Associative Operation with Four Vectors: Is it True?

In summary, 4-momentum is a concept that combines the energy and momentum of a particle into a single four-dimensional quantity. The equation for calculating 4-momentum is p = (E, p<sub>x</sub>, p<sub>y</sub>, p<sub>z</sub>), where E is the energy of the particle and p<sub>x</sub>, p<sub>y</sub>, and p<sub>z</sub> are the momentum components in the x, y, and z directions. It is conserved in a closed system and has a relationship with mass according to Einstein's theory of relativity. 4-momentum has various real-world applications in fields such as particle physics, ast
  • #1
bgy
8
0
hi,

Is it true that

2*(p+p_1)p_3(p+p_1)p_2 - (p_3)(p_2)(p+p_1)^2 = (p_3)(p_2)(p+p_1)^2 ,

where p,p_1,p_2,p_3 are four vectors? Or simply: associative this operation?
 
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  • #2
cant quite figure out what u are multiplying by what
why don't u try using latex format
 
  • #3
esalihm said:
cant quite figure out what u are multiplying by what
why don't u try using latex format

ok. See the attachment.
 

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What is 4-momentum?

4-momentum is a concept in physics that combines the energy and momentum of a particle into a single four-dimensional quantity.

What is the equation for calculating 4-momentum?

The equation for calculating 4-momentum is p = (E, px, py, pz), where E is the energy of the particle and px, py, and pz are the momentum components in the x, y, and z directions, respectively.

How is 4-momentum conserved?

4-momentum is conserved in a closed system, meaning that the total 4-momentum before a collision or interaction is equal to the total 4-momentum after the collision or interaction.

What is the relationship between 4-momentum and mass?

According to Einstein's theory of relativity, the mass of a particle can be expressed as m = √(p2 - E2), where p is the magnitude of the particle's 3-momentum (p2 = px2 + py2 + pz2) and E is the energy of the particle. This relationship shows that as the energy of a particle increases, its mass also increases.

What are some real-world applications of 4-momentum?

4-momentum is used in many areas of physics, including particle physics, astrophysics, and quantum mechanics. It is also used in practical applications such as in medical imaging technologies like PET scans, which use 4-momentum to track the paths of particles in the body.

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