# Calculating Invariant Mass Using Momentum and Rest Mass

• iloveflickr
In summary, the conversation discusses finding the invariant mass using lab-frame momentum and rest mass. The equation E^2 = m0^2c^4 + (pc)^2 is suggested as a solution, with E representing total inertial energy. The total inertial energy is defined as the sum of a particle's rest mass and kinetic energy.

#### iloveflickr

Hello,

I'm working on this problem and I'd like to know how to find the invariant mass using just the lab-frame momentum and rest mass.

I've found a lot of equations that deal with E, and I'm not completely sure what that is either.

Thanks

You have to tell us "this problem".

I have a proton with momentum = 1GeV hitting a neutron at rest, and I'd like to find the CM-momentum before collision.

Thanks

More work...

So here's what I have so far...

E* = (Ep* + En*),

where
Ep* = Mp + Pe
En* = Mn

Pe = momentum of electron in lab frame
Ep* = energy of proton in CM frame
En* = energy of neutron in CM frame
Mn/Mp = mass of neutron/proton

Is E* = Invariant mass? If so, I've got this problem done.

iloveflickr said:
Hello,

I'm working on this problem and I'd like to know how to find the invariant mass using just the lab-frame momentum and rest mass.

I've found a lot of equations that deal with E, and I'm not completely sure what that is either.

Thanks

As measured in an inertial frame of reference - If m0 = invariant mass of system, p = total momentum of system and E = total inertial energy of the system then

E^2 = m02c4+(pc)2. Simply solve for the invariant mass m0 of the system and you have you're answer.

Pete

Last edited:
pmb_phy said:
As measured in an inertial frame of reference - If m0 = invariant mass of system, p = total momentum of system and E = total inertial energy of the system then

E^2 = m02c4+(pc)2. Simply solve for the invariant mass m0 of the system and you have you're answer.

Pete

Thanks for your response. I found that exact equation in many texts and I haven't a clue what the total inertial energy of the system is.

In my particular problem, would it be E = KE(proton) + Mass(proton) + Mass(neutron)?

iloveflickr said:
Thanks for your response. I found that exact equation in many texts and I haven't a clue what the total inertial energy of the system is.

In my particular problem, would it be E = KE(proton) + Mass(proton) + Mass(neutron)?

The total inertial energy, E, of a particle is the sum of the particle's rest mass and its kinetic energy. The total energy, W, of a particle is the inertial energy + potential energy. That is to say that

E = K + E0

W = E + V

Best wishes

Pete

Thanks much.

## 1. What is the formula for calculating invariant mass?

The formula for calculating invariant mass using momentum and rest mass is given by m0 = √(E2 - p2c2)/c2, where m0 is the invariant mass, E is the energy, p is the momentum, and c is the speed of light.

## 2. Why is invariant mass important in particle physics?

Invariant mass is important in particle physics because it is a fundamental property of particles that remains constant regardless of the frame of reference. It allows physicists to study and classify particles based on their invariant mass, providing valuable insights into the nature of matter and energy.

## 3. How is momentum related to invariant mass?

Momentum and invariant mass are related through the equation p = m0γv, where p is the momentum, m0 is the invariant mass, γ is the Lorentz factor, and v is the velocity. This equation shows that the momentum of a particle is directly proportional to its invariant mass.

## 4. Can invariant mass be negative?

No, invariant mass cannot be negative. Invariant mass is a measure of the energy and momentum of a particle, and both energy and momentum are always positive quantities. Therefore, the square root in the formula for calculating invariant mass will always yield a positive value.

## 5. How is the concept of relativistic mass related to invariant mass?

The concept of relativistic mass is related to invariant mass in that both are measures of a particle's energy and momentum. However, relativistic mass is a frame-dependent quantity, meaning it changes depending on the observer's frame of reference, while invariant mass remains constant. Invariant mass is considered a more fundamental and useful concept in particle physics.