Relativistic Energy and four momentum

Click For Summary
SUMMARY

The discussion focuses on the relativistic energy and four-momentum conservation during a collision between two particles. The initial particle, with kinetic energy T0 and rest energy E0, strikes a stationary particle, resulting in a final kinetic energy T expressed as T = T0cos2(θ)/(1 + (T0sin2(θ)/2E0)). Participants emphasize the importance of writing conservation equations for total energy and linear momentum in both x and y components to approach the problem effectively.

PREREQUISITES
  • Understanding of relativistic energy concepts, including kinetic and rest energy.
  • Familiarity with four-momentum conservation principles in particle physics.
  • Knowledge of trigonometric functions and their application in physics.
  • Ability to formulate and solve conservation equations in collisions.
NEXT STEPS
  • Study the derivation of relativistic energy equations in particle collisions.
  • Learn how to apply four-momentum conservation in different collision scenarios.
  • Explore the implications of invariant mass in relativistic collisions.
  • Investigate the role of angles in scattering processes and their effects on energy distribution.
USEFUL FOR

This discussion is beneficial for physics students, researchers in particle physics, and anyone interested in understanding relativistic collisions and energy conservation principles.

golfingboy07
Messages
17
Reaction score
0
A particle of initial kinetic energy T0 and rest energy E0 strikes a like particle at rest. The initial particle is scattered at an agle theta to its original direction. Show that the final kinetic energy T is

T = T0cos2(theta)/(1+ (T0sin2(theta)/2E0))

what I have so far:

We know that T = E - E0 and that four momentum will be conserved. Also I think if we choose a suitible invariant it may simplify the problem

Could I get more suggestions/hints a starting point etc.

Thanks

GM
 
Physics news on Phys.org
The total energy before and after the collision is the same, as well as the total linear momentum, so I suggest you start by writing those 3 "conservation equations" (1 for energy, 1 for x-component momentum and 1 for y-component momentum)
 

Similar threads

Relativistic energy and momentum conservation
  • · Replies 8 ·
Replies
8
Views
6K
Initial conditions for orbits around a wormhole
  • · Replies 4 ·
Replies
4
Views
1K
Probability distribution of outgoing energy of particle
  • · Replies 1 ·
Replies
1
Views
2K
Time Independence of the Momentum Uncertainty for a Free Particle Wave
  • · Replies 3 ·
Replies
3
Views
2K
Collision of two photons using four-momentum
  • · Replies 5 ·
Replies
5
Views
4K
De-excitation of a moving atom with photon emission
  • · Replies 6 ·
Replies
6
Views
2K
Rocket propelled by a beam of photons
  • · Replies 10 ·
Replies
10
Views
4K
Fourier transform of t-V model for t=0 case
  • · Replies 0 ·
Replies
0
Views
2K
Four momentum proton-proton scattering question
  • · Replies 15 ·
Replies
15
Views
3K
Angle of reflection of a beam light on a moving mirror
  • · Replies 20 ·
Replies
20
Views
3K