Suppose we know a particle's four-momentum $p_{t}$ and $p_{x}$ components. If we draw the particle's four-momentum arrow on an energy-momentum diagram, we can use a hyperbola to determine
A) The particle's energy.
B) The particle's speed.
C) The particle's $x$-velocity.
D) The particle's momentum magnitude $|\vec{p}|$
E) The particle's mass.
F) The scaling on the $t$ axis.
G) Something else (specify).

Question

Quizplus · Accepted Answer

The particle's mass is invariant and can be determined from its four-momentum components using the relation $m^2c^2 = E^2/c^2 - |\vec{p}|^2$, where $E$ is the energy and $|\vec{p}|$ is the magnitude of the spatial momentum. The hyperbola on an energy-momentum diagram represents points of constant mass (squared), thus allowing us to determine the particle's mass.

Suppose We Know a Particle's Four-Momentum ptp_{t}pt​ And pxp_{x}px​ Components xxx -Velocity D) the Particle's Momentum Magnitude

Suppose We Know a Particle's Four-Momentum $p_{t}$ And $p_{x}$ Components $x$ -Velocity
D) the Particle's Momentum Magnitude