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SPECIAL THEORY OF RELATIVITY |
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all rights reserved 2002
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Momentum
For
non-relativistic objects Newton defined momentum, given the symbol p,
as the product of mass and velocity -- p = m v. When
speed becomes relativistic, we have to modify this definition -- p =
gamma (mv) Notice
that this equation tells you that for any particle with a non-zero mass, the
momentum gets larger and larger as the speed gets closer to the speed of light.
Such a particle would have infinite momentum if it could reach the speed of
light. Since it would take an infinite amount of force (or a finite force acting
over an infinite amount of time) to accelerate a particle to infinite momentum,
we are forced to conclude that a massive particle always travels at speeds less
than the speed of light. Some
text books will introduce the definition m0 for the mass of
an object at rest, calling this the "rest mass" and define the
quantity (M = gamma m0) as the mass of the moving object.
This makes Newton's definition of momentum still true provided you choose the
correct mass. In particle physics, when we talk about mass we always mean mass
of an object at rest and we write it as m and keep the factor of gamma
explicit in the equations. |
