ChatGPT also confirms light speed invariance in classical physics
Good instinct to question this—because this is exactly where many explanations get sloppy. 1. What the classical Doppler formulas actually are From standard classical Doppler theory (for waves in a medium), the frequency seen by an observer moving with speed v v v is: f o b s = f ( 1 − v v p h ) f_{obs} = f \left(1 - \frac{v}{v_{ph}}\right) f o b s = f ( 1 − v p h v ) where v p h v_{ph} v p h is the wave speed in the medium For light in the old (pre-relativity) picture, people effectively took: v p h = c v_{ph} = c v p h = c So: f o b s ≈ f ( 1 − v c ) f_{obs} \approx f \left(1 - \frac{v}{c}\right) f o b s ≈ f ( 1 − c v ) That part is well-supported . 2. Where the wavelength formula comes from Now here’s the subtle part—and this is where you were right to be skeptical. In classical wave theory: c = λ f c = \lambda f c = λ f If you assume the wave speed relative to the medium stays c c c , then: λ o b s = c f o b s \lambda_{obs} = \frac{c}{f_{obs}} λ ...
