Information About

Four-momentum
  CATEGORIES ABOUT FOUR-MOMENTUM
   
minkowski spacetime
   
relativity
   
APPAREL
BABY
BEAUTY
BOOKS
CAR TOYS
CELL PHONES
DVD'S
ELECTRONICS
GOURMET FOOD
GROCERIES
HEALTH & PERSONAL
HOME & GARDEN
JEWELRY
MUSIC
MUSIC INSTRUMENTS
OFFICE PRODUCTS
SOFTWARE
SPORTING GOODS
TOOLS & HARDWARE
TOYS
VIDEO GAMES
SHOPPING HOME
MORE SHOPPING...



:
\begin{pmatrix}
p_0 \ p_1 \ p_2 \ p_3
\end{pmatrix} =
\begin{pmatrix}
-E \ p_x \ p_y \ p_z
\end{pmatrix}


The four-momentum is useful in relativistic calculations because it is a Lorentz vector. This means that it is easy to keep track of how it transforms under Lorentz Transformation s.


MINKOWSKI NORM: P<SUP>2</SUP>


Calculating the Minkowski Norm of the four-momentum gives a Lorentz Invariant quantity equal (up to factors of the Speed Of Light ''c'') to the square of the particle's Proper Mass :
  U {E^2 \over c^2} - ec p^2 = m^2c^2 </math>
  Is The Reciprocal Of The Metric Tensor Of "http://wwwinformationdelightinfo/information/entry/special_relativity" class="copylinks">Special Relativity Because <math>p^2\!</math> is Lorentz invariant, its value is not changed by Lorentz transformations, ie boosts into different frames of reference




CONSERVATION OF FOUR-MOMENTUM


The conservation of the four-momentum yields two conservation laws for "classical" quantities:
# The total Energy E = - p0 is conserved.
# The classical three- Momentum ec p is conserved.

Note that the mass of a system of particles may be more than the sum of the particles' rest masses, since Kinetic Energy in the system center-of-mass frame counts as system mass. As an example, two particles with the four-momentums {-5 Gev, 4 Gev/''c'', 0, 0} and {-5 Gev, -4 Gev/''c'', 0, 0} each have (rest) mass 3 Gev/''c''2 separately, but their total mass (the system mass) is 10 Gev/''c''2. If these particles were to collide and stick, the mass of the composite object would be 10 Gev/''c''2.