Changes

It happens that, under relativity, the momentum of a particle in motion is given by

It happens that, under relativity, the momentum of a particle in motion is given by

:<math>p = \sqrt{1-v^2/c^2}\ m\ v</math>

:<math>p = \frac{1}{\sqrt{1-v^2/c^2}}\ m\ v</math>

instead of the "classical" formula

instead of the "classical" formula

:<math>p = m v\,</math>

:<math>p = m v\,</math>

As can be seen, the difference is only significant for particles travelling at speeds comparable to the speed of light, that is, "relativistic" speeds.

As can be seen, the difference is only significant for particles travelling at speeds comparable to the speed of light, that is, "relativistic" speeds.

Some people have gotten around this by using a subscript zero to denote the particle's rest mass, and defined something called the "relativistic mass", denoted '''m''', as

Some people have gotten around this issue by using a subscript zero to denote the particle's rest mass, and defining something called the "relativistic mass", denoted '''m''', as

:<math>m = \sqrt{1-v^2/c^2}\ m_0\,</math>

:<math>m = \frac{m_0}{\sqrt{1-v^2/c^2}}\,</math>

so that the momentum formula will look more natural in terms of this "relativistic mass" '''m'''.

so that the momentum formula will look more natural in terms of this "relativistic mass" '''m'''.

:<math>p = m v\,</math>

:<math>p = m v\,</math>

The factor

The factor

:<math>\sqrt{1-v^2/c^2}</math>

:<math>\frac{1}{\sqrt{1-v^2/c^2}}</math>

shows up in a number of places in relativity, and is called the ''Lorentz factor'', commonly denoted with the Greek letter <math>\gamma\,</math>.  This means that the formula for momentum is

shows up in a number of places in relativity, and is called the ''Lorentz factor'', commonly denoted with the Greek letter <math>\gamma\,</math>.  This means that the formula for momentum is

:<math>p = \gamma m v\,</math>

:<math>p = \gamma m v\,</math>