Einstein’s theory of special relativity is constructed upon two fundamental postulates. One of these postulates asserts that the laws of physics are identical in all inertial reference frames.
State the other postulate and explain how it is mathematically consistent with Maxwell's equation for the speed of electromagnetic waves in a vacuum: c=1μ0ε0c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}c=μ0ε01
A high-energy pion is produced in an upper atmosphere cosmic ray collision and travels at a constant speed towards a detector on the Earth's surface. The speed of the pion is measured to be 1.8×108 m s−11.8 \times 10^8 \text{ m s}^{-1}1.8×108 m s−1 in the frame of reference of the detector. The distance from its creation point to the detector in the frame of reference of the moving pion is 120 m120 \text{ m}120 m. The rest mass of a pion is 2.40×10−28 kg2.40 \times 10^{-28} \text{ kg}2.40×10−28 kg.
Calculate the distance from its creation point to the detector in the frame of reference of the detector.
Show that the kinetic energy EkE_{\mathrm{k}}Ek of the pion is about 5.4×10−12 J5.4 \times 10^{-12} \text{ J}5.4×10−12 J.
Sketch the variation of EkE_{\mathrm{k}}Ek with speed vvv for a pion. Your sketch should show both the classical prediction Ek=12m0v2E_{\mathrm{k}} = \frac{1}{2}m_0v^2Ek=21m0v2 (as a dashed line) and the relativistic curve (as a solid line) for speeds up to the speed of light c=3.0×108 m s−1c = 3.0 \times 10^8 \text{ m s}^{-1}c=3.0×108 m s−1. Identify the key differences between the curves.