What is the Meaning of 4-Momenta and How is it Used?

  • Thread starter Thread starter ManyNames
  • Start date Start date
ManyNames
Messages
136
Reaction score
0
What does ''4-momenta'' mean, and what context is it used?
Thanky'all
 
Physics news on Phys.org
Special relativity can be more easily handled by using Minkowski geometry in 4D. That means that we represent spacetime as a 4D surface. So vectors now have 4 components. Furthermore, lengths of vectors are defined by slightly different function than the usual one in Euclidean 3D of "square everything, sum and square root". Various quantities are then combined into one geometrical object. For example, we can talk about the distance (in both space and time) between two spacetime points as one 4-vector -- the advantage being that thing like the length of the vector, the "invariant interval", is the same in every frame. Just like a normal vector's length doesn't depend on the direction you look at it, 4-vectors don't change length because you're traveling at a different speed. 4-momentum is just the momentum and energy combined into one geometrical object.

See http://en.wikipedia.org/wiki/Four-vector
 
Thank you
 

Thread 'Describing the Big Bang'

I started reading a National Geographic article related to the Big Bang. It starts these statements: Gazing up at the stars at night, it’s easy to imagine that space goes on forever. But cosmologists know that the universe actually has limits. First, their best models indicate that space and time had a beginning, a subatomic point called a singularity. This point of intense heat and density rapidly ballooned outward. My first reaction was that this is a layman's approximation to...
View full post »
Thread 'Dirac's integral for the energy-momentum of the gravitational field'

Thread 'Dirac's integral for the energy-momentum of the gravitational field'

See Dirac's brief treatment of the energy-momentum pseudo-tensor in the attached picture. Dirac is presumably integrating eq. (31.2) over the 4D "hypercylinder" defined by ##T_1 \le x^0 \le T_2## and ##\mathbf{|x|} \le R##, where ##R## is sufficiently large to include all the matter-energy fields in the system. Then \begin{align} 0 &= \int_V \left[ ({t_\mu}^\nu + T_\mu^\nu)\sqrt{-g}\, \right]_{,\nu} d^4 x = \int_{\partial V} ({t_\mu}^\nu + T_\mu^\nu)\sqrt{-g} \, dS_\nu \nonumber\\ &= \left(...
View full post »

Thread 'A sufficient condition for integrability of equation ##\nabla g=0##'

In Philippe G. Ciarlet's book 'An introduction to differential geometry', He gives the integrability conditions of the differential equations like this: $$ \partial_{i} F_{lj}=L^p_{ij} F_{lp},\,\,\,F_{ij}(x_0)=F^0_{ij}. $$ The integrability conditions for the existence of a global solution ##F_{lj}## is: $$ R^i_{jkl}\equiv\partial_k L^i_{jl}-\partial_l L^i_{jk}+L^h_{jl} L^i_{hk}-L^h_{jk} L^i_{hl}=0 $$ Then from the equation: $$\nabla_b e_a= \Gamma^c_{ab} e_c$$ Using cartesian basis ## e_I...
View full post »

Similar threads

A How Does Linear Framedragging Affect Parallel Moving Masses in Flat Spacetime?
Replies
11
Views
2K
B What is the difference between the two 4-momenta in photon-electron collisions?
Replies
7
Views
1K
I Why do particles around us have finite momenta?
Replies
21
Views
2K
I Angles between 4-vectors in special relativity?
Replies
5
Views
1K
I Ray tracing in the movie Interstellar
Replies
9
Views
1K
I States and observables in quantum mechanics
Replies
5
Views
919
I Compton Scattering w/Moving Electron: Turner's Eq 5.29
Replies
2
Views
1K
Canonical Momenta Action Electromagnetism
Replies
4
Views
2K
I Electroweak Feynman Rules: Confusion about the photon-W boson interaction term
Replies
2
Views
2K
B What does the Minkowski spacetime interval represent and how is it determined?
Replies
20
Views
2K

Hot Threads

Recent Insights

Back
Top