Thread: Light sphere question View Single Post
 Mentor cfrogue, atyy already presented some pretty convincing math, but let me try two other ways: 1) Lorentz transform approach: We have the standard form of the Lorentz transform 1a) t' = ( t - vx/c^2 )γ 1b) x' = ( x - vt )γ And we have any arbitrary equation in the primed frame 1c) x' = ct' To obtain the corresponding equation in the unprimed frame we simply substitute 1a) and 1b) into 1c) 1d) ( x - vt )γ = c(( t - vx/c^2 )γ) Which simplifies to 1e) x = ct 2) First principles approach: We know that the second postulate is that c is the same in all reference frames, so we can immediately write that the speed of the light pulse is c. This implies 2a) x = ct + B Since we know that the origins coincided with the flash we know that x=0 and t=0 is a point on the light pulse, so we can use that to solve for B 2b) 0 = c0 + B 2c) B = 0 Substituting 2c into 2a gives 2d) x = ct Note that approach 1 is a general approach that will work for any equation that you care to write. Approach 2 is specific to this problem since we are dealing with light pulses and will not work in general. I would typically recommend approach 1.