Do photons slow down this much in the Sun's gravitational field?

Question

I just heard someone mention that photons take 40 thousand years to travel from the centre of the Sun to its surface which is roughly 700,000 kilometres. How is that possible if the speed of light/photons is 300,000 km/second?

Answer 1

Photons (as electromagnetic waves) always travel at the speed of light (in a vacuum and in this case between particle collisions - see below) which is about $\approx 3 \times 10^8 \ \text{ms}^{-1}$. They are being "slowed down", but not the way you think and not because of the suns' gravitational field, of which this has nothing to do with.

More precisely, although the photons travel from the core to the photosphere, which is a certain distance, the path they take is not direct.

Because the sun is dense, a photon emitted at the core will be absorbed by another nearby proton almost immediately, and then that proton will vibrate and re-emit another in a random direction. This happens over and over again many times so that when it reaches the sun's surface, thousands of years have passed. This process is described by what is called a random walk.

The distance that a photon can travel before it is absorbed, is given by what's called the mean free path, given by the equation

$$l = \frac{1}{\sigma n}$$

"where $n$ is the number of target particles per unit volume, and $\sigma$ is the effective cross-sectional area for collision."

As you can appreciate, the number of target particles (protons) will be significantly high making the mean free path extremely small, so the number of collisions is significantly high. in other words, the photon travels a substantial distance from the Suns' core to its surface, which takes thousands of years. After which it takes a measly 9 minutes to reach us,

$^1$ Also be careful with terms like "same" photon, since elementary particles (of a particular type) are indistinguishable (even in principle), so to give any particle a specific identity is technically incorrect. See this article about identical particles.

Answer 2

Gravity has little to do with it. The sun is a dense plasma and particles of plasma prolifically scatter photons (both elastically and inelastically). Hence the photon does not travel from the center to the surface in a straight line.

Answer 3

I should to clarify that gravitational field changes the wavelength of light (consequently the momentum of the photon in the vacuum) but not the speed of the photon since $$ p = \frac{\hbar}{\lambda} $$ and the speed of light in the vacuum remains absolute according to the relativity principle.

The reason of the apparent slow down of the speed of light in the sun is explained extensively in the previous answers.

Answer 4

The energy produced in the core takes that long to reach the surface. It's not the same photon taking that long. Photons are constantly emitted and absorbed, and the energy also spends time as kinetic energy of the electrons and protons in the plasma.

The core gets hot. It takes 40k years (or whatever the correct number may be) for it to cool, working its way though the entire bulk of the sun's material.