A cosmic ray particle passes through a 1 -cm-thick...

Name: Problem 66, Chapter 24: Essential University Physics Global Edition
Uploaded: 2023-04-03T22:19:45-08:00
Channel: James Kiss
Description: A cosmic ray particle passes through a 1 -cm-thick energymeasuring detector at very nearly the speed of light. What's the uncertainty in the particle's energy as measured in the detector's reference frame?

A cosmic ray particle passes through a 1 -cm-thick energymeasuring detector at very nearly the speed of light. What's the uncertainty in the particle's energy as measured in the detector's reference frame?

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Key Concepts

Energy-Time Uncertainty Principle

This principle, a fundamental aspect of quantum mechanics, states that the uncertainty in energy measurement multiplied by the uncertainty in the time interval of that measurement has a lower bound, typically expressed as ?E ?t ? ?/2. It implies that when energy is measured over a very short time interval, there is an inherent uncertainty in the energy value obtained.

Measurement Duration and Finite Detector Size

In practical measurements, the finite size of a detector imposes a limit on the duration over which a particle can be observed, as the time the particle spends in the detector is limited by its transit time across the detector's thickness. This finite time interval leads directly to an energy uncertainty in accordance with the energy-time uncertainty principle.

Relativistic Kinematics

When particles move at speeds close to the speed of light, their transit times through a physical system must be calculated using relativistic considerations. The particle’s nearly light-speed travel means that the time it takes to traverse a set detector thickness is very short, thereby magnifying the effect of the energy-time uncertainty principle on the measured energy.

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