Question

What is the gamma or Lorentz factor for something that is moving at half the speed of light relative to its surroundings?

a) 0.5
b) 1
c) 2
d) 1.5

Answer 1

The Lorentz factor for an object moving at half the speed of light is approximately 1.1547, which is not listed among the options provided.

Step-by-step explanation:

The gamma or Lorentz factor, often denoted as γ (gamma), for an object moving at a velocity (v) relative to the speed of light (c) is given by the equation:

γ = 1 / √(1 - v^2/c^2)

For something moving at half the speed of light (v = 0.5c), we can calculate the Lorentz factor as follows:

γ = 1 / √(1 - (0.5c)^2/c^2) = 1 / √(1 - 0.25) = 1 / √(0.75) ≈ 1.1547

Thus, none of the options (a) 0.5, (b) 1, (c) 2, or (d) 1.5 correctly represent the Lorentz factor for an object moving at half the speed of light. The correct Lorentz factor is approximately 1.1547.