Lorentz factor

The dimensionless Lorentz factor (gamma ) describes in the special theory of relativity, time dilation, and the reciprocal of the length contraction in the coordinate transformation between relatively moving inertial frames. It was developed by Hendrik Antoon Lorentz in the context of the project drawn up by Lorentz transformation, which forms the mathematical basis of the special theory of relativity.

The Lorentz factor is defined as:

• Denotes the relative velocity of two reference systems.
• The speed of light is independent of the reference system constant of nature.

For relatively static reference systems

, But still small compared to the velocity of light

So is

Lorentz factor in accelerations

The time derivative of is interesting to formulate the relativistic form of Newton's second law for accelerations in the direction of movement, as the relativistically correct relationship is. The rule is:.

It follows directly:

And we obtain for the time derivative of the Lorentz factor:

And thus for the correct relationship between force and acceleration in the direction of movement

Lorentz factor as a function of momentum p

The Lorentz factor can also be expressed as:

With

• The relativistic momentum of the object in
• Its mass

This spelling is found mainly in theoretical physics.

The proof of equivalence can be delivered on an identification with the "normal" Lorentz factor in the results of the relativistic momentum.

Lorentz factor as a function of the kinetic energy of

The Lorentz factor can also be expressed as:

With

• The kinetic energy of the object in
• Its rest energy

• Special Theory of Relativity
• Dimensionless size