4-momentum of particles in lab and CM frame

Click For Summary
SUMMARY

The discussion focuses on the calculation of kinetic energy for identical particles in different reference frames during a head-on collision. According to Griffiths' "Introduction to Elementary Particles," the total 4-momenta are analyzed in both the lab frame and the center of mass (CM) frame. In the CM frame, the zeroth component is represented as 2E/c, while in the lab frame, it is E' + mc², where mc² accounts for the rest energy of the stationary particle. This distinction clarifies why the lab frame includes the rest energy term, unlike the CM frame.

PREREQUISITES
  • Understanding of 4-momentum in special relativity
  • Familiarity with kinetic energy concepts
  • Knowledge of reference frames in physics
  • Basic principles of particle collisions
NEXT STEPS
  • Study Griffiths' "Introduction to Elementary Particles" for detailed explanations
  • Explore the concept of 4-momentum in special relativity
  • Learn about energy transformations in different reference frames
  • Investigate particle collision dynamics and their implications in physics
USEFUL FOR

Students and professionals in physics, particularly those studying particle physics, special relativity, and energy conservation in collisions.

MarekS
Messages
33
Reaction score
0
The question:
Suppose two identical particles, each with mass m and kinetic energy T, collide head-on. What is the kinetic energy of one in the rest system of the other?

The solution:

Is given on pg 109 of Griffiths' Introduction to Elementary Particles.

Griffiths writes down the total 4-momenta of the system in the lab frame and in the CM frame.

The zeroth component in the CM frame is 2E/c. So I guess that E is the energy of one of the particles in that frame.

The zeroth component in the lab frame is E'+mc^2, however. Why is mc^2 added for the lab frame? Why not have 2E'/c as in the CM frame?

Thank you!
 
Physics news on Phys.org
MarekS said:
The zeroth component in the lab frame is E'+mc^2, however. Why is mc^2 added for the lab frame? Why not have 2E'/c as in the CM frame?

The mc^2 is the energy of the particle that is at rest. E' is the energy of the particle that's moving.
 

Similar threads

Momentum and energy in Center-of-Momentum frame
  • · Replies 6 ·
Replies
6
Views
3K
Understanding the Conservation of Momentum in Special Relativity Collisions
  • · Replies 2 ·
Replies
2
Views
2K
What is the Threshold Energy of a Neutrino in the Centre of Mass Frame?
  • · Replies 10 ·
Replies
10
Views
3K
Compton Scattering Angle - CM FRAME
  • · Replies 2 ·
Replies
2
Views
3K
Two particle collision - One in excited state
  • · Replies 10 ·
Replies
10
Views
2K
Decay of a particle of mass M into two particles
  • · Replies 1 ·
Replies
1
Views
4K
How Does Special Relativity Affect Photon Emission Angles?
  • · Replies 4 ·
Replies
4
Views
2K
Relativistic collision of two protons to produce a proton-antiproton
  • · Replies 21 ·
Replies
21
Views
13K
Relativistic Harmonic Oscillator Lagrangian and Four Force
  • · Replies 1 ·
Replies
1
Views
2K
Finding CM frame velocity in special relativity
  • · Replies 9 ·
Replies
9
Views
6K