Understanding Particle Decay and Momentum Conservation in Relativity

In summary, the conversation is about finding the momentum of children particles from the rest frame of the parent particle after it decays into two other particles. The person asking the question found a helpful article on Wikipedia, but is confused by the mathematical working. They are questioning how the equation 2(p_M*p_1) can be expanded into only two terms instead of four. Another person responds by explaining that each momentum in the equation is a four-momentum and the multiplication involves vector multiplication, resulting in two terms. The minus sign is also explained as being due to the law of multiplying co- and contra-variant four-vectors.
  • #1
planesinspace
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I am answering a question about a particle decaying into two other particles and one needs to find the momentum of the children particles from the rest frame of the parent. I found a very helpful article on Wikipedia under 'Particle Decay', however I am really confused by their mathematical working and wondering if anyone can explain it or agree with me that Wiki has made a mistake :)

I can't copy all the equations so the link is here: http://en.wikipedia.org/wiki/Particle_decay
its under the Sub heading Conservation of four momentum.

I don't understand how they can expand 2(p_M*p_1) into only 2 terms when under normal (a+b)(c+d) expansions you get four. Unless there is some weird vector multiplication I don't understand?

Any help GREATLY appreciated!
 
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  • #2
That easy. Each momentum p in these equations is a four-momentum, so for p this reads p = (E, p). The multiplication is just the vector multiplication, where the first term involves the E's, whereas the second term involves the three-momentum p. The minus sign appears due to the law how to multiply co- and contra-variant four-vectors.
 
  • #3
Thankyou!
 

1. What is particle decay?

Particle decay is a process in which a particle spontaneously transforms into one or more other particles. This can occur due to various factors, such as the instability of the particle or the presence of certain interactions.

2. How does particle decay relate to relativity?

Particle decay is closely related to relativity, as it involves the conversion of mass into energy. According to Einstein's famous equation E=mc², mass and energy are equivalent and can be converted into each other. In particle decay, the original particle loses some of its mass, which is then converted into the energy of the new particles.

3. Can particle decay violate the laws of relativity?

No, particle decay does not violate the laws of relativity. While it may seem like mass is being created or destroyed, it is actually just being converted into energy. This is consistent with the principle of conservation of mass-energy in relativity.

4. What is the role of time dilation in particle decay?

Time dilation, a phenomenon predicted by relativity, plays a crucial role in particle decay. As particles move at high speeds, time appears to pass slower for them. This means that particles with shorter lifetimes in their own frame of reference can appear to have longer lifetimes in a different frame of reference, allowing them to travel farther before decaying.

5. How is particle decay studied and measured?

Particle decay is studied and measured through various experimental techniques, such as particle accelerators and detectors. These tools allow scientists to observe and analyze the products of particle decay, providing valuable information about the particles involved and the fundamental forces at work.

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