< 1 2 >
Lorentz factor
The Lorentz factor γ is the factor by which time, length, and mass change for an object while that object is moving.
Calculation
Measurements have shown that the speed of light c is the same in all directions in a stationary and uniformly moving reference system.
S (t, x, y, z) < − − − − − − − − − − − − − − x − − − − − − − − − − − − − − − > x-axis → v < − − − − − − − − − − x' − − − − − − − − − − > S (t', x', y', z')
The coordinates t, x, y, z and t', x', y', z' coincide at the moment t = t' = 0. For a light signal emitted at that moment in the direction of the x-axis the following applies
and
For high speeds v it should be noted that t ≠ t'. We need a factor to explain the change in length, so we write
 ⋅ γ.png){kind=small}
and
Now we calculate this factor as follows
and
By substitution we get
so that
HistoryThe Dutch physicist Hendrik Lorentz (1853 - 1928) is known for the Lorentz transformations. |