "Speed"]*QuantityVariable[Superscript["v", "′"], "Speed"])

symbol description physical quantity
V velocity in stationary observer reference frame "Speed"
u velocity of moving observer with respect to stationary observer "Speed"
v′ velocity in the moving observer reference frame "Speed"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Relativistic Addition of Velocities"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Relativistic Addition of Velocities"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Relativistic Addition of Velocities"], {QuantityVariable[ Superscript["v","\[Prime]"],"Speed"] -> Quantity[0.5`, "SpeedOfLight"], QuantityVariable["u","Speed"] -> Quantity[0.7`, "SpeedOfLight"]}]
Out[3]=

Source Metadata

  • Creator:
  • Date: 1905

Publisher Information