# Relativistic scattering Lab and CM frames

• trelek2
In summary, the conversation discusses the concept of the speed of the center of mass frame in relation to the lab frame for non-relativistic and relativistic scattering. It is mentioned that in both cases, the speed of the center of mass frame is equal to the speed of the electrons in the center of mass frame. The conversation also mentions using the Lorentz velocity addition formula to prove this in the relativistic case, and that the proof is valid for both cases.
trelek2
Hi!

I have the following problem:
Example: collision of 2 electrons
For non-relativistic scattering it is easy to show that the speed of the CM frame with respect to the lab frame is equal to the speed of the electrons in the CM frame, expoloiting the fact that in the lab frame, one of the electrons is at rest.

Now this also holds in the relativistic regime. I'm not really sure where does this follow from. Is it valid to take the lorentz velocity addition formula, and taking the speed of the particle in the lab frame to be 0 we see that for x-coordinate the speed of the electron in CM frame must then be uqual to to the speed of CM frame in lab frame. Saying that the lab and CM frames are in standard configuration makes this proof general enough?

I think your proof is correct. What's different between the relativistic and nonrelativistic cases is that in the relativistic case, the velocities in the c.m. frame are not half the velocity of the projectile in the lab frame.

Hello!

The relationship between the lab and CM frames in relativistic scattering can be derived using the Lorentz transformation equations. In the lab frame, one of the electrons is at rest and the other has a velocity v. In the CM frame, both electrons have the same velocity v' (since the CM frame is moving with the same speed as the electrons). Using the Lorentz transformation equations, we can relate the velocities in the two frames, and we get that v' = (v + u)/(1 + vu/c^2), where u is the velocity of the CM frame with respect to the lab frame. Since v=0 in the lab frame, we get v' = u, which means that the speed of the electrons in the CM frame is equal to the speed of the CM frame in the lab frame. This holds for any standard configuration of the lab and CM frames, making the proof general enough. I hope this helps!

## 1. What is the purpose of a Relativistic scattering Lab?

A Relativistic scattering Lab is used to study the interactions between particles at high energies. It allows scientists to understand the fundamental forces of nature and the structure of matter.

## 2. What is the difference between the CM frame and the Lab frame in a Relativistic scattering experiment?

The CM (center-of-mass) frame is a reference frame where the total momentum of the system is zero. In a Relativistic scattering experiment, this frame is used to simplify calculations and better understand the interactions between particles. The Lab frame, on the other hand, is the frame of reference of the laboratory where the experiment is being conducted.

## 3. How is energy conserved in a Relativistic scattering Lab?

In a Relativistic scattering Lab, energy is conserved through the use of special relativity equations. These equations take into account the increase in mass of particles at high energies and ensure that the total energy of the system remains constant.

## 4. What is the role of the Lorentz transformation in a Relativistic scattering Lab?

The Lorentz transformation is a mathematical tool used to convert measurements between different reference frames, such as the CM and Lab frames in a Relativistic scattering Lab. It helps to account for the effects of special relativity, such as time dilation and length contraction, on the measurements taken in the experiment.

## 5. How do scientists use the data collected from a Relativistic scattering Lab to make discoveries?

Scientists use the data collected from a Relativistic scattering Lab to analyze the behavior of particles at high energies and make predictions about the fundamental forces of nature. By comparing the experimental results with theoretical predictions, they can gain a deeper understanding of the underlying principles of the universe.

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