A neutral K meson at rest decays into two πmesons, which travel in opposite directions along the

step 1 To solve this problem, I will use the formula V -dess is equal to b minus u by 1 minus V u by c

A neutral K meson at rest decays into two πmesons, which...

A neutral $K$ meson at rest decays into two $\pi$ mesons, which travel in opposite directions along the $x$ axis with speeds of $0.815 \mathrm{c} .$ If instead the $K$ meson were moving in the positive $x$ direction with a velocity of $0.453 c,$ what would be the velocities of the two $\pi$ mesons?

Key Concepts

Relativistic Velocity Addition

This concept involves transforming velocities between different inertial frames when the speeds involved are significant fractions of the speed of light. The relativistic velocity addition formula replaces the classical (Galilean) sum of velocities to ensure that no observed speed exceeds the speed of light. It is a fundamental tool in special relativity for analyzing the motion of particles as seen by different observers.

Lorentz Transformations

Lorentz transformations provide the mathematical framework to convert time and space coordinates from one inertial frame to another moving at a constant velocity relative to the first. They are essential for understanding how velocities, positions, and times of events, such as particle decays, change in different reference frames under the constraints of special relativity.

Conservation of Energy and Momentum in Relativistic Decays

In particle physics, the conservation laws of energy and momentum are applied even in the realm of high speeds as dictated by special relativity. When a particle decays, like in the scenario of a kaon decaying into two pions, these conservation principles ensure that both energy and momentum are conserved across different reference frames. This forms the basis for calculating the resultant speeds and directions of the decay products when analyzed under a Lorentz transformation.

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