Chapter 6: Photons and Massless Particles
Photons are massless yet carry energy and momentum. They always travel at c in all frames, have zero proper time, and obey E = pc. Their behavior illustrates the extreme limits of special relativity.
Photon Properties
E = pc
For massless particles, the energy-momentum relation gives E = pc (since m = 0).
E = hf
Photon energy is quantized: E = hf = hc/λ (Planck's relation).
p = h/λ
Photon momentum from E = pc and E = hf: p = h/λ (de Broglie relation).
No Rest Frame
Photons always travel at c—there's no frame where a photon is at rest.
Relativistic Doppler Effect
\( f_{\text{obs}} = f_{\text{source}} \sqrt{\frac{1 - \beta}{1 + \beta}} \)
(for motion directly toward/away)
Redshift (receding)
Source moving away: observed frequency lower, wavelength longer (redder).
Blueshift (approaching)
Source moving toward: observed frequency higher, wavelength shorter (bluer).
Radiation Pressure
Light carries momentum, so it exerts pressure when absorbed or reflected:
\( P = \frac{I}{c} \) (absorbed) or \( P = \frac{2I}{c} \) (reflected)
Applications: solar sails, laser cooling, comet tails pointing away from Sun.