Relativistic quantities

Time and length are not the only relative quantities. Momentum and energy are also relativistic quantities, meaning their value depends on the frame of reference of the observer. Different frame of references may measure different values of energy and momentum for an object.

Momentum

You may recall that the classical equation of momentum is p=mv, however momentum is a relativistic quantity, so it’s ‘real’ equation is:

The above equation is useful to explain why objects cannot reach the speed of light. As the speed of an object approaches the speed of light, the denominator would approach 0, and hence the relativistic momentum would approach infinite. It is impossible for an object to have infinite momentum, so it is clearly impossible for an object to travel at the speed of light.

Energy

The total energy of a moving object is given by:

The rest energy of an object is given by:

The total energy of a moving object is also given by:

Combining the above equations gives us:

The above equation is useful to calculate the kinetic energy of a moving object. Kinetic energy is a relative quantity, so its value is different for different frame of references.