# Squared length of 4-momentum g(p,p)?

• berlinspeed
In summary, the squared length of 4-momentum g(p,p) is a mathematical quantity used to measure the magnitude of a particle's momentum in a four-dimensional space-time. It is calculated by taking the dot product of the 4-momentum vector with itself. It is different from the magnitude of 4-momentum and is not a conserved quantity. The squared length is directly proportional to the mass of a particle, as described by the equation E=mc^2.
berlinspeed
Homework Statement
Can someone explain why the squared length of p^2 = p dot p = -m^2 and not -m^2*c^2?
Relevant Equations
p^2 = p dot p = -m^2
Explained in statement.

That depends on two things:
1. What is the metric you use

2. What are the units you are using.

## 1. What is the definition of the squared length of 4-momentum g(p,p)?

The squared length of 4-momentum g(p,p) is a mathematical quantity that measures the magnitude of a 4-momentum vector in special relativity. It is calculated by taking the dot product of the 4-momentum vector with itself.

## 2. How is the squared length of 4-momentum g(p,p) related to energy and momentum?

In special relativity, the squared length of 4-momentum g(p,p) is equal to the square of the energy divided by the square of the speed of light. It is also equal to the square of the momentum divided by the square of the speed of light.

## 3. What is the significance of the squared length of 4-momentum g(p,p) in particle physics?

The squared length of 4-momentum g(p,p) is a fundamental quantity in particle physics, as it is used to calculate the invariant mass of particles. It is also used to determine the energy and momentum of particles in high-energy collisions.

## 4. How is the squared length of 4-momentum g(p,p) affected by Lorentz transformations?

The squared length of 4-momentum g(p,p) is invariant under Lorentz transformations, meaning that it has the same value in all inertial reference frames. This is a key concept in special relativity and is used to describe the behavior of particles at high speeds.

## 5. Can the squared length of 4-momentum g(p,p) be negative?

Yes, the squared length of 4-momentum g(p,p) can be negative in certain cases. This occurs when the 4-momentum vector is spacelike, meaning that it has a greater magnitude in space than in time. In contrast, a timelike 4-momentum vector will always have a positive squared length.

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